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Mathematical Competence and Performance in Geometry of High School Students

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The primary objective of the study was to determine the mathematical competence and performance in Geometry of high school students. More specifically, the study ascertained if selected variables like gender, third year grade in English, learning styles, class size and classroom structure significantly affect the high school students' performance in Geometry and their mathematical competence in terms of mathematics concepts and problem solving skills. Respondents of the study were the 212 high school students who were taken at random from the three national high schools. The data were analyzed using SPSS Program. Results of the study revealed the following: The classrooms of Geometry classes were "highly structured". The high school students in Mambusao taking Geometry have varied learning styles. They had low level of mathematical competence and low academic performance in the said subject. Students who have high preference in reading/writing and are tactile/kinesthetic learners perform significantly higher. The learning styles of high school students, class size, classroom structure, and level of mathematical competence significantly affect their performance in geometry. While, grade in English, learning styles of the high school students and class size significantly affect their level of mathematical competence.
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Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
53
Mathematical Competence and Performance in Geometry of High School
Students
Charina C. Gloria
Capiz State University
Burias, Mambusao, Capiz 5807 Philippines
ABSTRACT
The primary objective of the study was to determine the mathematical competence and performance in Geometry of high school
students. More specifically, the study ascertained if selected variables like gender, third year grade in English, learning styles, class
size and classroom structure significantly affect the high school students’ performance in Geometry and their mathematical
competence in terms of mathematics concepts and problem solving skills. Respondents of the study were the 212 high school
students who were taken at random from the three national high schools. The data were analyzed using SPSS Program. Results of the
study revealed the following: The classrooms of Geometry classes were “highly structured”. The high school students in Mambusao
taking Geometry have varied learning styles. They had low level of mathematical competence and low academic performance in the
said subject. Students who have high preference in reading/writing and are tactile/kinesthetic learners perform significantly higher.
The learning styles of high school students, class size, classroom structure, and level of mathematical competence significantly affect
their performance in geometry. While, grade in English, learning styles of the high school students and class size significantly affect
their level of mathematical competence.
Keywords: Mathematical Competence, Mathematical Concepts, Problem Skills, Performance
1. INTRODUCTION
High performance in every test in the classroom, in the
division, in the region and in the national level administered
by the teacher under Department of Education’s supervision is
one of the major goals of every teacher and every learning
institution.
It is a familiar notion that people learn mathematics in
different ways. Some people remember best what they have
seen. Others are good in words. Some may be competent in
solving problems but have difficulty learning mathematics
formulae. There are students who are good with their hands or
who have creative, artistic talent and flair but who have
difficulty with more formal mathematics learning and who do
not see themselves as able learners at all [1].
Students usually get low grades in their performance in
mathematics due to lack of concept, understanding of the
fundamental manipulation or mathematical skills and most of
all the love of mathematics, and this may create difficulty and
negativism towards the subject. Nevertheless, teachers must
look at their profession and try to find out what they can share
in the learning process.
According to [2], for teachers to be truly effective they should
bring together these four basic components: an appreciation of
the discipline of mathematics itself- what it means to “do
mathematics”, an understanding of how students learn and
construct ideas, an ability to design and select task so that
students learn mathematics in problem solving environment
and the ability to integrate assessment with the teaching
process in order to enhance learning and improve daily
instruction.
Mathematics concept is an idea or mental impression, the
content of which is primarily related to computation,
quantitative relationship, systematic reasoning or structure or
configuration [3].
Problem-solving on the other hand, is an extremely complex
process for students because it involves a complicated rather
than simple recall of facts or the application of well- learned
procedures. The ability to solve mathematical problems
develops slowly over a long period of time because success of
adopting so depends in the assimilation of mathematical
content knowledge skills. Problem solving skills is one of the
most important goals of mathematics education. Thus, the
learner should be provided with maximum opportunities to
think and imagine that learning abstract concepts that is
accepted generally as a difficult subject can be easily grasped
and comprehended [4]. According to [5], “one is effective in
problem solving if he has acquired knowledge, skills and
understanding in meeting various situations”. [6] added that
one cannot solve mathematical problem if he lacks basic facts,
without competence in computation, understanding of
mathematical operation, or ability to sequence in logical order
.
It is on the above premise that this study was conducted.
2. STATEMENT OF THE PROBLEM
In the past decade, it has been suggested that problem-solving
techniques can be made available most effectively through
making problem solving, the focus of the mathematics
curriculum. Although mathematical problems have
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
54
traditionally been a part of the mathematics curriculum, it has
been only comparatively recently that problem solving has
come to be regarded as an important medium for teaching and
learning mathematics [7]. With these developments in
mathematics instruction, the researcher was motivated to
undertake this investigation to ascertain the level of
mathematical competence and performance in Geometry of
high school students in Mambusao District for 2010-2011.
Specifically, the study sought answers to the following
questions:
1. What is the classroom structure level of geometry
classes?
2. What are the learning styles of the respondents?
3. What is the level of mathematical competence of the
respondents in terms of mathematics concepts and
problem solving skills?
4. What is the level of performance of the respondents
in Geometry?
5. Is mathematical competence related to high school
students’ performance in Geometry?
6. Is there a significant difference in the performance in
geometry when respondents are grouped according to
personal related factors such as gender, third year
grade in English, learning styles; and classroom
profile such as class size and classroom structuring?
7. Is there a significant difference in the mathematical
competencies of the respondents when grouped
according to student-related factors such as: gender,
third year grade in English, learning styles and
classroom profile such as class size and classroom
structuring?
3. LITERATURE REVIEW
Mathematics Concepts in Geometry
Geometry is a rich source of knowledge, both theoretical and
practical, that it should be studied seriously. A working
knowledge of simple geometric shapes together with their
properties and relationships will contribute to the development
of students reasoning and analytical minds [8].
Solving problems in Geometry is a challenge, but it can also
be fun when you know how. Understanding the concept and
working geometry problems takes practice. The more types of
problems that you do, the better you will become in quickly
deciding what the problem asks and reaching a solution [9].
Many students learned mathematics as a set of disconnected
rules, facts, and procedures. Oftentimes, mathematics teachers
find it difficult to recognize the important mathematical
principles and relationships underlying the mathematical work
of students. Those responsible for the professional
development of teachers are increasingly coming to
understand the need for long term opportunities for teachers to
deepen their understanding of mathematical content [10].
Motivating students to love mathematics is the goal of every
mathematics teacher. Teachers consider themselves to be
always on the right track, so they expect wonderful outcomes
from their teaching. Mathematics can be meaningful by
allowing the learners to explore mathematical concepts,
relationships and possibly in the most interesting situation
where they could gain mastery of skills of valuable meaning
and have ready application in one’s everyday life [3].
