Analysis of math teaching methodology

Ref. number:2016-1-MK01-KA201-021659
The project is funded by the ERASMUS + program of the European Union
Collection of related good
practices in Europe and beyond
"MATHDebate - The Voice of Students
- Searching Excellence in Math Education
through Increasing the Motivation for Learning"
ANALYSIS OF MATH
TEACHING METHODOLOGY

MATHDebate –
The Voice of Students – Searching Excellence in Math
Education through Increasing the Motivation for
Learning (2016 – 2018)
Ref. number:2016-1-MK01-KA201-021659
www.mathdebate.eu
Analysis of math teaching methodology
(Collection of related good practices in Europe and beyond)
September 2017

Reviewers:
1. Snezana Mirascieva, PhD,
Full professor at Didactic and Teaching Methods,
Faculty of Educational Sciences,
Goce Delcev University – Stip
2. Agim Rushiti, PhD
Associated Professor at Mathematics and Math Teaching Methods
Faculty of Computer Sciences,
Mother Teresa University – Skopje
CIP - Каталогизација во публикација
Национална и универзитетска библиотека "Св. Климент Охридски", Скопје
51:37.02-047.44(049.2)
ANALYSIS of math teaching methodology [Електронски извор] : (collection of
related good practices in Europe and beyond) / [coordinator Tatjana Atanasova -
Pachemska]. - Stip : University "Goce Delcev", 2017
Начин на пристап (URL): https://e-lib.ugd.edu.mk/naslovna.php. - Текст во PDF
формат, содржи 151 стр., илустр. - Наслов преземен од екранот. - Опис на изворот
на ден 08.11.2017. - Публикацијата е во рамки на проектот: Erasmus+ MATHDebate
Project - The voice of students - searching excellence in math education through
increasing the motivation for learning (2016 - 2018) Ref. number:2016-1-MK01-KA201-
021659. - Библиографија: стр. 151
ISBN 978-608-244-445-1
а) Математика - Методика - Анализи - Дебати
COBISS.MK-ID 104848394

Contribution for the preparation of this Analysis
The Analysis of Teaching Methodology is the first intellectual outcome of the collaborative work
of all the Partners for the development of the European Erasmus+ MATHDebate Project,
namely the following:
Coordinate Organization:
Goce Delcev State University - Stip, Macedonia (Tatjana Atanasova – Pachemska, Limonka
Koceva Lazarova, Marija Miteva) along with 6 partners from Macedonia, Bulgaria, Romania and
Cyprus.
Partner Organizations:
Union of researchers of Macedonia – SIM – Skopje, Macedonia (Biljana Jolevska – Tuneska,
Nikola Tuneski, Sanja Pachemska, Zoran Trifunov), Municipal Primary school “Ljuben Lape"
– Skopje (Dobrila Jovanovska Gjorgon, Aleksandra Peshevska Mitanovska, Sonja Daneva),
General Secondary School “St. Kliment Ohridski” – Aksakovo, Bulgaria (Penka Atanasova
Ganeva, Snezhana Semova Anastasova, Tinka Stoyanova Ivanova), South-West University
“Neofit Rilski” – Blagoevgrad, Bulgaria (Anton Stoilov), Secondary School "Mihai
Eminescu" – Alba Iulia, Romania (Rodica Florica Marinescu, Camelia Barbatu, Emilia Grad),
Cyprus Mathematical Society – Cyprus (Gregoris Makrides, Andreas Skotinos).
Contact the coordinator:
Tatjana Atanasova – Pachemska at tatjana.pacemska@ugd.edu.mk
Tel.: (+389)32550109
www.mathdebate.eu
©2017 MATHDebate Project
Disclaimer: "The European Commission support for the production of this publication does not
constitute an endorsement of the contents which reflects the views only of the authors, and the
Commission cannot be held responsible for any use which may be made of the information
contained therein."
The website of MATHDebate project is www.mathdebate.eu.
ISBN: 978-608-244-445-1

Contents
INTRODUCTION ....................................................................................................................... 1
Neediness for collecting of good practices in Europe and beyond.............................................. 8
What is a description of good practice?...................................................................................... 8
What is actually made?.............................................................................................................11
Analysis ....................................................................................................................................17
Why did we need an analysis?..................................................................................................17
Content of Collection of good practices.....................................................................................18
Conclusion................................................................................................................................23
ANNEX - Collection of Good Practices in Europe and beyond ..................................................24
ARITHEMTIC ........................................................................................................................25
“Find missing term”- sequences introduced in early age the ..............................................25
“Make your own money”-practicing simple mathematical operations..................................26
Comparing Decimals Game ...............................................................................................28
Math class assisted by parents ..........................................................................................30
Discovery learning .............................................................................................................32
Game and simulation .........................................................................................................34
Algorithmic method ............................................................................................................36
Didactic games in mathematics..........................................................................................38
Individual work in mathematics lesson ...............................................................................41
..............................................................................................................................................43
COMMUNICATION SKILLS ..................................................................................................44
Explicit instruction or Direct Instruction Lesson ..................................................................44
Cooperative learning..........................................................................................................45
‘Famous mathematicians’-throw-out history of mathematics ..............................................47
Peer Tutoring .....................................................................................................................49
Project ...............................................................................................................................51
The Pyramid (snowball method).........................................................................................53
The mosaic method ...........................................................................................................55
The Cluster method ...........................................................................................................57

Brainstorming.....................................................................................................................58
The gallery walk.................................................................................................................60
Flipped Classroom.............................................................................................................62
Measuring angels with jigsaw method................................................................................65
JIGSAW PUZZLES............................................................................................................68
Students Teams Achievement Division – STAD method....................................................70
Storytelling method ............................................................................................................73
Think-pair-share (TPS).......................................................................................................76
DEBATE ............................................................................................................................78
Discussion method in mathematics....................................................................................82
The Racing games feast of mathematics ...........................................................................84
Research approach to mathematics presented through presentations by students............87
Method of Math Work Stations...........................................................................................89
Creative drama – drama +math=dramath...........................................................................91
INTEGRATED CLASSROOM................................................................................................95
Geometry and fashion design ............................................................................................95
Geometry and Bulgarian folklore........................................................................................97
MATH AND DATA ANALYSIS.............................................................................................100
Data Simulations..............................................................................................................100
Didactic games in mathematics........................................................................................102
Survey method.................................................................................................................105
REAL LIFE PROBLEMS......................................................................................................109
Problem solving ...............................................................................................................109
Math-lab approach...........................................................................................................112
Motivational tasks / entertaining tasks and games ...........................................................114
Motivational problems in math education .........................................................................116
Maths problems with practical application ........................................................................119
SPECIFIC CASE STUDY ....................................................................................................122
The Portfolio ....................................................................................................................122
INSERT (Interactive Noting System for Effective Reading and Thinking) method ...........124
The Racing games feast of mathematics .........................................................................126
VISUALIZATION AND ICT ..................................................................................................130
Where you can, use computers to do the drudge work.....................................................130

The cube method.............................................................................................................132
‘Brainteasers season’.......................................................................................................134
Solving mathematical problems using concrete materials ................................................135
‘Part of a whole’- introducing fractions in early age ..........................................................136
Visuals and graphics........................................................................................................138
Coordinate Geometry Method in Solving Problems..........................................................140
Experimental method in mathematics ..............................................................................142
E-lesson in mathematics as a form of training.................................................................145
Modeling ..........................................................................................................................147
Mathematics - a tool for modern thinking /”Creative” classroom/......................................149
References .............................................................................................................................151

Teachers should be seriously prepared to answer to the requirements of the
economy based on knowledge, and the ability to “offer product” with appropriate
knowledge, qualifications and competences on the labor market
(T.A.Pachemska, Project Coordinator)

1
INTRODUCTION
The mathematics is all around us. The ability for understanding mathematics and
mathematical judgment is a crucial for the future of the students. In today complex society,
learning and understanding mathematics and natural sciences has become necessary for full
development of everyone. The development of each country economy depends of the individual
simulation, development of new modern technologies and reinforcement of the connections
between science disciplines. The importance of mathematics in the recent period is increased
because of the huge application of the computers, information technologies, modelling and
simulation. Because of that is so important to ensure the best mathematical education for the
children already in primary school.
On ICME, 2004 it is discussed about the importance of primary mathematics education
that cannot be overemphasized never. It is in the primary years that students from any part of
the world learn number concepts and numeration, shapes and figures, and basic measurement
skills, among other beginning mathematical skills. Yet, ironically, in the primary grades mathe-
matics learning becomes more problematic than could be expected. Indeed, it is never true that
teaching primary school mathematics is without effort.
Generally, the main goal of teaching mathematics is mathematization of students’
thinking. The clarity in students’ thinking, the simplicity in students’ assumptions and deduce
logical conclusions are in the basis of the mathematics. One of the most important goals of the
mathematics is to develop skill to the students for understanding of the abstract mathematical
concepts and solving of the real-life problems.
Besides the huge importance and application of the mathematics in the other sciences,
and the application of the mathematical knowledge in everyday life, but in many countries in the
world the mathematics is not popular subject between the students. Most students do not like
mathematics because they usually do not get the desired results. This usually lead to the
anxiety and even phobia for the mathematics. Generally, they face up with conquering the basic
mathematical concepts, but also, they could not use the mathematical knowledge in other
sciences and in various practical situations. Although mathematics is so important and it is on a
pedestal between the sciences, among pupils it is perceived as a difficult, abstract, boring and
no practical subject, [1]. These students’ attitudes towards mathematics are one of the reasons

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for low success of the students on all education levels. Many researchers, as Akinsola,
Moenikia and Singh in [2], [3], [4], respectively have shown that the fear of mathematics is a
factor for low success in mathematics. Generally, the students’ attitudes towards mathematics
and their success in mathematics are in positive correlation. A contribution in the study of
attitudes toward mathematics was by Neale, who underlined that, “attitude plays a crucial role in
learning mathematics and positive attitude toward mathematics is thought to play a key role in
causing students to learn mathematics” [5]. Neale in [5] defined mathematical attitude as “a
liking or disliking of mathematics, a tendency to engage in or avoid mathematical activity, a
belief that one is good or bad at mathematics, and a belief that mathematics is useful or
useless”. Tait–McCutcheon in [9] has observed that the concept of attitude includes at least
three verbs: to think, to feel, and to behave. Thus, students’ attitudes toward mathematics affect
how well or how often they do it, and how much enjoyment they derive from it, Moenikia [8]. All
teachers, especially teachers of math, have struggled to create authentic student interest in the
concepts learned in class. Students often go through the motions of the class period because
they are required to do so without any genuine interest. This must be changed by considering
adding any of these four suggestions into the classroom: taking problems from their real lives,
using a creative approach, use pop culture, or by making math music videos. Awarding of the
students’ attitudes towards mathematics would be useful for the teachers. At the beginning of
each semester, attitude test could be applied to the students, so that teachers can identify the
students who have negative attitude toward mathematics and can take required precautions. In
order to make student active, to increase their motivation, and attitudes, mathematics should be
associated with everyday life. Using concrete materials in learning environments positively
increases students’ mathematics achievement and their attitudes towards mathematics. When
students are satisfied with the activities in the learning environment, learning would be more
permanent and meaningful. Therefore, this situation is important for students to have positive
attitude. The improvement in attitudes is likely to be more significant when taking into
consideration different environments, but the main contribution is determined in the class
environment. Gillet, Filak have researched on this topic and have shown that teacher support
regarding autonomy affected student motivation, among other aspects, in [6, 7]. To overcome
these phenomena, it is necessary, to develop new methods by the teachers, activities in which
the students will be active in the realization of the teaching process. The classical approach in
the teaching, creates a passive student, so the students must be encouraged to take a part in
analysis of the mathematical curriculum.

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The process of teaching mathematics should be realized in situations which provide:
The students are learning to enjoy in mathematics – the school is the best place to
achieve that.
The students are learning the mathematics’ importance – the equalizing of the
mathematics with formulas and schemas is the worst thing, which can be given to the student.
Such approach by the teacher can damage the students’ thinking and understanding. The
learning where and how some mathematical technique could be used is more important than
the studying of that technique, which could be easy, read in the book.
The students are learning to set and to solve the problems – they are studying to
talk, to communicate and to work together in the process of solving mathematical problems.
Learning that mathematics is an indispensable part of their lives is the best mathematical
education.
The students are learning abstraction in order to acquire the relations and
structures - they are using the abstraction to acquire some relations, to see the structures of
something, to determine the authenticity of some statement. The logical thinking is the best gift,
which could be obtained with the mathematics and to use in everyday communication.
The students are learning the basic concepts in mathematics – arithmetic, algebra,
geometry, all of them offer conquering of the abstraction, the structure and the generalization.
The students are included in the process of teaching mathematics everyday – the
task of every teacher is to activate not only the talented, but and the other students.
By the NCTM, “Effective mathematics teaching requires understanding what students
know and need to learn and then challenging and supporting them to learn it well.”
Students learn mathematics through the experiences that teachers provide.
Teachers must know and understand deeply the mathematics they are teaching.
There is no one "right way" to teach.
Effective teaching requires deciding what aspects of a task to highlight, how to
organize and orchestrate the work of students.

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Effective teaching requires continuing efforts to learn and improve. Teachers need
to increase their knowledge about mathematics and pedagogy.
"One of the teaching approaches which contribute particularly well to successful learning in
mathematics is - well planned opportunities for children and young people to learn through
investigate, active approaches" Learning Together: Mathematics - HMIE.
In the last period are realized many projects in which the main area of the research is
the mathematical education. These projects were realized in order to enhance the process of
teaching mathematics. In some of them, it is worked for changing of the students’ attitudes
towards mathematics as a school subject. Also in many projects are elaborated many
procedures for solving of some mathematical problems. The methods, which could be used in
the process of teaching mathematics, are also elaborated in some projects. There are many
realized projects in order to increase the mathematical knowledge through solving mathematical
problems. The Erasmus+ project: Math – Labyrinth – Increasing the level of knowledge thought
solving mathematical problems is such project. However, in neither one it is not considered
the possibility for active including of the students in the process of teaching
mathematics in a way where the student will choose the method on which the teacher could
present some mathematical content. The active participation of the students in the process
of teaching mathematics, in terms of choosing the method for working on some lesson in
mathematics, would contribute a different attitude of students towards mathematics as a
school subject. On the one hand, positive attitudes and interest in learning mathematics
will be imposed, and on the other hand, their knowledge of mathematics as well as their
ability to use the acquired mathematical knowledge will be increased
Available on: https://education.gov.scot/improvement/Pages/num2higherordermaths.aspx
Download: 06.09.2017

5
In order to make the teaching of mathematics accessible to all student and at the same time
pleasant, the project MATHDebate - The Voice of Students – Searching Excellence in
Math Education through Increasing the Motivation for Learning (2016 – 2018) is realizing.
In the project pupils, teachers from schools and academic staff take part, and its main aim is to
develop a new method for realization of teaching mathematics, which would increase the
students’ motivation for learning mathematics, but also would change their attitudes for
the importance of the mathematics in the school and their lives.
What is teaching method?
A teaching method is a way in which a teacher organizes and manages the teaching-
learning situation, presents clear explanations and vivid descriptions, assigns and checks if
learning interacts effectively with learners through questions and probes, answers and
reactions, and praise and criticism (Schulman, 1999). According to Carl (1995), a teaching
method is a way of facilitating interaction between the teacher and learners in order to realize
set goals. Learning that is motivating therefore should be:
• An active process in which the learner is maximally involved;
• Guided through the use of a variety of teaching methods, which in the end offer learners
a variety of learning experiences, that will enable them later to generalize and
discriminate information (Carl, 1995).
In order to motivate learners Scot (1994) posited that learner- centered teaching
methods should be used to ensure that:
• There is a close link between the learning needs of the learner and the teacher's
teaching;
• Feedback is given in phases so that the learner feels that his/her hard work is being
recognized and rewarded by the teacher;
• All learners are challenged and extended in their learning; and
• Whatever is being taught is directly linked to the learners' real life experiences.

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According to these, we want to develop the new teaching methodology and use it to the
students aged 11-15 to like Mathematics and learn more. Using debate on mathematical
problems and ICT methodology for learning will lead to enlarge students’ skills of
mathematics and their abilities to solve practical and word problems. Students will be an
active part of educational process using this new methodology. Students gained
knowledge and skills in mathematics can be applied in other areas of science. Thought
MATHDebate method also literacy and communication skills are developed.
A project of this kind is an excellent opportunity for making arguments between
minds, criticizing different opinions on some topic, all of it with one goal: achieving very
good mathematical skills of the students. At the end, we expect bigger motivation for
learning mathematics to be achieved and this will lead to excellence in mathematical education.
Тhis project would be very beneficial for the schools, as it would help the
teachers, in attempt to produce motivated and responsible learners, who relate positively
to each other, to staff and to the surrounding community. By making mathematical learning
more attractive and accessible, we make sure that the students are well-prepared for the exams
they will take, which are essential for their future development. In addition, it would help young
students to develop self-confidence and to successfully deal with significant life changes and
challenges. Nonetheless, it would enable them to make a positive contribution to the society, by
developing the expertise and experience needed to claim their rights and to understand their
responsibilities, and by preparing them for the challenges and opportunities of working life.
Improving students' motivation to learn mathematics is crucial for many distinct reasons.
At the EU level, the Education and Training 2020 strategy underlines the importance of
providing efficient and equitable education of high quality in order to improve employability and
allow Europe to retain a strong global position. In order to achieve this objective, continued
attention must be paid to raising the level of basic skills such as literacy and numeracy (Council
of the European Union, 2009).
In the last ten years all the schools in many countries (Macedonia FYR too) face with
great difficulties to make students to like and learn mathematics. Although it is an essential
subject for future career development of the students it is usually thought than mathematics is
very difficult, not interested and not connected with other subject area. The knowledge of the
students is decreasing every year. This can be seen by PISA and TIMSS studies conducted in
many schools.

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When the students are in position to select their high school (after ninth grade), because
of the fear of studying Mathematics they usually choose their vocation without any Mathematics
in it, like low school, language schools, medical schools, arts, etc. The technical and science
study programs at Universities are not popular and have lack of students. For example, there is
none unemployed math teacher in a state with very big percent of unemployment.
The state Ministry of education in Macedonia FYR made this question as a national
priority and they made reforms to increase the level of Mathematics knowledge. Reducing the
share of low-achieving students in mathematics is a priority in every European country, defined
as one of the benchmarks for 2020. It also corresponds with one of the four strategic objectives
for the European Council's framework: "Improving the quality and efficiency of education and
training; acquiring key competences and making the level of education and training more
attractive and efficient "(C119 of 28.5.2009)
In efforts that the Ministry of education made to solve this problem, in 2016 Mathematics
was introduced as an obligatory subject for graduate students on the state matura
examinations. However, the students did not fulfill this because of strong negative debate.
This motivated us to make research about new methodology and create innovative ways
of teaching and learning Mathematics using modern technologies, and this also satisfies the
European priority to "support the professional development of teachers as mediators of
creativity and innovation; promote the incorporation of creativity and innovation at all levels of
education and training" (C 141 of 7.6.2008)
We want the teachers together with the Universities professors and volounters in
associations that work on this topic to share their experiences and thoughts and develop new
methodology for learning math skills though democratic process of choosing teaching
methodology. Using this method, they will learn more, they will be more motivated, they will use
innovative technologies to study, and big percent of the students will like to continue with their
education in the field of science and technology area. This is an approach focused on student-
centered and problem-based active learning, and fostering critical thinking skills.
The focus will be students aged 11-15, i.e. in the last three years of the elementary
schools.

