BIBLIOGRAPHY
WUZHEN SHU, April 2006. Teaching Mathematics Among Selected Public
Schools In La Trinidad, Benguet, Philippines and Huai Hua City, Hunan, China: A
Comparative Study. Benguet State University, La Trinidad, Benguet.
Adviser: Percyveranda A. Lubrica, Ph.D.
ABSTRACT
This study aimed to determine the socio-economic profile of Mathematics
teachers and grade VI pupils in the selected schools; to evaluate the extent of use of
teaching approaches and methods in Mathematics; to determine the extent of providing
activities to pupils in learning Mathematics; to identify the area of need of teachers to
improve their teaching Mathematics; to determine the performance of students in
Mathematics; to identify the specific area in Mathematics that the grade VI pupils are
competent in; and to determine the relationship between the socio-economic profile of
teachers and the extent of use of methods in teaching mathematics, teaching approach,
extent of provision of activities in learning Mathematics, and degree of needs for
improving their teaching.
Findings show that the great majority of Mathematics teachers range in age from
21 to 40 years in the four schools. The teachers are dominantly females. Almost all of
them are bachelor’s degree holders, and have been teaching for six to ten years. Their
salary range from PhP 8,000 to above PhP 18,000.

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The grade six pupils range in age from 11 to 12 years. Females dominate the
males in the four schools . Most of their parents have blue or white collar job.

The teaching approaches frequently used are discovery, conceptual, process and
unified. The process and conceptual approach is most frequently at BSU, an the unified
approach is frequently used in the other three schools.
Varied teaching methods are used by teachers in teaching Mathematics. Most
frequently used at BSU Elementary Laboratory School are activity method, inductive
method and problem-solving method; at La Trinidad Central School are discussion,
investigatory, integrated, problem-solving, and modular; at Ying Feng Road Elementary
School are reporting, activity and investigatory; and at Xing Guang Elementary
Laboratory School are those methods which are frequently of use in teaching
Mathematics.

The teachers provide varied activities during the teaching learning process in
Mathematics. However, Ying Feng Road Elementary School (YFRES) showed a very
frequent provision of the activities in teaching Mathematics. The leading activity is
practice and drill, followed by giving quizzes. The use of traditional form of evaluation
through a pencil-and-paper test is very common to all teachers.

The Mathematics teachers of BSU Elementary Laboratory School feel that to
improve their teaching in Mathematics, they should attend in-service trainings and
seminars, make modules, conduct action research, update current strategies, improvise
teaching aids, use modern technology and use other textbooks. Those in La Trinidad
Central School feel that they have fewer needs to improve their teaching in Mathematics.
Those in Yin Feng Road Elementary School feel that they need to attend in-service
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training and seminars, update of current strategies and improvise teaching aids. Those in
Xing Guang Elementary Laboratory School feel the need to improve teaching aids and
update current strategies in teaching.

The pupils in Ying Feng Road Elementary School have the highest performance
in Mathematics, followed by those at Xing Guang Elementary Laboratory School, La
Trinidad Central School and BSU Elementary Laboratory School. La Trinidad Central
School have more low performing pupils. Conversely, BSU Elementary Laboratory
School, Ying Feng Road Elementary School and Xing Guang Elementary Laboratory
School have high performing group of pupils. The pupils are competent in addition of
whole numbers and decimal numbers, and least competent in division of whole number.
In using the same mathematical operation in fractions, all the pupils are most proficient in
multiplication and least proficient for division. In using the fundamental operations in
word problems, the pupils are more competent in solving problems using subtraction and
division than in using addition and multiplication. The pupils are proficient in
transforming a number to percent and have shown competence in all the other areas but
have not surpassed the acceptable criterion.
Age significantly and negatively relates to the use of methods, teaching approach
and provision of activities; and gender significantly and negatively relates to the use of
methods and approaches, provision of activities and areas needed to improve teaching of
teachers. Years in service significantly and negatively relates to frequency of use of
teaching methods and approaches in LTCS and BSU, activities in YFRES and XGELS;
and degree of need in improving teaching Mathematics in BSU and XG Elementary
Laboratory School.
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Educational qualification significantly affects the teachers’ extent of use of
methods and approach in teaching and provision of activities. Salary significantly relates
to use of methods and approaches in some schools except for BSU.

