Number Recognition Assignment

Number Recognition Assignment
Introduction
For this mathematical report the theme that has been chosen is Number recognition. The report will
investigate how children can learn the concept related to number through everyday experiences,
such as, playing and painting. The assignment will be linked to the Early Years Foundation Stage
(EYFS). The report will demonstrate the planning, implementing and evaluating a range of activities
which will support children in their mathematics knowledge focusing on numbers three and four
years old. Activities supported by the Early Years Foundation will be displayed in the plan and
evaluated in the report. The report will contain thorough key theories of learning linking to the
activities that will take place. The evaluation in the report ... Show more content on Helpwriting.net
...
This can be linked to Vygotsky's (1978) (cited in Nevid 2007) theory of Zone of Proximal
Development. The Zone of Proximal Development is closely linked to scaffolding. Vygotsky sees
the Zone of Proximal Development as the area where the child needs the most guidance. He looks at
the interaction of peers as a great way of developing skills. The Zone of Proximal Development
provides support for the learner's development. According to (Nevid 2007) the followers of
Vygotsky believe that parents and practitioners should use the skill of scaffolding in order to support
children when they are gaining new
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A Number Of Learning Style Theories Exist
A number of learning style theories exist. Learning style theorists according to Csapo and Hayen
(2006) have identified specific characteristics of learning and have organized these characteristics
into specific "classifications" of learners. Learning styles are individual differences in learning and
an individual's learning style "is the way he or she concentrates on, processes, internalizes, and
remembers new and difficult academic information or skills.
According to Gülbahar and Alper (2011) learning styles can be described as the means of
perceiving, processing, storing, and recalling attempts in the learning process. In Gülbahar and
Alper (2011) research, various cognitive and learning style theories and models have been proposed
over the course of many years, identifying and categorizing individual differences like Hill's
Cognitive Style Mapping (1976), Dunn and Dunn Learning Styles (1978), Howard Gardner's
Multiple Intelligence Theory (1983), Kolb's Learning Styles (1984), Gregorc Learning Styles
(1985), Felder Silverman Learning Model (1988), Grasha–Reichmann Learning Style Scales (1996),
and Hermann Brain Dominance Models (1996). These models of learning styles are currently being
used in today's society.
One approach is Kolb's (1984) Experiential Learning Theory, which is based on the works of Kurt
Lewin, John Dewey, Lev Vygotsky, and Jean Piaget. Kolb has described four basic learning styles:
accommodative, assimilative, divergent, and convergent which are based

The Theory Of Evolution Of A Population Over A Number Of...
Evolution is the change in genetic composition of a population over a number of continuous and
successive generations, which may have resulted from natural selection, inbreeding, hybridization,
or mutation. (Biology Online, 2008). This change occurs when there is genetic variation, a variation
of genomes between members of species, or groups of species thriving in different areas as a result
of genetic mutation. (Biology Online, 2009).
The two major mechanisms considered to be the driving force of evolution can be depicted in Figure
1 and 2. The first is natural selection, which is the theory of evolution proposed by Charles Darwin.
This is the principle by which each slight variation, if useful, is preserved and passed on to the ...
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They mainly inhabited the ground, however ascended trees in search of fruit as a source of food.
Platforms built in these trees from sticks and leaves were used to confine females which were also
used as sleeping places. Favourable conditions and abundant food resulted in disuse of the agility
and strength of humans. However, the time and force expended on these qualities were not lost, and
instead, passed onto the brain. Consequently, they gained acute intelligence which allowed them to
observe and imitate in exchange for their agility and strength. (Origin and early History of Man,
n.d).
The first record of human interference with the evolution and biodiversity of other species was
around 1.9 million years ago when humans first discovered sharp rocks (Ross, 2014). This discovery
could be seen as having both a positive and negative impact on the evolution of species around the
world.
For humans, this discovery lead to the creation of tools and weapons and the discovery of fire. It
provided them with the necessary equipment to attack and hunt down creatures which posed a threat
to their existence. However, by continuously killing off certain species from a time frame of about
4.8 megaannum (Ma) to 4500 years ago (ya), the actions of humans brought about the extinction of
animals such as mastodons, mammoths, American cheetah and giant kangaroos. (Dunn, 2012).
Smaller creatures which were

Article Analysis: 'Representations In Teaching And...
The article, "Representations in Teaching and Learning Fractions," explains the concept of teaching
and learning fractions using representations. One of the Common Core Concepts that is supported in
this article is CCSS.Math.Content.3.NF.A.2: Understand a fraction as a number on the number line;
represent fractions on a number line diagram (Grade 3). Watanabe talks about using linear model to
represent fractions. The article discuss about how number lines do not help children comprehend
fraction as numbers but only makes sense to those who already know fractions. Watanabe says that
some teachers think that number lines are "useful tools to teach children relationships between
whole numbers and fractions." The manipulatives that are discussed ... Show more content on
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Model is the instructional materials while "representation refers both to process and to produce." I
always thought these two terms were synonymous. I learned that the difference between the
comparison method and part–whole method is "the relationship between the whole and fraction
part." The whole part method is "the fractional part embedded in the whole" while the comparison
method is "the whole and the fractional part are constructed separately (p.459)." I learned that we
should write out the fraction words rather than the numbers because it is more consistent. For
example, we should write 1–half instead of 1/2. By writing the words instead of numbers, it helps
children identify the fraction units.
This article would be appropriate for third teachers as well as other elementary teachers because
Watanabe mentioned about how fraction is one of the challenging topics for elementary children.
Elementary is when the children starts to learn fractions. The article talks about whether these tools
or methods are helpful to students who are beginning to learn fractions. Watanabe comments that
number lines are often used in primary grades. The article mentions that children should understand
fractions as numbers before going

Pupil B Task: A Conceptual Analysis
Pupil B task was to build a tower of 8 blocks from a larger set. He coordinated all number manes
with the blocks but when asked how many have you got he replied 10. Baroody, 2009) highlighted
B's counting errors occur as counting one object in a set twice, as a result, gets an incorrect total.
Similarly, McGuire, Kinzie and Berch (2012) believes that if B could correctly count using the one –
to– one correspondence principle, he would have labeled each block with the correct number name.
Furthermore, this highlighted that B could not keep track of objects is he has counted and of those,
he has not counted(DCFS,2009). McGuire, Kinzie and Berch (2012) highlighted that this is a
common difficulty that many pupils encounter as they learn to count. ... Show more content on
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This is across various sectors ranging from psychological, cross–cultural to educational
investigations. In the process challenging the theories developed about how children learn and think
in different mathematical domains (Mohyuddin and Khalil, 2016). Although research findings
suggest that individual interventions targeting pupils' difficulties in mathematics are effective,
interventions may work better than these are targeting specific strengths and weaknesses ( Dowker
and Sigley,2010). Errors and misconceptions can be corrected if teachers provide the correct
alternatives to pupils. Counting sets the foundations of early algebra, therefore, it is important that
pupils are provided with appropriate activities to support their learning (Earnshaw and Hansen,
2011). There is a range of resources available to support pupils counting needs, however, more
needs to be done. Because while it is easy to diagnose learners' difficulties, finding solutions for
them is not that simple (Gillum, 2014). Research demonstrates that teaching pupils to avoid
misconceptions is not helpful and could result in hidden misconceptions (Hansen, 2014). Instead of
planning to avoid errors and misconceptions, teachers should carefully plan mathematical lessons
that allow children be confronted with examples that challenge and encourage them to make
connections between mathematical concepts and their own