As such, teachers aimed primarily to impart knowledge and
make it fully understand for maximum retention of the learner,
and in the process, develop his capability to enable him to
translate abstract concepts and theories into practical and
functional skills. The importance of achieving this latter goal
could not be overemphasized. This is so, since these
mathematical concepts are essential not only in the furtherance
of the learner’s academic pursuit, but more importantly in
facing his day-to-day life.
To improve students’ competence in learning mathematical
concept and skills, mathematics should be taught in
meaningful manner which are enjoyable and interesting. [4]
stated that to motivate students to learn is to give them the
most interesting and pleasurable activity. It may follow that
students should be provided with the varied activities and
exercises to last until students could attain the needed speed
and accuracy in mathematical operation. Teachers should
bring richness of knowledge and inspiration to their students
leading into broader and richer life someday.
In mathematics, concepts form the basis of formulation of
generalizations and rules could master the fundamentals of
mathematics as early as possible [4].
According to [1], mathematics has been called a symbolic
language that enables human to think about record, and
communicate ideas concerning the elements and the
relationship of quantity.
According [4] to make mathematics an interesting subject,
teachers should base their teaching on the principles of child
development and learning. Students learn better through
exploration and manipulation of object.
Students will value Mathematics if they see how it plays a role
in their real lives and in society. Thus, the task of the teacher is
to make mathematics learning meaningful to the students by
connecting the lesson to the real life experiences and allowing
students to experience mathematics through actual
measurements and exploration [11]
Lessons in mathematics should be explained more clearly so
that students will really understand the concepts that are being
taught to them. The use of instructional materials suited to the
lessons taken should also be mastered by teachers. Remedial
teaching in mathematics should be given to students to give
them a better understanding of their lessons. It is in this class
that students are encouraged to verbalize the difficulty which
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
55
they have encountered in learning mathematics. School
administrators should try to consider the problems expressed
by students so that this will be the bases for the solution to be
taken to help students to have a better understanding of
Mathematics. It is further recommended that teachers teaching
Mathematics should have a major in mathematics. [1]
Teaching- learning process is interesting if a teacher uses
teaching aids and devices that would attract and sustain the
interest of the students. Techniques, strategies, the use of
teaching aids and exposure to interesting physical environment
related to mathematics would enhance learning.
According to [20] teachers should find ways and means to find
better performance in mathematics by making the lesson more
interesting and meaningful and also by giving the students
mathematical concept.
Problem Solving Skills
Problem solving is an important component of mathematics
education. It is an essential discipline because of its practical
role to the individual and society. Through a problem-solving
approach, this aspect of mathematics can be developed.
Presenting a problem and developing the skills needed to solve
that problem is more motivational than teaching the skills
without a context. Such motivation gives problem solving
special value as a vehicle for learning new concepts and skills
or the reinforcement of skills already acquired [7], [11]
Approaching mathematics through problem solving can create
a context which simulates real life and therefore justifies the
mathematics rather than treating it as an end in itself.
The National Council of Teachers of Mathematics
recommended that problem solving be the focus of
mathematics teaching because, they say, it encompasses skills
and functions which are an important part of everyday life.
Furthermore it can help people adapt to changes and
unexpected problems in their careers and other aspects of their
lives. More recently the Council endorsed this
recommendation [11] with the statement that problem solving
should underlie all aspects of mathematics teaching in order to
give students experience of the power of mathematics in the
world around them.
[12] also advocated problem solving as a means of
developing mathematical thinking and as a tool for daily
living, saying that problem-solving ability lies 'at the heart of
mathematics' because it is the means by which mathematics
can be applied to a variety of unfamiliar situations. Problem
solving is, however, more than a vehicle for teaching and
reinforcing mathematical knowledge and helping to meet
everyday challenges. It is also a skill which can enhance
logical reasoning.
Many writers have emphasized the importance of problem
solving as a means of developing the logical thinking aspect of
mathematics. 'If education fails to contribute to the
development of the intelligence, it is obviously incomplete.
Yet, intelligence is essentially the ability to solve problems:
everyday problems and personal problems [13].
Training in problem-solving techniques equips people more
readily with the ability to adapt to such situations. A further
reason why a problem-solving approach is valuable is its
aesthetic form. Problem solving allows the student to
experience a range of emotions associated with various stages
in the solution process. Mathematicians who successfully
solve problems say that the experience of having done so
contributes to an appreciation for the 'power and beauty of
mathematics' [11] the "joy of banging your head against a
mathematical wall, and then discovering that there might be
ways of either going around or over that wall" [14]
One of the aims of teaching through problem solving is to
encourage students to refine and build onto their own
processes over a period of time as their experiences allow
them to discard some ideas and become aware of further
possibilities [15]. As well as developing knowledge, the
students are also developing an understanding when it is
appropriate to use particular strategies. Through using this
approach the emphasis is on making the students more
responsible for their own learning. Students can become even
more involved in problem solving by formulating and solving
their own problems, or by rewriting problems in their own
words in order to facilitate understanding. It is of particular
importance to note that they are encouraged to discuss the
processes which they are undertaking, in order to improve
understanding, gain new insights into the problem and
communicate their ideas [16].
According to [17], a learner becomes a good problem solver
when he can readily understand the important features of the
problem. He can sense whether his answer is correct or not. In
the teaching-learning process, appropriate strategies and
techniques maybe adopted to provide varied activities, namely
involvement, analogy, analysis, modified experimental
method, direct presentation, teaching by rule, by definition, by
rules, by using methods or by using games and simulation.
Computational skills and problem solving performance
involve more than thinking; rules, analyze the figures, sizes
and angles and how it derives to definite solutions;
competence and confidence to apply this knowledge in
practical word which surely determine how mathematics is
very important. Solving performance of students refers to how
an individual digest the problem mentally based on general
law such as the relationships between the sides and angles of
triangles and with the properties.
According to [4], students have difficulty in problem solving.
She further cited that there was no mastery of skills in the
fundamental operations although the students have a positive
attitude towards mathematics.
The main reason for learning all about math is to become
better problem solvers in all aspects of life. Many problems
are multi step and require some type of systematic approach.
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
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Most of all, there are a couple of things you need to do when
solving problems. Ask yourself exactly what type of
information is being asked for. Then determine all the
information that is being given to you in the question. When
you clearly understand the answers to those two questions, you
are then ready to devise your plan.
Learning how to solve problems in mathematics knows what
to look for. Math problems often require established
procedures and knowing what procedure to apply. To create
procedures, you have to be familiar with the problem situation
and be able to collect the appropriate information, identify a
strategy or strategies and use the strategy appropriately.
Problem solving requires practice. When deciding on methods
or procedures to use to solve problems, the first thing you will
do is look for clues which are one of the most important skills
in solving problems in mathematics. If you begin to solve
problems by looking for clue words, you will find that these
'words' often indicate an operation.
NCTM recommends teachers enable students to solve
problems because problem solving is the heart of mathematics.