Based on the results, the following conclusions are drawn: All the teaching
approaches are used in teaching Mathematics but the schools significantly vary in the
extent of use of the teaching approaches used in teaching Mathematics. Most applicable
among teachers is the use of unified approach where they use the student vocabulary in
the presentation of a topic in Mathematics. Relevant and concrete examples are needed in
the teaching of Mathematics.

The teachers do not significantly vary in the extent of use of the teaching methods
in Mathematics. Differences in the extent of use of the method is likewise observed
among the four schools.

The teachers are proficient in the use of the methods except for reporting. This
shows that teachers promote the collaborative or cooperative learning in Mathematics.

Enhancement activities are provided but not frequently. Mastery learning is not
much an emphasized in the teaching of Mathematics in the two schools in Mathematics
as manifested by the low extent of providing the activity.

There is a need to increase more time for teachers to spend in classroom teaching
for Mathematics. Textbooks are scarce and teachers lack research skills in all schools.

There is a need for pupils in all the schools to enhance their competencies using
the four fundamental operations in Mathematics and other areas of learning. Age, gender,
highest educational attainment and salary received by teachers are significantly and
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negatively related to the extent of use of teaching methods and approaches and provision
of activities to pupils in learning Mathematics.

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TABLE OF CONTENTS

Page
Bibliography..………………………………………………………………. i
Abstract ……………………………………………………………………..
i
Table of Contents …………………………………………………………...
vi
INTRODUCTION………………………………………………………….. 1
Background of the Study ………………………………………………
1
Statement of the Problem ……………………………………………...
2
Objectives of the Study ………………………………………………..
3
Importance of the Study ……………………………………………….
4
Scope and Delimitation of the Study ………………………………….
4
REVIEW OF RELATED LITERATURE ………………………………….
6
Professional Profiles of Teachers ……………………………………...
6
Profile of Pupils ……………………………………………………….
7
Teaching Approaches / Methods ………………………………………
7
Learning Activities in Mathematic…………………………………….
14
Level of Competencies in Different Areas in Math …………………..
16
Relationship Between Variables……………………………………….
22
Others Related Studies ………………………………………………...
23
Conceptual Framework………………………………………………...
27
Definition of Terms ……………………………………………………
30
Hypotheses of the Study ………………………………………………
34
vi

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METHODOLOGY ………………………………………………………….
36
Locale of the Study ……………………………………………………
36
Respondents of the Study ……………………………………………...
39
Research Design ……………………………………………………….
41
Instrumentation ………………………………………………………..
41
Data Gathering ………………………………………………………...
42
Statistical Treatment of Data …………………………………………..
42
RESULTS AND DISCUSSION ……………………………………………
43
Socio-economic Profile of Mathematics Teachers…………….………
43
Socio-economic Profile of Grade VI pupils ………………………...…
51
Teaching Approach Used By Teachers in

Teaching Mathematics.…………………………………………….
56
Teaching Methods Employed by Teachers in

Teaching Mathematics./……………………………………….......
58
Extent of Provision of Activities in

Teaching Mathematics ………………………………….................
62
Perceived Degree of Needs in Specific Areas in

Teaching Mathematics…..................................................................
66
Performance of Grade VI Pupils in Mathematics………………….......
68
Competencies of Grade Six Pupils in Varied

Areas in Mathematics ………………………………………….…
70
Competencies of Grade VI pupils in other Areas …………………….
75
Relationship between Socio-economic Profile of

Teachers and Selected Variables …………………………………
76


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SUMMARY, CONCLUSIONS AND RECOMMENDTIONS……………..
80
Summary ………………………………………………………………
80
Conclusion …………………………………………………………….
83
Commendations ……………………………………………………….
84
LITERATURE CITED ………………………………………………..……
86
APPENDICES …………………………………………………………...…
91
Approval Letter.......……………………………………………………
91
Teacher’s Questionnaire……………………………………………….
93
Pupil’s Questionnaire………………………………………………….
99
BIOGRAPHICAL SKETCH……………………………………………......
106