8
We believe that the implementation of the project will increase the
underachievement in the basic skills of mathematics, science and literacy through this
new effective and innovative teaching method and make excellence in mathematics
education.
This project will be able to make a comparison with the topics, matter, and types of
problems that students in different countries have and share the experience and knowledge with
Math teachers from the selected countries. The societies that are involved in the project will give
an insight into the practice of teaching and learning Mathematics in other countries and at the
same time, they can contribute to the realization of this project with the enormous experience
they have in European projects of this kind.
Neediness for collecting of good practices in Europe and beyond
The analysis of teaching methodology in the MATHDebate Project consists of activities
that produce the first output of the MATHDebate Project - Collection of related good practices in
Europe and beyond.
This collection of good practices is simply intended to serve as a base for math
educators to share practices and methods that have produced positive results of one sort or
another. It is a collection of materials that represent practitioners’ perspectives based in part
upon research, but mostly upon experience.
What is a description of good practice?
There has to be an expectation of what a pupil might be assumed to "know" when teaching a
topic. The aim of the teachers is to build on and advance that knowledge, to ensure that it has
been incorporated into the pupils’ mental structures appropriately, including knowing about the
limitations of use of that knowledge and providing opportunities for pupils to use and apply that
knowledge in a variety of contexts.
From a constructivist position it would appear that "good practice" is in providing almost any
situation, activity, game, web page activity whereby by some magic process pupils automatically
develop the concepts they need. These processes need to be more carefully identified and
carefully designed series of activities or even actual "tutoring/teaching/chalk and talk" where by
the learner is helped to properly develop the cognitive structures. The good practice should

9
enable the student for easier solving of practical problems. The teacher should be a guide to the
students and should prepare them for successful individual persons. So, he should teach them
all the steps which could be applied as strategies in the process of problems’ solving.
In order for a practice to be good, it should be taken the following into consideration:
• Good practice should include aspects of both teaching and learning.
Good learning takes place when students are given opportunities to solve problems by
developing their understanding and making links between different areas of mathematics and
applying skills.
Good teaching enables good learning to take place by treating students as thinking individuals
who can operate mathematically. It involves creating an appropriate environment in which
students can respond to high levels of expectation and challenge. They are kept on the edge of
thinking. By 1989 National Curriculum Non-Statutory guidance: “The teachers’ job is to organise
and provide the sorts of experiences which enable pupils to construct and develop their own
understanding of mathematics, rather than simply communicate the ways in which they
themselves understand the subject.”
• Different good practices in various places in the world.
One and the same practice can be differently accepted by the students in different parts of the
world. If one practice is good for students who study in a school in Europe, it does not
necessarily mean that the same practice would be the best choice for students who study in
schools in America. Whether a practice is good or not primarily depends on many factors: the
way of realization of the teaching process, previously acquired knowledge, in what social
environment students learn etc.

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• Good practice needs to be developed in all school’s levels.
• Models of good practices need to be shared.
• Good practice needs to be valued at all levels- school, community, district, state,
national and international.
The best practice involves:
• listening to the voices of student
• designing a student-centered curriculum
• Student enjoying learning
• doing to understand – active learning
• relating learning to the world of the student
• teachers as learners
• providing professional development
• Including practical examples
One of the goals of this analysis is to gather good practices of various teaching methods and
their implementation in the schools:
• to make a survey of math teaching methodology and other activities involving math
• to specify the modern technologies and the methodologies in use
• to collect best practices in schools which participate in the project.
Based on the received information and experiences a list of good practices is provided. This list
is a part of the analysis report, which will be published electronically. Some of the collected
methods will be uploaded on the e-platform (computer and mobile version) and will be a part of
MATHDebate process. In this way, they will be visible for all interested parties – teachers,
students, parents...
In the realization of the analysis of good practices participated all partner organizations from the
MATHDebate project:
1. Goce Delcev State University - Stip, Macedonia.
2. Union of researchers of Macedonia – SIM – Skopje, Macedonia
3. Municipal Primary school “Ljuben Lape" - Skopje
4. General Secondary School “St. Kliment Ohridski” – Aksakovo, Bulgaria

11
5. South-West University “Neofit Rilski” – Blagoevgrad, Bulgaria
6. Secondary School "Mihai Eminescu" – Alba Iulia, Romania
7. Cyprus Mathematical Society – Cyprus
All partners have made effort and they spend much of their time to do the research and to make
selection of good practices. The school partners have used their current experiences in the
classes with their students and also have used the internet resources to collect more examples
of good practices. The other partners institutions like involved Universities and associations
analyzed the offered good practices from the schools, added good practices from their
experiences and researches and after that analyzed all of them and systematized the findings
regarding the current teaching methodology in seven groups.
It was considered various methods which are good practices in Europe and beyond.
The collection of these practices is the first step to quality assurance for creation of a
methodology of standards, which is used as a base for the development of the interactive e-
platform and MATHDebate method.
This collection of good practices is an electronic database of all practices in teaching and
learning mathematics that are relevant to the students' age and interest.
The researchers focused their attention according to the type of practice that is relevant to our
proposal and rational; since the target group is mostly students at age 11-15 it was of immense
importance to concentrate on the activities that are relevant to type and scope for this age of
pupils.
What is actually made?
In the period of preparation of the analysis of the teaching methodology, it was taken many
activities to achieve the desired outcomes. During the period of the realization of this analysis,
the participants carried out the following activities:
• research of good practices (methods) in Europe and beyond;
• creation of methodology of standards;
• selection of methods that are relevant to project proposal;
• collection of good practices;
• creation of database;

12
• classification of the selected methods in seven groups, according to that in what kind of
mathematical content could be applied;
All the methods and approaches included in the Collection of good practices are set out in the
MATHDebate project itself and are relevant to the purpose and complexity of the issues of the
MATHDebate project.
All the participants in preparation of this analysis made decisions about who to be surveyed,
how the data to be collected, the sources of data that to be used, and the duration of data
collection during the Meeting 1.
The researchers focused their attention according to the type of practice that is relevant to the
target group: students at age 11-15 years.
All good practices as methods are classified in seven groups:
• Arithmetic
• Communication skills
• Integrated classroom
• Math and data analysis
• Real life problems
• Specific case studying
• Visualization and ICT
The classification of the methods is done according to the methods’ content, the possibilities for
their implementation at the classes (in what kind of classes they could be used), the
activities/actions that the practice involve and according to the resources which is needed for
method application in the teaching process.

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The first group Arithmetic
is referring to all methods
which could be applied in
order the students adopt
and solve problems that
include basic arithmetic
operations: addition,
subtraction, multiplication
and division, and more
advanced operations, such
as manipulations
of percentages, square
roots, exponentiation,
and logarithmic functions.
These methods could be
applied in realization of
algebra and arithmetic
classes, when the students
do algebraic operations
and work with numbers.
Available on:
https://www.theguardian.com/teacher-network/teacher-blog/2014/may/19/how-
to-teach-mental-arithmetic-maths
(Download on: 06.09.2017)
Mathematics provides a specific and rich
context for students to develop their ability
to read, write, visualise and talk about
complex situations involving a range of
mathematical ideas. Students can apply
and further develop their literacy skills and
strategies by shifting between verbal,
graphic, numerical and symbolic forms of
representing problems in order to
formulate, understand and solve problems
and communicate results.
The picture is taken on math class in Primary school
Ljuben Lape in Skopje.
(Debate)

14
The methods included in the second group Communication skills refer to students’
communication skills. Their main aim is to increase communication in math classes in order to
simplify the mathematical problems and to get solution of the problem. These skills, including
reading, writing, listening, and speaking, enhance mathematical understanding and problem-
solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze
mathematical ideas. The curriculum and evaluation standards recommend that opportunities be
afforded students to "use language to communicate their mathematical ideas" (NCTM 1989,
78).
Because of the great possibility for application of the mathematical knowledge in the other
sciences, it is needed to create a group of methods Integrated classroom. Integration focuses
on making connections for students, allowing them to engage in relevant, meaningful activities
that can be connected to real life. The methods in this category covers mathematical problems
from the other sciences. Mathematical problems in biology, geography, physics, and economy
could be treat by these methods.
The picture is taken on math class in Primary school Ljuben
Lape in Skopje.
The picture is taken on math class in Secondary
School "Mihai Eminescu" – Alba Iulia, Romania
(Gallery walk)
In this category Math and data analysis,
methods for data analysis are included. The
methods in this group could be applied for
quantitative or qualitative analysis. Each
method has specific technique. These
methods could be adequate for work with
statistical data and for solving of everyday
problems, which were researched by the
students.
Available on: https://www.pinterest.com/explore/student-
data-tracking/
Download: 06.09.2017

15
Informal "real life" mathematical problems are questions related to a concrete setting. They are
used in mathematics education to teach students to connect real life situations to the abstract
language of mathematics. This group Real – life problems consists of methods for solving
practical problems from day-to-day. These problems are covering wide range of practical
problems in different areas, with which the people are facing in their lives.
Available on: http://malini-math.blogspot.mk/2011/08/applications-of-trigonometry-in-real.html
(download on: 06.09.2017)
Through the years, teachers have struggled to make math meaningful by providing students
with problems and examples demonstrating its applications in everyday life. Nowadays
technology makes it possible for students to experience the value of math in daily life instead of
just reading about it.Case studies drawn from real life give meaning to theoretical concepts.The
group of methods for Specific case studying consists of methods for researching
(qualitative study/inductive research).

16
The case study method often involves
simply observing what happens to, or
reconstructing 'the case history' of a
single participant or group of
individuals. A case study is a report of
descriptive information on data of
research of an experiment, project,
event or analysis.
Mathematical visualization is an aspect
of geometry that allows one to
understand and explore mathematical
phenomena via visualization.
Mathematical visualization is used
throughout mathematics, particularly in
the fields of geometry and analysis. The
application of ICT helps the
visualization and problems’ solving.
These methods in the group
Visualization and ICT could be used
for solving problems where visualization
is necessary and in that way the
process of finding solution is simpler.
The picture is taken on math class in Secondary School "Mihai
Eminescu" – Alba Iulia, Romania
(Project)
The picture is taken on math class in Primary school Ljuben Lape in Skopje.

17
Analysis
What we have concluded about situation of the process of teaching mathematics in the target
schools which are part of the project?
It is deduced that in order of increasing of the motivation for learning mathematics it is needed
to change the approach in the process of teaching mathematics. The schools which are the
target are using different approaches based on the survey between the students and teachers
and it is perceived that are needed innovative approaches, especially in the part of learning of
mathematical tools in process of solving problems through curriculum.
It was determined at many tests on the level of the Republic of Macedonia, that the students
have problems in functional connecting of the knowledge in mathematics and other sciences.
Having in mind, the basic syntagma on the project “To hear the voice of the students”, the
teachers and other participants in the project partner institutions have make effort to research
the different approaches in the process of teaching mathematics in the countries which have the
best results on the international tests.
The analysis of the offered practices has as a goal to help to the teachers in changing the
environment for studying and learning, and to allow of the students to be a creator and partners
in the teaching process.
It is expected that this interaction between teachers and students, the ICT and other digital
technology and resources will increase the motivation for learning mathematics and will
contribute the increasing of knowledge. The teachers should use the information technology to
increase the number of innovative methods in the teaching process.
For some of the teaching methods which are part of this analysis, the targeted schools have not
enough teaching mechanism and devices. Because of that, it will be used videos and
simulations which are already made, in order some method to be simulated.
Why did we need an analysis?
The aim of this publication is not only to present and depict active methods, but also to confirm
that they encourage contemporary students to work in class, acquire knowledge and skills that
are necessary in life. Moreover, the analysis should encourage the teachers to include new and
innovative approaches in the process of teaching mathematics and to foster the students to take
an active part in the realization of the teaching process, according to the main motto of the
project – Students tell their opinion about the methods and they choose the method which is the
best for presenting of some teaching unit by the teacher.

18
Content of Collection of good practices
The Collection of good practices will be categorized in seven groups, according to that in what
kind of mathematical content they could be applied.
Remark: Some of the methods are included in more than one group. It means that they could be
applied in different situations and areas in mathematics.
Arithmetic
1. “Find the missing term”-sequences introduced in early age
2. “Make your own money”-practicing simple mathematical operations
3. Comparing Decimals Game
4. Math class assisted by parents
5. Discovering learning
6. Game and simulation
7. Algorithmic method
8. Didactic games in mathematics
9. Individual work in mathematics lesson
Arithmetic
Good practice
Communication skills Integrated classroom
Math and data analysis Real life problems
Specific case studying
Visualization and ICT

19
Communication skills
1. Explicit instruction or Direct Instruction Lesson
2. Cooperative Learning
3. “Famous mathematicians”- throw - out history of mathematics
4. Peer Tutoring
5. Project
6. The Pyramid (snowball method)
7. The mosaic method
8. The Cluster method
9. Brainstorming
10. The gallery walk
11. Flipped Classroom
12. Measuring angels with jigsaw method
13. Jigsaw puzzles
14. Students Teams Achievement Division – STAD method
15. Storytelling method
16. Think-pair-share (TPS)
17. Debate
18. Discussion method in mathematics
19. The Racing games feast of mathematics
20. Research approach to mathematics presented through presentations by students.
21. Method of Math Work Stations
22. Creative drama – drama +math=dramath

20
Integrated classroom
1. “Magic Maths” – innovative strategies for developing and embedding mathematics in
family learning.
2. “Famous mathematicians” – throw - out history of mathematics
3. Project
4. Brainstorming
5. Discovery Learning – inquiry Method
6. Experimental method in mathematics
7. Geometry and Bulgarian folklore
8. Geometry and fashion design
Math and data analysis
2. Survey project
3. Data Simulations
4. Debate
5. Didactic games in mathematics
Real life problems
1. “Magic Maths” – innovative strategies for developing and embedding mathematics in
family learning.
2. “Make your own money” - practicing simple mathematical operations
3. Math class assisted by parents
4. Problem Solving
5. Discovery Learning – inquiry Method

21
7. Math-Lab Approach
8. Algorithmic method
9. Motivational tasks / entertaining tasks and games /
10. Motivational Problems in Mathematical Education
11. Maths problems with practical application
Specific case studying
1. The Portfolio
2. INSERT (Interactive Noting System for Effective Reading and Thinking) method
3. Flipped Classroom
4. Students Teams Achievement Division – STAD method
5. Debate
6. The Racing games feast of mathematics
7. Motivational tasks / entertaining tasks and games
8. Motivational Problems in Mathematical Education
9. Mathematics - a tool for modern thinking /”Creative” classroom/
10. Creative drama – drama +math=dramath
Visualization and ICT
1. Where you can, use computers to do the drudge work
2. Brainteasers season
3. Solving mathematical problems using concrete materials
4. ‘Part of a whole’- introducing fractions in early age
5. Computer-assisted learning
6. The mosaic method

22
7. The cube method
8. The gallery walk
10. Math-lab approach
11. Visuals and graphics
12. Coordinate Geometry Method in Solving Problems
13. E-lesson in mathematics as a form of training
14. Experimental method in mathematics
15. Geometry and Bulgarian folklore
16. Geometry and fashion design
18. Modeling
Remark: The method that is included in few categories will be presented only one time with the
good practice template in the annex.

23
Conclusion
The Analysis of teaching methodology is a first step of the process of developing a new
methodology and creating innovative ways of teaching and learning Mathematics using modern
technologies. This aproach satisfies the European priority to "support the professional
development of teachers as mediators of creativity and innovation; promote the incorporation of
creativity and innovation at all levels of education and training”.
The done analysis of good practices would help to the teachers to change the conditions in the
classroom, the approach in teaching of the material from the curriculum. This analysis would be
beneficial for the students too, because by using of these good practices the students would be
able to choose the way on which their teachers will teach some lesson. The using of ICT in the
teaching process would be helpful for the teachers and the students for the increasing of the
digital competences in the process of successful development for the persons – carrier of the
economy in 21st century. The e-platform, which included the done analysis of good practices,
will be available for all who want to try and use this new tool to increase the motivation for
studying mathematics. In addition, will be listed the chosen teaching methods which are used in
different countries in Europe and beyond. For all teaching methods, the main information, which
were needed for the project, are included.
Better competence of the teachers since they will look on the teaching process from the
point view of the students and have better understanding for it, strengthening the
teachers' digital and linguistic competences, the possibility of networking and exchange
of good practices, competitiveness among teachers, comparability of the common
European educational space, are our main priorities.

24
ANNEX - Collection of Good Practices in Europe and beyond

25
ARITHEMTIC
FIELD CONTENT
PLEASE FILL THE CELLS ACCORDING TO
THE EXPLANATION IN THE COLUMN
CONTENT
1. TITLE
What is the name that best
describes the good
practice?
“Find missing term”- sequences introduced in
early age the
2. COUNTRY
In which country does the
good practice take place?
Macedonia
3. LINK
Please give a web link for
further information about
the good practice.
http://www.stepbystep.org.mk/WEBprostor/toolb
ox/Matematika_niz_igra.pdf
4. LANGUAGE Language of the source. Macedonian
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
Please summarise the
main characteristics of the
teaching practice.
The activity is practiced in groups. The students
get cards with numbers that they are supposed
to find the place for on a big poster posted in the
classroom.
6. RESOURCES
Required resources for
effective application of the
method.
Big poster, cards with numbers, clips
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
characteristics, which
describe the method as a
GOOD practice.
• Visualisation of the order of numbers in
sequences
• Working in groups
• Practicing addition and subtraction
8. HOW DOES IT
WORK?
Max 100 words.
Which activities/actions
does the practice involve?
The teacher or instructor splits the students in
groups of 2-3 students. Each group of students
gets a certain set of cards with numbers written
on it. On a display, there is a big poster with
parts of sequences (at early age, arithmetic) in
which there is a number missing. There are
more cards then numbers missing on the poster.
The task of every group is to check if their
numbers fit in some place on the poster. If they
have a card that does not fit anywhere, they
need to explain why it does not. The game
begins when there are no more cards left.
9. EVIDENCE
Links for videos, photos.
The source does not contain photos or videos to
the actual students work.
10. RESULTS
Max 75-100 words.
 Quantitative and
qualitative results
in relation to the
This practice is a fun and visual way of
introducing sequences, order and relation
between numbers for early age. The students
also have bounding and befriending time, as

26
teaching goals.
 What is the
users/target
group’s opinion of
the activity?
they work in groups. Students like this activity,
especially if they are not math-oriented,
because nobody is under pressure or in the
centre of attention.
11. ASSESSMENT
Suggested assessment
method for the students
As it is a group activity, students should be
assessed in two different ways: group
participation and group achievements. The
achievements of the group can be measured by
counting how many numbers were putted in the
right place. The group participation of a student
should be measured by the students in the
group, verbally, by asking them to explain who
did what and how. By practicing this we also
review the material and encourage student to
work together.
12. UPLOAD A FILE
Please send related
electronic documents
(lesson plan, evaluation
etc.) so that they can be
uploaded on the e-
platform.
https://drive.google.com/open?id=0B97-
RYVZgbqDeEZmWnMyQWFvX3M
RYVZgbqDUTQyUEZRb1pNenM
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
“Make your own money”-practicing simple
mathematical operations
2. COUNTRY
Macedonia
3. LINK
the good practice.
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Student should draw their own money and then
later use them to buy things from an improvised
market in the classroom.
6. RESOURCES
method.
Coloured paper, markers, scissors, improvised
fruit and vegetables.
7. WHY IT IS A Give at least three • Learning practical skill

27
GOOD
PRACTICE?
GOOD practice.
• Creativity
• Practicing addition, multiplication,
subtraction
• Working with data
8. HOW DOES IT
WORK?
Max 100 words.
Each student receives 5 rectangles out of 4
different colors. They are supposed to first
decorate their ‘money’. The colors should
represent 1 denar, 5 denars, 10 denars and 20
denars. The teacher (or volunteers from the
students) should sell the improvised groceries in
the classroom. Before the market ‘opens’ each
student should make a list of everything that
they want to buy for the next day in school.
Each fruit or vegetable has a different price. At
the end, each student should tell how many
pieces they got, each at what price, how many
they paid for each type of grocery, what change
did they got, etc.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
After this practise students can do addition
multiplication and subtraction faster and more
precise. Students feel that they can help in the
market when grocery shopping with their family.
Big part of this practice is planning their ‘budget’
and items that they need/want. Students start
understanding the difference between what they
want and what they need.
11. ASSESSMENT
The marking point should be scheduled based
on the following criteria:
• What portion of the items on the
shopping list is bought
• Correctly calculating the amount of
money, they should pay and get change
for.
• Getting the max number of pieces, they
could get from the list (optimizing the
budget)
• Their understanding about what they
could have bought more and what to
leave out.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
RYVZgbqDVUpFTzd3TFJxWG8
RYVZgbqDbVFfcEtTVkVRdWM

28
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Comparing Decimals Game
2. COUNTRY
USA
3. LINK
the good practice.
http://www.teacher.org/lesson-plan/comparing-
decimals-game
4. LANGUAGE Language of the source. English
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Students will play a game in which they choose
cards and choose the best place to put the
number they have chosen in order to get the
highest answer possible.
6. RESOURCES
method.
1 copy of the 2 page worksheet (attached)
1 deck of cards per pair of students (with Jacks,
Queens and Kings removed)
1 pencil
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Students will read, write, and compare decimals
to thousandths. Students will compare two
decimals to thousandths based on meanings of
the digits in each place, using >, =, and <
symbols to record the results of comparisons
8. HOW DOES IT
WORK?
Max 100 words.
Since you’re the oldest, select a card from the
deck. Think aloud as you choose where to place
the number you selected. Call on a student to
select the next card and have him decide where
to put his card and state the value based on the
place he chose. Continue until all of the spaces
are filled in. Read your final number in the
correct form. Call on a student to read the class’
number and help them to read it in correct form.
Ask students who has the greater number.
On page 2, write your number in the Player 1
space and the class’ number in the player 2
place. Ask them which one of the symbols
belongs in the middle, <, =, or >
Explain that player one always writes their
number in the Player 1 place and player 2
always in the player 2 place, but you will write a
different symbol based on who’s number is

29
greater.
Circle or highlight the greater number to show
which partner won this round.
Give students time to play the game with their
partners.
You may choose to have them play multiple
rounds with one partner or change partners after
each round.
9. EVIDENCE
The source did not contain photos or videos of
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The students learn the value of the number
depends on the place he number is set into.
They learn to compare numbers with decimal
spaces.
The students think of this practice as it is a
game and do not feel the pressure of getting the
wrong answer.
11. ASSESSMENT
Students analyze and compare the results of the
game, teacher can check the comparison in part
2 of the worksheet and assess students in this
way.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
http://www.teacher.org/wp-
content/plugins/download-
attachments/includes/download.php?id=20057

30
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Math class assisted by parents
2. COUNTRY
Romania
3. LINK
the good practice.
http://everydaymath.uchicago.edu/parents/
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
A group of pupils are taught the information
needed to reach a certain level of performance
Each pupil will respond to at least two
theoretical questions and solve at the
blackboard an exercise which will be evaluated
by his colleagues
6. RESOURCES
method.
worksheets, marker
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Awakening the interest of any student for the in-
depth study of mathematics, closely related to
the national exam
* The opportunity for each parent to
observe their child compared with their
classmates, both in terms of training and
emotionally.
8. HOW DOES IT
WORK?
Max 100 words.
Make an overview of the theoretical concepts
learned in plane geometry (7th grade) and
geometry in space (8th grade) through
questions asked by their fellow students.
Each student is given a sheet with algebra
problems proposed to be solved.
The board is divided into six parts.
Each student randomly draws a ticket with a
problem to be solved at the board.