Students must be exposed to a variety of problems- problems
that vary in context. In level of difficulty and in mathematical
methods required for their solutions. Students must learn to
analyze the conditions in a problem, to restate them, to plan
strategies for solving it, to develop several solutions and to
work collaboratively with others in search of the solution.
Most of all students must develop the discipline and
perseverance to solve a problem no matter how complex it is.
Performance in Geometry
The mathematics performance is on the average and they
encountered moderate difficulty in the subject with both
algebra and geometry as highly difficult subjects [18].
Likewise [19], found out that the performance of the college
freshmen students of Polytechnic College of Antique for the
Second Semester of 2001-2002 in arithmetic computation and
problem solving skills was satisfactory.
In the study of [20], revealed that the performance of Grade V
pupils in Mathematics of Tapaz East District for SY 1997-
1998 was satisfactory. She recommended that teachers should
find ways and means to help their pupils get better grades in
Math by making the lesson more interesting and meaningful
and by giving the pupils mathematical exercises so that they
will master the mathematical concept.
[4] found that the performance in problem solving in
mathematics of Grade IV pupils in the District of Ivisan,
Capiz, was unsatisfactory.
Factors Affecting the Mathematical Competence and
Performance in Geometry
Gender
Several studies have been conducted relating gender to
performance of students in mathematics.
A study conducted by [1] concluded that there was no
significant difference in the academic performance of first year
high school students categorized as males and females which
implies that gender does not have a direct bearing on students’
academic performance in mathematics.
This finding is further supported by [21] that there were no
gender differences in mathematics learning from kindergarten
to third grade. Differences in gender began to emerge in the 4th
grade but they were not significant. Girls were slightly
superior with boys in computation while boys were found
slightly superior to girls in mathematical reasoning.
However, [3] claimed that gender was related to academic
achievement and indicated that females performed better than
males. Also, a study conducted by found that females
performed better in mathematics [3].
[22] in his study found that female respondents are better
performers in Algebra than the males.
[19] found that female students performed better than males in
arithmetic computation and problem solving skills.
In the study of [18] results showed that females perform
significantly better than males. The study further revealed that
there was a positive significant correlation between gender and
academic achievement and mathematical performance.
Learning Styles
Everyone has a learning style. One’s style of learning, if
accommodated, can result in improved attitude toward
learning and increased productivity, academic achievement,
and creativity. Learning style is a composite of characteristics,
cognitive, affective and physiological factors that serves as
relatively stable indicators of how a learner perceives, interacts
with and responds to the learning environment. Some may
prefer to learn by listening to someone talking about the
information. Others prefer to read the concept in order to learn
it, while some need to see a demonstration of the concept.
Learning style theory proposes that different people learn in
different ways and that it is good to know what one’s own
preferred learning style is. Knowing one’s learning style
improved self-esteem. When children understand how they
learn and how they struggle to learn, they can be more in
control of their environment and can ask for what they need
[23].
Knowing one’s learning style preferences can help plan for
activities that take advantage of the student’s natural skills and
inclinations. There are many different learning styles.
Identifying preferred learning style leads to meta-cognition
(self-awareness). A preferred learning style is like your
favorite shoes. But favorite shoes are not always appropriate,
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
57
so you have to try something different. There is no right or
wrong learning style. Although one may prefer one style over
another, preferences develop like muscles, the more they are
used, the stronger they become. To gain a better understanding
of one as a learner you need to evaluate the way you prefer to
learn or your learning style. Students can learn any subject
matter when they are taught with methods and approaches
responsive to their learning style strengths [25].
The learning style of the students is based on the theory of
constructivism. This theory elaborates that the learner chooses
and finds the type of learning suitable to his experiences [25].
This statement was corroborated suitably to his experiences
and learning style.
The concepts learning style is based on the theory that an
individual responds to educational experiences with consistent
behavior and performance patterns. The complexity of the
construct psychometric problems is related to its measurement
and the enigmatic relationship between culture, the teaching
and learning process [25].
In the study conducted by [1] she found out that there was no
significant relationship between learning style and academic
performance of first year high school students in Lapaz
National High School. This result was contrary to the finding
revealed in the study of [1] that a highly significant
relationship was established between the students’ learning
styles and academic performance.
Class Size
Class size as a possible factor in pupil and teacher efficiency
was mentioned by writers of textbooks in educational
administration, in school surveys, and in the reports of school
superintendents and committees, before any controlled studies
were made. These writers frequently set up empirical
standards of class size, basing them upon experienced and
opinions. The following statements have been chosen as
typical of the sources mentioned. “In order that the very best
work may done, class in the school ought not to contain more
than from 35 to 40 pupils. When classes are of this size, it is
possible for the teacher to give the time and attention requisite
to the achievement of the best results. “All school
administrators agreed that 40 is the super-maximum number of
pupils that should under any circumstances be seated in any
elementary schools [24].
Classroom Structure
A significant issue in education reform today is the effect of
classroom structure on the cognitive development of students.
The management of a classroom includes control of its
physical conditions, proper utilization of materials for
instruction, classroom routine and discipline.
The physical aspects includes the location, size, shapes,
lighting, ventilation, acoustic and provisions for sanitation.
While the location and the size of the room are not within the
teacher’s control, the ingenious and creative teacher can
transform even the dullest room in the building to be
attractive, restful and comfortable. The educational climate of
the room should be conducive to learning.
Other aspects related to classroom management are:
Lighting. Lighting and illumination of the room should be
adequate. Good lighting facilities affect the health and the
learning of the pupils/students. There are several factors that
should be considered into the provision of good lighting
facilities. These are the size of the room, the light available,
the location of the doors and windows, the colors of the walls,
shades and manipulation of blinds.
The general physical appearance of the room can stimulate
pleasant feelings, attitudes, thoughts, ideas, and appreciations
that are essential to learning. The climate can enhance the
morale of the learners, and, in effect, work hard and learning
becomes more meaningful [26].
Classroom structure is made of the activities and physical
composition of school-based learning environment. Classroom
structure can be ordered in ways that influence or manipulate
student behavior; teachers routinely learn these different ways
in order to address everyday student behavior and learning, as
well as to address special needs and more specialized learning
as students grow older.
"A classroom that is well structured can result in increased
learning opportunities, and can increase opportunities for
appropriate social interactions. A well-structured classroom
can also decrease frustration, which may result in fewer
challenging behaviors. For a staff, it can increase efficiency in
that staff members can spend less time dealing with
challenging behavior and more time working on increasing
desired skills... A well-structured classroom should be a
positive, pleasant place where students and staff alike want to
be."
According to [27] one of the factors that affect the efficiency
of learning is the condition in which learning takes place. He
noted that the physical conditions needed for learning is under
environmental factors. This includes the classroom, textbooks,
and equipment. In school and at home, the condition for
learning must be favorable to produce desired results. It is
difficult to do a good job of teaching in a good type of
building and without adequate equipment and instructional
materials. According to the same author, instructional
materials are not instructional in themselves. In reality, they
are only aids to instruction. They are used to gain knowledge,
concepts, ideas, and deals through the senses of hearing,
seeing and touching. The use of different senses will also add
effectiveness in causing learning to be meaningful and
functional.
