local_media6355515740080111993.pptx

MATHEMATICAL MODELING: EFFECTS ON
PROBLEM SOLVING PERFORMANCE AND
MATH ANXIETY OF STUDENTS

INTRODUCTION
 Mathematics is very important in our lives.The application of mathematics is evident not only
in the field of education, but in almost every aspect that we could think of: when we budget
our monthly income, manage our time, and even in the infrastructures we see outside. In the
Philippine education system, mathematics is one of the top priorities in terms of the number
of hours allocated per class in all levels.The Department of Education (DepEd) mandated 50-
minute time allocation everyday in the old curriculum (Revised Basic Education Curriculum)
and 1 hour for 4 days for the new curriculum (K to 12 Curriculum). Mathematics is also one of
the subjects included in assessing one’s achievement in terms of national level competency
like the National Career Assessment Examination and the National Achievement Test. In
wanting to develop mathematical competency in the subject, to promote good camaraderie
skills between students, and to establish rapport between teachers and students, various
mathematics trainings for students and teachers are held in the country such as the
MathematicsTeachers Association of the Philippines (MTAP) trainings and the Mathematics
Trainers’ Guild apart from the different mathematics enrichment and remedial programs
advocated by various schools both in the private and public sectors.

GAPS
 Teachers, on their part, are finding ways to make their classes love mathematics
by trying out new techniques and teaching methods which would make students
interested and engaged.With regard to that, there are plenty of teaching
methods and strategies that the teachers could use, but this study utilized the
integration of mathematical modeling because according to Kaiser, Blomhøj and
Sriraman (as cited in Blomhøj, 2009), the introduction of mathematical modeling
and applications is probably, together with the introduction of information
technology, the most prominent common features in mathematics curricula
reforms around the world.

STATEMENT OFTHE PROBLEM
 The main purpose of this study was to determine the effects of the integration of
mathematical modeling to the problem solving performance and math anxiety of
students. Specifically, it sought to find answers to the following specific questions: 1.
Is there a significant difference between the pretest and posttest mean scores of the
control and experimental groups in terms of:
1.1. Problem-solving performance?
1.2. Level of math anxiety?
2. Is there a significant difference between the posttest mean scores of the control
and experimental groups in terms of:
2.1. Problem-solving performance?
2.2. Level of math anxiety?

RESEARCH DESIGN
 The study employed the experimental design particularly the pre and
posttest design, to compare the performance of the participants taught
using the integration of mathematical modeling with another group, the
control group, which was taught using guided practice.The
experimental research design is appropriate to this study because it is
the only design that can truly test a hypothesis concerning cause-and-
effect relationship (Sevilla, et.al. , 1992).

PARTICIPANTS OFTHE STUDY
 The study employed intact groups and group matching techniques in selecting the participants of the
study.The participants came from the Grade 9 students enrolled in Eastern Bacoor National High
School. From the twelve heterogeneous sections, two sections (each composed with 46 students)
were randomly chosen using the fishbowl technique to represent the control and experimental group.
Between these two sections, a coin was tossed to determine which among the sections shall be the
control group or the experimental group.
 To ensure that no other underlying factors would interfere with the results of the study, aside from
the variables presented in the conceptual paradigm, both groups were handled by the same teacher,
their classroom location is within the same area, and their class schedule interval is comparable.
 Group matching techniques were used so that each group will have an equal distribution of learners
according to their mathematical ability: above average, average, and below average.The basis of
their classification is their 2nd grading period grade in Mathematics.The scale used in the
classification of the student’s ability level was adopted from Basco (2008) as seen in table 1.