The Theory Of Conservation Of Mass, Numbers And Weight Of...
Field experiment base in The reapplication of a classic Piagetian task relating to Conservation of
mass, numbers and weight. Arlet J Vega Guerra Course # EDU 502 CRN #24704 Psychological
Foundations of Education Dr. EM Rentas Nova Southeastern University March 24, 2017 First to
begin with the experiment it was necessary to understand the definition of Conservation: a conscious
perception that tangible amounts don't vary whenever their appearances are modified. Preservation
is a substantial factor in Piaget's cognitive development theory. Using the basic concepts of the
Piaget's conservation theory and applying those simple tasks I was able to appreciate how the
cognitive development of kids work in the different stage of their learning. Applying the experiment
I also obtained a better understanding from the point of view of some kids about the Theory of
Conservation of mass, numbers and weight of Piaget. The experience was just focus in the
preoperational and concrete stage of this theory due to the age of my participants. I gave this test to
a friend of mine children's, I chose her because she was the only one that I knew has kids within the
suitable range which applied to this procedure and she was also willing to allow their children to
help me do the tasks in their home. For the reapplication of the Piagetian tasks related to the
conservation of mass and numbers, I utilized the following material: two

Charles Galton 's Theory Of Differential Psychology
Francis Galton was born into a wealthy quaker family, their fortune coming from his banker father.
Of course, his mother wasn 't a nobody; she was the daughter of the Erasmus Darwin, a man of
many things, one of which was medicine. At an early age, Francis was expected to become a doctor
by his father, which didn 't leave him with much of a choice, since his father could cut him off at any
time. So he went to Trinity and studied medicine and mathematics, until he had a nervous
breakdown from the pressure at 21. Fortunately, his dad died soon after, leaving him with a lot of
money to do whatever he wanted and no need to go into a field that he didn 't want to do. Galton
was one of the first experimental psychologists and the founder of Differential psychology. It is the
study of characteristic differences and variations of groups or individuals, especially through the use
of analytic techniques and statistical methods. He was most known for his work in intelligence. He
believed that aspects of human nature could be measured scientifically. Galton tried to measure
intelligence through reaction time tests. For example, the faster someone could register and identify
a sound, the more intelligent that person was. Galton believed that intelligence as well as some
physical and mental characteristics of humans were inherited and biologically based. Based on
studies of prominent individuals and their family trees, he concluded that intellectual ability is
inherited the same

The Impact Of Arabic Numerals In Medieval Europe
Impact of Arabic Numerals on Medieval Europe Medieval European society was changed by the
introduction of the Arabic numerals into their society. The Islamic Golden Age introduced lots of
innovative thought into the world, and eventually those ideas made their way into Europe, one of
which was the Arabic numerals. They revolutionized the way that daily tasks, like merchant
bookkeeping, and academia were approached. Medieval Europe was transformed by the Islamic
Golden Age and that is highlighted through the transformation Arabic numerals had on society.
Preceding the Islamic Golden Age, Indian culture had a revolution of thought which was seen in the
Islamic Empire. One thing from Indian culture that transcended into Islamic culture was the concept
of zero. This was something that was not considered in earlier mathematic studies. It read in "Math
Roots: Zero: A Special Case," "the Arabs recognized the value of the Hindu system, adapted the
numerals and computation, and spread the ideas in their travels." The Arabic people saw the power
in this numbering system because there was a place holder number. This concept was accepted into
Islamic thought; however, it was not received well in Europe. For the greater part of the European
society, it was a strange system, in comparison to the Roman numeral system, and was not widely
accepted. At the beginning of Arabic numeral introduction into European society, scholars and
mathematicians were primarily the only ones who accepted

A Summary On Marie Sophie Germain
Family[edit] Marie–Sophie Germain was born on 1 April 1776, in Paris, France, in a house on Rue
Saint–Denis. According to most sources, her father, Ambroise–Franҫois, was a wealthy silk
merchant,[3][4][5] though some believe he was a goldsmith.[6] In 1789, he was elected as a
representative of the bourgeoisie to the États–Généraux, which he saw change into the
Constitutional Assembly. It is therefore assumed that Sophie witnessed many discussions between
her father and his friends on politics and philosophy. Gray proposes that after his political career,
Ambroise–Franҫois became the director of a bank; at least, the family remained well–off enough to
support Germain throughout her adult life.[6] Marie–Sophie had one younger sister, named
Angélique–Ambroise, and one older sister, named Marie–Madeline. Her mother was also named
Marie–Madeline, and this plethora of "Maries" may have been the reason she went by Sophie.
Germain 's nephew Armand–Jacques Lherbette, Marie–Madeline 's son, published some of Germain
's work after she died (see Work in Philosophy).[4] Introduction to mathematics[edit] When
Germain was 13, the Bastille fell, and the revolutionary atmosphere of the city forced her to stay
inside. For entertainment she turned to her father 's library.[7] Here she found J. E. Montucla 's L
'Histoire des Mathématiques, and his story of the death of Archimedes intrigued her.[4] Sophie
Germain thought that if the geometry method, which at that time referred to all of pure

Middle Range Nursing Theories Are Abstract, Testable...
Middle Range Nursing Theory Middle range nursing theories are abstract, testable theories that
contain a limited number of variables. According to Chinn and Kramer (2011), middle range nursing
theories can lead to new practice approaches as well as examine factors that influence the desired
outcomes in nursing practice. One beneficial and widely used middle range nursing theory is the
theory of unpleasant symptoms, developed collaboratively by Lenz, Pugh, Milligan, Gift, and Suppe
in 1995. The theory of unpleasant symptoms has three related components: the symptoms
experienced by the individual, factors that affect the nature of the symptom experience, and the
consequences of the symptom experience (Lenz, Pugh, Milligan, Gift, & Suppe, 1997). Symptoms
can be measured individually or in combination with other symptoms, and they can often be
characterized by intensity, duration and frequency, level of distress, and quality. Physiological
factors, psychological factors, and situational factors each relate to each other and can influence the
symptom experience (Lenz, Pugh, Milligan, Gift, & Suppe, 1997). Physiological factors include
normal functioning of body systems, whereas psychological factors include the mental state and
knowledge of symptoms. Situational factors are compromised of the social and environmental
aspects that may affect the patient's experience. The final component of the theory of unpleasant
symptoms is the outcome of the symptoms experience, or