31
The classmates are divided into six groups.
Each group seeks to solve the problem of one of
the colleagues from the board and intervene
when needed.
In the end, the teacher makes an assessment
on the way the activities were carried on.
9. EVIDENCE
The source does not contain photos or videos of
the actual student work.
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The whole activity was very interesting and
instructive.
Following this activity, each student, under
the guidance of the teacher and checked closely
by their parents, can improve school
performance.
11. ASSESSMENT
Students who have solved the problems well
receive extra work for improving their
knowledge, and the others try to get up-to-date
with what they need to know.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

32
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Discovery learning
2. COUNTRY
Macedonia
3. LINK
the good practice.
https://www.learning-theories.com/discovery-
learning-bruner.html
http://www.teach-
nology.com/teachers/methods/theories/discover
y.html
http://www.learnnc.org/lp/pages/5352
4. LANGUAGE Language of the source. USA
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Discovery learning is an inquiry-based,
constructivist learning theory that takes place in
problem solving situations where the learner
draws on his or her own past experience and
existing knowledge to discover facts and
relationships and new truths to be learned [1].
As a result, students may be more likely to
remember concepts and knowledge discovered
on their own [2].
6. RESOURCES
method.
http://floridarti.usf.edu/resources/format/pdf/Clas
sroom%20Cognitive%20and%20Metacognitive
%20Strategies%20for%20Teachers_Revised_S
R_09.08.10.pdf
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
1. encourages active engagement
2. promotes motivation
3. promotes autonomy, responsibility,
independence
4. develops creativity and problem solving
skills.
5. tailors learning experiences
8. HOW DOES IT
WORK?
Max 100 words.
Students interact with the world by exploring
and manipulating objects, wrestling with
questions and controversies, or performing
experiments.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
In the process of learning through discovery, the
focus is on the search for solutions from
elements already known
The deductive way of learning through discovery

33
 What is the
users/target
the activity?
is specific to learning activities it which
identifying ways of working (for example,
multiplication as repeated addition) is required.
Students form their correlation capabilities by
applying the results found in the proposed
exercises.
11. ASSESSMENT
Can be done by self-assessment, filling check
lists (analytic or holistic); by simple tracking
student’s work.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

34
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Game and simulation
2. COUNTRY
USA
3. LINK
the good practice.
http://www.thirteen.org/get-the-
math/files/2011/10/vidgamesfulllesson.pdf
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
A procedure which employs skills and/or chance
and has a winner
Predominantly used to practice and reinforce
basic skills, additionally can be used to
introduce new concepts and develop logical
thinking and P.S. strategies
A simulation can be defined as a reconstruction
of a situation or a series of events which may
happen in any community.
A simulation required each pupil to make
decisions based on previous training and
available information.
After the pupils make a decision, they are
provided with opportunities to see or discuss
one or more possible consequences of this
decision—in some ways simulations are really
sophisticated games such as monopoly.
6. RESOURCES
method.
Computer, game, board.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
characteristics which
GOOD practice.
1.Usually highly motivating
2.Pupils enjoy playing games
3.More likely to generate greater
understanding and retention
4.Games are an active approach to learning
5.Good attitudes to math are fostered
through games
8. HOW DOES IT
WORK?
Max 100 words.
Pikado.docx
http://www.thirteen.org/get-
themath/files/2011/10/vidgamesfulllesson.pdf
9. EVIDENCE
Links for videos, photos. The source does not contain photos or videos of

35
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
 It is related to pupil’s own experience
and thus motivating
• It is an active approach to learning
• It fosters retention
• It develops new roles functions for both
teacher and pupil
• It fosters cooperation among students
• It relates mathematics to ‘real-life
situations’.
When designed well, both simulations and
gaming environments can facilitate students’
learning of both specific domain knowledge and
concepts, and several cognitive skills like
pattern recognition, decision-making and
problem-solving
gaming could be used effectively to provoke
interest, teach domain knowledge
games strengthened students’ engagement,
information processing, problem-solving, social
development, and academic abilities.
Other educational strengths of using games and
simulations include developing a variety of
cognitive objectives, transferable process skills,
student-centered learning, initiative, creative
thinking, affective objectives, sense of
completion, and knowledge integration
Student effectiveness increases when they are
afforded opportunities to contribute to the game
design and create new games
• Students’ motivation, skills, and ability to
explore, experiment and collaborate increased
by playing computer games
• With realistic games, students not only
become smarter and intellectually engaged but
also realize their desire for hard fun, delayed
gratification, rewards, making right decisions,
participation, depth of understanding, challenge,
and using their pattern recognition and problem-
solving skills
11. ASSESSMENT
E-test
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
Pikado.docx
http://www.thirteen.org/get-the-
math/files/2011/10/vidgamesfulllesson.pdf

36
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Algorithmic method
2. COUNTRY
Bulgaria
3. LINK
the good practice.
https://diuu.bg/emag/3647/3/
4. LANGUAGE Language of the source. Bulgarian
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
The problem with the algorithms is a problem for
detection and analysis of mental activity, as in
solving tasks and in life in general.
In mathematics algorithmic approach leads to
larger specialization and improvement. It is
important to ensure the most favorable
conditions for the processing and utilization of
information from students and maximum
development of their cognition.
Construction of efficient algorithms of training
involves a logical analysis of the submitted
material for studying and using concepts and
simple rules of mathematical logic.
6. RESOURCES
method.
Theoretical sources. Textbooks. Workbooks and
manuals.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
-Algorithmic method reveals an opportunity for
leadership and management of the learning
process.
- Are developing intellectual and practical skills.
- Students learn how to learn and what to learn.
- Creative thinking;
8. HOW DOES IT
WORK?
Max 100 words.
1. Choose a theme for the application of the
method ( The introduction of formulas to
calculate the roots of quadratic equation)
2. Logic activities:
- conditions for application;
- researcing possibilities of number of solutions;
3. Determination of training actions – (performed

37
mathematical operations)
4. Determining the way of their connection –(
logical circuit of the algorithm)
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Training algorithms enhances creative search,
guesswork, intuition.
Serve to develop a number of important
qualities of logical and creative thinking of
students as suggesting such a method in which
students prepare to independently detect the
required algorithm.
11. ASSESSMENT
individual assessment:
- Learning algorithm;
- Application of the algorithm;
- Detecting situations of application of the
algorithm;
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
-

38
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Didactic games in mathematics
2. COUNTRY
Bulgaria
3. LINK
the good practice.
www.math.bas.bg/smb/2010_PK/tom/pdf/340-
346.pdf
priobshti.se/…i/izpolzvane-na-didakticheski-
igri...
4. LANGUAGE Language of the source. Bulgarian language
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Didactic game in mathematics education
is viewed as a powerful means of stimulating
active cognitive activities in students; increase
their interest in mathematics and leads to easier
absorption of learning content.
Didactic game plays a crucial role in enhancing
the activity of students in the learning process,
helps to facilitate absorption of educational
content, urges on active cognitive activity
greater number of students and increases their
interest.
Actual pedagogy game is complicated, but
simultaneously it is an opportunity for
harmonious and spontaneous communication
between students and teachers. Throughout the
game the students concentrate and mobilize
themselves and are able to make great efforts to
achieve the goal of the game.
6. RESOURCES
method.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
During the game participants acquire skills and
habits of concentration and independent
thinking; they develop their attention and pursuit
of knowledge; They do not notice that they learn
to recognize and remember new or assimilate
and apply the acquired knowledge; orient
themselves in photographic situations by
completing the stock of ideas and concepts;

39
develop certain habits and imagination. Even
the usually passive students in class in
mathematics include willingly make efforts not to
mislead their peers throughout the game. So
didactic game becomes a transformative
creative activity located in close cooperation
with other types of academic work.
8. HOW DOES IT
WORK?
Max 100 words.
Orientation:
The teacher defines the theme, makes a
characteristic of the game and an overview of its
moves and rules.
Preparations for holding the game:
Getting to know with the script, assignment of
roles, preparing for their performance, providing
procedures for the management of the game.
Conducting the game:
The teacher monitors the conducting of the
game, controls the sequence of the participants’
actions, provide the necessary support, reports
the results.
Discussion of the game:
Implemented actions, positive and negative
sides during the game, as well as the arisen
difficulties are being analyzed; possible ways of
the game realization including possible
amendments to the rules are also being
discussed.
A significant part of the didactic games are
gaming actions that regulate the rules of the
game, stimulate cognitive activities of
participants, provide an opportunity to
demonstrate their ability to transform
knowledge, skills and habits to achieve the
objectives of the game.
Cognitive content is the basis of didactic game
and lies in the utilization of those skills and
knowledge that apply in solving educational
problems embedded in game. Didactic game
has a certain game result which is the end the
game and gives its completeness.It occurs
primarily in the form of solution to the academic
task and brings the student satisfaction.

40
9. EVIDENCE
Links for videos, photos. -
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
By playing children mastered the rules of
intellectual and practical activities in accessible
formats. Intellectual game is an effective form of
conducting lessons in mathematics as the
knowledge acquired with interest are the
soundest. Students take up the game and not
pay attention to the fact that in the process of
playing they have to solve serious tasks.
The use of didactic games in teaching
mathematics enables students to develop, refine
and consolidate their observation, to form team
working skills, teaches them to listen and
respect other opinions, to develop their creative
abilities. Children are much more free,
responsible, creative, active and independent.
The game helps to create and maintain a
benevolent, positive psychological climate in the
students’ team.
11. ASSESSMENT
-
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
https://drive.google.com/open?id=0B4ls-
AtzeWJ9OW5FbzBOSlNOSFU

41
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Individual work in mathematics lesson
2. COUNTRY
Bulgaria
3. LINK
the good practice.
www.math.bas.bg/omi/DidMod/Articles/statiaKP
.pd
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Individual work is defined as work which is
performed without the direct participation of the
teacher, but it’s being assigned as a task to the
students within a particular period. Students
consciously strive to achieve the objective of the
task, make every effort and express the results
of their mental or physical action in one form or
another.
Individual work is a means of educating
students to self-activity, as well as a means of
developing their independence of thinking and
actions. By means of an active individual work
students need to acquire new knowledge, to
consolidate, check and apply the ones that have
already been acquired; in the course of carrying
out their individual activity they should form the
ability to rely on themselves.
6. RESOURCES
method.
Worksheets, selection of tasks by the
teacher
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
• Development of a higher level of
cognitive autonomy.
• Consolidate the theoretical knowledge.
• Distinguish the essential from non-
essential links in the process of teaching
mathematics.
• Reinforcement of knowledge and skills by
solving various tasks.
• Performing comparative analysis between
studying math concepts.

42
8. HOW DOES IT
WORK?
Max 100 words.
Individual work of consolidation,
expansion and improvement of acquired
knowledge.
What is necessary for implementation of
individual work?
1. Individual work needs to be realized by
students; they have to be aware of its purpose
and meaning. When students are assigned
tasks for individual work they need to be in the
clear with the aim to be achieved after their
solution.
2. Compliance with the degree of
formation of mental and practical skills as well
as students’ learning habits with their skills to
work independently.
3. Implementation of the principles of
accessibility and systematic.
4. Using of instructions in oral, written or
visual form before students start their individual
work.
5. Individual work must be followed by
analysis.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The selected tasks are of increasing
complexity for each additional step. The
students climbed all existing stairs have
mastered the learning content and receive the
highest mark if the tasks had been solved
correctly. When time limit is up compulsory
correction is done by presenting of task
solutions. Students themselves check their
solution with red pens, correct their mistakes
and evaluate themselves according to the
teacher’s instructions.
11. ASSESSMENT
Test, discussion
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
AtzeWJ9b3dUOW95c3FSZms
AtzeWJ9LXVTZ0xYa1lfYk0

44
COMMUNICATION SKILLS
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Explicit instruction or Direct Instruction Lesson
2. COUNTRY
USA
3. LINK
the good practice.
https://iris.peabody.vanderbilt.edu/module/math/
cresource/q3/p06/#content
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Explicit or direct instruction involves teaching a
specific skill or concept in a highly structured
environment using clear, direct language. This
type of instruction is focused on producing
specific learning outcomes and sometimes
involves the use of scripted lessons.
6. RESOURCES
method.
Book, board.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Clearly identifies the expectations for learning;
Provides precise instructions;
Connect new learning to previously learn.
8. HOW DOES IT
WORK?
Max 100 words.
Orientation to the Lesson: Teacher
gains students’ attention; Teacher relates
today’s lesson to a previously related one;
Teacher uses essential questions to activate
students’ thinking
Initial Instruction: Teacher leads
completion of several sample problems;
Teacher models and instructs students to model
problem completion; Teacher points out difficult
aspects of problem
Teacher-Guided Practice: Students
complete problems under teacher supervision;
Teacher monitors each student’s success in
problem completion; Teacher assists students
independently; Students may discuss problems

45
with each other
Independent Practice: Students
complete sample problems independently;
Students may complete homework as
independent practice
Check: Teacher checks student performance on
independent work
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
This practice enables students to model
different mathematical problems to solve and
discuss them independently. Also, this practice
helps students independently perform their
homework based on instruction received during
the class.
The group's opinion on the activity is
positive because they take all the necessary
instructions from the teacher to solve
independently the mathematical problems.
11. ASSESSMENT
Competition
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
/
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Cooperative learning
2. COUNTRY
USA
3. LINK
the good practice.
5. SUMMARY
(DESCRIPTION
Max 50 words. Cooperative learning is a teaching method that
uses small, heterogeneous (that is, mixed-

46
OF THE
METHOD)
teaching practice.
ability) groups to maximize the learning of each
of those groups’ members.
6. RESOURCES
method.
Book, notebook, flipchart
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Lead to greater motivation toward learning
Increase time on task
Improve self-esteem
8. HOW DOES IT
WORK?
Max 100 words.
Teacher assigning students to small groups for
a cooperative-learning task.The students then
work together to solve a mathematic problem.
9. EVIDENCE
https://iris.peabody.vanderbilt.edu/wp-
content/uploads/module_media/math_media/mo
vies/math_08_angle.mp4
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Discussing and solving problems as a group can
help students to move from a concrete level of
understanding to a more abstract level of
understanding. Cooperative learning also helps
students to develop social skills by creating a
context for interaction.
Research has demonstrated that some
cooperative learning programs (i.e., Team-
Accelerated Instruction [TAI], Student Teams-
Achievement Divisions [STAD]) have yielded
favourable results for improving computation
skills.
11. ASSESSMENT
Competition
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
/

47
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
‘Famous mathematicians’-throw-out history of
mathematics
2. COUNTRY
USA
3. LINK
the good practice.
http://atlantis.coe.uh.edu/archive/math/math_les
sons/mathles2.html
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Students in groups of two will research a
particular mathematician.
6. RESOURCES
method.
World Map, stick pins, colour paper for creating
a timeline
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
• Identifying with a mathematician
• Increase research skills
• Presentation skills
8. HOW DOES IT
WORK?
Max 100 words.
The teacher should become familiar with all
resources available at the school for student
research on mathematicians. Web sites can be
bookmarked or lists of mathematicians posted
from web sites for students to easily use as
resources. World map is in the room with small
cards and pins for identifying home countries of
the mathematicians. The teacher "proposes" the
area of investigation. The teacher can excite the
students about this projects by telling the
students about some of the famous
mathematicians. The students in the class may
have some knowledge from past studies that
can be shared in class. Facts about
mathematician's lives is not the focus of this
lesson. The students should come away with an
interest in learning more about these
mathematicians and an overall appreciation for
these mathematicians. The students, when
creating their models, should have the
opportunity to discuss their model with other
students and with the teacher. Applying the the

48
knowledge that was learned from the research
of the mathematician to the created model
design will be the problem-solving part of this
lesson for students. Every student will have a
different "construction" of knowledge, so the
assignments will vary considerable.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Students, especially students that struggle with
math learn to understand that all formulas are
invented by humans, that somebody actually
thought of them and it took some time to get
there. They identify themselves with a person
that is good in mathematics and find common
grounds with him/her. Students feel encouraged
to do mathematics, as it is not something that is
done only by prodigies.
11. ASSESSMENT
Assessment methods should measure the level
of involvement in the practice: how dedicated
and open to the problem the student was, how
good and detailed the research was, and last
how deducted the student was into
impersonating the name that they got. The
teacher and students have decided upon
evaluation criteria which has been posted in the
classroom from the beginning of the
assignment.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
http://atlantis.coe.uh.edu/archive/math/math_les
sons/mathles2.html

49
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Peer Tutoring
2. COUNTRY
USA
3. LINK
the good practice.
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
In peer tutoring, two students work together on
an instructional activity. Two peer-tutoring
approaches (i.e., Peer Assisted Learning
Strategies Math, Class Wide Peer Tutoring)
have been shown to be highly effective for
teaching mathematics. These strategies have
several features in common: Reciprocal peer
tutoring (i.e., during the session, each student in
the pair serves as a coach and as a tutee).
6. RESOURCES
method.
No special resources are needed
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Students work together; each student in the pair
serves as a coach and as a tutee; students
switch roles.
8. HOW DOES IT
WORK?
Max 100 words.
Frequent verbal interaction and feedback
between the coach and tutee
Use of positive reinforcement
A competitive game format
Teacher monitoring and feedback
9. EVIDENCE
https://iris.peabody.vanderbilt.edu/wp-
content/uploads/module_media/math_media/mo
vies/math_07_PALS.mp4
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
In peer tutoring, two students work together on
an instructional activity (e.g., learning
multiplication tables, practicing two-digit addition

50
teaching goals.
 What is the
users/target
the activity?
with carrying). The pairs of students can be of
the same or different ability levels.
Peer tutoring was not designed as a method of
teaching new skills. Rather, it provides students
opportunities to practice a newly learned skill or
to review mathematics skills while receiving
feedback.
The users opinion of this actuvity is positive
because it is interesting.
11. ASSESSMENT
Test
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
/