 Table 1. Basis of Classification in terms of students’ mathematical ability (Basco, 2008)
As revealed in table 1, there are three classifications of mathematical ability namely: below
average; average and above average.The researchers made sure that this three types of
students are well represented in each of the two groups under study.
Grade Classification
86 and above Above Average (AA)
80-85 Average (A)
79 and below Below Average (BA)

RESEARCH INSTRUMENTS
 The instruments that were used in gathering data from the participants are the
following: Problem Solving PerformanceTest, composed of multiple choice items
and free-response items, which seeks to measure the problem solving
performance of the students; Mathematics AnxietyTest, adopted from Montiel
(1995), which seeks to measure the math anxiety level of students in terms of the
following constructs: Social Responsibility Anxiety, MathematicsTest Anxiety, and
Numerical Anxiety; Lesson Plans which serves as a guide for teaching both
groups; Class Observation Form which serves as a checklist for the observer
regarding the execution of the lesson on both groups; and a questionnaire
followed by an interview of the selected students from the experimental group
conducted to elicit students’ experiences and reactions during the integration of
mathematical modeling in their classroom.

DATA GATHERING PROCEDURE
 Prior to the execution of the study, both groups took a pretest to gauge
their problem solving performance and math anxiety level through the
problem solving performance test and mathematics anxiety test.
Overall, the findings seem to imply that aside from the schedule,
teacher, classroom location, and the assumption that the IQ of the
participants are comparable based on their grades last period, the
pretest scores of both groups show that they are comparable and that
they have the same entry level on the subject.Table 2 reveals the
respondents’ pre-test mean score on problem solving performance and
anxiety.

Table 2. Result of t-test for the Comparison of the Pretest Mean Scores of the Control and
Experimental Groups on Problem Solving Performance and Math Anxiety
Variable Test Items Group Mean SD Computed t-
value
Critical t-
value
Interpretation
PSP MC Control 8.33 2.39 0.669
1.6620
Not Significant
Experimental 8.72 3.17
FR Control 0.35 0.67 0.631 Not Significant
MC & FR Control 8.67 2.50 0.497 Not Significant
MA SRA Control 27.11 4.63 0.621
1.6620
Not Significant
MTA Control 90.78 15.46 0.963 Not Significant
NA Control 108.52 19.50 1.165 Not Significant
TOTAL Control 226.50 33.54 0.208 Not Significant
*PSP – Problem Solving Performance, MA – Math Anxiety
*MC – Multiple Choice Items, FR – Free-response Items
*SRA – Social Responsibility Anxiety, MTA – Mathematics Test Anxiety,
*NA – Numerical Anxiety, TOTAL – Combined SRA, MTA, and NA
Table 2. Result of t-test for the Comparison of the Pretest Mean Scores of the Control
and Experimental Groups on Problem Solving Performance and Math Anxiety

 It is evident in table 2 that no significant difference were reflected from each of the mean scores and mathematics
anxiety level which means that both of the two groups (the experimental and control groups) were equal in those
variables.
 There were two kinds of treatment: the integration of mathematical modeling for the experimental group and the
guided practice for the control group. Both groups were taught the same topics: Quadrilaterals,Triangle Similarities,
andThe PythagoreanTheorem.The execution of the study lasted for three weeks only (December 1- 18, 2014). Extra
handouts, visual aids and other learning materials for the pupils in both groups were provided.This was necessary in
order to control the effects of teaching materials and references.To ensure that the teacher-researcher would not
show any bias during the execution of the study, two teachers from Eastern Bacoor National High School made a
classroom observation for every execution of different activities.
 In terms of the structure in teaching, both groups were handled in a student-centered approach where activities and
group works are integrated in every lesson proper. However, the experimental group performed a different way of
presenting their solutions that would engage them to think further than what is expected from them.The
experimental group was exposed to mathematical modeling to deeply interpret the scenario or phenomena that they
are meant to explain or answer.
 To determine the performance of the students in the experimental group, an indicator was used to provide objective
scoring for each group.This indicator was adopted, as shown in table 3, from the “Six Level of Assessing
Mathematical Modelling” by Ludwig and Xu, (as cited in Journal f Mathematik-Didaktik 31.1, 2009:77-97).