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INTRODUCTION
Background of the Study
Knowledge not land or capital is the most valuable human resource in the
emerging information age. Thus, schools around the world of whatever nature are
pushing forward towards excellence, a means for a country to achieve industrialization,
which is enjoyed by several western countries and a fraction of Asian nations.
Since Mathematics is a part of the school curriculum and one of the pre-requisites
in fulfilling the requirements of every educational system, it must be the focal point of
every government in the world. Mathematics is the basis of all subjects. There are no
natural sciences or social sciences to speak of without Mathematics application.
Unfortunately a lot of poor scenarios have been observed by some educators and
researchers. Students face big problems and difficulties in dealing with the Mathematics.
A a result, they develop a phobia or dyscalculia of mathematical or arithmetic concept
and experience difficulty in performing Mathematics calculations. In many instances, a
child or pupil would carry on this kind of disability for the rest of his/her life and would
never overcome it.
In China, many elementary schools have pupils experiencing difficulties in
studying Mathematics. Pupils easily forget and sometimes get confused in computing or
using different kinds of formulas. Hence, most of the pupils spend a great deal of time
studying the said subject.
The educational system is also one of the problems of China. Although progress is
on its way, the system creates some loopholes. For instance, teachers are not given the
leeway to make the subject matter more interesting because of the regulation that the
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teaching contents of all schools should be followed with the same format, same teaching
plans, and teaching procedures in one specific subject matter. Secondly, books are
required to be covered from first to last page. Thus, this study.
Statement of the Problem

This study particularly compared the teaching of Mathematics among elementary
grade VI Pupils in selected schools in the Philippines and that of China. Specifically, the
researcher endeavored to find the answers to the following questions:
1. What is the socio-economic profile of Mathematics teachers and grade
VI pupils in the selected schools?
2. What is the extent of use of teaching approaches and methods in
Mathematics?
3. What is the extent of providing activities to pupils in learning
Mathematics?
4. Which area in Mathematics should teachers need to improve?
5. What is the performance of students in Mathematics?
6. In what areas are the grade VI pupils competent in Mathematics?
7. What is the relationship between the socio-economic profile of teachers and
a. the extent of use of methods in teaching mathematics,
b. Teaching approach,
c. Extent of provision of activities in learning Mathematics, and
d. Needs for improving their teaching?

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Objectives of the Study
The main purpose was to compare the status of teaching Mathematics in selected
schools in the Philippines and China. The specific objectives of the study are the
following:

1. To determine the socio-economic profile of Mathematics teachers and
grade VI pupils in the selected schools.
2. To evaluate the extent of use of teaching approaches and methods in
Mathematics.
3. To determine the extent of providing activities to pupils in learning
Mathematics.
4. To identify the areas that need improvement in the teaching of
Mathematics.
5. To determine the performance of students in Mathematics.
6. To identify the specific areas in Mathematics that the grade VI pupils are
competent in their learning.
7. To determine the relationship between the socio-economic profile of
teachers and
a. the extent of use of methods in teaching mathematics,
b. Teaching approach,
c. Extent of provision of activities in learning Mathematics,
d. degree of needs for improving their teaching.

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Importance of the Study

The product of this study will benefit first and foremost the four selected schools.
It gives ideas of how teachers can integrate the changes and other technical aspects of
education necessary in the improvement of the educational curriculum and system. It
gives them pointers on how to facilitate learning in Mathematics and make pupils
competitive. School administrators can be guided as they continue of improve the quality
of education as they see the feedback in regard to academic performance of pupils and to
competencies of their teachers. Teachers may get some ideas and other concepts on how
they can improve themselves and their craft, and on how to be effective inside and
outside the school and classroom. Guidance counselors may also gain an advantage in
this study. They can be enlightened of the problem regarding study habits and
Mathematics phobias and other related disability. Eventually, they come up with some
programs and services that could help students in overcoming such problems.
Most importantly , this study would help the researcher improve her teaching in
all aspects of teaching Mathematics. She can gain an insight into when and how to use
new and effective educational technology. Finally, she can gain knowledge of how to
adjust to the diverse personalities of students and thus to modify her own personal
attitude and personality so that she can generate a general interest of the pupils in
learning Mathematics.
Scope and Delimitation of the Study

This study centers on the identification and comparison of teacher-related, pupil-
related, and learning-related factors that have a high significance to or influence on the
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mathematical performance of the pupils of selected public schools in Huai Hua City and
La Trinidad, Benguet. Included in the study are only grade six pupils who are currently
enrolled and their teachers.