Routine Activities Theory
Cody Haag
Reaction Paper
1) How was card counting viewed by various people/groups (counters, casinos, and family
members) in the text?
Card counting was viewed different ways by different people throughout the book. The team from
MIT viewed card counting as a way to beat blackjack. They did not view it as cheating, but a way to
put the cards in their favor to have a better chance of winning. Card counting is not full proof even if
the odds were in their favor they could still lose at blackjack, but they normally won more than they
loss. The team also did not considering it cheating because they did not do anything to change the
outcome of the cards. They did not switch cards or do anything like that. They used their brains to
calculate the ... Show more content on Helpwriting.net ...
I believe this because the theory requires three things. It requires a motivated offender, a suitable
target, and a lack of capable guardianship. All three things are in the card counters thought process.
They are the motivated offenders to get money. They see the casinos as the suitable targets, and
throughout the book the casinos lack capable guardianship. In Criminological Theory it talks about
how life has a routine to it. They use a rush hour example in the book to show how you predict it is
going to happen because it is part of a routine. In the book the team would hit the casinos on big
holidays and fight nights because they knew it would be crazy. Which meant they would be able to
play without getting caught, and they knew the routine of the casinos. Inertia, which refers to the
size and bulk of a target, is another factor that can make a target suitable. (J. Mitchell Miller 92) The
size and bulk of the target, which I see as the profit they saw to gain from hitting the casinos made
they a very suitable target to them. The casino are also a suitable target because lack of capable
guardianship. Even though they have security and cameras there are just too many people, and too
much commotion to keep track of everyone. This made the card counters see this because with their
skills they do they would not get caught because the casinos just had to watch too many

Accounting Standards And The Codification System
DATE: January 19, 2016
TO: Chris Yost, CPA
FROM: Holly Thobe, Junior Accountant
SUBJECT: Using the Accounting Standards Codification
All Staff Accountants must learn how to research GAAP accounting standards using FASB's
accounting standards Codification system. The purpose of this memo is to provide instructions on
how to research the accounting standards using the new Codification system. Users will discover
how to research the accounting standards using the Codification system, explore the updated
revenue recognition standards, and learn how to access updates from the system.
FASB Accounting Standards Codification
The FASB Codification database is easy to use when researching the accounting standards once the
basics are fully understood. The FASB Codification database can be accessed by logging in at
http://aaahq.org/ascLogin.cfm and using the following codes (case sensitive): Username –
AAA51207 Password – HFdU64n
The Codification uses a hierarchy to organize its subject matter. Area is the largest collection, and
then comes topic, subtopic and section. Each topic, subtopic and section is identified with a number
and a title. The numbers provide a simple way to find specific accounting guidance. A three–digit
number and a title identify topics. The first digit of the numerical identifier resembles the area of the
topic. Subtopics are either exclusive or shared. Exclusive subtopics have unique content and shared
subtopics have common content. To identify

Sophie Germain's Contribution To The Middle Age Of Paris
Sophie Germain was born April 1st, 1776 in Paris, France. Sophie's family was rich and counted as
upper Classmen. Sophie was the middle child out of 2 others, Marie–Madeline Germain and
Angelique–Ambroise Germain. She was brought into the world around times when it was frowned
upon for women to be educated, not to mention that it was also a revolution year too. Sophie spent
most of her time in the house reading in her Father's collection of books. "Their eldest and youngest
daughters, Marie–Madeleine and Angelique–Ambroise, were destined for marriage with
professional men. However, when the fall of the Bastille in 1789 drove the Germains' sensitive
middle daughter into hiding in the family library, Marie–Sophie's life path diverged from them all.
From the ages of 13 to 18 Sophie, as she was called to minimize confusion with the other Maries in
her immediate family, absorbed herself in the study of pure mathematics." One day she came across
a book about a deceased Mathematician by the name of Archimedes. Sophie was so engaged by his
work that she looked more into it as it interested her a lot. Sophie died on June 27th, 1831 in
birthplace of Paris, France. She wanted to find out more, what did Archimedes try to finish? At a
young age, Sophie's parents did not agree with her studying mathematics because it was not allowed
for women to study a lot, it was too dangerous according to the law. Plus, there was no school
because of the Revolution War. That law did not stop Sophie

Personal Statement For Biology
To me, the study of math is not just memorizing convoluted formulas and complex theorems.
Instead, it is an exploration of unique and foreign purviews, wrangling with new concepts, and
always searching to find the true meaning of each end result. This in particular applies to the study
of number theory in mathematics. The most basic assumptions of the integers can be cracked open
and dissected by number theory, and it will forever hold its place as the foundation of math. Last
summer, I attended PROMYS (Program in Mathematics for Young Scientists) and fully enjoyed my
time spent deducing and proving complicated number theory problems. There, I gained my first
taste of non "school math", and was intrigued by the startling harmony of numbers ... Show more
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I am fascinated by the way that biology holds the secrets of our origins and existence. Biology is a
field created by humans, where we study our own networks of cells joined by molecular and
chemical reactions. The slightest change in a chromosome or strand of DNA may result in a
radically changed organism, and as the technology available to carry out experiments and
observations increases, the ability we have to improve the world directly increases. However,
biology does not require advanced equipment to unearth details about the natural world. I like that
biology may be as simple as observing the unusual behaviors of squirrels foraging in a backyard, the
different crystalline patterns of snowflakes each winter, or investigating how honeysuckle plants
twine around a trellis. All of these seemingly simple observations can be explored even deeper, to
the cellular level, and many more investigative questions will naturally accompany them. Nearly
everything in this field is connected, which is why it is so important to view the big picture and
attempt to draw conclusions from old discoveries. This is why biology can be connected to all career
fields and how it can provide the answers to so many large scale problems in our government,
environment, and general

Final Thoughts ( Book )
Ellyce Uy
44755122
MATH335 201
*300+ words
Final Thoughts (Whole Book) This book is not like any other, and as a whole had four main impacts
on me. First it taught me about the complexity of elementary mathematics and not to underestimate
it. Secondly, it taught me about the consequences becoming overly dependent on mathematical aids
(leading to doing and not understanding). Thirdly, it taught me the reasons behind why we do certain
mathematical procedures. Lastly it gave me tips for future teaching and parenting.
One of the main themes in this book is challenging the notion of how simple it is to teach
elementary kids. In fact it is profound. Often times, professional mathematicians are so enveloped in
their complex and high–level ... Show more content on Helpwriting.net ...
This reminds us not to underestimate and overlook elementary mathematics that appears basic.
Mathematical diversions, therefore, cannot be taught without the students' understanding of the
basic mathematical foundations. It is like learning to play an instrument; one must know the basics
before being able to play a piece.
Learning about the long and tiresome process of transforming ordinary fractions into decimal
fractions has made me realize how much I had taken for granted using calculator for the past decade.
There are downsides to relying more on the calculator than relying on "old–fashioned" mind.
"Patterns as Aids" becomes a problem when a student follows rules without understanding and
calculates large numbers mentally using tricks but fails to understand the purpose of the processes or
steps. Therefore it is better to understand less but thoroughly, than to be an expert in memorizing
tricks and rules without any understanding. Principles must be taken apart, and each ingredient
learned and taught individually. When something sounds hard or difficult, it usually means we did
not break the problem into portions. Often I take for granted and overlooked simple aspects of math
that I automatically perform. This book also mentions the importance of using word