LEVEL CHARACTERISTICS
0
The student has not understood the situation and is not able to sketch or write anything concrete about the
problem.
1
The student only understands the given real situation, but is not able to structure and simplify the situation or
cannot find connections to any mathematical ideas.
2
After investigating the given real situation, the student finds a real model through structuring and simplifying,
but does not know how to transfer this into a mathematical problem (the student creates a kind of word
problem about the real situation).
3
The student is able to find not only a real model, but also translates it into a proper mathematical problem, but
cannot work with it clearly in the mathematical world.
4
The student is able to pick up a mathematical problem from the real situation, works with this mathematical
problem in the mathematical world, and has mathematical results.
5
The student is able to experience the mathematical modelling process and to validate the solution of a
mathematical problem in relation to the given situation.
Table 3. Six Level for Assessing Mathematical Modelling Competency

DATA ANALYSIS PROCEDURE
 The following statistical tools were used in this study. Mean and standard
deviation.These were used to describe the respondents’ scores in the problem
solving and math anxiety test before and after using the pictorial models.T-test
for dependent samples.This was utilized to determine if a significant difference
between the pretest and posttest mean scores of the respondents. Results and
Discussion
 Table 4 shows the result of t-test between the pretest and posttest mean scores of
both groups in terms of their problem solving performance and math anxiety. For
their problem solving performance, findings showed that there is a significant
difference between the two groups which suggests that both group showed
improvement in their mean scores while for their math anxiety, findings show that
both groups were able to reduce their level of anxiety from moderately anxious to
low anxious.

Variable Test Items Group Pretest
Mean
Score
Post test
Mean
Score
Computed t-value Critical t-
value
Interpretation
PSP MC
Control 8.33 15.72 15.239
1.6794
Significant
Experimental 8.717 17.94 22.682 Significant
FR
Control 0.35 6.98 12.562 Significant
MC & FR Control 8.67 22.70 17.460 Significant
MA
SRA
Control 27.11 22.52 7.635
1.6794
Significant
MTA Control 90.78 85.41 2.167 Significant
NA
Control 108.52 103.94 1.096 Not Significant
Experimental 113.24 96.11 5.150 Not Significant
TOTAL Control 226.50 213.15 1.946 Significant
*PSP – Problem Solving Performance, MA – Math Anxiety MC – Multiple Choice Items, FR – Free-response Items
*SRA – Social Responsibility Anxiety, MTA – Mathematics Test Anxiety, NA – Numerical Anxiety, TOTAL – Combined SRA, MTA, and NA
Table 4. Result of t-test for the Comparison of the Pretest and Posttest Mean Scores of the
Control and Experimental Groups on Problem Solving Performance and Math Anxiety

COMPARISON OF RESPONDENT’S POSTTEST
MEAN SCORE AND MATH ANXIETY LEVELS.
 Table 5 shows the result of t-test between the posttest mean scores of both groups in terms of their
problem solving performance and math anxiety. For the problem solving performance, the experimental
group obtained a higher mean score than the control group while for the math anxiety, the experimental
group obtained a lower mean score than the control group.
 Based on the mean scores of both groups, the experimental group performed better which suggests that
mathematical modeling is more effective than guided practice in improving the problem solving
performance of students in mathematics.This is in agreement with the study of Dudley (as cited in
Oswalt, 2012) who stated that the primary purpose of a modeling task is to teach students reason, logic,
and problem- solving.Temur (2012) also stressed that modeling has an important place in developing a
problem solving technique. It has been found out by Fey et al. (as cited in Wethall, 2011) that students who
were taught using a modeling approach outperformed the students using a traditional approach on
problems that require interpretation of results of algebraic calculations.This is also evident in the posttest
answers of students on part II where it can be shown that students from the mathematical modeling
group have a systematic way of answering the word problems given. Students also showed how the
concepts learned in the class can be applied when solving a certain problem compared with the other
group who proceeded with the computation part of the problem. In a study by Chuan (2003),
mathematical modeling was used to further teach students in terms of problem solving and it was proven
effective in improving student’s critical thinking and creativity. Also, Mathematical modeling encourages a
deeper comprehension of mathematical ideas and trains students to reflect, interpret, and formulate a
plan when presented with a non-traditional problem (Oswalt, 2012).