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
58
4. METHODOLOGY
The descriptive correlational design was used in this study.
According to Best, in [4],descriptive research deals with
describing, recording, analyzing, and interpreting conditions
that exist. It involves some types of comparison or contrast
and attempts to discover relationships between existing non-
manipulated variables. Good and Scates in [4] added that
descriptive research is of large value in proving facts on which
professional judgment maybe based.
On the other hand, correlational research method seeks to
investigate whether a relationship exists between two or more
variables. It enables the researcher to make more intelligent
predictions [11].
5. RESULTS AND DISCUSSION
Personal and School Related Characteristics of the
Respondents
Data in Table 2.0 reveals that more than a half of the
respondents were female (55.7%) and less than a half of them
were male (44.3%). This suggests that the females had
exceeded the distribution of the males in the study.
Shown in the same table are the third year grades in English of
the student-respondents. It appeared that more than two-fifth
of them had very low grade in English (44.3%). This was
closely followed by around four tenth (40.1%) with low grade;
a little less than one fifth (14.6%) were with average English
grade and two (0.9%) had high grade in English. The English
mean grade of 80.90 showed that students had low grade in
English which implies that most of these respondents do not
possess adequate linguistic skills to assist them in grasping
easily the mathematical concepts lessons in Geometry.
As to class size, data show that majority of them attended big
class (69.3%); more than a fourth belonged to average class
(26.9%); and a smaller percentage of students were assigned to
a small class (3.8%) This result implies that the geometry class
attended to by the respondents was quite big in number, hence
might be overcrowded during the class session.
Table 2. Distribution of respondents according to
their personal and school related characteristics
VARIABLE
FREQUENCY
PERCENT
Gender
Male
94
44.3
Female
118
55.7
TOTAL
212
100
Third Year
Grade in
English
Very Low
94
Low
85
Average
31
High
2
TOTAL
212
MEAN =
80.90 (Low)
Class Size
Small
8
Average
57
Big
147
TOTAL
212
Level of Classroom Structure
Data in Table 3.0 revealed that a little more than three fifth of
the respondents (61.8%) claimed that their classrooms were
highly structured; more than a fifth (22.2%) said that they
were “uncertain” while more than a tenth (15.6%) had very
highly structured room and one (0.5%) said the classroom was
poorly structured.
The mean of 3.71 showed that the Geometry classrooms of the
respondents’ were “highly structured”. This suggests that
Geometry classrooms are ideally designed for quality
instructional outcomes.
Table 3. Distribution of respondents according to
their classroom structure.
CATEGORY FREQUENCY PERCENT
Poorly Structured 1 0.5
Uncertain 47 22.2
Highly Structured 131 61.8
Very Highly Structured 33 15.6
TOTAL 212 100
MEAN = 3.71 (Highly Structured)
Learning Styles
The mean scores on the learning styles of the respondents are
presented in Table 4.0. The same highest mean scores
(M=3.60) appeared to be on those where respondents highly
preferred reading and writing and
tactile learning styles, respectively. This was closely followed
by the visual learning style (M=3.53), and the last was the
auditory learning style with a mean of 3.43. All mean scores
however, were verbally interpreted “high” in all composite of
learning styles. This indicates that student respondents were
highly visual, auditory and tactile learners and had high
preference for reading and writing style. This implies that
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
59
students employed varied learning styles according to the
learning activities they are into during their geometry class.
This is likely to say that respondents learn in different ways.
Table 4. Learning styles of the respondents
LEARNING STYLES MEAN VERBAL
INTERPRETATION
Visual 3.53 Highly Visual
Auditory 3.43 Highly Auditory
Reading/Writing Preference 3.60 High Preference
Tactile/Kinesthetic 3.60 Highly Kinesthetic
Mathematical Competence Level
Table 5.0 reflects the mathematical competence level of the
respondents in terms of mathematical concepts and problem
solving skills. As revealed, the level of competence in
mathematical concepts of the students seemed “low” as this
registered a mean percentage score of 36.95. As to their level
of competence in problem solving skills, respondents were
also found “low” as revealed by the mean percentage of 34.20
for this component. The over-all mathematical competence of
the respondents was generally low, (M=35.75%) implying that
students were not proficient in geometry.
Table 5. Mathematical competence of the respondents
COMPETENCE MEAN V.I
Mathematical Concepts 36.95 Low
Problem Solving Skills 34.20 Low
GRAND MEAN: 35.75 Low
Mathematical Concept Competence Level
The distribution of the respondents as to their level of
competence in mathematics concepts is shown in Table 5a.
Results reflected a low mathematical concept level for a little
less than two-third of the student respondents (63.2%). The
same numbers and percentages of respondents (18.4%) were
with very low and average levels of mathematical concepts,
respectively. The mean percentage of 36.95 indicated a “low”
level in mathematical concepts among student respondents.
This implies that mathematical concepts in geometry lesson
seemed difficult for the students to grasp.
Table 5a. Distribution of respondents as to their level
of competence in mathematical concepts
COMPETENCE FREQUENCY PERCENT
Mathematical Concepts
Very Low 39 18.40
Low 134 63.20
Average 39 18.40
TOTAL 212 100.00
MEAN = 36. 95% (Low)
Level of Problem Solving Skills
The distribution of the respondents as to their problem solving
skills (Table 5b) showed that less than three-fourth of them
(70.3%) had low problem solving skills. Only one (0.5%) was
found with high problem solving skills, while those in lesser
percentages were found to have very low (17%) and average
(12.3%) problem solving skills respectively. The mean
percentage of 34.20 suggests a low level problem solving
skills among student respondents implying that most of them
were not fully armed with knowledge as revealed by their low
mathematical concepts level. Thus, it follows that these
respondents might not have acquired enough logical reasoning
skills to create a context simulating real life.
Table 5b. Distribution of respondents as to their level
of mathematical competence in problem solving
skills.
COMPETENCE FREQUENCY PERCENT
Problem Solving Skills
Very Low 36 17
Low 149 70.3
Average 26 12.3
High 1 0.5
TOTAL 212 100
MEAN = 34. 20% (Low)
Performance Level in Geometry
Performance in geometry (Table 6.0) appeared to be very low
among more than two-fifth of the respondents (45.3%); while
more than a third (35.4%) were found with low level
performance; less than a fifth (17%) were average performers
and only 2.4 percent had “high” performance. The mean of
80.76 indicates a low level performance in geometry subject
by the student-respondents.
This result conformed with the findings of [4] that
performance in Mathematics of Grade IV pupils was
unsatisfactory. However, the result contradicted [19] study
who found out that college freshmen of PCA performed
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
60
satisfactorily in arithmetic computation and problem solving
skills.