Pupil-related factors include pupils’ personal profile according to age, sex, and
parents’ occupation, including perspective and attitude of pupils toward Mathematics.
Learning-related factors focus on the mental ability level of pupils sampled in the four
phases of learning, namely, acquisition, mastery, generalization, and maintenance.
Classroom management related to timetable or distribution of time spent in learning
concepts and theories and to activities given by the teacher is considered. Teacher-related
factors zero in on how teachers use materials in teaching Mathematics effectively,
approaches and techniques used in processing problem solving and other arithmetic
operations; and on the activities that the pupils are doing during Mathematics classes in
order to understand the concepts and theories and their application. The most important
thing in the educational system, the Mathematics curriculum is also included.


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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REVIEW OF LITERATURE
Socio-economic Profile of Respondents
Professional Profile of Teachers
It is an accepted fact that the quality of education depends to a large extent on the
quality of teachers. The professional profile of the teacher is an indicator of the standard
of education in a country.
The quality of education is said to be dependent upon the quality of teachers,
supervisors and administrators that the system employs (Guerrero, 1989). One of the
measures of the quality of teachers and administrators is their academic and their
professional training. Their academic and professional training is reflected on their
educational attainment, field of specialization, number of years of teaching and
participation to seminars and workshops relative to the improvement of instruction
(Lubrica,1996).
The question on the professional profile of teachers has been the subject of many
investigations and discussions for the past many years. Researchers looked into the
different aspects of educational program with the aim in view of bringing out what needs
to be done to improve the system. The following are some pertinent studies that are
related to the present investigation (Lubrica,1996)
Toledo (1982) conducted a research among Mathematics teachers of Benguet
State University and found that Mathematics has not advanced professionally. The same
finding was gathered by Ocampo (1987) with the implementation of the Performance

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Appraisal System for teachers. Ocampo also found that secondary teachers pursued their
professional advancement by earning some M.S units.
Profile of Pupils
According to Madali (1979), several factors have been identified to play
significant roles in the achievement of students in Mathematics. Among these factors are
heredity, environment and past achievements. This is also seconded by Sorenson (1979)
who revealed that sex had something to do with attitude toward certain subjects.
However, Santos (1980) made a comparative study of the mathematical abilities of boys
and girls to find out whether sex is a determining factor in the differences in
mathematical abilities of boys and girls; whether the intelligence of an individual affects
his or her ability to understand the mathematical principles; and to discover other factors
that directly cause or affect the differences in mathematical abilities. It was found that sex
does not affect the differences in mathematical abilities; that the intelligence of an
individual does not affect his ability to understand the mathematical principles; and that
some of the other factors that directly cause or affect the differences in mathematical
abilities were lack of textbooks, lack of extensive drill work, absence of remedial
teaching, lack of interest on the part of the teacher and inability of the students to
comprehend and understand the different problems in Mathematics.
Teaching Approaches / Methods
Salandanan, Santos, and Diaz (1988) mentioned two problems that a mathematics
teacher has to deal with. First is to provide his mathematical experiences suitable to the
state of development of their existing concept and to fit his method of presentation to the
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pupil’s concrete or formal level of thinking. The second is to develop the pupil’s ability
to analyze new material himself so that he can synthesize his own concepts in ways most
meaningful for him independently. They further added that to solve these problems in
ways that will meet the needs of the learners, the teacher needs to know and to use
different teaching strategies.