Variable Test Items Group Mean SD Computed t-
value
Critical t-
value
Interpretation
PSP
MC
Control 15.72 2.40 3.468
1.6620
Significant
FR
MC & FR
MA
SRA
Control 22.52 5.83 0.038
1.6620
Not Significant
MTA
NA Control 103.94 22.73 1.940 Significant
TOTAL Control 213.15 45.31 2.034 Significant
*PSP – Problem Solving Performance, MA – Math Anxiety
*MC – Multiple Choice Items, FR – Free-response Items
*SRA – Social Responsibility Anxiety, MTA – Mathematics Test Anxiety,
*NA – Numerical Anxiety, TOTAL – Combined SRA, MTA, and NA
Table 5. Result of t-test for the Comparison of the Posttest Mean Scores of the Control
and Experimental Groups on Problem Solving Performance and Math Anxiety

FINDINGS
 Based on the data gathered, the following are the findings of this study.
1.There is a significant difference between the pretest and posttest mean scores of the
respondents in the problem-solving in terms of multiple-choice items and free-response
type and combined.
2.There is a significant difference between the respondents’ prior and after mathematical
anxieties in terms of social responsibility, mathematical test anxiety except for numerical
anxiety, however, significant difference has noted for its combination.
3.There is a significant difference between mean performances of the respondents in
the two independent groups both in the multiple-choice items and free-response items
and its combination.
4.There is a significant difference between math anxiety levels of the group who use
mathematical modeling and the group who use guided practice, in terms of all its
component namely: Mathematics test anxiety; numerical anxiety except for social
responsibility anxiety. However, the use of the combination of all its components has
been found to be significant.

CONCLUSION
 Based on the findings of the study, the following conclusions were drawn.
1. Both the use of mathematical modeling and guided practice in the classroom
significantly increase problem-solving performance of the grade 9 high school students
2.The use of mathematical modeling significantly improve grade 9 high school students’
math anxiety level specifically in terms of social responsibility anxiety and mathematics test
anxiety. However, it does not affect students’ numerical anxiety.
3. Mathematical modeling is more effective compared with the use of guided practice in
teaching problem –solving topics in mathematics
4.The use of mathematical modeling, compared with the use of guided practice, in teaching
problem-solving, is more effective in reducing the grade 9 high school students’ math
anxiety level specifically in terms of numerical anxiety, mathematics test anxiety and its
combination. However, in terms of social responsibility anxiety, both of the two strategies
were equally effective.

RECOMMENDATION
 Based on the findings, the following recommendations are proposed to help future researchers,
curriculum developers, teachers, and school administrators:
1. In terms of instruction, it is recommended for teachers to integrate modeling tasks during their topic
discussion since it can help elicit positive reactions from students and help improve camaraderie between
students.
2. In terms of the execution of the mathematical modeling tasks, it is recommended to create a task that would
also elicit individual work for students since in this study, the modeling tasks were only centered on groupings.
3. It is also recommended that more alternative modeling activities, other than the one presented in this study,
be created in such a way that it would be applicable in a day to day basis since in this study, the integration of
modeling activities is presented twice per topic discussion only.This is to also to avoid saturation.
4. Consider improving of the use of mathematical modeling that would affect students’ numerical anxiety.
5. More researches about the integration of mathematical modeling in classroom are recommended which seek
to determine the effects on other factors such as the creative thinking of students and other aspects of problem
solving.
6. For future researchers of the study, it is recommended that the duration of the study be for the whole grading
period or more than 3 months so that the effect of the integration of the modeling activities will be fully realized
and shown by the students. Also, extending the duration of the study can be a test to see how the students can
retain the methods of solving problems using mathematical modeling.

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