Math Experience In My Life
At an early age, I was bad at math, yet I knew it would be my passion. Throughout elementary
school, I gave into the idea that I lacked intelligence enough to pursue mathematics seriously in
school, and later on in my life. Nonetheless, math found itself back into my life during my middle
school years and solidified its presence within my life.
I was the dumb kid in class, unable to add and subtract, unable to memorize the multiplication table.
Before, I found joy in knowing. To this date I remember what seemed like witchcraft as my father,
on one of his rare visits home from work, showing me how squares worked when I was five. The
Japanese education system in my first and second grade placed value in the ability to memorize
rules and tables. The better one was at memorization, which felt to me the mindless recounting of
multiplication and division and the ability to just know the answer, was needed for success. I wanted
to know why the number four was four. What it really meant. What does it mean that there are two
less from six? Why were Eight things divided by two equal the same as the square of two? I was
interested in the hows and the whys of numbers, not just its identity. For this reason, I was not
deemed successful and was not seen as a student with prospects. Despite my seeming lack of talent
in the mathematical field, I knew, I knew somehow that math was my passion. I was successful in
the math classes in the elementary school in America. All that was required of

Interdisciplinary Disciplines : Mathematics And Informaticss
Interdisciplinary Disciplines: Mathematics & Informatics Nichole Erickson Arizona State University
During the process of determining my major here at Arizona State University, I contemplated many
different disciplines. The first three years of my undergraduate coursework was focused on the study
of software engineering after transferring from a community college where I had a liberal arts focus,
but had taken many mathematics courses. The culmination of these studies, along with two summer
internships, helped determine my current interdisciplinary degree focused in Mathematics and
Informatics. While separate disciplines, they are interdisciplinary in nature, not just with each other
but with many other disciplines as well. This paper will examine both disciplines, highlighting areas
of similarity, with the purpose of emphasizing how the two are linked in an interdisciplinary way.
The paper will also discuss how I hope to utilize these two areas in a future career. The first
discipline, Mathematics, as one of the Natural Sciences, can be traced throughout human history.
Formally, Mathematics is defined by Merriam–Webster as, "the science of numbers and their
operations, interrelations, combinations, generalizations, and abstractions and of space
configurations and their structure, measurement, transformations, and generalizations Algebra,
arithmetic, calculus, geometry, and trigonometry are branches of mathematics." (Merriam–Webster,
2017). Generally, the purpose

Who Is Ramanuj A Hero's Journey?
The Life of Ramanujan based on Joseph Campbell's model of analysis
Srinivasa Ramanujan was one the greatest mathematicians in India. With no formal training in pure
mathematics, he made significant contributions to the analytical theory of numbers and made an
outbreak in continued fractions, elliptical functions and infinite series. He is deeply religious and
credits his mathematical capacities to divinity. He once told his friend, "An equation for me has no
meaning, unless it expresses a thought of God". Starting with the ordinary world, Joseph Campbell
gives a detailed description of a hero's journey. I consider Ramanujan to be my hero as he fulfills all
the stages of joseph Campbell's theory of hero's journey.
Joseph Campbell gives a detailed description of the 12 stages in a ... Show more content on
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A stamp picturing Ramanujan was released by the Government of India in 1962 – the 75th
anniversary of Ramanujan's birth – commemorating his achievements in the field of number theory,
and a new design was issued on 26 December 2011, by the India Post. Ramanujan's birthday is
annually celebrated as the Ramanujan's day. In 2011, on the 125th anniversary of his birth, the
Indian Government declared that 22 December will be celebrated every year as "The National
Mathematics Day". Then Indian Prime Minister Manmohan Singh also declared that the year 2012
would be celebrated as the National Mathematics Year. Several movies are released portraying
Ramanujan's life, one of the most famous among them is "The Man Who Knew Infinity: A Life of
the Genius Ramanujan" by Robert Kanigel. The novel "The Indian Clerk" by David Leavitt explores
in fiction the events following Ramanujan's letter to Hardy. There is also a museum dedicated to
depicting Ramanujan's life story. It is located in Chennai and has many photographs of his home and
family, along with letters to and from friends, relatives,

Leonhard Euler's Life And Accomplishments
Leonhard Euler was an 18th century physicist and scholar who was responsible for developing many
concepts that are an integral part of modern mathematics. Leonhard Euler is considered one of the
most renowned and respected mathematician of all times. Euler is known for the tremendous
contributions he made to the field of mathematicians. Many concepts of today's mathematics
originated from the works of this phenomenal mathematician. Euler works spanned many fields
including mechanics, fluid dynamics, optics, astronomy, and music theory. His interest in
mathematics began in his childhood from the teachings of his father, Paul Euler. Johann Bernoulli,
another great mathematician in his time, was a friend of Leonard's father was a major influence in
Euler. According to Gottschling, Leonard works covered many areas such as algebra, geometry,
calculus. Trigonometry, and number theory. Two numbers are named after Euler which are Euler's
Number in calculus, ... Show more content on Helpwriting.net ...
He began his study of theology in 1723 but after gaining his father 's friend, Johann Bernoulli, he
changed his study to mathematics. He completed his studies at the University of Basel. Around the
same time, Johann Bernoulli two sons, Daniel and Nicholaus were working at the Imperial Russian
Academy of Sciences in Saint Petersburg. On July 31, 1726, Nicholaus died of appendicitis and at
that point Daniel assumed his brother's position. He recommended his previous now vacant position
to be filled by his friend Euler. Euler arrived in Saint Petersburg on May 17,1727. He was promoted
to a position in the mathematics department. He stayed with Daniel Bernoulli whom he also worked
with. After the death of Peter II, Euler rose through the ranks of the academy and became professor
of physics in 1731. Daniel Bernoulli left the academy to return to Basel. Euler was appointed to the
vacated position of senior chair mathematics. This new post improved his financial