Furthermore, the teacher needs to do the following to execute lesson in
Mathematics successfully: manage his classroom efficiently and with minimum
disruptions; elicit active participation from his student; recognize and solve students’
learning difficulties (inability to read at grade level, physical handicaps, emotional
problems, low skill level, etc.); communicate Mathematical concepts precisely in the
proper inductive sequence, at a level consistent with the children’s abilities; adapt the
pace and direction of instruction to the group he is teaching; provide an atmosphere
where mistakes are accepted as a part of learning and where students feel free to ask
question when they do not understand a concept; motivate students to want to learn
mathematics; develop in students positive attitudes toward mathematics; and select and
use methods appropriate for given behavioral objectives and concepts.
Lardizabal et al. (1991) stated that practices have gradually replaced undesirable
features of so-called lesson-hearing procedures. This is due in part to the gradual
acceptance of the newer philosophy of education, i.e., education is not merely a process
of learning facts and storing knowledge, but it is conceded with the social, emotional, and
mental development of the individual.
Including the ability to meet social needs they further added that before taking up
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specific techniques for organizing classroom activities, it is best to consider first the
social needs of pupils and students in planning classroom experiences which can be
expressed in terms of abilities required to satisfy them.
Moreover, they mentioned that not every class can provide activities that will
contribute to the realization of all the preceding outcomes but many activities can
contribute to the realization if they are handled in the right way. The result will be a
greater range of pupil participation in learning experiences. With this perspective, the
teacher should understand the need for different methods of organizing classroom
activities and the need to make a wise choice of the types of activities that should be used
under varying conditions. They mentioned the following approaches and techniques
which can be used in teaching: the integrative technique, the discovery approach, the
process approach, the conceptual approach, mastery learning, programmed instruction
team teaching, simulation, module, etc.
In China, the teacher fulfills his teaching tasks using styles/techniques or
strategies which includes teacher-teaching methods and student-learning methods.
Teaching and learning is a bilateral activity so in order for the teacher to fulfill his
teaching tasks, there should be concrete methods and measures to attain the objectives of
teaching-learning process.
Mathematics teacher should have a broad systematic understanding of the main
teaching methods so that he can teach according to the concrete teaching content.
Generally, teaching methods in Mathematics are classified as the traditional and
the modern. Traditional teaching method includes explanatory method where the teachers
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teach through systematic narration. The teachers reading and oral communication to
transmit knowledge characterize it. This method is guided by the scientific, systematic,
enlightenment, artistic, and emotion principles.
Lecture method is a traditional method. The teacher is tasked to ask questions to
the students and at the same time he expects some feedbacks from the students. It is
through this method that the reasoning and expression of ideas of the students are
developed. For this method to be effective, the teacher must carefully decide on what
questions to ask, from easy to difficult. The questions should be enlightening and on the
level of the students. Lastly, he should be able to summarize the lesson.
The show or demonstration method falls under traditional method too. Here,
visual materials are shown to students to explain the lesson. Discussion, on the other
hand, encourages the students to discuss among themselves and ask question for the
teacher to answer. Meanwhile, the Reformed Chinese Educational Method or the modern
method includes several teaching methods in Mathematics such as self-study, unit
method, drills, and exercises and other methods used by foreign countries such as the
programmed instruction, example, and discovery method.
Caet (1979) attempted to appraise the instruction of elementary Mathematics in
the Division of Pagaduan City during SY 1978-1979. The study dealt specifically on such
areas as the attitudes of teachers towards professional growth; the extent of making use of
instructional materials; methods and technique of teaching and evaluative instrument to
make instructions effective. The respondents of the study were 232 teachers of the
Division of Pagaduan City who taught elementary Mathematics. The findings are
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summarized as follows:

1. The majority of the teachers teaching elementary Mathematics were
academically prepared and educationally qualified to teach the subject.

2. All teachers were often and always interested to teach the subject; they had the
right attitude towards professional growth, reflecting this attitude by attending in-service
training, reading professional books and magazines, attending summer and Saturday
classes and some even went to the extent of taking educational leave of absence.

3. More than three-fourths of the teachers always used prescribed textbooks,
supplementary materials, teaching guides, manuals, workbooks and magazines to make
their Mathematics instruction effective.

4. The majority of the teachers such as self activity, discovery, project method and
others.

5. Most of the teachers always used mastery learning and discussion techniques.

6. Almost all the Mathematics teachers evaluated the outcomes support of their
objectives using the criterion-referenced measures.

7. The Mathematics teachers were given enough supervisory support for
improvement from the Principals and the Division Mathematics supervisor through
regular visits and observations.
Salamonis (1970) suggested three central factors that would contribute to
successful teaching and would likewise affect the effective implementation of the
curriculum. These factors are as follows: teacher’s knowledge of the subject matter,
teacher’s knowledge of the learning theory, and teacher’s knowledge of techniques and
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strategies.

It was also explained that the teacher should have a sound background in the
subject matter and related areas, and a willingness to learn more. Along with the
knowledge of the learning theory, the teacher should know who are being taught and
should be familiar with all the aspects of learning. Such aspects must be recognized when
they arise in the classroom and must be known how to utilize in the service of education.
In line with the knowledge-teaching techniques and strategies, the teacher must be able to
analyze what is required in the situations and to select the most suitable techniques and
strategies.