51
FIELD CONTENT
PLEASE FILL THE CELLS ACCORDING
TO THE EXPLANATION IN THE COLUMN
CONTENT
1. TITLE
What is the name that
best describes the
good practice?
Project
2. COUNTRY
In which country does
the good practice take
place?
Romania
3. LINK
Please give a web link
for further information
about the good
practice.
http://webcache.googleusercontent.com/sea
rch?q=cache:48Fx6H-
cQUwJ:www.tvet.ro/Anexe/4.Anexe/Teste%
2520de%2520evaluare2006/Textile%2520pi
elarie/Despre%2520proiect.doc+&cd=5&hl=r
o&ct=clnk&gl=ro
4. LANGUAGE
Language of the
source.
Romanian
5. SUMMARY
(DESCRIPTION OF THE
METHOD)
Max 100 words.
main characteristics of
the practice.
- it takes place over several weeks
- the theme and the working groups
(heterogeneous) are determined
- Students look for information, combine it,
formulate problems and seek solutions
- The project involves a final product as a
result of collecting and processing data
- The final product combines the text with
drawing, collage or model
6. RESOURCES
effective applying of
the method.
- theoretical knowledge from the school
curriculum
- Internet, media sources
- material resources from which to
manufacture the final product
7. WHY IT IS A GOOD
PRACTICE?
Give at least three
describe the method
as a good practice.
- is a cooperative method; Mutual learning is
a type of effective learning
- It values each student, using them
individually at different stages of the project
- Can measure performance and progress
due to workload individualization
- socialization
8. HOW DOES IT WORK?
Max 100 words.
Which actions does
the practice involve?
- the theme is suggested by the teacher, but
consulting the students
- working groups (5-6 students) are formed
-the teacher names the group leaders, and
they choose their group members.
- the idea of making the final product lies
with each group, in accordance with the
theme
- each group leader is concerned with the
work allocation within the group so that each
member can contribute, as well as with the
work schedule (meetings)

52
- the project is done in school, but also
outside it
- the students discuss the execution stage
throughout the project
- each student uses creativity to do the task
- the teacher advises the groups
- the final product is presented in an
organized environment
- evaluation is done as follows: self-
assessment, evaluation between groups,
teacher assessment - with strengths and
weaknesses
9. EVIDENCE
Links for videos,
photos.
https://youtu.be/LMCZvGesRz8
https://drive.google.com/drive/folders/0B3gt
wSuuS-LgNXhPQWV5VU9nS1E
10. RESULTS
Max 75-100 words.
 Quantitative
and qualitative
results in
relation to the
goals.
 What is the
users/target
group’s
opinion of the
activity?
- promotes the overall development of
personality, by using knowledge from
various school subjects, by integrating
knowledge, capabilities, skills and attitudes /
values
- stimulates students' responsibility by
enabling them to select the themes and the
means of achieving the goals
- assesses students in learning
- focuses on identifying / formulating
problems and then on solving them
- engages students in real-life situations
- shifts the emphasis from "learn about" to
"know how"; promotes learning through
direct contact with things (active school)
- encourages self- thinking, rather than
memorizing or recognizing the information
- are interactive, engage students in
understanding the evaluation process
11. ASSESSMENT
Suggested
assessment method
for the students
Competition, assessment of the posters for
projects, students’ voting for posters
12. UPLOAD A FILE
Please send related
(lesson plan,
evaluation etc.) so that
they can be uploaded
on the e-platform.
/

53
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The Pyramid (snowball method)
2. COUNTRY
Romania
3. LINK
the good practice.
http://www.projekt-
matematyka.eu/images/Modern_Methods_of_T
eaching.pdf
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
The method follows the gradual accumulation of
students' opinions.
Its basic principle is mixing individual activities
with group activities.
6. RESOURCES
method.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Allows each participant to take turns working
with one colleague, then with the members of a
group and then with the whole class.
The Pyramid stimulates discussion boldness
even in the shyest students, especially in the
initial pair.
8. HOW DOES IT
WORK?
Max 100 words.
The teacher gives the students the problem in
question
Students solve the task individually, write down
the answers and the misunderstandings.
They form groups of two students, who discuss
the results reached and write down the newly
emerged unknowns.
Two initial groups gather in larger groups who
discuss about chosen solutions.
The entire class discuss the task.
9. EVIDENCE

54
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The method facilitates communication and
student creativity
It stimulates the imagination of all participants
It stimulate competitivity, but also on the
cooperation because it ensures collective and
active participation of all members of the class
11. ASSESSMENT
The solutions found are analyzed with the whole
class; the same thing is done with the issues
that still require answers.
The best solution is chosen, the whole class
reaching a consensus.
By applying this method, it is difficult to assess
each participant.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

55
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The mosaic method
2. COUNTRY
Romania
3. LINK
the good practice.
https://www.youtube.com/watch?v=aXkRe5hdQ
RU
https://www.youtube.com/watch?v=hT-
Wik7TRn8
https://www.youtube.com/watch?v=15XPHLlqV
ZE
4. LANGUAGE Language of the source. Romanian
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
This is the interdependent groups method. It is a
strategy based on peer learning. Each student
has a learning task where they have to become
expert. All responsibility lies with the
transmission of assimilated information towards
other colleagues.
6. RESOURCES
method.
Flip chart, marker
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
- increasing pupils' motivation, because they are
aware that they can influence learning
- Greater efficiency of applying the acquired
knowledge
- The lesson is more interesting for each
student, because each student is involved in
understanding the contents which then he has
to be able to apply in real life
8. HOW DOES IT
WORK?
Max 100 words.
mosaic method is done in five stages:
1. Preparation of the material:
- the teacher sets a theme for study and divides
it into four or five sub-themes.
- the main elements that the student need to
focus on when studying the material
independently are established
- makes an expert sheet with the 4-5 sub-
themes that will be offered to each group
2. organizing the students in teams (4-5
students)

56
- Each student in a team receives a letter (A, B,
C, D) and his task is to study by himself the
theme from the sheet A, B, C, D
- Each student studies the task received on his
own
3. creating the groups of experts
- groups of experts with the same letter are
created, to discuss the problem together
- they talk based on data and materials at their
disposal, and new items are added. Each
member is taught as well as possible,
afterwards having the responsibility of teaching
the colleagues from the initial team
4. returning to the original team learning
- Every expert presents, concisely and
attractively, to his colleagues the theme
prepared by him
- The group members are encouraged to
discuss, ask questions and take notes
5. evaluation
- the groups share their results with the whole
class
9. EVIDENCE
https://www.youtube.com/watch?v=5JMhC4_NB
yQ
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
boosting students' confidence
- development of argumentative communication
activities within the group
development of individual and group
responsibility
optimize learning by teaching someone else's
acquisitions
11. ASSESSMENT
interdependence between members and
individualization of each contribution leads to
each individual's affirmation and to increased
self-confidence
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
http://www.creeaza.com/didactica/didactica-
pedagogie/PREZENTAREA-
INVESTIGATIILOR-PR123.php
http://www.teachhub.com/jigsaw-method-
teaching-strategy

57
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The Cluster method
2. COUNTRY
Romania
3. LINK
the good practice.
https://eric.ed.gov/?id=EJ946291
https://www.academia.edu/1025684/The_efficie
ncy_of_cluster_method_in_improving_the_creat
ive_writing_skill_of_6th_grade_students_of_pri
mary_school
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
- can be used especially when updating the
structures previously learned or in the evocation
stage, students having to establish connections
between the elements studied and being
actively involved in the thinking process.
6. RESOURCES
method.
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
- after solving the task, the students will use the
concepts and links created to develop concrete
ideas about the new concept. This exercise
encourages participation of the whole class.
8. HOW DOES IT
WORK?
Max 100 words.
. - students will write a new word or a nucleus
phrase in the center of a sheet of paper.
- Students are invited to write as many words or
phrases that come to mind about the selected
topic.
- Words (ideas) will be linked by lines to the
central notion or, if appropriate, to one
suggested by the students.
- At the end of the exercise the entire structure
will be commented and explained.
- The whole class takes part in the "cluster" and
they attempt to discover new connections
related to the proposed word/ phrase.
9. EVIDENCE
https://ro.pinterest.com/explore/division-
strategies/?lp=true

58
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
- this technique is meant to encourage students
to think freely and to stimulate idea connections.
- It is a way of achieving associations of ideas or
of providing new meanings to previously
acquired ideas.
- Clusters can be done individually or as a group
activity.
11. ASSESSMENT
Debate, discussion
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
https://iteach.ro/pg/blog/vasilica.ghita/read/6702
8/elevii-cu-ces-o-activitate-la-disciplina-
matematica
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Brainstorming
2. COUNTRY
USA
3. LINK
the good practice.
https://www.forbes.com/sites/susanadams/2013/
03/05/4-steps-to-successful-
brainstorming/#593eb4595992
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Consists of expressing the opinions freely,
without any prejudices.
- ideas on how to resolve a problem are needed;
criticism will under no circumstances be
admitted.
- all ideas are written on the board, followed by
a break for the ideas to sink in, during which
everybody reflects on them
- the Ideas are taken one by one and are
grouped by category. Symbols, keywords, etc.
- The next step is the critical analysis, followed
by evaluation, argument, counter-argument of
the ideas previously issued. Then the original
ideas are selected, or the feasible solutions to

59
the problem to be solved.
6. RESOURCES
method.
Files
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
- can assess students' knowledge on a certain
topic, usually at the beginning of a chapter
- Is a creative deliberation in order to generate
in a short period of time, within a group, a
multitude of ideas that can help to solve a
problem.
8. HOW DOES IT
WORK?
Max 100 words.
Development technique
- Enunciation of theme and side talks
- Reformulating the theme "How to ...?"
- Choosing an essential reformulation and
writing it down: "How many ways can we ...?"
- warming-up
- Brainstorming itself.
- The most interesting idea
The evaluation aims to identify the most
interesting ideas that can be applied in practice,
and demonstrating that participants effort in the
brainstorming was not in vain, their ideas being
followed by action.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The fundamental objective of this method is the
free expression of opinion, without prejudices.
All ideas are accepted, even the wacky,
unusual, strange and fantastic, as they come in
the minds of students, whether or not they lead
to solutions.
To advance in learning, the students need to be
trained in the exchange of ideas.
11. ASSESSMENT
Competition
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
https://dschool-
old.stanford.edu/sandbox/groups/dstudio/wiki/2f
ced/attachments/660d8/Brainstorming-
Method.pdf?sessionID=d07c198d92501ebb3ee
e4ff3da193b387130fcbf

60
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The gallery walk
2. COUNTRY
Romania
3. LINK
the good practice.
https://innerspacejournal.wordpress.com/2012/1
0/24/metode-si-tehnici-de-invatare-prin-
colaborare-interactive-turul-galeriei/
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
- Students are divided into groups of 4-5
members heterogeneous, depending on the
number of students in class
- The teacher gives students the assignment
- Each group will produce a product on
previously established theme
- Flip-chart products will be exhibited on the
walls of class
- A designated student group presents, if need
be, the in front of all students
- Analysis of all works (each product is
reviewed, completed, corrected and evaluated
by other groups)
- the groups re-examine their own products,
comparing to the others
6. RESOURCES
method.
- Flip-chart sheets, markers, tape, handouts
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
- It is a method of learning through cooperation;
- encourages students to express their opinions;
- the gallery walk involves interactive and deeply
formative assessment of products made by the
students (groups);
8. HOW DOES IT
WORK?
Max 100 words.
- Follows the expression of personal
views on the proposed theme
- Students learn to listen, to understand
and accept others' ideas or to reject
them by demonstrating the validity of
sustained ideas
- Stimulates creativity of participants,
individual and collective thinking

61
- Develops social capabilities of the
participants - intercommunication and
mutual tolerance, respect for each
other's opinion
- Attracts and arouses students'
interest, creating interactions between
them
9. EVIDENCE
Links for videos, photos. https://youtu.be/pSt5echeRrM
https://youtu.be/6LIXhXJeccg
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
- Promotes interaction between
participants' minds, between their
personalities, leading to a more active
learning and obvious results
- Stimulates individual effort and
productivity and is important for
selfdiscovering the students' own
capacities and limits
- There is an intergroup dynamic with
favorable influences on personality,
and the subjects working in teams are
able to apply and synthesize
knowledge in varied and complex
ways
- Develop and diversify their skills,
abilities and social skills of students
- Minimize the phenomenon of
emotional blockage of creativity
11. ASSESSMENT
Voting for posters
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional file

62
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Flipped Classroom
2. COUNTRY
USA
3. LINK
the good practice.
http://mulletstein.weebly.com/unit-5-
geometry.html
https://net.educause.edu/ir/library/pdf/eli7081.pd
f
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
The flipped classroom is a pedagogical model in
which the typical lecture and homework
elements of a course are reversed.The flipped
classroom is where students watch the
video lesson and learn the material at home
then come to school and have class time to
work on problems where the teacher and fellow
students are available to answer
questions. This teaching technique addresses
the typical math classroom problem: Students
passively listen to the lecture, begin the
homework (only getting to the easy ones), go
home and get stuck. Instead, students are able
to tackle the "difficult" part of the learning-the
problems-in the classroom where there is
immediate help available from the teacher and
peers.
6. RESOURCES
method.
geometry.html
http://www.flippedmath.com/
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
 Increases student engagement
 Strengthens team-based skills
 Offers differentiated instruction
 Provides opportunity for teacher to meet
with students one-on-one
 Increases opportunity for higher-order
thinking skills
 Fosters 21st Century learning
environments
 Increases contact time with students
 Increases student responsibility and
buy-in
 Maximizes learning opportunities even
when absent

63
 Direction instruction meets constructivist
learning
 Passive listeners become active
learners
 Easier to make real-life connections to
content
 Forces teacher into the role of "guide"
 Increases hands-on learning time
 Learning is student-driven
 Anytime tutoring
 Parental Involvement
8. HOW DOES IT
WORK?
Max 100 words.
How Does The Flipped Classroom Work?
Technological pre-learning: In the flipped
classroom, the class is not organized around the
teacher’s lectures. Instead, students are
required to learn the material before class,
allowing them to clear up any
misunderstandings while the teacher is
available. This “pre-learning” is often
accomplished online, with the teacher
posting instructional videos for students to
watch at home.
Reading and writing: Students read textbooks or
conduct online investigations outside of class.
Teachers have them write reactions to the
readings or prepare questions to ask during
class time.
Classroom assistance: Once students are in the
classroom, they are able to obtain one-on-one
help from teachers and teacher’s aides. The
teacher may split the students up into groups to
work on projects or hold discussions.
Meanwhile, he or she is in the room offering
help to students who have questions or who are
struggling.
Enrichment activities: The classroom experience
may also be supplemented by labs, hands-on
projects or field trips. Activities like these are
often successful in capturing student interest,
making them more likely to continue to study
concepts on their own.
9. EVIDENCE
geometry.html
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
The biggest advantage of the flipped
classroom approach is the element of active
participation. When taught in the traditional
lecture-and-note manner, students often grow
bored and find themselves interested in

64
users/target
the activity?
everything but the content covered by the
teacher. Proponents of the flipped classroom
argue that it is better to let students learn the
material at their own pace in a comfortable
home environment with the help of readings,
videos and online material. Then they can
pursue interactive learning activities in the
classroom while receiving personalized attention
from the teacher.
11. ASSESSMENT
 Watch, summarize, question protocol
 Embed video into a Google Form to
include questions - instantly group
students by level of understanding.
 Student Interviews (individual or small
group)
 Performance assessments
 Projects
 Class discussion
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
07b Flipped Classroom Lesson Plan
Template.docx
FlippedLessonPlanTemplate-website.docx
FlippedClassroom.docx
Flipped Lesson Plan Template.doc
07e Flipped Classroom Student Learning
Checklist.docx
07d Flipped Lesson Plan Presentation
Rubric.docx
07c Flipped Classroom Lesson Plan
Rubric.docx

65
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Measuring angels with jigsaw method
2. COUNTRY
UK
3. LINK
the good practice.
https://www.mathspad.co.uk/teach/lessonPlans/
anglesJigsawProject.php
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
The jigsaw classroom is a research-
based cooperative learning technique.
The “Jigsaw Method” is a teaching strategy of
organizing student group work that helps
students collaborate and rely on one another.
This teaching strategy is effective for
accomplishing multiple tasks at once and for
giving students a greater sense of individual
responsibility
The Jigsaw method is a cooperative learning
technique in which students work in small
groups. Jigsaw can be used in a variety of ways
for a variety of goals, but it is primarily used for
the acquisition and presentation of new material,
review, or informed debate..
6. RESOURCES
method.
Ruler, agglomerate
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
This Strategy allows for:
• An efficient way to learn content.
• Development of listening,
engagement, and empathy skills.
• A way for students to work
independently.
• Interaction among all students.
8. HOW DOES IT
WORK?
Max 100 words.
Here is the basic way this popular teaching
strategy is used in classrooms:
Step 1: Organize students into a group of 4-6
people.
Step 2: Divide the day’s reading or lesson into
4-6 parts, and assign one student in each group
to be responsible for a different segment.
Step 3: Give students time to learn and process

66
their assigned segment independently.
Step 4: Put students who completed the same
segment together into an “Expert group” to talk
about and process the details of their segment.
Step 5: Have students return to their original
“Jigsaw” groups and take turns sharing the
segments they’ve become experts on.
Step 6: Have students complete a task or a quiz
that’s reliant on them having understood the
material from the contributions of all their group
members.
During this whole process, where’s the teacher?
At first, the teacher facilitates the arranging of
groups, explaining of roles, and timing for each
portion. Notice that the teacher doesn’t have to
lecture or be the focal point of attention. When
the students are in groups for steps 4 and 5, the
teacher should walk amongst the groups and
lend support or explanation where necessary.
With this simple approach to group work, each
individual has something unique to contribute to
their group’s outcome. No one else in the group
is doing the same task, so each student
experiences a higher sense of ownership and
accountability to the members of their group.
The teacher may find it valuable to appoint one
student in each group as the “Leader” who can
manage time, make sure each student
contributes their part, and ensure the group is
accomplishing the goals. The most mature
student in each group might be the best option;
however, teachers should consider how the
disengaged, the diffident, or the problem
students might benefit from being the leader.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The jigsaw method allows the teacher to break
students into groups and assignments into
smaller pieces, all for accomplishing tasks with
more detail and collaboration. “Jigsaw” draws a
direct image to a jigsaw puzzle. Just as the final
image of a puzzle is constructed from many
separate pieces fitting together, so too are
academic tasks completed when members of
the team offer unique, jigsaw-cut efforts to the
group
When working independently, students are

67
accountable strictly to themselves.
The jigsaw method gives students a sense of
ownership and belonging – feelings hard to
experience when working alone.
In addition to having shared responsibility to the
group setting, students gain the benefit of
learning from those different from themselves.
While individual students could be required to
do the entirety of a project on their own, the fact
that they have the opportunity to listen to the
perspectives of others enhances the quality of
their education.
Jigsawing requires students to listen and learn,
and the group is rewarded when each individual
contributes their skills and knowledge to the
whole. Not only is learning improved, but
tolerance and understanding is as well
11. ASSESSMENT
Test tasks and check lists
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
Measurin-angels-with-jigsaw-method.docx
https://www.mathspad.co.uk/teach/angles.php#i
nter

68
FIELD CONTENT
CONTENT
1.TITLE
describes the good
practice?
JIGSAW PUZZLES
2.COUNTRY
UK
3.LINK
the good practice.
https://www.jigsaw.org/#steps
http://www.teachhub.com/jigsaw-method-
teaching-strategy
4.LANGUAGE Language of the source. English
5.SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
Teachers arrange students in groups. Each
group member is assigned a different piece of
information. Group members then join with
members of other groups assigned the same
piece of information, and research and/or share
ideas about the information. Eventually,
students return to their original groups to try to
"piece together" a clear picture of the topic at
hand. That's the simple overview.
6.RESOURCES
method.
The resources below will fill in the details and
provide examples of the technique in action.
7.WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
The cooperative learning strategy known as the
"jigsaw" technique helps students create their
own learning.
With this simple approach to group work, each
individual has something unique to contribute to
their group’s outcome. No one else in the group
is doing the same task, so each student
experiences a higher sense of ownership and
accountability to the members of their group.
8.HOW DOES IT
WORK?
Max 100 words.
STEP ONE
Divide students into 5- or 6-person jigsaw
groups.
The groups should be diverse in terms of
gender, ethnicity, race, and ability.
STEP TWO
Appoint one student from each group as the
leader.
Initially, this person should be the most mature
student in the group.