Life Is Mathematics: Looking at the movie Pi. Essay
Life Is Mathematics: Looking at the movie Pi.
Well that pretty much says it all. What is it? It is a very good movie. This is an Independent film. It
is a number which can only be defined in the mind. The first time I watched this movie was when I
was at my best friend's house last year around 2am. We watched it on VHS, but didn't finish it. I
came back here and found someone who had it on their computer; we burned it to a CD in a DivX
format. "DivX(TM) is a leading MPEG–4 compatible video compression technology, with over 50
million users worldwide" (e.Digital Corp.). Now I can watch it whenever I want to.
This movie is in black and white. It is not old, but it is not in color. That adds to the effect of the ...
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However, every time I watch, it I pick up on something else. I pick up on some other allusion or
some other spin on a story.
I am a math major so this movie is fun to watch because one aspect of it is math. There is a little bit
of history in it. The golden ratio, the golden spiral, and how density was discovered. These are all
things a math major should know. It is nice to see them incorporated in a movie about math.
Using math you can do anything you want. This is illustrated by a quote I found in a book about
Math Theory.
One Hungarian physicist once remarked in the course of writing a textbook that although he would
often be referring to the motions and collisions of billiard balls to illustrate the laws of mechanics,
he has neither see nor played this game and his knowledge of it was derived entirely from the study
of physics books. (Barrow 21)
One way to understand Mathematics is to look at language; mathematics is a language in itself and
in some cases it can help you understand another culture, without having to live in that culture.
There are many references to the Kabbalah in this movie.. More than references, the movie talks
about it directly. In the movie it is said that the Kabbalah was written by god and every letter is a
number. When you take it apart word by word, you get a series of number. In the movie they show
that the word for father is one number, the

The Effect of Schema on Memory
The Effect of a Schema on Memory
Psychology MSc, University of Hertfordshire
Abstract
Schema Theory is a principle in which cognitive processes are influenced by social and cultural
factors. According to schema theory the knowledge we have stored in our memory is reorganised
into a set of schemas which is based upon our general knowledge and our previous experience.
Experiments have proved that despite seeing and interacting with an object almost every day, our
ability to remember said object is greatly influenced by the schemas we already have. This
experiment will be conducted in an almost identical way to that of French and Richards and look at
the effect of schemas on memory. It was predicted that participants use their previous ... Show more
This experiment will be conducted in an almost identical way to French and Richards experiment
and look to determine the effect of schemas on memory. It was predicted that like French and
Richards experiment the participants use their previous knowledge of Roman numerals to
mistakenly draw the clock.
Method
Participants
The participants in this experiment were recruited through opportunistic sampling, the class
members of a Psychology Masters Course in Hertfordshire University. The class was made up of
both male and female students of a variety of ages.
Design
This experiment used between–participants, experimental design as all the participants were in three
separate conditions which were then compared. The Independent Variable in this experiment was the
different condition, whether they were in the surprise memory condition, the forewarned memory
condition or the copy condition. The Dependent Variable is the extent to which they could correctly
recall/copy the clock.
Apparatus
This experiment used an instruction sheet which indicated the relevant instructions for each
condition. (This is included in Appendix 1). The experiment also used an identical clock for all the

conditions with roman numerals depicting the numbers, where four was shown as IIII. (This is
included in Appendix 2). The rest of the apparatus included paper, pens and a stop watch.
Procedure
In this experiment the participants were split up into three conditions. The

Number Theory Outcast Analysis
In the number theory podcast it is discussed how we go from twenty and four to twenty four. Bob
and Mike also discuss why we say it the way we say it. I personally like the feeling of saying twenty
four rather than twenty and four. It sounds more appropriate and grammatical. Bob and Mike speak
about how in old English they wrote "twenty and four" and even "four and twenty". But, in modern
english the and is eliminated and we pronounce it "twenty four". The conjunction and is eliminated.
The modern way arises randomly. The change came due to "laziness" according to Bob. The easier
approach took over universally. It is more natural to write the higher number first rather than the
lower. Lower before higher delays comprehension also according

Srinivasa Ramanujan
Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made contributions to
the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite
series. Ramanujan was born in his grandmother's house in Erode on December 22, 1887. When
Ramanujan was a year old his mother took him to the town of Kumbakonam, near Madras. His
father worked in Kumbakonam as a clerk in a cloth merchant's shop. When he was five years old,
Ramanujan went to the primary school in Kumbakonam although he would attend several different
primary schools before entering the Town High School in Kumbakonam in January 1898. At the
Town High School, Ramanujan did well in all his school subjects and showed himself as a ... Show
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Ramachandra Rao told him to return to Madras and he tried, unsuccessfully, to arrange a scholarship
for Ramanujan. In 1912 Ramanujan applied for the post of clerk in the accounts section of the
Madras Port Trust. Ramanujan was appointed to the post of clerk and began his duties on 1 March
1912. Ramanujan was quite lucky to have a number of people working round him with training in
mathematics. In fact the Chief Accountant for the Madras Port Trust, S N Aiyar, was trained as a
mathematician and published a paper On the distribution of primes in 1913 on Ramanujan's work.
The professor of civil engineering at the Madras Engineering College, T. Griffith was also interested
in Ramanujan's abilities and, having been educated at University College London, knew the
professor of mathematics there, namely M. Hill. He wrote to Hill on 12 November 1912 sending
some of Ramanujan's work and a copy of his 1911 paper on Bernoulli numbers. Hill replied in a
fairly encouraging way but showed that he had failed to understand Ramanujan's results on
divergent series. The recommendation to Ramanujan that he read Bromwich's Theory of infinite
series did not please Ramanujan much. Ramanujan wrote to E. W. Hobson and H. F. Baker trying to
interest them in his results but neither replied. In January 1913 Ramanujan wrote to G H Hardy
having seen a copy of his 1910 book Orders of infinity. Hardy studied the long list of unproved
theorems which Ramanujan enclosed with

Islamic Influence On The Modern World
The muslims from the Islamic empire had created everything from the elegant architecture such as
mosques to a completely new level in the field of medicines. This time period takes place in the 7th
and 8th centuries and lies between its two primary cities, Baghdad and Cordoba. During the Golden
Age, the ideas of the Arabs, Egyptians, and Europeans came together. The Islamic contributions
affected the modern world by creating unique geometric and floral designs, making new discoveries
in geography and taught the study of arithmetics.
The natives of the Islamic empire had produced many new and dazzling forms of arts and literature
calligraphy and architecture, that was popular around that time period and in the modern world of
today. During ... Show more content on Helpwriting.net ...
Geometric and floral design was significant because it helped to make everyday items, such as
plates, and turn it into a work of art using these designs. Also, it helped to illuminate the Qur'an and
helped to decorate the mosques. Geography was important because the muslims created more
accurate maps, that helped the travelers to get information of a region's location, physical features,
and natural resources. Lastly mathematics helped the world because the Muslims help spread a very
important number, 0. It was important also because of the muslim scholar who had invented the
arabic numbers, which are used today. Without this useful innovations, it would be difficult to make
such progress people would have in the modern