Table 6. Respondents’ level of performance in
geometry
PERFORMANCE FREQUENCY PERCENT
Very Low 96 45.3
Low 75 35.4
Average 36 17.0
High 5 2.4
TOTAL 212 100.0
MEAN = 80.76 (Low)
Relationship between Mathematical Competence and
Performance in Geometry
Mathematical Concept Competence and
Performance in Geometry.
The results of the analysis using Pearson Product Moment
Correlation (r) indicate that mathematics concept competence
is highly correlated to performance in geometry. (r= 0.463; p <
0.05), therefore, the null hypothesis which states that these two
variables are not related is rejected.
The result seems to suggest that performance in geometry is
highly affected by the competence of the high school students
in mathematical concept. It seems to suggest that the higher
the mathematical competence, the higher is the performance in
geometry.
Table 7. Correlation matrix on the relationship
between Performance in geometry and mathematical
concept competence.
VARIABLE
PERFORMANCE
IN GEOMETRY
COMPETENCE
r
r prob
r
r prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.463
**
0.000
COMPETENCE
0.463**
0.000
1.0
0.000
** Highly significant
Mathematical Skill Competence and Performance in
Geometry.
Shown in Table 7a is the relationship between mathematics
skill competence of the respondents and their performance in
Geometry. The r value (r= 0.405; p < 0.05) reveals a highly
significant relationship between the two variables, therefore,
the null hypothesis which states that these variables are not
related is rejected.
The result seems to indicate that the more competent the
student in problem solving skills, the higher is his/her grade in
geometry.
Table 7a. Correlation matrix on the relationship
between performance in geometry and mathematical
skill competence
VARIABLE
PERFORMANCE IN
GEOMETRY
COMPETENCE
r
r prob.
r
r
prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.405**
0.000
COMPETENCE
0.405**
0.000
1.0
0.000
** Highly significant
Mathematical Competence (taken as a whole) and
Performance in Geometry
Presented in Table 7b is the results of the analysis of the
relationship between mathematics competence of the
respondents when taken as a group and their performance in
geometry. The r value (r=0.518; p < 0.05) clearly shows a
highly significant relationship between the two variables,
therefore, the null hypothesis which states that mathematics
competence is not related to performance in geometry is
rejected.
The findings seem to suggest that the higher the mathematics
competence of the students in concepts and skill, the higher is
their grades in geometry.
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
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61
Table 7b. Correlation matrix on the relationship
between performance in geometry and mathematical
competence (taken as a whole).
VARIABLE
PERFORMANCE
IN GEOMETRY
COMPETENCE
r
r prob
R
r
prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.518**
0.000
COMPETENCE
0.518**
0.000
1.0
0.000
** Highly significant
Differences in the Performance in Geometry When The
Respondents are Classified According to
Student Related Factors
Performance in Geometry and Gender
Table 8 shows the performance of the respondents when
classified according to gender. Results of the analysis using t-
test (t(210)= 4.775, p<0.05) revealed a highly significant
difference in the performance in geometry of the two groups of
respondents. Female respondents (M- 81.914) performed
better in geometry than their male counterpart (M = 79.35).
The finding clearly suggests that the null hypothesis claiming
that there is no significant difference in the performance of
students in geometry when they are classified according to
gender is rejected.
The result of the study confirmed [3] claiming that gender was
related to achievement with the females performing higher
than males. Likewise, this result [22] findings that females
performed better than males in Algebra, respectively.
Table 8. T-test results on the differences in
performance in geometry when the respondents are
classified according to gender
COMPARED
GROUP
DF
M
SD
t-value
Two-
Tailed
Probability
Male
210
79.35
3.98
4.775**
0.000
Female
81.91
3.79
** Highly significant
Performance in Geometry and Grade in English
Result of the analysis of the relationship between performance
of the students in geometry and their average third year grade
is reflected in Table 9. The r value of 0.797 strongly suggests a
highly significant relationship between the two variables, so
that the null hypothesis indicating absence of relationship of
these two variables mentioned is rejected. The result implies
that the higher the grade of the students in English, the higher
is their performance in geometry.
Table 9. Correlation matrix on the relationship
between performance in geometry and grade in
English
VARIABLE
PERFORMAN
CE IN
GEOMETRY
GRADE IN
ENGLISH
r
r prob
r
r
prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.797**
0.000
GRADE IN
ENGLISH
0.797
**
0.000
1.0
0.000
** Highly significant
Performance in Geometry and Learning Style
Performance in geometry and visual learning style
To understand better if learning styles affect performance in
Geometry, an analysis was done using Pearson Product
Moment Correlation and the result is shown in Table 10.
It can be gleaned from the table that there is no significant
relationship between performance in geometry and visual
learning style of the respondents (r= 0.078, p>0.05). The result
implies that students who use visual learning style are not
assured to perform well in geometry.
Performance in Geometry and auditory learning style
The result of the analysis of the geometry performance of the
students and their auditory learning style revealed that there is
no significant relationship between the two variables (r=
0.101, p>0.05). This suggests acceptance of the null
hypothesis that performance in geometry is not related to the
auditory learning style of the students.
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
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62
Table 10. Correlation matrix on the relationship
between grade in Geometry and perceived visual
learning style.
VARIABLE
PERFORMANCE
IN GEOMETRY
VISUAL
LEARNING
STYLE
r
r prob
r
r
prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.078ns
0.259
VISUAL
LEARNING
STYLE
0.078ns
0.259
1.0
0.000
ns - Not significant
Table 10a. Correlation matrix on the relationship
between performance in geometry and perceived
auditory learning style
VARIABLE
PERFORMANCE IN
GEOMETRY
AUDIT
ORY
LEARN
ING
STYLE
r
r prob
R
r prob.
PERFORMAN
CE IN
GEOMETRY
1.0
0.000
0.101ns
0.144
AUDITORY
LEARNING
STYLE
0.101ns
0.144
1.0
0.000
ns - Not significant
Performance in geometry and reading/writing
preference learning style
Shown in Table 10b is the result of the analysis of the
relationship between performance of the respondents in
geometry and their reading/writing preference learning style.
The results of the analysis show that there is a significant
correlation between the two variables tested (r= 0.174, p<
0.05). This signals the rejection of the null hypothesis.
The finding implies that the higher the reading/writing
preference learning style used by the high school students, the
higher is their performance in geometry.
Table 10 b. Correlation matrix on the relationship
between performance in geometry and perceived
reading/writing preference learning style
VARIABLE
PERFORMAN
CE IN
GEOMETRY
READING/
WRITING
PREFERENCE
LEARNING
STYLE
r
r prob
r
r prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.174*
0.011
READING/WRITIN
G PREFERNCE
LEARNING
STYLE
0.174*
0.011
1.0
0.000
* Significant at 5% level
Performance in geometry and tactile learning style
The result of the analysis of the relationship between
performance of the respondents in geometry and their
tactile/kinesthetic learning style is presented in Table 10c. The
result of the analysis shows that there is a significant
correlation between the two variables tested. This proves
enough evidence to reject the null hypothesis.