69
STEP THREE
Divide the day’s lesson into 5-6 segments.
For example, if you want history students to
learn about Eleanor Roosevelt, you might divide
a short biography of her into stand-alone
segments on: (1) Her childhood, (2) Her family
life with Franklin and their children, (3) Her life
after Franklin contracted polio, (4) Her work in
the White House as First Lady, and (5) Her life
and work after Franklin's death.
STEP FOUR
Assign each student to learn one segment.
Make sure students have direct access only to
their own segment.
STEP FIVE
Give students time to read over their segment at
least twice and become familiar with it.
There is no need for them to memorize it.
STEP SIX
Form temporary “expert groups” by having one
student from each jigsaw group join other
students assigned to the same segment.
Give students in these expert groups time to
discuss the main points of their segment and to
rehearse the presentations they will make to
their jigsaw group.
STEP SEVEN
Bring the students back into their jigsaw groups.
STEP EIGHT
Ask each student to present her or his segment
to the group.
Encourage others in the group to ask questions
for clarification.
STEP NINE
Float from group to group, observing the
process.
If any group is having trouble (e.g., a member is
dominating or disruptive), make an appropriate
intervention. Eventually, it's best for the group
leader to handle this task. Leaders can be
trained by whispering an instruction on how to
intervene, until the leader gets the hang of it.
STEP TEN
At the end of the session, give a quiz on the
material.
Students quickly come to realize that these
sessions are not just fun and games but really
count.
9.EVIDENCE
Links for videos, photos. No photos in the source
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
Whatever level or subject you teach, the jigsaw
method offers you a chance to neutralize the
problems of competitive classroom behaviours
and build a cooperative environment. Consider
how you’ll use this easy technique to boost the
learning, relationships, and collaboration in your

70
users/target
the activity?
classroom this year!
11. ASSESSMENT
Quiz, game
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Students Teams Achievement Division – STAD
method
2. COUNTRY
UK
3. LINK
the good practice.
www.innovativelearning.com/educational_psych
ology/.../cooperative_learning.doc
https://www.ukessays.com/essays/education/stu
dent-teams-achievement-divisions-model-
cooperative-learning-method-education-
essay.php
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
A cooperative learning method for mixed-ability
groupings involving team recognition and group
responsibility for individual learning.
This method shares intergroup cooperation and
intergroup competition with the previous one.
The teams are composed of high, average, and
low performing students, and of boys and girls
of different racial or ethnic backgrounds. Thus,
each team is a microcosm of the entire class.
There are five main steps a teacher should
follow when STAD is implemented. The teacher
first introduces new materials to be learned. The

71
team members then study worksheets on the
material until they master the material. Individual
quizzes are taken on the material studied. The
teacher then combines the scores to create
team scores. Members of the winning team are
given certificates and a weekly one-page class
newsletter recognizes the teams with the
highest scores.
6. RESOURCES
method.
Book, files, worksheets
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Promote collaboration and self-
regulating learning skills
• Good interaction among students
• Improve positive attitude toward
subject
• Better self-esteem,
• Increased interpersonal skills
8. HOW DOES IT
WORK?
Max 100 words.
The students are divided into heterogeneous
groups of four or five members. The teacher
presents a topic to all the class, with all the
explanations and exemplifications s/he
considers necessary. The students work in
teams for different sessions where they discuss,
compare, widen, formulate questions, elaborate
conceptual maps, basis of orientation,
memorize, etc. and make sure all the members
of the group have learned what they were asked
to.
After that, the teacher assesses each student
individually and transforms the individual
qualification in group qualification using a
system known as “performance in divisions”.
This method compares the performance of each
student as regards the reference of a group of a
similar level. Thus we make sure each student
can contribute to the success of his/her team,
given his/her possibilities, and it can also be the
case that a student with a lower performance
level provides a higher score to his/her team
than another student with a higher performance
level because she has been better placed in
his/her division.
9. EVIDENCE
Links for videos, photos. No evidence photos in the source
10.RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
STAD also add an extra source of learning
within the groups because some high achievers
act as a role of tutor, which result in high
achievements. Finally, it enables the students
according to the requirements of the modern
society by teaching them to work with their

72
the activity?
colleagues competently and successfull
Students in groups learn cooperatively resolve
the matter according to the basic competencies
to be achieved.
The group was formed of students who have
different skills, good level of high, medium, and
low. If possible, group members are from
different ethnic or religious serta memperhatikan
gender equality.
Award more emphasis on group rather than
individual.
Students work together in achieving its
objectives by upholding the norms of the group.
Actively assist and motivate students to succeed
shared passion.
Active role as a peer tutor to further enhance the
success of the group.
Interaction among students with increasing their
ability to argue.
The main idea behind the model STAD is to
motivate the students to encourage and help
each other to master the skills presented by the
teacher.
11.ASSESSMENT
Provision of test or quiz
12.UPLOAD A FILE
Please send related
uploaded on the e-
platform.
Linear equations - Stad method.docx

73
FIELD CONTENT
CONTENT
1. TITLE
best describes the good
practice?
Storytelling method
2. COUNTRY
place?
UK
3. LINK
about the good practice.
https://hal.archives-ouvertes.fr/hal-
01289881/document
https://conference.pixel-
online.net/edu_future2012/common/download/P
aper_pdf/354-ITL54-FP-Albool-FOE2012.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
the teaching practice.
Storytelling is a powerful pedagogical tool. The
teacher, the storyteller, and the performer share
a similar purpose: to inform, engage, and
entertain their audience. They all seek to
communicate their message in the most
compelling and provocative way possible.
Telling a story engages the audience in a
unique way. Storytelling, then, is yet another
device in the repertoire of a good teacher. It is
not only a potent tool for the teacher as a way of
organizing information, but as a dynamic means
for students to express what they have learned.
The magic of storytelling changes the
atmosphere in the classroom and in so doing
enhances the learning environment. Stories
serve to open the mind so that the hearer is
ready to take things in. In short, stories appeal
to the heart, and, once the heart is won, the
mind is open to learn!
Stories promote lively imagination on the part of
students. When students listen to a story, they
create mind pictures, make inferences and
predictions, and fill in the gaps. They in a sense
become involved in creating the story, thus
forming a relationship with the narrative. When
packaged as a story, the oral delivery of
information promotes greater involvement than
does written language.
6. RESOURCES Required resources for
Computer, board, flipchart

74
effective application of
the method.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
describe the method as
a GOOD practice.
Using storytelling as a method of instruction and
assessment supports educational
objectives. These include:
• improving verbal skills
• gaining self-confidence
• discovering the meaning of events
• developing a love for language and
stories
• encouraging higher levels of cognitive
thinking
• gaining a more in-depth understanding
of narration
• improving imaginative skills
• internalizing the traditional structure
and conventions of stories
• improving writing skills
• Improves listening skills
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
When preparing one's notes for a class lesson,
a teacher decides how best to present the
material. Consider packaging the information in
the form of a story rather than a lecture. When
deciding how to help the students to process
information, or to assess what students have
learned, consider having the students recreate
the information in the form of a story and then
tell it. Here are some ways that storytelling can
be applied to the classroom setting.
• Create a story to illustrate new concepts
or ideas.
• Express a topic or theme by narrating a
story about it.
• Explain historical events by narrating
them as stories.
• Invent and tell the story of historical
figures meeting one another or about
characters from different stories
meeting.
• Put knowledge that needs to be
assessed in a narrative form and tell the
story to the teacher and class.
• Take a familiar story and retell it with
characters and situations based on
curricular material
• Place yourself in a familiar story and
narrate the events from your first-person
point of view.
As a pedagogical tool, teachers should
use storytelling to explore cultural diversity, to

75
survey storytelling methods, to discover a
variety of ways to create stories, to integrate the
curriculum, to foster imagination, and to
investigate the power of narrative. Stories go
beyond the mere presentation of facts; instead,
they involve the students by engaging the
imagination and promoting conceptual
connections to the information being presented.
9. EVIDENCE
https://www.youtube.com/watch?v=q8-
Efax54xQ
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
In order to appeal to different learning
styles, it is necessary to transcend the
traditional presentation of fact and
theory. Stories are concrete; they exemplify
concepts better than abstract, non-creative
methods. Teaching storytelling also teaches
presentation, communication, and writing skills.
Storytelling is such an effective tool for the
teacher because it is a powerful form of
communication. Both the student and the
teacher benefit from it. Students learn from
hearing stories because they pay closer
attention, understand the message more readily,
and retain key points longer. Teachers become
better educators because being able to tell a
story effectively enhances the perception of the
teacher as a leader. A teacher who can adeptly
tell a tale reveals an approachable, likeable, and
human side to his or her personality. This helps
to close the distance between the teacher and
the students by making the teacher's status less
threatening.
11. ASSESSMENT
Test, checklist
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
-IntroductionToTheCartesianPlane (1).pptx
A-fly-on-a-ceiling.doc

76
FIELD CONTENT
CONTENT
1. TITLE
practice?
Think-pair-share (TPS)
2. COUNTRY
place?
USA
3. LINK
https://www.teachingchannel.org/videos/think-
pair-share-lesson-idea
http://oame.on.ca/main/files/thinklit/ThinkPairSh
are.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Think-pair-share (TPS) is a collaborative
learning strategy in which students work
together to solve a problem or answer a
question about an assigned reading. This
technique requires students to (1) think
individually about a topic or answer to a
question; and (2) share ideas with classmates.
Discussing an answer with a partner serves to
maximize participation, focus attention and
engage students in comprehending the reading
material.
6. RESOURCES
the method.
Electronic board, blackboard, notebook
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
It helps students to think individually about a
topic or answer to a question.
It teaches students to share ideas with
classmates and builds oral communication
skills.
It helps focus attention and engage students in
comprehending the reading material.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
Decide upon the text to be read and develop the
set of questions or prompts that target key
content concepts.
Describe the purpose of the strategy and
provide guidelines for discussions.
Model the procedure to ensure that students
understand how to use the strategy.
Monitor and support students as they work
through the following:
Think: Teachers begin by asking a
specific higher-level question about the text or

77
topic students will be discussing. Students
"think" about what they know or have learned
about the topic for a given amount of time
(usually 1-3 minutes).
Pair: Each student should be paired with
another student. Teachers may choose whether
to assign pairs or let students pick their own
partner. Remember to be sensitive to learners'
needs (reading skills, attention skills, language
skills) when creating pairs. Students share their
thinking with their partner, discuss ideas, and
ask questions of their partner about their
thoughts on the topic (2-5 minutes).
Share: Once partners have had ample time to
share their thoughts and have a discussion,
teachers expand the "share" into a whole-class
discussion. Allow each group to choose who will
present their thoughts, ideas, and questions
they had to the rest of the class. After the class
“share,” you may choose to have pairs
reconvene to talk about how their thinking
perhaps changed as a result of the “share”
element.
9. EVIDENCE
https://www.teachingchannel.org/videos/think-
pair-share-lesson-idea
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
Think-Pair-Share/Partner share is a
great strategy for helping students
verbalize their thinking and increase
student engagement and learning at all
levels. The one talking is the one
learning. The Think-Pair-Share strategy
is a versatile and simple technique for
improving students' reading
comprehension. It gives students time
to think about an answer and activates
prior knowledge. TPS enhances
students' oral communication skills as
they discuss their ideas with one
another. This strategy helps students
become active participants in learning
and can include writing as a way of
organizing thoughts generated from
discussions.Think-Pair-Share... • can be
used throughout the lesson. • provides a
chance to connect new information. •
uses social learning techniques.

78
11. ASSESSMENT
Test in the paired students
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files
FIELD CONTENT
CONTENT
1. TITLE
describes the good practice?
DEBATE
2. COUNTRY
Macedonia
3. LINK
further information about the
good practice.
/
4. LANGUAGE Language of the source. /
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Please summarise the main
characteristics of the
teaching practice.
A debate involves students in researching and
analyzing a controversial topic based on a stance
which will lead to a series of oral presentation of
standpoints and arguments by the two opposite
teams. Debating can be employed as an
instructional strategy wherever the learning
material and circumstances are open to opposing
points of view (Example: Does operation
subtracting exists?)
6. RESOURCES
method.
Classroom with debate placed desks, flipchart for
marking the key points from the debate,
conclusions and further questions.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Declarative, Functioning, Take Time to Answer,
Active, Process Oriented Method

79
8. HOW DOES IT
WORK?
Max 100 words.
Which activities/actions does
the practice involve?
The participants in a debate consist of three
groups: The affirmative team which stands for the
debate topic, the negative team which stands
against the debate topic, and a group of
audiences.
Teachers may have to be the hosts of the debate,
and ensure the debate is running at an
appropriate pace. They also assess the
performance of the students during the debate,
and provide feedback to enhance their learning
afterwards.
Each debate team normally consists of 3 or 4
members, with the captain initiating the motions
and presenting the summaries. The other team
members will assist in the development of
arguments, take notes on the opposing arguments
delivered by the opposing team, and brainstorm
ideas and questions for rebuttals as the debate
proceeds.
9. EVIDENCE
https://g16languagebhlmackay.files.wordpress.co
m/2015/10/screen-shot-2015-10-23-at-9-03-
46.png
http://kevinfitton.com/education/Debate%20in%20t
he%20Classroom.gif
10. RESULTS
Max 75-100 words.
qualitative results in
relation to the
teaching goals.
 What is the
users/target group’s
opinion of the
activity?
Allow students to look at both sides of an issue;
improve students' communication and expression
skills in a public setting; enhance techniques of
searching information, improve skills for gathering,
evaluating and synthesizing data from various
sources to develop arguments; foster appreciation
of opposing viewpoints; enhance debating/arguing
techniques against opposing opinions; allow more
interactive exchange among students and
teachers.
11. ASSESSMENT
Set up rules for the debate. After the debate, ask
students to write an essay to reflect their own
opinions and the knowledge gained through the
debate.
MARKIN
G
RUBRIC
S
Excelle
nt
Proficie
nt
Average
Preparat
ion:
Prepare
d a very
broad
Satisfact
ory
preparati
Demonst
rated
preparati

80
scope of
informati
on and
deep,
critical
analysis
of the
given
topic;
informati
on is
collected
from a
wide
range of
sources
and
perspect
ives
which
effectivel
y
contribut
e to
develop
ment of
argumen
ts
on of
informati
on and
analysis
for the
given
topic;
major
issues
about
the topic
was well
covered
on for
the basic
informati
on of the
given
topic,
but no
evidence
of
analysis
coming
from the
student
was
shown
Organiz
ation
and
Present
ation
Logical
flow in
the
presenta
tion of
argumen
ts;
informati
on
organize
d in a
coherent
manner;
powerful
and
persuasi
ve
presenta
tion
Generall
y clear
flow of
argumen
ts;
presenta
tion is
persuasi
ve but
with
minor
problem
s
Able to
give the
basic
framewo
rk of the
presente
d ideas,
but lack
of
persuasi
ve
power
Use of
Argume
nts
Plenty of
very
strong
and
persuasi
Many
fairly
strong
argumen
ts but a
Argume
nts are
generall
y on the
right

81
ve
argumen
ts
few are
not
persuasi
ve
track but
not
convinci
ng and
strong
enough
Rebuttal Excellen
t
defense
and
attack
against
the
opposite
side;
able to
identify
the
weaknes
s of the
opposite
side
Satisfact
ory
defense
and
attack
against
the
opposite
side;
attempte
d to find
out
weaknes
s of the
opposite
side
Fail to
defense
for some
issues; a
few
successf
ul
attacks
against
the
opposite
side
12. UPLOAD A
FILE
Please send related
electronic documents (lesson
plan, evaluation etc.) so that
they can be uploaded on the
e-platform.
http://www.csun.edu/~ds56723/phil338/hout338ru
bric.htm
http://ar.cetl.hku.hk/am_debate.htm#5
http://www.educationworld.com/a_lesson/lesson/le
sson304b.shtml

82
FIELD CONTENT
CONTENT
1. TITLE
practice?
Discussion method in mathematics
2. COUNTRY
place?
Bulgaria
3. LINK
www.ivanpivanov.com/uploads/sources/55_Inte
raktivni-metodi-za-obuchenie.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
The discussion method in teaching
mathematics is a process of interaction
controlled by the teacher, through which
students acquire information and experience. It
is an effective method that promotes student-
centered learning than teaching. Students are
able to actively participate in discussions, which
enhance their understanding and capture their
attention. The discussion method promotes
democratic thinking among students. Students
are able to freely share their ideas, speak their
opinions and challenge each other to arrive at a
common decision.
Teamwork gives quality results, due to the use
of knowledge and resourcefulness of many
people.
6. RESOURCES
the method.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Stimulates the original thinking of
students.
• Provides an opportunity for each of the
students to take part in the learning
process.
• Generate a quantity of ideas and
opinions.
• Allows everyone to convey their own
point of view.
• Emphasis on learning instead of
teaching.

83
• Develops democratic way of thinking.
• Spirit of tolerance is inculcated.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
Discussion in the form of dialogue can be used
to reinforce students’ knowledge. In order to
provide an opportunity for the students to
assimilate something more than technical skills
and contribute to their mathematical education
teachers emphasize on establishing a warm,
supportive environment that invites students to
discuss willingly. Those tasks that begin with
the question ‘What do you think?’ enable
students to think mathematically and to assess
situations from a mathematical point of view.
During the process of discussion students are
able to freely share their ideas, express their
opinions, bring the relevant arguments and
challenge each other to arrive at a common
decision.
9. EVIDENCE
Links for videos, photos. No evidence photos
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
 Students are being given an opportunity
to expand their existing knowledge.
 Learning material that has already been
known is clarified.
 Students are enabled to develop their
abilities to think rationally.
 Learners gain experience to solve
problems unaided.
 Students are empowered to express
different opinions and bring the relevant
arguments.
11. ASSESSMENT
Individual assessments are given to those
students that have been actively involved in the
discussion and been able to give reason for
their standpoints.
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files

84
FIELD CONTENT
CONTENT
1. TITLE
practice?
The Racing games feast of mathematics
2. COUNTRY
place? Bulgaria
3. LINK
www.math.bas.bg/…MITE2/Grozdev-
Chehlarova-paper.pdf
www.math.bas.bg/…tii/33-vazrajdane-na-
praznicite...
www.researchgate.net/…/Sava_Grozdev/public
ation/...
4. LANGUAGE Language of the source. Bulgarian, English
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Celebrations of mathematics are useful for all
students from the first to the last class of
education, they leave a lasting impression in the
mind. An important part of the celebration of
mathematics are racing games. Participants
broadcast three teams with three contestants.
First played for team standings, then individual
standings. Between stages have educational
interesting facts and tasks for the audience.
6. RESOURCES
the method.
Prepared didactic software to celebration of
mathematics -type presentation.
Supplies for the competition – sheets, pens;
Prizes for participants;
Invitations for the guests;
Logo for each participant and guest;
Diplomas (I, II, III place for team and individual
ranking);
Decoration ;
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
Participation in racing games on the celebration
of mathematics contribute to:
• formation of skill orientation in time;
• to improve the ability to plan and implement
the plan;
• for reflection and evaluation at your own
opportunities, achievements and personality
changes as a result of training.