The Story Of Mathematics From The Book ' The Infinite '
In 1912, the "unsinkable" ship Titanic ruptured its hull on a large iceberg, causing a completely
unexpected disaster that shocked the world. Looking at this iceberg, or any other for that matter, the
average observer likely draws the conclusion that what he sees is a good portion of the entire slab of
frozen water. However, the observer only sees about 10 percent of its entirety: in order to view the
whole iceberg, he must look below the surface to understand how such a seemingly "small" iceberg
could sink a such a huge ship. And just as any observer should look deeper in order to understand
the sinking of the Titanic, I did the same with mathematics when I read Taming the Infinite: The
story of mathematics from the first numbers to chaos theory. Never before had I even considered the
ideas discussed in the book written by Ian Stewart. What I found within ruptured a mental hull in
brain, allowing the history of math to flow into my mind. Before reading the first two chapters, I had
always assumed that I had a fairly decent grasp of math; however, after completing the assignment I
realized the vastness of its history which reaches into depths I'd never enter into otherwise. In my
previous math classes, ranging from Algebra I to AP Calculus, I never had been assigned to anything
dealing with the actual history of math. So, much to my surprise as stated earlier, I found many
aspects of the book to be infinitely fascinating. In the first chapter, I was astonished to learn

Mathematics Of Creative Writing : Exposing The Invisible Tool
Mathematical Proportions in Creative Writing: Exposing the Invisible Tool
In the academic world, creative writing and mathematical proportions are often considered to be
located at opposite ends of the spectrum, but they are not as different as they seem. Authors often
need to carefully plan and divide their story to create an end result that is a balance between
exposition and dialogue, romance and action, or tragedy and comedy. That is where mathematical
proportions come in–ratio and fractions in particular. Every author uses ratio and fractions, whether
they know it or not, and the proper use of them determines the quality of their writing. Who would
read a book that's 70% exposition or 100% dialogue? Therefore, in this essay I will ... Show more
Fractions can also be used to represent ratios or even division equations and all rational numbers.
While fractions come in many different forms such as mixed numbers, improper, vulgar and proper
fractions, the function of a fraction is generally the same–to represent parts of a whole. To simplify
the matter further–if you can solve a division problem, then you are able to use fractions. In fact,
you use fractions all the time without a hint of doubt. For instance, when we tell the time, use or
recipe or figure out the price of an object after a sale–it is all fractions. We use them every day, but
why? What is the inclination to measure ingredients in halves, quarters and two–thirds? Why do we
reflexively say "Half past 3" when telling the time? It is all because parts of a whole are far more
common than complete collectives of any one thing. So let us take a step back and analyze a
fraction: 2/5. 2 is considered the numerator, and 5 is the denominator. 5 would be the whole–for
instance, there are 5 stuffed bears in total. But then 2 is the amount we have from the whole–as in,
we only have 2 of the 5 stuffed bears. A slightly more challenging problem would be saying that a
$50 shirt is ½ price. To solve this, we would simply convert 50 into an improper fraction (a fraction
in which the numerator is larger than the denominator), 50/1 and multiply it by ½. This would result
in the improper fraction, 50/2. You would then simplify

The Contribution Of Leonhard Euler
Leonhard Euler was a fascinating and talented man who made significant contributions in
mathematics, physics, engineering and astronomy (Stockstill). The incredible amount of work he
produced in mathematics has made his name famous around the globe. He has produced more work
than any other professional in mathematics (Australian Mathematics). His work in calculus, graph
theory, and mathematical notation has greatly influenced mathematics (Euler Website). Euler was a
great 18th–century mathematician but also worked in music theory and mechanics (Mastin). His
prolific work in various fields and his determination to continue work after facing great physical
challenges makes Euler more than a great mathematician, it makes him one of the most ... Show
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He wrote his book Mechanica in 1737, which looked a Newtonian dynamic through a mathematical
lens for the first time. He worked with Newton most notably with the construction of the famous
equation F = ma. During this time he wrote papers on number theory, differential equations, calculus
variations and rational mechanics. However, this time in his life was also very difficult. He
developed health problems. Euler got a severe fever which was followed by eye problems (Finkle).
He began to lose sight in his right eye in 1738 and lost complete sight in 1740.
This year also brought him great success. He had great fame from winning the Paris Academy of
Science competition once again (O 'Connor). He left St. Petersburg due to a poor political climate in
Russia at the time (DeSagher). He believed that the Russian police were following him and found an
opportunity to leave Russia (DeSagher). He took a position at the Berlin Academy Of Sciences
under Frederick the Great (Stockstill). He produced an amazing amount of work there. He wrote 380
articles while at the Berlin Academy (O 'Connor). During this time he wrote one of his most popular
works to date "Letters to a German Princess" (O 'Connor). This was popular because it explained
some of his very complex concepts in simple terms. There were 200 "letters" inspired by the
instruction he gave to the Princess of Anhalt–Dessau (Australian Mathematics).
He still kept

What Makes An Effective Mathematical Educator? Essay
Introduction
What makes an effective mathematical educator? What knowledge and skills are required to teach
the mathematical concept of patterns effectively? Are educators impacting the development of
children's understanding of patterns? This essay will embody the skills and knowledge required to
be an effective educator of mathematics and the concept of patterns. It looks and the role of an
educator in the development of a child's understanding of patterns in the classroom setting. It
explains the need for an educator to have a positive attitude towards mathematics and patterns as
children are very perceptive and negative attitudes and feelings can be transferred to the students we
are teaching.
Key Understandings of Patterns
The First Step in Mathematics (FSiM, 2004) states there are six key understandings of patterns, each
part as equally important as the next. These six key understandings outline the mathematical
concepts associated with patterns, they provide educators with the curriculum content and with the
pedagogical guidance, to make informed decisions on what and how they will to teach patterns to
their students. Educators are given the task of ensuring each student is exposed to and is developing
their knowledge of patterns, allowing them to achieve the desired outcome through these six key
understandings'. Educators need to have knowledge of the six key understandings of patterns to be a
valuable support to a child's learning. My results on my Early