The finding seems to indicate that the higher the tactile
learning style employed by the high school students, the
higher is their performance in Geometry.
Table 10c. Correlation matrix on the relationship
between performance in geometry and perceived
tactile learning style
VARIABLE
PERFORMANC
E IN
GEOMETRY
TACTILE
LEARNING
STYLE
r
r prob
r
r prob.
PERFORMANCE IN
GEOMETRY
1.0
0.000
0.156*
0.023
TACTILE
LEARNING STYLE
0.156*
0.023
1.0
0.000
* Significant at 5% level
Volume 5 No.2, February 2015 ISSN 2224-3577
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63
Performance in geometry and learning styles (taken
as a whole)
The analysis of the relationship between performance of the
respondents in geometry and their degree of use of the
different learning styles is presented in Table 10d. The results
of the analysis suggest a significant correlation between the
two variables tested (r= 0.164, p< 0.05). This presents enough
evidence to reject the null hypothesis. The finding implies that
the higher the value placed by the respondents on the use of a
combination of different learning styles, the higher is their
performance in geometry.
The result of this study contrasted the findings of [11] that
learning styles and academic performance of the first year high
school students were not related.
Table 10d. Correlation matrix on the relationship
between performance in geometry and perceived
learning style (taken as a whole)
VARIABLE
PERFORMAN
CE IN
GEOMETRY
LEARNING
STYLE
r
r
prob
R
r
prob.
PERFORMANCE
IN GEOMETRY
1.0
0.000
0.164*
0.017
LEARNING
STYLE
0.164
*
0.017
1.0
0.000
* Significant at 5% level
Performance in Geometry and Class Size
Table 11 contains the results of the analysis of the relationship
between performance of the students in Geometry and class
size using one-way Analysis of Variance. The finding
indicates a highly significant difference in the performance of
the respondents in geometry when they were classified
according to class size (F = 38.805, p<0.05). Therefore the
null hypothesis stating absence of relationship between the
two variables is rejected. This finding of the study implies that
class size significantly affect performance of the students in
geometry. This can be explained perhaps by the fact that small
class size is more manageable than big class size.
The finding further indicates that students who belonged to
small class size had the highest performance in geometry (M=
87.16); followed by average class size ( M= 83.60); and the
lowest performance was that of the students who belonged to
big class size (79.44). Performance of students in small class is
significantly higher than that of average and big class sizes.
Likewise, performance in geometry of those who were in the
average class size is significantly higher than that of the big
class size.
Table 11. ANOVA on the differences in the
performance in geometry when respondents are
classified according class size
CATE-
GORY
SV
Sum of
Squares
Df
Mean
square
F
Si
g
Class
Size
Betwe
en
Group
s
947.54
2
473.77
38.8
05**
0.
0
0
0
Withi
n
group
s
2551.67
209
12.209
Total
3499.21
211
** Highly significant
Performance in Geometry and Perceived
Classroom Structure
Shown in Table 12 is the analysis of the relationship between
performance in Geometry and students perception as to their
classroom structure. The result indicates a highly significant
correlation between the two variables tested (r= 0.393, p< 0.05),
therefore the null hypothesis is rejected due to insufficient evidence
to prove that the null hypothesis indicating absence of relationship
between performance in Geometry and perceived classroom structure
is true.
The result of this study implies that the more highly structured the
classroom as perceived by the students, the higher is their
performance in Geometry.
This result affirm the contention [26] that the general appearance of
the room can stimulate pleasant feelings, attitudes, thoughts, ideas
and appreciations that are essential to learning and in effect learning
becomes more meaningful.
Table 12. Correlation matrix on the relationship between
performance in geometry and classroom structure.
VARIABLE
PERFORMANCE
IN GEOMETRY
CLASSROOM
STRUCTURE
r
r prob
R
r prob.
PERFORMANC
E IN
GEOMETRY
1.0
0.000
0.393
*
0.000
CLASSROOM
STRUCTURE
0.393**
0.000
1.0
0.000
** Highly significant
Volume 5 No.2, February 2015 ISSN 2224-3577
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64
Differences in the Mathematical Competence of the
Respondents when Classified According to Student
Related Variables and Classroom Management
Mathematical Competence and Gender
Mathematical concept competence and gender
Presented in Table 13 is the result of the analysis of the
difference in mathematical competence of the respondents
when they were classified according to gender. The finding
reveals that there is no significant difference in the
mathematical concept competence of the two groups of
respondents (t(210)= 1.135, p>0.05). This finding shows that
there is sufficient evidence to accept the null hypothesis. This
implies that regardless of gender, competence in mathematical
concept of the high school students is the same.
Table 13. T-test results on the differences in
mathematical concept competence when the
respondents are classified according to gender
COMPA
RED
GROUP
DF
M
SD
t-value
Two-
Tail
Probabil
ity
Male
210
36.03
12.43
1.135ns
0.258
Female
37.97
12.29
ns - Not significant
Competence in mathematical skill and gender
The result of the analysis of the difference in mathematical
skills of the respondents when classified according to gender is
shown in Table 13a. The finding reveals that there is no
significant difference in the Mathematics skill of the two
groups of respondents (t(210)= 1.352, p>0.05).
This finding simply suggests accepting the null hypothesis
indicating absence of significant difference in the
mathematical competence of the respondents when they are
classified according to gender. This implies that regardless of
gender, mathematical skills of the high school students is the
same.
Table 13a. T-test results on the difference in
competence in mathematics skills when the
respondents are classified according to gender
COMPARED
GROUP
DF
M
SD
t-value
Two-
Tailed
Probability
Male
210
32.71
11.75
1.352ns
0.178
Female
36.04
13.00
ns - Not significant
Mathematical competence (taken as a whole) and gender.
As shown in Table 13b, the result of the analysis of the
difference in mathematical competence of the respondents
when they were classified according to gender.
The finding indicates that there is no significant difference in
the mathematical competence of the two groups of respondents
(t(210)= 1.444, p>0.05). This shows that there is sufficient
evidence to accept the null hypothesis and implies that
mathematical competence of the high school students is not
affected by gender.
Table 13b. T-test results on the differences in
mathematical competence (taken as a whole) when
the respondents are classified according to gender
COMPAR
ED
GROUP
D
F
M
SD
t-
value
Two-Tail
Probabilit
y
Male
21
0
34.70
10.24
1.444n
s
0.150
Female
36.80
10.69
ns - Not significant
Mathematical Competence and Grade in English
Presented from Table 14 to Table 14b are the results of the
analyses of relationship between mathematical competence of
the respondents and their grade in English. The analyses of the
two variables reveal that there is a highly significant
relationship between the two variables tested. Matching
mathematical concept competence (r=0.344, p<0.05) and skills
Volume 5 No.2, February 2015 ISSN 2224-3577
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©2015 IJST. All rights reserved
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65
in solving problems in geometry (r=0.347, p<0.05) and when
taken as a whole (r=0.407, p<0.05) the competence of the
students and their grade in English reveal a highly significant
relationship. This implies that the higher the grade of the
students in English, the higher is their mathematical
competence.