85
• improve is the ability to work in a team;
• strong emotional impact and form a love to
math;
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
Preparation for the celebration:
• Selection of tasks for the contestants and the
audience
• Preparation of software product for the
celebration;
• Preparation of scenarios for the celebration
• Development of a logo for each participant
and guest
• Purchase Awards, making diplomas,
invitations to guests
• Preparation of consumable for competition
• Decorate the room
Conduct of the celebration: There are two
presenters on the celebration. Acquaint
participants and guests with the regulation of
the competition . The competition is in three
rounds. In the first round of all participants are
broadcast three teams of three contestants.
The second round is the team standings, and
the third - for individual standings. In each
round are solved three problems for time.
Between each two rounds have interesting facts
for the audience and tasks for the audience - so
filled time in which contestants solve problems
and the celebration has a learning function for
the audience. After each round explains the
decision of tasks. Commission examines the
decisions and broadcast winners.
9. EVIDENCE
No evidence photos
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
The competition is very emotional. Participants
are always satisfied after its completion, also the
audience and guests, since they were not just
passive spectators but and participants. For
contestants competition also has an educational
and educative function.
The limitation of time to solve problems is
essential. This limitation requires and
accordingly educate concentration in learning
the task, in solving it, replying or refusal of it.
Assist in the formation of the ability to make a
decision. Educates responsibility - no time for

86
continuous verification of the correctness of the
result reached. Time constraints contribute to
the understanding of the need for knowledge of
rational methods of work of more methods to
solve problems, more knowledge. In some
cases, intuition is crucial to reach an answer -
and it is based on associations, analogies of
preliminary accumulation of knowledge, skills,
tactics and behavior.
11. ASSESSMENT
Competition, test
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files

87
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Research approach to mathematics presented
through presentations by students
2. COUNTRY
Bulgaria
3. LINK
the good practice.
http://conf.uni-ruse.bg/bg/docs/cp15/6.4/6.4-
8.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Contemporary student should be provoked to
expand their knowledge in mathematics, to seek
additional information about the studied
material. Preparing a presentation on a given
topic stimulate thinking and creative activity.
Students play the role of researchers. The
presentation of presentation allows them to
"enter" into the role of teacher, increases their
confidence.
6. RESOURCES
method.
Laptop, projector, presentation.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
- Provoke interest of students;
- Seek and receive new information;
- Offers a variety;
- Developing skills for independent work and
teamwork;
8. HOW DOES IT
WORK?
Max 100 words.
In relation with the theme "Measuring units" the
students have a task to explore the use of other
measuring unit than those in the lesson. The
task boost their interest. They presented reports
and presentations.
9. EVIDENCE
No evidence photos
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
- Formed new attitude towards mathematics as
a fun and interesting science;
- Stimulate is research skills;
- A new learning environment;

88
 What is the
users/target
the activity?
- Attracting the students' attention;
- Students self-seeking sources of information;
11. ASSESSMENT
Individual assessments of performance,
creativity and presentation presentations.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
AtzeWJ9dnkyM2dYM3FkazA

89
FIELD CONTENT
CONTENT
1. TITLE
best describes the
good practice?
Method of Math Work Stations
2. COUNTRY
place?
Bulgaria
3. LINK
about the good
practice.
diuu.bg/ispisanie/broi23/23dpp/23dpp2.pdf ;
http://conf.uni-ruse.bg/bg/docs/cp/9/9-40.pdf
4. LANGUAGE
Language of the
source.
Bulgarian language
5. SUMMARY
(DESCRIPTION OF THE
METHOD)
Max 50 words.
• There are diverse assignments
with varying degrees of
complexity on each of the
stations. Tasks should be varied
in type and form so as to
different senses to be used.
• Common theme of tasks.
• Learning by doing is being
emphasized. Students go
through the stations and work on
the tasks.
• Stations can be operated
individually, in partnership or in
groups.
• There has been a set time for
passage through the stations.
• Current control.
• ‘The Road’ through the stations
of every student is being noted in
the so-called progress datasheet.
• The materials wrought are being
stored in an individual folder.
• Evaluation of work done.
6. RESOURCES
the method.
Worksheets with the corresponding
tasks for each station, progress
datasheet.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
• Through this working method the student
is being given a chance to be an active side.
• Teacher is being acted as a partner,
consultant or advisor.
• Deepening and generalization of

90
knowledge.
• Developing skills and self-control.
• Developing Social Skills.
• Suitable for interdisciplinary work.
• Ability to individualization and
differentiation of learning.
• Mastering the ability to make
decisions.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
• Promoting of individual work and
training.
• Teamwork.
• Learning through communication.
• Internal differentiation at choice.
• Individual support at various levels of
difficulty.
• Encouraging poorer students through
individual support.
• Promoting talented with creative
optional stations.
• Increasing motivation.
9. EVIDENCE
Links for videos,
photos. No evidence photos
10. RESULTS
Max 75-100 words.
 Quantitative
and qualitative
results in
relation to the
teaching goals.
 What is the
users/target
group’s opinion
of the activity?
By using this method competences are
being formed. It helps build basic
knowledge and experience through action is
being gained. It is expected to achieve the
following:
• Coping with the tasks set and keeping the
order of work.
• Observing time regulated.
• Interesting in the subject of work.
• Good and detailed solution shaping.
• Sharing lessons learned.
• Presentation Skills.
• Ability to make decisions.
• Forming co-operative skills.
• Conforming to different opinions.
11. ASSESSMENT
method for the
students
12. UPLOAD A FILE
Please send related
(lesson plan,
evaluation etc.) so that
they can be uploaded
on the e-platform.
AtzeWJ9U2F0dE9meFJNYzA

91
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Creative drama – drama +math=dramath
2. COUNTRY
Turkey, Greece
3. LINK
the good practice.
http://broadwayeducators.com/teaching-
mathematics-in-the-classroom-through-theatre/
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
The drama is as empirical aspect of learning.
The student may learn from what they are doing
in drama.
Drama is a performing art, an outlet for self-
expression, and a way of learning. Drama is an
effective learning tool because it involves the
student intellectually, physically, socially, and
emotionally. Activities in improvisation,
pantomime, play-making, and scene
reenactment serve to develop the creative
potential in the participants and help to develop
critical thinking skills.
6. RESOURCES
method.
https://pdfs.semanticscholar.org/1a92/264a18d1
dae1664b834d59ba2661bd5a307f.pdf
file:///C:/Users/user/Downloads/ENHANCING_I
NNOVATIVE_PRACTICES_IN_MATHEM.pdf
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
Creative drama method has been used to
enable the person to be active, to learn by
realizing, makes him a productive and creative
person and also it helps the person to improve
healthy social communication skills
The benefits of using creative drama as a
teaching methodology coincide with the
established goals of education. These include:
developing the imagination and creativity
fostering critical thinking and problem-solving
skills
exploring and evaluating ideas
discovering positive ways of dealing with

92
conflict
expressing feelings and interpreting the
feelings of others
enhancing communication skills
improving literacy skills
8. HOW DOES IT
WORK?
Max 100 words.
In the introduction part, to lead everyone goes in
a relaxed mood, ready to work together in a
harmony, trust each other and also have fun,
warm-up activities were used. These activities
also gave students some hidden clues about the
rest of the lesson.
In the development part, dramatic moments
were introduced in which students faced with
the tension of time, an obstacle to overcome,
mission to accomplish, or status to challenge.
These tensions forced them to remove the
obstacle, or accomplish the mission in given
time. In order to get rid of these tensions, they
had to create some ideas, discuss their ideas
with their friends. In some lessons, the teacher
participated in the activities by taking some roles
in them. This helped the teacher to control the
students, and the teaching/learning process. It
also provides more effective relationships
between the teacher and students.
Finally, in quieting part, the key points of the
concept covered summarized either by the
teacher or by the students. Students reviewed
what they have learned either by answering or
solving the questions posed by the teacher, or
presenting what they have learned by creating a
scenario that requires the use of knowledge
learned.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Creative drama offers children the chance to
explore themselves through the lives of fictional
“others” in a safe space that enables mistakes
to be made and learned from (Jindal-Sanpe et.
al., 2011). Creative drama provide collaborative
learning and learning by discover. Therefore,
mathematics and creative drama is learned
through exploring.
Participation in drama activities provides the
teacher with another way to assess the student.

93
Through dramatic play, students reveal how
they organize ideas, solve problems, work in a
group, deal with conflict, and use their
imagination. Observing how students
dramatize an event offers valuable insight into
how they perceive, interpret, understand, and
analyse the material at the core of the lesson.
Drama is a teaching tool that allows students to
participate, demonstrate, and observe in a
"controlled," or non-threatening,
environment. In other words, it provides another
"non-traditional" opportunity for students to learn
and to demonstrate learning. At the same time,
drama helps students get in touch with their
creativity and spontaneity as well as to develop
confidence in the expression of their
ideas. Finally, it teaches self-discipline,
acceptance of and positive response to
criticism, and cooperation with others.
11. ASSESMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

95
INTEGRATED CLASSROOM
FIELD CONTENT
CONTENT
1. TITLE
practice?
Geometry and fashion design
2. COUNTRY
place?
Bulgaria
3. LINK
http://www.fashion-lifestyle.bg/textiles_broi68
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Teachers are often asked the following
question by their students, ‘Where shall we
need knowledge learned in mathematics?’
To convince students that life is math and
something else we can put them in certain life
situations. When generalized students’
knowledge about geometric shapes through
practical work ‘Geometry and Fashion Design’
students can make clothing models.
6. RESOURCES
the method.
A sketchpad, colored pencils.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Provoking students’ interest.
• Pupils find out themselves an answer
of the question ‘Why do we
need mathematics?
• Developing creative imagination.
• Educating sense of aesthetics.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
Preparatory part
Students are assigned a task to investigate
the application of
geometric figures in contemporary fashion

96
trends.
Working part
Create a lady’s toilet that meets the following
requirements:
● be made of triangles only;
● be made of quadrangles only;
● be made of triangles and quadrangles.
Having had models prepared students answer
the question, ‘In which of the cases the least
fabric is needed?’.
9. EVIDENCE
AtzeWJ9OW5xd3lsS1VNdkk
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
● Establishing connections between
mathematics and everyday
life.
● Students' attention is being riveted.
● Students are being given an opportunity
for personal
involvement.
● Students that have difficulties in learning
new material are
enabled to show themselves.
● Students are promoted to use their own
ideas and practical
skills.
● Students feel more motivated to learn
and work.
11. ASSESSMENT
Assessing creativity and aesthetic
presentation.
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files

97
FIELD CONTENT
CONTENT
1. TITLE
practice?
Geometry and Bulgarian folklore
2. COUNTRY
place? Bulgaria
3. LINK
https://sites.google.com/site/knigadete/matemati
ceski-folklor
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
When we say mathematics and Bulgarian
folklore always remember those fun tasks fruit of
our mercurial Bulgarian people. This practice is
considered another application of geometry in
our folklore and traditions. How do students with
the help of geometry can create notorious
Bulgarian martenitsi / white and red / dedicated
on March 1, devise using symmetry beautiful
Bulgarian embroidery so characteristic of our
costumes.
6. RESOURCES
the method.
Colored paper, scissors, glue, sketchbook,
colored pencils and markers.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
- Provoke interest of students;
- Develop creative imagination;
- Place the application of mathematics to
another in a different light;
- Find participation in mathematics defined
various fields;
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
1 / Preparatory part;
6-grade students is on assignment to develop
traditional Bulgarian martenitsi using only
geometric shapes triangle, rectangle, circle and
its parts.
Grade 8-With a central axial symmetry, rotation
and translation to draw samples of Bulgarian
embroidery.
working part
6kl.-Create martenitsa that meets the following
requirements:
-to only of triangles and quadrangles

98
-to only of circles and its parts
8kl.- Create Bulgarian embroidery that meets
the following requirements:
-to is composed of a symmetry
-to a set of several symmetries
9. EVIDENCE
AtzeWJ9cTJuNTdoV0tWYms
AtzeWJ9THFtaFdPUV91Vm8
AtzeWJ9c0ZXWG93dXpvM1E
AtzeWJ9Z0VvOU9nUUw3Q3c
AtzeWJ9a2dsVzNmV3Zuelk
AtzeWJ9TlJWNlI0TlhYOEk
AtzeWJ9Y0c5dTFPNnVtWms
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
Development of martenitsas embroideries and
develop creative attitude in mathematics.
Acquaint them with some of the traditions of the
Bulgarian people. Serve to develop a number of
important qualities of logical and creative
thinking of students, as they are in the role of
artists and designers. It allows for use of own
practical skills. Possibility of personal
involvement and expression of students, which
is more difficult to deal with mastering the
material.
11. ASSESSMENT
Individual assessment:
-Create original designs.
- Artistic and aesthetic craftsmanship.
- Precise execution.
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files

100
MATH AND DATA ANALYSIS
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Data Simulations
2. COUNTRY
USA
3. LINK
the good practice.
http://static.clexchange.org/ftp/documents/imple
mentation/IM1996-01EffectiveUseOfSims.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Teaching with data simulations means giving
students opportunities to simulate data in order
to answer a particular research question or
solve a statistical problem. There are several
ways to use simulations: physical simulations of
a process, using probability models to simulate
data to estimate the chance of a particular
outcome, or simulating data while varying
parameters to illustrate a concept or deepen
students' understanding of a process. Another
use of simulation is to generate data under a
certain theory to test whether a particular
outcome is surprising.
6. RESOURCES
method.
Computer
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Simulation is an important tool used by
statisticians to solve problems, so students
need to learn how to use simulation as a
statistical problem-solving tool.
• Simulating data can help students visualize
and build a deep understanding of difficult
and abstract statistical concepts, and to see
dynamic processes, rather than static
figures and illustrations.
• Simulations provide students a way to
informally address questions involving
statistical inference, before formally
studying this topic later in a class.
• Simulations provide a way to actively
engage students in making and testing
conjectures about data, developing their
reasoning about statistical concepts and
procedures.

101
8. HOW DOES IT
WORK?
Max 100 words.
How simulations are used is of great
importance. Simulations can involve physical
materials (drawing items from a bag, tossing
coins, sampling candies) or involve generating
data on the computer (drawing samples from a
population or generating data based on a
probability model). Even when using computer
simulations, always begin with a concrete
simulation (e.g., having students take random
samples of words from the Gettysburg address
before taking simulated samples using their
Sampling Words applet).
9. EVIDENCE
http://serc.carleton.edu/sp/library/datasim/exam
ples.html
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
/
11. ASSESSMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
http://serc.carleton.edu/sp/library/datasim/exam
ples.html

102
FIELD CONTENT
CONTENT
1. TITLE
practice?
Didactic games in mathematics
2. COUNTRY
place?
Bulgaria
3. LINK
www.math.bas.bg/smb/2010_PK/tom/pdf/340-
346.pdf
priobshti.se/…i/izpolzvane-na-didakticheski-
igri...
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Didactic game in mathematics education is
viewed as a powerful means of stimulating
active cognitive activities in students; increase
their interest in mathematics and leads to easier
absorption of learning content.
Didactic game plays a crucial role in enhancing
the activity of students in the learning process,
helps to facilitate absorption of educational
content, urges on active cognitive activity
greater number of students and increases their
interest.
Actual pedagogy game is complicated, but
simultaneously it is an opportunity for
harmonious and spontaneous communication
between students and teachers. Throughout the
game the students concentrate and mobilize
themselves and are able to make great efforts to
achieve the goal of the game.
6. RESOURCES
the method.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
During the game participants acquire skills and
habits of concentration and independent
thinking; they develop their attention and pursuit
of knowledge; They do not notice that they learn
to recognize and remember new or assimilate
and apply the acquired knowledge; orient
themselves in photographic situations by
completing the stock of ideas and concepts;

103
develop certain habits and imagination. Even
the usually passive students in class in
mathematics include willingly make efforts not to
mislead their peers throughout the game. So
didactic game becomes a transformative
creative activity located in close cooperation
with other types of academic work.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
Orientation:
The teacher defines the theme, makes a
characteristic of the game and an overview of its
moves and rules.
Preparations for holding the game:
Getting to know with the script, assignment of
roles, preparing for their performance, providing
procedures for the management of the game.
Conducting the game:
The teacher monitors the conducting of the
game, controls the sequence of the participants’
actions, provide the necessary support, reports
the results.
Discussion of the game:
Implemented actions, positive and negative
sides during the game, as well as the arisen
difficulties are being analyzed; possible ways of
the game realization including possible
amendments to the rules are also being
discussed.
A significant part of the didactic games are
gaming actions that regulate the rules of the
game, stimulate cognitive activities of
participants, provide an opportunity to
demonstrate their ability to transform
knowledge, skills and habits to achieve the
objectives of the game.
Cognitive content is the basis of didactic game
and lies in the utilization of those skills and
knowledge that apply in solving educational
problems embedded in game. Didactic game
has a certain game result which is the end the
game and gives its completeness.It occurs
primarily in the form of solution to the academic
task and brings the student satisfaction.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
By playing children mastered the rules of
intellectual and practical activities in accessible

104
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
formats. Intellectual game is an effective form of
conducting lessons in mathematics as the
knowledge acquired with interest are the
soundest. Students take up the game and not
pay attention to the fact that in the process of
playing they have to solve serious tasks.
The use of didactic games in teaching
mathematics enables students to develop, refine
and consolidate their observation, to form team
working skills, teaches them to listen and
respect other opinions, to develop their creative
abilities. Children are much more free,
responsible, creative, active and independent.
The game helps to create and maintain a
benevolent, positive psychological climate in the
students’ team.
11. ASSESSMENT
Competition, game
12. UPLOAD A
FILE
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platform.
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105
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Survey method
2. COUNTRY
Macedonia
3. LINK
the good practice.
http://www.nctm.org/Publications/Mathematics-
Teacher/2015/Vol109/Issue5/Engaging-
Students-in-Survey-Design-and-Data-
Collection/#THELESSON’SGOALSANDIMPAC
T
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
A survey is a method of collecting information. It
may collect information about a population’s
characteristics, self-reported and observed
behaviour, awareness of programs, attitudes or
opinions, and needs. Repeating surveys at
regular intervals can assist in the measurement
of changes over time. Information collected
using surveys is invaluable in planning and
evaluating policies and programs.
Information is collected from a group of people
in order to describe some aspects or
characteristics of the population of which that
group is a part.
The main way in which the information is
collected is through asking questions by the
members of the group constitute the data of the
study.
Information is collected from a sample rather
that from every member of the population.
6. RESOURCES
method.
Survey, worksheets, computer
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Students were enthusiastic and highly motivated
Enables strengthening their ability to write and
implement well-designed surveys and also helps
students to increase their critical thinking
8. HOW DOES IT
WORK?
Max 100 words.
STEP 1: DEFINING THE PROBLEM
The problem to be investigated by means of
Survey should be:
- Sufficiently interesting

106
- Important
Strategy for defining survey question:
- Hierarchical Approach
STEP 2: IDENTIFYING THE TARGET
POPULATION
Unit of Analysis
- Is the major entity that is being analyzed
in a study?
- It is the “what” or “who” that is being
studied
- It includes individuals, groups, social
organizations and social artifacts.
Target Population
- The group of persons (objects, institutions and
so on) that is being studied.
STEP 3: CHOOSING THE MODE OF THE
COLLECTION
Direct Administration to a Group
Mail Surveys
Telephone Surveys
Personal Interviews
STEP 4: SELECTING THE SAMPLE
- The subject of the survey should be
selected from the population.
- the subjects they intend to question
possess the desired information
- Individuals who possess the necessary
information but who are uninterested in
the topic of the survey (or who do not
see as important) are unlikely to
respondents.
- conduct a preliminary inquiry among
potential respondents
STEP 5: PREPARING THE INSTRUMENT
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
This lesson gave students the opportunity to see
that surveys can be powerful tools when they
are well designed and implemented. Students
were enthusiastic and highly motivated to
examine their own behaviour behind the wheel
by analysing data they had generated. They
came to appreciate that the results from surveys
can be unintentionally misleading or
purposefully deceptive. They also realized that

107
the strength of the evidence used to answer a
question depends on the quality of the data
collected. This exploration strengthened their
ability to write and implement well-designed
surveys and also led to a welcome bit of
scepticism and critical thinking when reading the
results of surveys. For students, this was a
valuable mathematics lesson and a potentially
life-saving experience.
11. ASSESSMENT
populacija-primerok-
со%20ИКТ%20и%20истражување.doc#Prilog2
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
populacija-primerok-со ИКТ и
истражување.doc
Data-Collection-Lesson-Plan.docx
Data-Collection-Lesson.pptx
Data-Collection-Worksheet.docx

109
REAL LIFE PROBLEMS
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Problem solving
2. COUNTRY
/
3. LINK
the good practice.
http://www.free-management-
ebooks.com/news/six-step-problem-solving-
model/
4. LANGUAGE Language of the source. English, Macedonian
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Problem solving models are used to address the
many challenges that arise in the workplace.
While many people regularly solve problems,
there are a range of different approaches that
can be used to find a solution.
Complex challenges for teams, working groups
and boards etc., are usually solved more quickly
by using a shared, collaborative, and systematic
approach to problem solving.
6. RESOURCES
method.
The group may use tools, such as a Gantt chart,
timeline or log frame. Between Steps Five and
during Step Six the operational/technical
implementation of the chosen solution takes
place.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
The Six Step Problem Solving Model provides a
shared, collaborative, and systematic approach
to problem solving.
 Each step must be completed before moving
on to the next step. However, the steps are
repeatable. At any point, the group can return to
an earlier step, and proceed from there.
 The goal is not to solve but to evolve,
adjusting the solution continually as new
challenges emerge, through repeating the Six
Step Process.
8. HOW DOES IT
WORK?
Max 100 words.
 Step 1) Define the Problem – Identify
problems through problem formulation and
questioning. The key is asking the right
questions to discover root causes.