Essay on Carl Friedrich Gauss
Carl Friedrich Gauss was born in Braunshweigh, Germany, now lower Saxon Germany, where his
parents lived and they were considered a pretty poor family during their time. His father worked
many jobs as a gardener and many other trades such as: an assistant to a merchant and a treasurer of
a small insurance fund. While his mother on the other hand was a fairly smart person but
semiliterate, and before she married her husband she was a maid, the only reason for marrying him
was to get out of the job because she was so tired of it. She was very unhappy in the marriage trying
her hardest to put the unhappiness behind her, so that she could make sure that Carl always had her
loving devoted attention and support at whatever he did and was sure to ... Show more content on
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Buttner was astonished, he could not believe that Carl was finished so fast, and had no idea how he
had done it. So Carl proceeded in telling him that: "the method was to realize that pair wise addition
of terms from opposite ends of the list yield identical intermediate sums: 1+100=101, 99+2=101,
3+98=101 and so on for a total sum of 50 x 101= 5050. (Wikipedia)". After all these shenanigans
and many, more Carl caught the eye of the Duke of Braunshweig. The Duke found him in school
when he was in eleventh grade studying with a teacher named Mr. Bartels, who was convinced to let
him work in the gymnasium were he made very quick progression in all his studies. Then the
professors form Collegium and a Private Conclure to the duke offered friendship and encouragement
and good offices at court. When finally it was time and the Duke sent him through Collegium
Carolinum (now Technische Universitat Braunshweig) where he attended from 1792 to 1795 and
after that the Duke sent him to another university called the University of Gottingen form 1795 to
1798, where he studied his little heart out. While in Collegium in 1797, he collected a very ripe and
seasoned education filled with science and classical education way beyond those his age. He was
way ahead of those his age in ways such as already been able to dig his hands into elementary
geometry, algebra and analysis. Even before he got to the

Theories Of Counseling And Psychotherapy, And The Number...
According to McCarthy & Archer (2013), there are more than 400 different theories of counseling
and psychotherapy, and the number keeps growing (McCarthy & Archer, 2013). In McCarthy &
Archer's (2013) book titled, Theories of counseling and psychotherapy, they focus on the 10
mainstream approaches in therapy (McCarthy & Archer, 2013). With various options available for
treatment in therapy or counseling, the possibilities are endless to utilize on clients. Although,
McCarthy & Archer (2013) also point out that one approach has not been found to be more effective
than others, what is certain is that the 10 chosen therapeutic approaches are the most popular
(McCarthy & Archer, 2013). A counselor possesses various skills and knowledge, and although they
may be viewed as the experts in their arena, some therapeutic approaches would appreciate them not
taking on such obvious roles. Such approach ensures that the client–counselor relationship is
established as well as rapport. Other approaches, where clients may seek answers may want a more
straight forward approach, where the counselor is the expert and provides suggestions, which how to
solve their problems. Certainly, the field of counseling is sensitive, as a counselor is dealing with a
person's emotions and state of mind, and where self–disclosure is not always attainable. Therapy is
anything but ordinary, as there is no norm or expectation from one client to the next. It can also be
quite diverse in a cultural, ethical,

The Perfect Number
People often wonder, "What is the perfect number?" What they do not know is that there is more
than just one perfect number; there are many. Today's research tells us that there are forty–eight
perfect numbers. A perfect number is a number that is equal to the sum of its positive divisors,
excluding its self. 6=1+2+3 28=1+2+4+7+14 18=1+2+3+6+9 (= 21)
To answer the question of what a perfect number is you need to know how to solve for a perfect
number, who has been involved in coming up with perfect numbers, the criteria, and interesting
facts about perfect numbers. Perfect numbers are more complex than just deciding whether a
number is considered "perfect" or not. First, what you have to do to get a perfect number. Every
scholar has invented their own formula to result in a perfect number. The most common formula is
to take the factors of a number and add them together. If the sum of the factors, except the number
itself, results in the original number then the number is perfect. Euclid invented a formula that is
also used to solve for perfect numbers: 2p–1 (2p – 1) Ex.1: 21 (22 – 1)= 6 Ex.2: 22 (23 – 1)= 28
In this formula p stands for a prime number, therefore in the first example two is the prime number
being used. You have two as the base because this is what the formula calls for, and then you
subtract one from your prime number, two, to get two to the first power. Then inside your
parenthesis you have two to the second power, the base taken from the formula

History Of Roman Number Symbols
The history of Roman Number Symbol are represented by letters. The Roman numerbs are
represented by seven different letters are I, V, X, L, and D. Therefore, these roman letters represent
1, 5, 10, 100, and 500. Ancient Roman use these seven letters to make a lot of different numbers and
to be written of the Roman alphabet. In the Etruscans was an ancient civilization of Italy developed
their own numeral system with different symbols. A common theory of the origin Roman numeral
system was represented by hand signal. For example, the Roman numeral system by hand signal
was used like one, two, three and four signaled by the equivalent amount of fingers that were used.
Then, "The number five is represented by the thumb and fingers separated, making a 'V' shape and
The number ten is represented by either crossing the thumbs or hands, signaling an 'X' shape"
(Pollard). Therefore, the numbers; six, seven, eight and nine are represented by one hand signaling a
five and the other representing the number 1 through to 4. The hand signal was used for counting by
either crossing the thumbs, fingers separated, and signaled, which helped to hand ... Show more
The tally sticks had been used for thousands of years and continued to be used until the 19th
century. For instance, the tally sticks was used to either additive nor subtractive, whereas the
numbers one, two, three and four were represented by the equivalent amount of vertical lines. If
these numbers described in the article would be written in tally sticks a Roman numerals. For
instance, "Four could be written as either IIII or IV" (Reddy). Another example, seven on a tally
stick would look like, IIIIVII, when shortened it would look like VII. These Roman numbers are the
same like the Roman number symbol. Another reason, larger numbers in tally sticks like 500 and
1000 would be a 'D' and 'M' in a circle

Mistakes Made By Learners As A Result Of Carelessness
Hansen (2006) explains errors as 'mistakes made by learners as a result of carelessness,
misinterpretation of symbols and texts, lack of relevant experience or knowledge related to a
Mathematical topic'. From her research she found that misconceptions, eventually led to errors.
Drews (2005) defines misconceptions as the 'misapplication of a rule, an overgeneralization or
under–generalization or an alternative conception of the situation'. Misunderstandings are the result
of a failure to grasp what was being taught; therefore reinforcement of the correct method needs to
be issued.
Errors, misconceptions and misunderstandings are all found within the classroom and are customary
for children to use within their work. Vygotsky (1962) states that children 'think and learn socially
through experience, interaction and support (Smith et al, 2003). 'The activities enable children to
experiment, make decisions, errors and correct themselves' (Bruce, 2005). As a teacher it is crucial
to identify the misconstrued knowledge/concepts and the underlying problems in the most accurate
way. It is through discussion with the child, their ideas and perceptions, that the true reasons for the
misconceptions become evident.
The National Numeracy Strategy (DfE, 1999) requires teachers to 'identify mistakes, using them as
positive teaching points by talking about them and any misconceptions that led to them'. Children
regularly make errors, misconceptions and misunderstandings in Mathematics,