Table 14. Correlation matrix on the relationship
between mathematical concept competence and grade
in English
VARIABLE
MATHEMATICA
L COMPETENCE
GRADE IN
ENGLISH
r
r prob
R
r
prob
.
MATHEMA
TICAL
COMPETEN
CE
1.0
0.000
0.344**
0.00
0
GRADE IN
ENGLISH
0.344**
0.000
1.0
0.00
0
** Highly significant
Table 14a. Correlation matrix on the relationship
between mathematical skill competence and grade in
English
VARIABLE
MATHEMATICAL
COMPETENCE
GRADE IN
ENGLISH
r
r prob
r
r
prob.
MATHEMATICAL
COMPETENCE
1.0
0.000
0.347**
0.000
GRADE IN
ENGLISH
0.347**
0.000
1.0
0.000
** Highly significant
Table 14b. Correlation matrix on the relationship
between mathematical competence (taken as a whole)
and grade in English
VARIABLE
MATHEMATICAL
COMPETENCE
GRADE IN
ENGLISH
r
r prob
r
r
prob.
MATHEMATICAL
COMPETENCE
1.0
0.000
0.407**
0.000
GRADE IN
ENGLISH
0.407**
0.000
1.0
0.000
** Highly significant
Mathematical Competence and Learning Style
Tables 15 to 15b present the results of the analyses of the
relationship between mathematical competence of the
respondents and their learning style. When the mathematical
concept competence in terms of problem solving skill was
matched with the respondents learning style, the results of the
analysis using Pearson Product Moment Correlation revealed a
significant relationship between the two variables. The result
was consistent when the test was done when competence was
taken as a whole. This was the basis in rejecting the null
hypothesis stating absence of relationship between
mathematical competence and learning style of the high school
students.
The result implies that the higher that value assigned by the
students in the use of the combination of different learning
styles, the more competent they would be in geometry
concepts and skills.
Table 15. Correlation matrix on the relationship
between mathematical concept competence and
learning style
VARIABLE
MATHEMATICAL
COMPETENCE
LEARNING
STYLE
r
r prob
r
r
prob.
MATHEMATICAL
COMPETENCE
1.0
0.000
0.150*
0.029
LEARNING
STYLE
0.150*
0.029
1.0
0.000
* Significant at 5% level
Volume 5 No.2, February 2015 ISSN 2224-3577
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66
Table 15a. Correlation matrix on the relationship
between mathematical skill competence and learning
styles
VARIABLE
MATHEMATICAL
COMPETENCE
LEARNING
STYLE
r
r prob
r
r
prob.
MATHEMATICAL
COMPETENCE
1.0
0.000
0.143*
0.037
LEARNING
STYLE
0.143*
0.037
1.0
0.000
* Significant at 5% level
Table 15b. Correlation matrix on the relationship
between mathematical competence (taken as a whole)
and learning style
VARIABLE
MATHEMATICAL
COMPETENCE
LEARNING
STYLE
r
r prob
r
r
prob.
MATHEMATICAL
COMPETENCE
1.0
0.000
0.174*
0.011
LEARNING
STYLE
0.174*
0.011
1.0
0.000
* Significant at 5% level
Mathematical Competence and Class Size
The differences in the mathematical competence of the
student-respondents when they were classified according to
class size are shown in Table 16 to Table 16b. When the
relationship between mathematics concept competence and
class size was compared using F-test (F= 13.283, p<0.05), the
result indicates a significant difference in the mathematical
competence of the respondents. It was further revealed that
there was a significant difference in the problem solving skills
of the respondents (F= 6.334, p<0.05) when classified
according to class. The result was consistent when taken as a
whole (F= 14.606, p<0.05). This was the basis for rejecting the
null hypothesis which states that there is no significant
difference in the mathematical competence of the students
when classified according to class size. It was found in the
study that the mathematical competence of the students who
were in the small class size is significantly higher than those in
the average and big class sizes.
Table 16. ANOVA on the differences in
mathematical concept competence when respondents
are classified according to class size
CATEG
ORY
SV
Sum
of
Square
s
Df
Mean
squar
e
F
Sig
Class
Size
Betwe
en
Group
s
3634.2
3
2
1817.
12
13.283
**
0.0
00
Withi
n
group
s
28591.
33
20
9
136.8
0
Total
32225.
57
21
1
** Highly significant
Table 16a. ANOVA on the differences in
mathematical skills when the respondents are
classified according to class size
CATEGO
RY
SV
Sum
of
Square
s
Df
Mea
n
squa
re
F
Sig
Class Size
Betwe
en
Group
s
1879.6
7
2
939.
83
6.334
**
0.00
2
Withi
n
group
s
31012.
32
20
9
148.
38
Total
32891.
98
21
1
** Highly significant
Volume 5 No.2, February 2015 ISSN 2224-3577
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67
Table 16b. ANOVA on the differences in
mathematical competence (taken as a whole) when
the respondents are classified according class size.
CATEGOR
Y
SV
Sum of
Squares
Df
Mean
square
F
Sig
Class Size
Betwee
n
Groups
2863.20
2
1431.6
0
14.606*
*
0.00
0
Within
groups
20485.1
0
20
9
98.015
Total
23348.3
0
21
1
** Highly significant
Mathematical Competence and Perceived Classroom
Structure
Shown in Table 17 to 17b are the results of the analysis of the
mathematical competence of the respondents when classified
according to class structure. In all the tests done to determine
if there is a significant difference in the mathematical concept
skill and problem solving skill of the respondents classified
according to their perceived classroom structure, it was found
that there is no significant difference. The results simply
suggest that regardless of the perceived classroom structure,
mathematical competence of the students are the same in all
categories. This implies that mathematical competence of the
students in geometry is not affected by their perception as to
their classroom structure.
Table 17. ANOVA on the differences in
mathematical concept competence when the
respondents are classified according class structure.
CATEGO
RY
SV
Sum of
Square
s
Df
Mean
square
F
Sig
Class
Structure
Betwe
en
Group
s
623.43
2
311.7
1
2.062
ns
0.13
0
Within
groups
31602.
14
20
9
151.2
06
Total
32225.
57
21
1
ns - Not significant
Table 17a. ANOVA on the differences in
mathematical skill competence when the respondents
are classified according to class structure.