110
 Step 2) Determine the Root Cause – During
this process, assumptions are uncovered and
underlying problems are further revealed. Also,
this is an opportunity to collect and analyze
data.
 Step 3) Develop Alternative Solutions –
Decisions are made within the group to
determine the appropriate solution and process
through creative selection.
 Step 4) Select a Solution – Once the group
has formed solutions and alternatives to the
problem(s), they need to explore the pros and
cons of each option through forecasting
consequences.
 Step 5) Implement the Solution – Develop an
action plan to implement and execute the
solution process.
 Step 6) Evaluate the Outcome – This final
stage requires an evaluation of the outcomes
and results of the solution process. Ask
questions such as: Did the option answer the
questions we were working on? Did this process
address the findings that came out of the
assumptions?
9. EVIDENCE
Links for videos, photos. Problemska%20zadaca.doc#Sliki
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
 Problem solving method can be an
effective method for teaching
mathematics in the hands of an able
and resourceful teacher of mathematics.
 Mathematics classrooms must be
challenging and engaging environments
for all students, where students learn
significant mathematics.
 Students are called to engage in solving
rich and relevant problems. These
problems offer several entry points so
that all students can achieve, given
sufficient time and support.
 Lessons are structured to build on
students’ prior knowledge
 Students develop their own varied
solutions to problems and thus develop
a deeper understanding of the
mathematics involved.
 Students consolidate their knowledge
through shared and independent
practice.

111
 Teachers select and/or organize
students’ solutions for sharing to
highlight the mathematics learning (e.g.,
bansho, gallery walk, math congress).
11. ASSESSMENT
Problemska%20zadaca.doc#Prilog
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
Problemska zadaca.doc

112
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Math-lab approach
2. COUNTRY
Macedonia
3. LINK
the good practice.
https://repository.nie.edu.sg/bitstream/10497/24
10/1/TL-5-1-19.pdf
http://teachingasleadership.org/sites/default/files
/Related-Readings/IPD_Ch6_2011.pdf
4. LANGUAGE Language of the source. English, Macedonian
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
The Mathematics Laboratory Approach is a
method of teaching whereby children in small
groups work through an assignment/task card,
learn and discover mathematics for themselves.
The children work in an informal manner, move
around, discuss and choose their materials and
method of attacking a problem, assignment or
tas
6. RESOURCES
method.
Cards, board, computer etc.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
The method is based on the principle of learning
by doing.
This method is psychological as we proceed
from known to unknown.
It is based on the student’s self-pacing.
It helps in making clear certain fundamental
concepts, ideas etc.
It develops the self-confidence and teaches the
students the dignity of labor.
The children learn the use of different
equipment’s, which are used in laboratory.
It develops in the child a habit of scientific,
enquiry and investigation.
This method presents mathematics as a
practical subject.
It stimulates the interest of the students to work
with concrete material.
It provides opportunities for social interaction
and co-operation among the students.
It is child-centered and therefore it is a
psychological method.
It helps the students to actively participate in the
learning process and therefore the learning

113
becomes more meaningful and interesting.
8. HOW DOES IT
WORK?
Max 100 words.
Procedure:
Aim of The Practical Work: The teacher clearly
states the aim of the practical work or
experiment to be carried out by the students.
Provided materials and instruments: The
students are provided with the necessary
materials and instruments.
Provide clear instructions: Provide clear
instructions as to the procedure of the
experiment.
Carry out the experiment: The students carry
out the experiment.
draw the conclusions: The students are required
to draw the conclusions as per the aim of the
experiment.
9. EVIDENCE
Links for videos, photos. Plostina%20na%20topka.docx#Photos
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
This method is based on the maxim “learning
by doing.”
This is an activity method and it leads the
students to discover mathematics facts.
In it we proceed from concrete to abstract.
Laboratory method is a procedure for
stimulating the activities of the students and
to encourage them to make discoveries.
This method needs a laboratory in which
equipment and other useful teaching aids
related to mathematics are available.
For example, equipment related to geometry,
mensuration, mathematical model, chart,
balance, various figures and shapes made up of
wood or hardboards, graph paper etc.
11. ASSESSMENT
instructional paper with a checklist for evaluating
Plostina%20na%20topka.docx#Ocenuvanje
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
Plostina na topka.docx
MATH-LAB.docx

114
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Motivational tasks / entertaining tasks and
games
2. COUNTRY
Bulgaria
3. LINK
the good practice.
https://www.researchgate.net/publication/29348
3022_MOTIVACIONNITE_ZADACI_V_OBUCE
NIETO_PO_MATEMATIKA
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Mathematics education is impossible without
solving problems attend in each lesson, they are
a means to achieve the training aims.
Motivational tasks must be the starting point of
each phase of training .They should be
challenging, emotional, related to real life, to
bring awareness training and prerequisites for
sustainable utilization of mathematical
knowledge. There are three main groups -
historical tasks; tasks with errors; entertaining
tasks and games; tasks with theoretical possible
solution, but not practicable; practical and daily
life tasks of students. In this practice will look
entertaining tasks and games.
6. RESOURCES
method.
handbook - Mathematical folklore; various
publications on the Internet
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
-entertaining tasks and games allow students in
the learning process to discover for yourself
some or other mathematical facts;
- incite them to thinking;
- striving to broaden and deepen their
knowledge;
- improve the skills
8. HOW DOES IT
WORK?
Max 100 words.
Sample tasks that are suitable for students from
5th to 7th grade:
1. Guessing age and number of the building
where you live - write the number of the building
where you live on a sheet. Multiply it by 2 and
add 5 to the result. The resulting number
multiply by 50 and add it to 365. To the last
result add your age and say the resulting
number. From the resulting number subtract

115
615. The first two numbers that you received are
numbers of the building where you live and the
latter two are your age.
2.Diophant spent 1/6 of his life in childhood;
1/12 in adolescence; after the seventh part
spent in childless wedlock and yet five years, he
had a son who died half years from his father,
then Diophant lived another four years.
3. Find a two digit number having properties: the
number of tens is less with 4 than the number
of units.If the number written with the same
numbers but in reverse order subtract the given
number is obtained 27.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Entertaining tasks and games provoke in
students:
- Anticipation and anxiety, joy of learning
mathematics;
- Awaken and develop sustainable interest
among students towards learning mathematics
and its application;
- Awaken students to independent, search,
creative work;
- Expand and deepen perceptions of students
about cultural and historical value of
mathematics;
11. ASSESSMENT
individual assessment;
- for speed
-for resourcefulness
- for wit
- for original solution
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

116
FIELD CONTENT
CONTENT
6. TITLE
describes the good
practice?
Motivational problems in math education
7. COUNTRY
Bulgaria
8. LINK
the good practice.
https://www.researchgate.net/publication/29
3483022_MOTIVACIONNITE_ZADACI_V_
OBUCENIETO_PO_MATEMATIKA
10. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Motivational tasks must be the starting point of
each phase of training. They should be
challenging, emotional and connected to real
life. Motivational tasks imported into
mathematics education awareness and create
significant preconditions for sustainable
utilization of mathematical knowledge. These
tasks allow students in the learning process to
discover for yourself or some other
mathematical facts, incite them to think over the
questions, made over all striving to broaden and
deepen the knowledge to skills development.
11. RESOURCES
method.
handbook - Mathematical folklore; various
publications on the Internet
12. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
- Incite and develop sustainable interest among
learners to learning mathematics and its
application;
- Incite students to self-seeking, a creative work;
- Show the learner practical significance of the
subject;
- Show students the reasons for the emergence
of one or another theory;
- Expand and deepen introduce learners to the
cultural and historical value of mathematics.
13. HOW DOES IT
WORK?
Max 100 words.
Groups tasks that contribute to the formation of
motivation for learning in students:
First group: Historic tasks

117
does the practice involve? These are such tasks, most of which are
composed by famous mathematicians in the
past or reach us via mathematical folklore.
Second group: Tasks with errors
A) mistakes made by students want errors to be
detected by other students in the class -these
errors are for others in the class and they are
result of incorrect analogies.
B) errors committed intentionally by the teacher
C) sophisticate, paradoxes.
Sophisticate and paradoxes help correct
consciously and thorough utilization of
knowledge in mathematics. Here we must pay
attention to the students not only learned what
state regulations, but also on those things that
are not true and mainly why not true. It is better
to understand how a mistake can lead them
ignoring a rule.
Third group: Fun tasks and games
These are such tasks carried away students to
actively participate in math.
Fourth group: Tasks of practice and everyday
life.
14. EVIDENCE
No evidence
15. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Entertaining tasks and games provoke in
students:
- Anticipation and anxiety, joy of learning
mathematics;
- Awaken and develop sustainable interest
among students towards learning mathematics
and its application;
- Awaken students to independent, search,
creative work;
- Expand and deepen perceptions of students
about cultural and historical value of
mathematics.
16. ASSESSMENT
individual assessment;
- for speed

118
-for resourcefulness
- for wit
- for original solution
17. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
AtzeWJ9ZmdSV2N6VnRnSlU
AtzeWJ9UEo5SU1aVEs2blU

119
FIELD CONTENT
CONTENT
1. TITLE
practice?
Maths problems with practical application
2. COUNTRY
place?
Bulgaria
3. LINK
http://sbornik.biz/class5.php?tag=%D0%9
7%D0%B0%D0%B4%D0%B0%D1%87%D
0%B8%20%D1%81%20%D0%BF%D1%8
0%D0%B0%D0%BA%D1%82%D0%B8%
D1%87%D0%B5%D1%81%D0%BA%D0%
BE%20%D0%BF%D1%80%D0%B8%D0%
BB%D0%BE%D0%B6%D0%B5%D0%BD
%D0%B8%D0%B5
http://sbornik.biz/class6.php
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
Solving problems with practical applications
convince students that mathematics taught in
school is closely related to the real world.
Mathematics is a science that requires not only
learning rules, but their application in real-life
situations. Finance, science, technology,
construction, trade, lifestyle - mathematics helps
students daily to feel themselves
knowledgeable and helpful.
6. RESOURCES
the method.
-
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Students are able to:
• Recognize the role of mathematics in
the world around us
• Work with real-life data;
• Comprehend the text, translate it into
the language of mathematics.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
Tasks with practical application reinforce
students’ knowledge on a given subject, offering
problem solving, which in turn orient students in
the relationship between objects. The plot of

120
involve? these tasks can be from various fields of human
knowledge and practice. Students learn to show
abilities, effective use of mathematical
knowledge to deal with specific situations.
What is required to solve the tasks is as
follows:
• Text comprehension;
• Hypotheses formulation;
• Modeling skills.
9. EVIDENCE
Links for videos, photos. -
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
 Awareness of the fact that mathematics
is all around us;
 A set of cognitive and practical skills;
 Acquiring experience for solving
problems in certain life situations;
 Developing thinking and reinforcing
knowledge;
 Acquiring certain natural science or
technical knowledge;
 Finding out connections between theory
and practical activities of human life;
 Provoking interest in certain
mathematics knowledge and skills;
 Being aware of the meaning of math
study material;
11. ASSESSMENT
-
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
-

122
SPECIFIC CASE STUDY
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The Portfolio
2. COUNTRY
Romania
3. LINK
the good practice.
https://www.ericdigests.org/2000-2/portfolio.htm
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Includes representative materials of what a
person has worked during a period of time. May
contain written solving of some work tasks,
notes, learning diaries, tests, homework, extra
problems solved, biographies of mathematicians
previously studied. Ideally, the portfolio contains
things that demonstrate student's progress in
learning mathematics.
Pupils must be given clear instructions about
what the portfolio should contain and the
evaluation criteria of portfolios must be known
by the students.
The student is free to include in the portfolio
material that he considers necessary. Some
elements of the portfolio are assessed
separately.
6. RESOURCES
method.
Files
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Integrated approach to learning and the use of
alternative valuation methods stimulate the
creation of a relationship of collaboration, trust
and mutual respect between teacher and
students and between students. The student
doesn't feel controlled, but supported. The
teacher must be more an organizer of learning
situations and a linking element between the
student and the society, which mediates and
facilitates access to information.

123
8. HOW DOES IT
WORK?
Max 100 words.
Task:
Store in a file all written math materials - notes,
homework, tests, extra solved problems,
biographies of mathematicians previously
studied.
The portfolio must contain at least the following
parts:
- A title sheet
- contents
- At least a written sheet (essay, describing
steps in solving a problem, etc.)
- Some math homework, to demonstrate
understanding the math process
- All written material produced during and for
math lessons (other than the homework)
- At least two tests demonstrating suggestive
progress.
- An essay conclusively linked to your
experience at math.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
- promotes the overall development of
personality by harnessing acquisition in different
subjects by integrating knowledge, capabilities,
skills and attitudes.
- Stimulates the responsibility of the student by
giving them the freedom of selecting the themes
and the solving options
- Assesses students' learning
- Focuses on the identification / formulation of
problems and then on solving them.
- Engages students in real-life situations; has
practical, social and economic significance and
implications in moral education.
- Encourages self-thinking rather than
memorization or recognition of information.
- Is interactive, engages students in
understanding the evaluation process
11. ASSESSMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

124
FIELD CONTENT
CONTENT
1. TITLE
practice?
INSERT (Interactive Noting System for
Effective Reading and Thinking) method
2. COUNTRY
place?
/
3. LINK
faculty.tamuc.edu/jthompson/Resources/INSE
RT.doc
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
- uses a text encoding way that allows learners
to read and understand actively and
pragmatically a certain content
- Used in the learning stage, as students' prior
knowledge, evidenced by evoking specific
activities, are used as basis for reading /
listening the text.
6. RESOURCES
the method.
Book, board, worksheets
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
a GOOD practice.
- develops vocabulary and ability to express and
use mathematical language
- own model of understanding and processing of
a mathematical text is highlighted
- students are faced with making connections
between information, making associations of
ideas, using written material to find new
meanings, information or work procedures in
relation to a given topic.
8. HOW DOES IT
WORK?
Max 100 words.
does the practice
involve?
-During the reading stage, students mark on the
text or in their notebooks:
knowledge / information / working procedures
confirmed by text - denoted by check
knowledge / information / work procedures
denied / contradicted by text - denoted by "-"
knowledge / information / work procedures they
haven't known before - marked with "+"
- the individually obtained information is
discussed in pairs / groups, then communicated
to the teacher. The teacher centralizes them in a
table on the blackboard.
Uncertain knowledge can be the theme of a

125
debate or can be research topic for future
lessons.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative
results in relation
to the teaching
goals.
 What is the
users/target
group’s opinion
of the activity?
- students are encouraged to monitor their own
understanding
- students are personally involved in the process
of acquiring knowledge and skills, as they
deliberately value and correlate their own
schemes of understanding and action in the
learning process.
Students build their own system of action in new
learning situations, system that uses schemes
of action that belong to critical thinking
11. ASSESSMENT
/
12. UPLOAD A
FILE
Please send related
uploaded on the e-
platform.
No additional files

126
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The Racing games feast of mathematics
2. COUNTRY
Bulgaria
3. LINK
the good practice.
www.math.bas.bg/…MITE2/Grozdev-
Chehlarova-paper.pdf
www.math.bas.bg/…tii/33-vazrajdane-na-
praznicite...
www.researchgate.net/…/Sava_Grozdev/public
ation/...
4. LANGUAGE Language of the source. Bulgarian, English
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Celebrations of mathematics are useful for all
students from the first to the last class of
education, they leave a lasting impression in the
mind. An important part of the celebration of
mathematics are racing games. Participants
broadcast three teams with three contestants.
First played for team standings, then individual
standings. Between stages have educational
interesting facts and tasks for the audience.
6. RESOURCES
method.
Prepared didactic software to celebration of
mathematics -type presentation.
Supplies for the competition – sheets, pens;
Prizes for participants;
Invitations for the guests;
Logo for each participant and guest;
Diplomas (I, II, III place for team and individual
ranking);
Decoration ;
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Participation in racing games on the celebration
of mathematics contribute to:
• formation of skill orientation in time;
• to improve the ability to plan and implement
the plan;
• for reflection and evaluation at your own
opportunities, achievements and personality

127
changes as a result of training.
• improve is the ability to work in a team;
• strong emotional impact and form a love to
math;
8. HOW DOES IT
WORK?
Max 100 words.
Preparation for the celebration:
• Selection of tasks for the contestants and the
audience
• Preparation of software product for the
celebration;
• Preparation of scenarios for the celebration
• Development of a logo for each participant
and guest
• Purchase Awards, making diplomas,
invitations to guests
• Preparation of consumable for competition
• Decorate the room
Conduct of the celebration: There are two
presenters on the celebration. Acquaint
participants and guests with the regulation of
the competition . The competition is in three
rounds. In the first round of all participants are
broadcast three teams of three contestants.
The second round is the team standings, and
the third - for individual standings. In each
round are solved three problems for time.
Between each two rounds have interesting facts
for the audience and tasks for the audience - so
filled time in which contestants solve problems
and the celebration has a learning function for
the audience. After each round explains the
decision of tasks. Commission examines the
decisions and broadcast winners.
9. EVIDENCE
AtzeWJ9NTZJWFl0TERHUG8
AtzeWJ9STdnZzVVdmRHTGc
AtzeWJ9ZlE1elVKSjZCY2M
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
The competition is very emotional. Participants
are always satisfied after its completion, also the
audience and guests, since they were not just
passive spectators but and participants. For
contestants competition also has an educational

128
users/target
the activity?
and educative function.
The limitation of time to solve problems is
essential. This limitation requires and
accordingly educate concentration in learning
the task, in solving it, replying or refusal of it.
Assist in the formation of the ability to make a
decision. Educates responsibility - no time for
continuous verification of the correctness of the
result reached. Time constraints contribute to
the understanding of the need for knowledge of
rational methods of work of more methods to
solve problems, more knowledge. In some
cases, intuition is crucial to reach an answer -
and it is based on associations, analogies of
preliminary accumulation of knowledge, skills,
tactics and behavior.
11. ASSESSMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

130
VISUALIZATION AND ICT
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Where you can, use computers to do the drudge
work
2. COUNTRY
U.S.
3. LINK
the good practice.
http://www.intmath.com/blog/how-to-make-
math-class-interesting
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
For the vast majority of your students (who will
not eventually become mathematicians), it's
more important they understand the concepts
and which process to use when confronted with
different real problems. They then should learn
how to use computer algebra systems (or
graphics calculators) to solve such problems.
6. RESOURCES
method.
http://www.intmath.com/blog/mathematics/free-
math-software-downloads-849
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Students skilled to use math software’s;
Learning becomes interesting;
The students easily solve problems.
8. HOW DOES IT
WORK?
Max 100 words.
To improve this practice math teaching method
we need computers and math software. It help
students to solve problems easier, for example if
they need to graph a line they can easy make it
with those software, just by giving necessary
coordinates.
9. EVIDENCE
/

131
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The expected results from this practice are to
enable students to use the computer to solve
mathematical problems with the help of
mathematical software, and to visualize them.
Also facilitating and encouraging math learning.
Students have very good thoughts about this
practice because they consider it to be very
interesting to solve mathematical problems with
the help of computers, while at the same time
they also develop informatics skills.
11. ASSESSMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

132
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
The cube method
2. COUNTRY In which country does the
Romania
3. LINK
the good practice.
http://webserv.lgrcat.ro/ssmrb/evenimente/Sesiu
ne_09_11_2013/15.pdf
5. SUMMARY
(DESCRIPTION
OF THE
METHOD)
Max 50 words.
teaching practice.
- Creation of a cube whose sides are the words:
describe, compare, analyze, associate, argue
- Announcing the theme
- Dividing the class into 6 homogeneous groups.
examining each topic from the perspective of
the requirement from one side of the cube
6. RESOURCES
method.
- Flip-chart sheets. markers, tape, handouts,
cube
7. WHY IT IS A
GOOD
PRACTICE?
Give at least three
GOOD practice.
- Each of the 8 groups receives one of the
above tasks about faces, edges, vertices
- Describe shapes, sizes, elements
- Compare what is similar, what is different
- Analyze
- Associate - what makes you think of
- Argue - list a number of reasons that support
your assertion
- Geometric body - cube, flip chart, marker
8. HOW DOES IT
WORK?
Max 100 words.
- The cube method is used if you wish to
analyze a situation from multiple perspectives. it
allows students to develop skills necessary for
complex approaches
- The method can be applied using only some
sides of the cube
9. EVIDENCE Links for videos, photos.
http://www.suntparinte.ro/metoda-
cubului#prettyPhoto/0/
http://www.tvladimirescutgv.ro/LECTII/Lectie%2
0descrierea%20clasa%20omogena/grupa_ii.ht
ml

133
10. RESULTS
Max 75-100 words.
▪ Quantitative and
qualitative results
in relation to the
teaching goals.
▪ What is the
users/target
the activity?
- Each student brings his contribution on a topic
previously chosen
- Each team draws up the final answer
- The final form is displayed on the board or on
the walls of the class and is analysed by other
teams
- Trains students in a continuous and
collaborative participation
- Develops teamwork attitude of tolerance
towards others
11. ASSESSMENT
/
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
https://www.google.ro/search?q=proiect+de+lect
ie+matematica+metoda+cubului&ei=4k3JWfLhD
8OE6QTHlpD4Aw&start=20&sa=N&biw=1366&
bih=676

134
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
‘Brainteasers season’
2. COUNTRY
Macedonia
3. LINK
the good practice.
http://www.learn-with-math-games.com/math-
brain-teasers.html
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
The aim of this practice is to develop the critical
thinking of students. For that purpose, a set of
brainteasers is introduced.
6. RESOURCES
method.
Projector, computer
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Developing new ways of thinking
• Introducing a diversity of opinions and
criticizing
• Critical attitude toward the problem
setting
8. HOW DOES IT
WORK?
Max 100 words.
The teacher opens the class with some of the
classical mathematical logic problems. Then
introduces a web-page with brainteasers and let
students decide which one of them to do next.
At the end of the class each student receives a
different set of problems (in a previously seen
setting) that they should try and answer by
themselves.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
After this practice students are more focused on
the details after reading a word problem. They
tend to notice the ‘weak spots’ in logic
statements better than previously. Both students
that do math with ease and not are excited
about solving problems that do not involve the
standard curriculum based problems. The
students are refreshed from the standard way of
learning mathematics. Teachers could clearly
see that they are excited and anticipating for the
next problem.