Teacher Reflection Paper
Introduction Mathematics is an important part of everyday life and as teachers in the early years, we
are responsible for teaching children the fundamentals of mathematics and helping develop
children's passion for learning mathematical concepts. Knaus (2013) states that "An effective
teacher of mathematics will ask questions to provoke children's thinking and introduce the language
of mathematics to help children see the connections between the world and mathematical concepts
(pg.3). As I progress through my degree and complete each Math unit, I have begun to recognise
mathematical understanding and concepts, I need to develop if I am going to become an excellent
teacher of mathematics. Standard 1.2 of the Australian Association of Mathematics Teachers
[AMMT] (2006) confirms that 'excellent teachers of mathematics understand how mathematics is
represented and communicated, and why mathematics is taught (p.1). The first section of this essay
will reflect on my mathematical understandings followed by a section reflecting of my knowledge
and ability to help children confidently demonstrate and develop mathematical skills and processes.
Lastly a conclusion of how this will benefit me to become an excellent teacher. Mathematical
Understandings After taking the First Five Years Mathematics Competency Test, I could identify
mathematical areas and concepts that I need to develop to enable me to become a better teacher of
mathematics. Once I completed the Competency

Evaluating Janet's Vocabulary
Reason for Referral and My Suggestions Janet is experiencing academic difficulty in mathematics
and timed tasks, however her language skills (vocabulary and comprehension) appear to be strong,
yet her parents feel it would be best to evaluate Janet in order to draw on her strengths and help pin
point her limitations. As the psychologist that will be evaluating Janet, I will be administering the
following tests:
Wechsler Intelligence Scale for Children– IV (WISC–IV) o "Consists of 15 subtests, 10 of which are
designated as core subtest used in the computation of composite scores and full Scale IQ, and five of
which are designated as supplemental" (Gregory, 2010, p.172).
Wechsler Individual Achievement Test –II (WIAT–III) o "Consists ... Show more content on
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My reasoning for using this theory over another would be "the architectural system (hardware)
refers to biologically based properties necessary for information processing, such as memory span
and speed of encoding/decoding information" (Gregory, 2010,, p.154). Memory span and speed of
decoding is very important when dealing with mathematical work such as how remember our
multiplication table, which some individuals remember by using mnemonic techniques while still
others struggle. According to Gregory (2010), individuals who are able to use the metacognition
approach to learning tend to have higher performance levels than those individuals that do not use
the metacognition approach. Two Other Theories of Intelligence in Comparison "Gardner's original
Theory of Multiple Intelligences consists of three components, seven "intelligences," and eight
supporting criteria of what comprises an "intelligence." The Three Components include: a definition
of intelligence, a challenge to the notion of a general intelligence (g), and a challenge to the
conviction that g can be reliably measured." (Helding,

Compilation of Mathematicians and Their Contributions
I. Greek Mathematicians
Thales of Miletus
Birthdate: 624 B.C.
Died: 547–546 B. C.
Nationality: Greek
Title: Regarded as "Father of Science"
Contributions: * He is credited with the first use of deductive reasoning applied to geometry. *
Discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are
equal and that vertical angles are equal. * Accredited with foundation of the Ionian school of
Mathematics that was a centre of learning and research. * Thales theorems used in Geometry:
1. The pairs of opposite angles formed by two intersecting lines are equal. 2. The base angles of an
isosceles triangle are equal. 3. The sum of the angles in a triangle is 180°. 4. An angle ... Show more
The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name
Theon of Alexandria as a more likely author. 4. Phaenomena, a treatise on spherical astronomy,
survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who
flourished around 310 BC.
* Famous five postulates of Euclid as mentioned in his book Elements
1. Point is that which has no part. 2. Line is a breadthless length. 3. The extremities of lines are
points. 4. A straight line lies equally with respect to the points on itself. 5. One can draw a straight
line from any point to any point.
* The Elements also include the following five "common notions": 1. Things that are equal to the
same thing are also equal to one another (Transitive property of equality). 2. If equals are added to
equals, then the wholes are equal. 3. If equals are subtracted from equals, then the remainders are
equal. 4. Things that coincide with one another equal one another (Reflexive Property). 5. The
whole is greater than the part.
Plato

Birthdate: 424/423 B.C.
Died: 348/347 B.C.
Nationality: Greek
Contributions: * He helped to distinguish between pure and applied mathematics by widening the
gap between "arithmetic", now called number theory and "logistic", now called arithmetic. *
Founder of the Academy in Athens, the first institution of higher learning in the

Ethical Theory Number Three States: The Designer Code Of...
Ethical theory number three states; What would others in my situation do? The best way to answer
the question on behalf of the creative industry is to look at the Designer Code of Ethics. Following
the AIGA Standards of Professional Practice, section 6.1 advises that; "A professional designer shall
avoid projects that will result in harm to the public." (AIGA 2015) I have addressed on the previous
page the harm in sexually enhancing children by dressing them up in items designed for an adult
audience and also the issues in advertising lingerie to children and exposing messages they do not
quite understand. So following this code an ethical designer would turn down the role as the
campaign is harming to the children involved. Guidance from

Wk6AssgnNixL
Latin American Subtraction Algorithm
Lisa Nix
Walden University
Dr. Mary Robinson, Instructor
MATH–6562G–1, Base Ten Number System & Operation: Addition/Subtraction
October 21, 2013
Latin American Subtraction Algorithm The Latin American subtraction algorithm is based on the
fact that the difference between the two numbers does not change while adding the same amount to
the minuend and subtrahend (Indiana University Southeast, n.d.). This algorithm appears to be one
that requires precision to detail as it is different from the traditional subtraction algorithm the
majority of students have been taught. Regardless of teacher preference, providing students with
various strategies allows them to experience the diversity in problem ... Show more content on
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A: Exemplary Work
A = 4.00; A– = 3.75
All of the previous, in addition to the following:
B: Graduate Level Work
B+ = 3.50; B = 3.00;
B– = 2.75
All of the previous, in addition to the following:
C: Minimal Work
C+ = 2.50; C = 2.00;
C– = 1.75
F: Work Submitted but Unacceptable
F = 1.00
Adherence to Assignment Expectations
The extent to which work meets the assigned criteria.
Assignment exceeds expectations, integrating additional material and/or information.
Assignment

Reflection Paper
1. How did you demonstrate mutual respect for, rapport with, and responsiveness to students with
varied needs and backgrounds, and challenge students to engage in learning?
While the students completed the erosion experiments, I asked may open–ended questions. I wanted
the students to understand why they thought their answers was correct. This helped the students stay
engaged. All students, regardless of their backgrounds, did well in the experiment. I walked around
while the students were completing the experiments and assessments. Students who varied with
needs had support of their "team". Each team, or group, had four to five students.
Engaging Students in Learning
2. Explain how your instruction engaged students in developing conceptual understanding and
procedural fluency in math, and scientific literacy in science.
Students were engaged in developing conceptual understanding by answering why the thought their
answer was correct. When making fractions out of the collected data, I encouraged students to tell
me why the denominator and numerator were placed where they were. I asked many question that
began with the word "why". I also encouraged students to make a mixed number into an improper
fraction. The students used their procedural fluency to calculate the mixed number into an improper
fraction. Students were engaged in scientific literacy by explain to me what the already knew about
erosion. The students predicted before each experiment what would happen. The

Number Recognition Assignment

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