CATEGOR
Y
SV
Sum of
Squares
Df
Mean
squar
e
F
Sig
Class
Structure
Betwee
n
Groups
21.51
2
10.75
0.068
ns
0.93
4
Within
groups
32870.4
8
20
9
157.2
8
Total
32225.5
7
21
1
ns - Not significant
Table 17b. ANOVA on the differences in
mathematical competence when the respondents are
classified according to class structure.
CATEGO
RY
SV
Sum of
Square
s
Df
Mea
n
squar
e
F
Sig
Class
Structure
Betwe
en
Group
s
280.69
2
140.
34
1.27
2ns
0.28
3
Withi
n
groups
23067.
62
20
9
110.
37
Total
23348.
30
21
1
ns - Not significant
ACKNOWLEDGMENT
The researcher wishes to express her sincere gratitude and
appreciation to the following persons who have extended their
unconditional help toward the completion of this study.
First of all, to the Almighty God, for His infinite mercy,
guidance and bountiful blessings that made the researcher
overcome all the difficulties and problems in life.
Volume 5 No.2, February 2015 ISSN 2224-3577
International Journal of Science and Technology
©2015 IJST. All rights reserved
http://www.ejournalofsciences.org
68
Dr. Genoveva N. Labaniego, Campus Administrator, for the
great help extended and for approval of this study.
Dr. Victoria N. Garnace, Research Coordinator, for her quality
instructions, untiring assistance and constructive suggestions
which contributed to the improvement and success of this
study.
Dr. Eveleth C. Gamboa, Schools Division Superintendent,
Division of Capiz, for allowing her to conduct the study in
Mambusao District.
Mrs. Felvita L. Lipardo, Principal of Mambusao East National
High School, for her kindness, moral support and
encouragement to finish this study.
Prof. Milagros O. Potato, her thesis adviser, for her valuable
advice and continuous motivation.
Dr. Roman V. Belleza and Prof. Veronica E. Albaladejo,
Members of the Guidance Committee, for the sound advice
and support and Prof. Ma. Lourdes I. Ilarde, External Member,
for her kindness extended.
Dr. Guillermo L. Legada, Jr., Graduate School Coordinator for
the valuable suggestions and encouragement.
Prof. Nenita Flores, Dean of the College of Education for the
inspiration.
Grateful acknowledgments are likewise extended to Dr.
Grizelda L. Lava for the valuable inputs and for the great help
extended; and Prof. Genalyn L. Baranda for her precious time
in editing the manuscript.
To the principals and teachers of the three secondary schools
in Mambusao for the goodwill and for allowing the researcher
to administer the questionnaire in their schools and for the
valuable assistance extended.
To her parents, brother and sisters and Clyde for the love and
prayers, which gave her inspiration to push forward the
research endeavor.
Her classmates and friends, for the motivation which have
strengthened her determination to go on.
Her co-teachers who in one way or the other extended their
support and encouragement.
Grateful recognition is given to CapSU, Mambusao, Capiz for
granting her free tuition while pursuing her Master’s Degree.
Special acknowledgment is extended to her beloved husband
James, whose endless sacrifices, fervent prayers, financial and
moral support made the researcher strive to succeed in her
educational pursuit.
To all of you, thank you so much. You will always have a
special place in her heart.
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Recent research in cognitive psychology and artificial intelligence (collectively called cognitive science) has made impressive progress in revealing the varieties and intricacies of mathematical problem solving. However, the connections between studies of mathematical problem solving and the practice of teaching mathematics are not always clear. That is to be expected. Due to the very nature of scientific inquiry, studies of problem solving must focus on questions of limited scope with simplified hypotheses, if only to provide a filter with which to separate signal from noise. Also, cognitive scientists tend to focus on what is in the world of mathematical problem solving, which is essential. But mathematics educators have an equal charge to consider what ought to be and how it might be achieved. With this in mind, it is clear that research in cognitive science on mathematical problem solving can inform mathematics educators of the current state of affairs and can even suggest constructs that promise powerful ways of thinking about teaching problem solving, but it cannot dictate mathematics curricula or methods of teaching. To improve mathematics teaching and learning, mathematics educators must consider the students' passage through an entire curriculum. Thus, those involved in curriculum development will of necessity always be traveling untrodden terrain, always working beyond established databases. My purpose in this paper is to discuss an attempt at developing mathematics curricula that draws from research on problem solving and mathematical cognition, but goes beyond it in addressing issues unique to mathematics education—primary among them, mathematics education's concern with the learner throughout a mathematical program. By itself, a collection of models of problem solving on relatively restricted problem sets is insufficient as a basis for designing a mathematics curriculum. A curriculum developer must augment it with some sort of model of a learner passing through the curriculum. As I have noted, cognitive science has developed a wealth of constructs that have powerful implications for mathematics curriculum development. I wish to make clear from the start, however, that I am writing from the perspective of a practicing mathematics educator. The examples that will be given come largely from my experience as a teacher of mathematics, albeit one who is fairly well informed of the methods and constructs of cognitive science. Perhaps another caveat is necessary. Ideas are significant only within the context of an overriding universe of discourse. The significance for mathematics education of much of recent research on mathematical problem solving can be appreciated only when we consider the aims of mathematics education. If one thinks of learning mathematics as tantamount to memorizing mathematical "facts," or an accretionary building of elaborate sets of behaviors, then much of what follows will be irrelevant. If, however, one accepts that the aim of mathematics education is to promote mathematical thinking, then this paper will be of interest. A predominant theme of this paper, as one would guess from the title, is that learning 1 The author wishes to express his gratitude to the Department of Mathematical Sciences, San Diego State University, for its support in preparing the materials reported in this paper.
Students Learning Styles and Academic Achievement in Math
  • C Bacalangco
BACALANGCO, C. 2011. Students Learning Styles and Academic Achievement in Math. Unpublished Master's Thesis, University of the Philippines.
Mastery of Mathematics Concepts by the High School Freshmen of PSPC Mambusao
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ALTABANO, M. B. 2002. Mastery of Mathematics Concepts by the High School Freshmen of PSPC Mambusao. Unpublished Master's Thesis, PSPC, Mambusao, Capiz.
Level of Mastery of the Mathematics Computation and Solving Problem Skills of the Grade V Pupils
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UMANI, E. G. 2003. Level of Mastery of the Mathematics Computation and Solving Problem Skills of the Grade V Pupils. Unpublished Master's Thesis, University of Iloilo.
Teaching and Problem Solving in Junior and Senior High Schools
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KRUNICK, S. & RUDNICK, J. 1996. "Teaching and Problem Solving in Junior and Senior High Schools". Retrieved September 16, 2011 from www.mathgoodies.com/articles/problemsolving.html
Doing Mathematics in Problem Solving
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  • Vault
M. VERO DE VAULT, "Doing Mathematics in Problem Solving". (The Arithmetic Teacher, II, No. 3 1987)
Geometry Textbooks for Third Year
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DE LEON, et al. 2002. Geometry Textbooks for Third Year. JTW Corporation, Quezon City.