135
11. ASSESSMENT
Assessment methods for this practice should
not be strict and should be more oriented toward
student ability to verbalize their opinion about
the solution of a certain problem.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
https://www.coolmath4kids.com/brain-teasers
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Solving mathematical problems using concrete
materials
2. COUNTRY
Kosovo
3. LINK
the good practice.
https://kec-ks.org/wp-
content/uploads/2016/06/BEP_HULUMTIMI-
N%C3%8B-VEPRIM-2.pdf
4. LANGUAGE Language of the source. Albanian
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
The main characteristics of these teaching
method is solving math problems using concrete
materials and games as: Mathematical
dictionary, fractional wall, calculator, paper
game, dominoes with fractions, memory cards
etc.
6. RESOURCES
method.
Concrete materials – paper, calculator, Lego
cubes, ..
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
Students are excited during the class, they learn
through the game, and this practice also makes
it possible to change the convictions of students
who Mathematics felt very difficult to learn.
8. HOW DOES IT
WORK?
Max 100 words.
This practice involves games and concrete
materials for math solving problems. Where the
teacher chooses the proper game or concrete
material to explain to students the new lecture,
for example during fractional learning they can

136
play the game dominoes with fractions.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
This practice has proved to be positive because
after its application the students have been
tested for teach units that have been developed
with this practice and they have shown good
results.
Students have also been questioned about this
practice and they have been very pleased
because math’s learning has been facilitated
and they have gained good thoughts about it.
11. ASSESSMENT
test
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
‘Part of a whole’- introducing fractions in early
age
2. COUNTRY
Macedonia
3. LINK
the good practice.
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Using Lego-cubes in in different colours,
students represent fractions as part of a whole.
For example, the fraction 3/5, can be
represented as 3green+2red=5 bricks. In other
words, 3 out of 5 bricks are green.
6. RESOURCES
Lego-cubes.

137
method.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Visualisation of fractions
• Putting context into numbers
• Visually interpret the concept: part of a
whole
8. HOW DOES IT
WORK?
Max 100 words.
Each student receives a set of Lego-cubes in
different colors. The teacher writes a fraction on
a paper and shows it to everybody. The
students are required to represent the fraction
with the Lego-cubes as part of a whole. If
somebody makes a different fraction, the
students are asked to read the fraction and then
represent it. Then it can go the other way
around, The teacher showing a ratio using
Legos, and the student verbalizing the given
fraction. Word problems, as representing 2/5 of
a pizza can also be used. The teacher can go
further by asking how much is there until 1.
9. EVIDENCE
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
The students enjoy building with Legos and
learning fractions in the same time. This is a
very visual way of learning, where the students
do not even feel that they are engaged in a
learning activity.
11. ASSESSMENT
If a student manages to represent a certain
fraction he/she is awarded 1 point.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
RYVZgbqDbnNkdXYyUklvckk
RYVZgbqDNXR1dlN6aTIxa1k

138
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Visuals and graphics
2. COUNTRY
USA
3. LINK
the good practice.
http://powerupwhatworks.org/strategy-
guide/visual-representations
http://powerupwhatworks.org/strategy-
guide/visual-representations-teach-tech
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Textbooks often include various visuals and
graphics for students to learn from. They are
crucial elements to accompany text and help get
the concepts across to students. However,
these graphics appeared to be much more
effective when paired with specific practice or
guidance. This guidance could be coming from
the teacher or from another classroom tool.
Teachers are starting to implement
computerized learning into the classroom for a
more personalized learning approach. In fact,
more than four in 10 teachers report the use of
e-readers and tablet computers in their
classrooms to complete assignments and assist
in learning.
6. RESOURCES
method.
Tablets, computers
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
All students can benefit from using visual
representations, although struggling students
may require extra support and practice. Visual
representations are a powerful way for students
to access abstract math ideas. Drawing a
situation, graphing lists of data, or placing
numbers on a number line all help to make
abstract concepts more concrete, whether done
online or offline. Developing this strategy early
will give students tools and ways of thinking that
they can use as they advance in their learning of
more abstract concepts.
8. HOW DOES IT
WORK?
Max 100 words.

139
/
9. EVIDENCE
https://www.youtube.com/watch?v=V-
9E_6ZWISk
https://www.youtube.com/watch?v=qlqkjH3iSQo
https://www.youtube.com/watch?v=C6aQiMjJ7R
Y
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
With virtual math programs, children can not
only see these graphics, but they can revisit
concepts that were especially difficult. They are
able to learn at their own pace and won't feel
rushed to move onto a concept they are not yet
ready to tackle.
11. ASSESSMENT
Electronic test
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

140
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Coordinate Geometry Method in Solving
Problems
2. COUNTRY
Bulgaria
3. LINK
further information about the
good practice.
http://math.bas.bg/
5. SUMMARY
(DESCRIPTION OF THE
METHOD)
Max 50 words.
Please summarise the main
characteristics of the
teaching practice.
The dynamics of present times challenges
the Bulgarian teachers to change their teaching
style and methodology. Contemporary students
are bored with the monotony of the traditional
lesson. They look forward to an interesting
approach that will attract and rivet their
attention. We share our experiences in practice
for implementing the coordinate system in
geometric tasks - producing various shapes (of
animals) using a coordinate system and find
their areas, dividing them into well-known
shapes.
6. RESOURCES
method.
● Worksheets with square grid and
notebooks.
● Drawing and measuring tools.
● Painting supplies.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
● Rationalizing of what has been
learned in math through
practical application.
● Using of imagination and logical
thinking.
● Acquiring of measuring skills.
● Applying the acquired knowledge
and skills to detect the
properties of figures and certain
regularities.
8. HOW DOES IT
WORK?
Max 100 words.
Preparatory part - A topic is being
formulated.
● Tasks to be solved are placed
individually as each student is
given a task from the coordinate
system for displaying a
sequence of points set by its
coordinates.
● Requirements related to the given

141
tasks have been
introduced.
● Students are being consulted at
different stages of their work.
● An individual assessment of the
obtained results is being
given to the students in relation to
assigned tasks and
requirements.
9. EVIDENCE Links for videos, photos.
/drive.google.com/open?id=0B4ls-
AtzeWJ9amVVREh6RWdmYzA
AtzeWJ9RndhUVY5a25fVlk
AtzeWJ9YndPVVEwNFJuUWs
AtzeWJ9NE9vWWxLM0tZakU
AtzeWJ9SHBTT3dJUkxBdEE
10. RESULTS
Max 75-100 words.
• Quantitative and
qualitative results in
relation to the
teaching goals.
• What is the
users/target group’s
opinion of the
activity?
• Research skills are being formed and
developed.
• Creative abilities are being promoted.
• Spatial thinking is also being developed.
• Shier students are encouraged to
participate in individual tasks.
• Cooperation and competitive behavior
are being stimulated.
• The irksome learning process converts
into diverting and interactive
experience.
• Students’ attention is being riveted.
They are given an opportunity to
participate themselves in the process of
learning.
• Pupils are enabled to use their own
knowledge and practical skills.
11. ASSESSMENT
ggested assessment method
for the students
• An individual assessment related to the
tasks assigned.
• Creative and aesthetic workmanship.
12. UPLOAD A
FILE
Please send related
(lesson plan, evaluation etc.)
so that they can be
uploaded on the e-platform.
-

142
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Experimental method in mathematics
2. COUNTRY
Bulgaria
3. LINK
the good practice.
http://www.dipku-
sz.net/izdanie/182/eksperimentt-po-matematika-
virtualen-i-realen
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
Contemporary Bulgarian students get
bored of the monotony of the traditional lesson
in math class. They expect something
interesting to revit their attention. Experiment in
mathematics is virtual or real. Caring out real
experiments in math class enable students not
only to receive knowledge in the form of
formulas, theorems and concepts, but also to be
able to find out connections between different
fields of knowledge. They clearly convince
themselves in their authenticity.
6. RESOURCES
method.
Patterns of geometric shapes and
bodies.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Provides opportunity for
students to visualize the
material.
• Connections between
formulas and concepts are
being established in an
experimental way; theorems
are also being evinced.
• Method offers a great
variety.
● Problems associated with
boredom by listening to the
lesson are being saved to the
teacher.
● Students are being motivated
to acquire knowledge.
● It is given meaning to what
has been learned.

143
8. HOW DOES IT
WORK?
Max 100 words.
6th grade - When displaying the formulas for the
volume of a
pyramid and cone.
Students have prisms and pyramids
patterns, cylinders and cones with equal areas
of bases and equal heights. By pouring water
from a pyramid into a prism and from a cone
into cylinder students establish in an
experimental way the following - the volume of
the pyramid or cone is 1/3 of the volume of the
prism or cylinder. They convince themselves of
equivalence of terms ‘volume’ and ‘capacity’.
8th grade - When introducing the concept
‘centroid’ in a triangle.
Students ascertain with great interest that
the centroid not only divides a median in a
certain respect, but it is also a center of gravity
of the triangle. Working in pairs they have
produced in advanced different triangles,
construct a centroid and experimentally find out
that if you break through the triangle in centroid
and tie a string through the hole it remains in
balance.
Proving the theorem about a circle inscribed in
a rectangle
By means of sticks students construct a
quadrangle around pre-made paper circle and
express their hypothesis about the relations
between the sides or angles. Once they
establish the relation between the sides, they
stain the related sides using a marker.
9. EVIDENCE
AtzeWJ9TDBaeWtjR1o0Z1E
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
● Students come out of ‘dryness’ of the
studied material and play
the role of researchers, discoverers of
properties.
● They establish connections between
problem solving and real-
life.
● They are enabled to form and develop

144
research skills;
● Spatial reasoning is being stimulated;
● Students' attention is being riveted.
● Students are being given an
opportunity for personal
involvement; they are empowered to
give a sample of their
knowledge and practical skills.
11. ASSESSMENT
-
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
-

145
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
E-lesson in mathematics as a form of training
2. COUNTRY
Bulgaria
3. LINK
the good practice.
http://conf.uni-
ruse.bg/bg/docs/cp15/6.4/6.4-8.pdf
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
The use of e-lessons in mathematics
education is a method that provoke students’
thinking to develop their individual skills, their
skills on working effectively in
a team environment , to assert creatively and
carry out their ideas. Multimedia exposure
makes lessons more interesting as it allows the
presentation of the material as a system of
images, figures, charts and facts in a particular
order.
The presentation of the educational
material presented on a large screen with text
and graphics, increases the didactic
opportunities of the lesson, reduces training
time and maintain students' interest.
6. RESOURCES
method.
Laptop, multimedia projector,
presentation
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
• Provides an opportunity for
visualization of the educational
material.
• Reducing teaching time.
• Maintain the students’ interest in
learning.
• Students are motivated to acquire
knowledge.
• individual and teamwork skills are
being developed.
8. HOW DOES IT
WORK?
Max 100 words.
• Solving problems to consolidate
students' knowledge on Area of a circle
• Knowledge application of geometric

146
does the practice involve? figures surface in tasks of combinatorial
character.
• The class is divided into three groups
and each group works on one of the
figures. A student of the group presents
and gives reasons for the solution.
• Update the notion ‘statistical table’,
percentage and constructing a pie chart
on tabulated data.
• the construction of a pie chart is being
displayed visually
9. EVIDENCE
Presentation
https://youtu.be/YI-b_beodZo
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
• Students participate during the lesson
actively and creatively, they are not in
the role of passive observers.
• The teacher receives information about
the extent of assimilation of pre-existing
material (through Tasks 1 and 2)
• By solving problems in groups is carried
out cognitive interpersonal
communication and interaction in
different working groups.
• A higher quality and effective learning is
being achieved.
• Students are being motivated to
participate more actively in the learning
process.
• Students like this type of presentation of
educational content and work with
willingness and interest.
• The passive learning process converts
into dynamic and interactive experience.
• A new learning environment is being
established; student’s self-activity is
being stimulated and a new attitude
towards mathematics is being formed.
11. ASSESSMENT
A verbal assessment of the group work is being
given. Students that have presented and given
reasons for the problem solution are evaluated
individually.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
AtzeWJ9N3BfdVJMY2RkVFE

147
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Modeling
2. COUNTRY
Bulgaria
3. LINK
the good practice.
http://www.iteach.ru ;
http://www.intuit.ru/department/education/intelte
ach/0/
http://pedagogicnews.uni-
ruse.bg/%D0%BC%D0%BE%D0%B4%D0%B5
%D0%BB-%D0%BD%D0%B0-
%D0%BF%D1%80%D0%BE%D0%B5%D0%B
A%D1%82%D0%BD%D0%BE-
%D0%B1%D0%B0%D0%B7%D0%B8%D1%80
%D0%B0%D0%BD%D0%BE-
%D0%BE%D0%B1%D1%83%D1%87%D0%B5
%D0%BD%D0%B8%D0%B5-%D0%BF/
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
The model is a simplified representation or
duplication of real things. The models are:
physical, theoretical logic, simulation,
mathematical. This practice describes the
mathematical - physical model. Knowledge
through action. Making of various models /
templates / geometric shapes and bodies with a
view to their knowledge, according to the
elements and properties, measuring basic
characteristics for the purpose of calculating the
surfaces, area and volume. This includes
precision and accuracy of workmanship and
aesthetics when choosing material and shaping
the final form.
6. RESOURCES
method.
Colorful cardboard drawing tools, glue, wooden
skewers, plasticine.
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
The models enable students to create models of
geometric shapes and bodies using their main
dimensions and characteristics with a view to
their better knowledge and learning. A visual
representation of the object, which contributes

148
to its recognition and determination. Students
use their creativity and develop their aesthetic
skills in craftsmanship.
8. HOW DOES IT
WORK?
Max 100 words.
1 / Choosing a theme for the application of the
method / Geometric shapes: triangle,
trapezium, parallelogram - 5th grade. Ribbed
and oval shaped bodies - 6th grade ./
2 / Task analysis.
3 / Building a net of elected bodies.
4 / Making of model / templates /
5.1 / If the model is a geometric shape
measuring basic characteristics for the purpose
of calculating the circumference and surface.
5.2 / If the model is geometrically form identifies
key characteristics for calculating area and
volume.
9. EVIDENCE
AtzeWJ9ZmdSV2N6VnRnSlU
AtzeWJ9UEo5SU1aVEs2blU
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
Development of models / templates / develop
creative attitude in mathematics. Serve to
develop a number of important qualities of
logical and creative thinking of students as
suggesting such a method in which students
prepare to self-discovery and exploration of
objects.
11. ASSESSMENT
Individual evaluation:
- Creative and aesthetic craftsmanship.
- True and precise execution.
- True cope with the measuring and calculation
process.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
-

149
FIELD CONTENT
CONTENT
1. TITLE
describes the good
practice?
Mathematics - a tool for modern thinking
/”Creative” classroom/
2. COUNTRY
Bulgaria
3. LINK
the good practice.
http://www.dipcu-sz.net/izdanie/183
www.j2e.com/toni-
66/lesson/4th+grade/10broinasistema
http://antoineta.wordpress.com/2015/10/04/
5. SUMMARY
(DESCRIPTION OF
THE METHOD)
Max 50 words.
teaching practice.
To be creative classroom principal place in it
must have creativity. It is a system of creativity,
combination of mental and personality that lead
to the formation of new ideas for solving the
theoretical and practical tasks. Modern younger
students demonstrate through their behavior
that they need training oriented towards
dialogue and cooperation, aiming to experience
active learning. Teachers should look for
creative approaches, productivity, flexibility,
originality, innovation, creativity and stimulate
new ideas.
6. RESOURCES
method.
white and colored paper, pencils, scissors,
drawing tools, color and plastic clips
7. WHY IT IS A
GOOD PRACTICE?
Give at least three
GOOD practice.
The creative classroom allows students to freely
imagine and create new things.
-to fantasize and combine
-to form and generate original ideas to modify
and use in the classroom in an original way.
8. HOW DOES IT
WORK?
Max 100 words.
1.Select a theme for the application of the
method ( Fun activities for studying natural
numbers)
2. Creation of mathematical abacus( the
purpose is to illustrate the decimal positioning
system)

150
3. Determination of training actions
4. Determining how they connect
9. EVIDENCE
No evidence photos
10. RESULTS
Max 75-100 words.
qualitative results
in relation to the
teaching goals.
 What is the
users/target
the activity?
-Training in creative classroom develops
creative thinking, guesswork, intuition.
Enhances creative searching.
-Form and develop research skills.
-Develop spatial reasoning.
-Encourages timid at work.
-Stimulate competitive behavior.
-It allows training to be interesting.
11. ASSESSMENT
Individual assessment:
-creative and aesthetic product.
- for participation, for the correct answer.
12. UPLOAD A FILE
Please send related
uploaded on the e-
platform.
No additional files

151
References
[1] N.G. Ignacio, L.J.B. Nieto, E.G. Barona,The affective domain in mathematics learning,
international electronic Journal of Mathematics Education, 1 (1) (2006), pp. 16-32.
[2] M.K. Akinsola, F.B. Olowojaiye, Teacher instructional methods and student attitudes
towards mathematicsInternational Electronic Journal of Mathematics Education, 3 (1)
(2008), pp. 60-73.
[3] Moenikia, M. & Zahed-Babelan, A. A study of simple and multiple relations between
mathematics attitude, academic motivation and intelligence quotient with mathematics
achievement. Procedia Social and Behavioural Sciences, 2, 1537-1542, (2010).
[4] K. Singh, M. Granville, S. Dika, Mathematics and science achievment: effects of
motivation, interest and academic engagement, The Journal of Educational Research,
Vol. 95, No. 6 (Jul. - Aug., 2002), pp. 323-332
[5] Neale, D., The role of attitudes in learning mathematics. The Arithmetic Teacher, Dec,
631-641, (1969).
[6] N. Gillet, R. J. Vallerand, and M. A. K. Lafrenière, “Intrinsic and extrinsic school
motivation as a function of age: the mediating role of autonomy support,” Social
Psychology of Education, vol. 15, no. 1, pp. 77–95, 2012.
[7] V. F. Filak and K. M. Sheldon, “Teacher support, student motivation, student need
satisfaction, and college teacher course evaluations: testing a sequential path
model,” Educational Psychology, vol. 28, no. 6, pp. 711–724, 2008.
[8] Moenikia, M. & Zahed-Babelan, A. A study of simple and multiple relations between
mathematics attitude, academic motivation and intelligence quotient with mathematics
achievement. Procedia Social and Behavioural Sciences, 2, 1537-1542, (2010).
[9] Tait–McCutcheon., S. L., Self-efficacy in mathematics: Affective, cognitive, and conative
domains of functioning. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents
and charting directions (pp. 507-513). Brisbane: MERGA.K. Elissa, “Title of paper if
known,” unpublished. (2008).
[10] ICME, 2004, Current problems and challenges in primary mathematics
education.

ISBN:978-608-244-445-1
This project has been funded with the support from the European Commission.
This publication reﬂects only of the author and the European Commission cannot be held
responsible for any use which may be made of the information contained therein.
Part of review:
... "Math teachers will have the opportunity to perceive the
challenges that math teaching process is faced with, in order to
prepare students for a "knowledge and skills - based economy" as
a fundamental EU priority after 2020" ... - S.Mirascieva
... "This is nice synthesis of positive practices collected from all
around the world, so learning mathematics may become
interesting and fun, but striving for quality and excellence at the
same time"... A.Rushiti

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