In order to determine the effectiveness of a teacher, an evaluation of teacher’s
performance is a necessity. The evaluation of teaching, as viewed by Rivera and
Sambrano (1982), aims to promote the growth and development of the teacher by means
of an analysis of the criteria of good teaching. It should help the teachers discover and
understand their strengths and weaknesses so that they can utilize their assets to a great
degree and correct their defects. More specifically, the evaluation of teaching aims to find
out the effectiveness of activities and experiences designed to help teachers formulate a
sound philosophy of education which relates to the roles of the teacher, the school and
other educational agencies in modern society and to understand the status, ethics and
organization
of
the
teaching
profession.


Within the area of teaching strategies, Alcorn (1964) said that the lecture method
can be functional only when it is correctly used, such as in explaining the problem,
illustrating or demonstrating a process or a point, telling a story, or introducing a new
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lesson. Other than that, the teacher should stimulate creative thinking among his
students. The teacher should foster students’ participation.

One does not learn by wholly listening. There is therefore a need for other
teaching techniques to illicit the active participation.

The task toward the effective implementation of the curriculum is through
effective teaching. Alcorn (1964) presented five strategies to effective teaching, as
follows: individual teacher effort; in-service education; planned service of supervision;
experimentation and research; and evaluation and accountability system.
These strategies, if properly installed, implemented and strengthened, will make a
good school in general and effective teaching in particular. The implementation depends
upon the competence of the school administrators and supervisors as well as the
dedication and cooperation of the teaching staff and other school personnel.
Tating (1993) said that the teacher occupies a most important place in modern
society. He is linked between industrial society and the educational system. He must
possess a thorough knowledge of his field and must have some experience in the world
for which he is preparing his students.






Borich (1992), as cited by Elliot et al. (2000), characterized effective teachers as
possessing five key behaviors: lesson clarity, instructional variety, task orientation, and
engagement in the learning process, and student success. Lesson clarity refers to how
clear the teacher makes his presentation to class. Instructional variety means that the
teacher’s teaching techniques remain flexible during the presentation of the lesson. Task
orientation and engagement in the learning process refer to the time spent in learning
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academic subjects. Berliner (1988), as cited by Elliot et al. (2000), stated that when
students’ academic learning time is increased, their achievement improves. Success rate
means the rate at which students understand and correctly complete their work.

Theories have been developed that include integrated approach to teaching and
learning, and commitment and understanding from the whole community (Drake, 1998;
Fleming, 1993; Stephens, 1991). Levak et al. (1993) claimed that flexibility which
allows teachers to utilize alternative approaches across disciplines, instead of forcing
connections where connections do not exist, seems to engender success.

Klein and Doty (1994) promoted models and structures related to teaching
approaches and this is related to interdisciplinary learning, which is proliferating .
These are based on active learning strategies that promote higher- order-critical-thinking
skills (defined as analysis, synthesis, application and evaluation). These methods include
collaborative / cooperative, learning discovery and problem- based learning.
Learning Activities in Mathematics
Serion (1980) pointed out that the pupils dislike Mathematics and its related
fields, and this attitude must have been due to the influence of frustrated elders.
Aside from the effect of the school and the parents, attitudes also develop from
suggestions. Hence, it is necessary that the pupils’ positive attitude toward Mathematics
should be developed early. It is because the most difficult attitudes to change are those
rooted in fears or highly personal emotional needs. With fears and prejudices, proper
attitudes towards Mathematics are not developed in children (Alken, 1970).

Mazon (1982) made a study on the difficulties of sixth grade pupils in problem
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solving in arithmetic through diagnostic teaching and found the following outstanding
causes of errors in the sixth grade: the pupils failed to understand the problem in whole or
in part; they were poor in silent reading; they lacked the knowledge of terms; they lacked
the necessary experience to reproduce the situation in the problem; they lacked the ability
to know the meaning and relations of some of the different quantities used in functional
arithmetic; they lacked the ability to identify the proper processes of operations; and they
lacked the ability to perform accurately the fundamental processes.

Furthermore, Dantis (1982), discovered the important factors conducive to the
teaching of Mathematics that school administrators may use in the improvement of
instruction. Respondents were 214 fourth year high school students of three private
sectarian schools in San Jose, Occidental Mindoro. It was recommended that
Mathematics teachers should do away with the common attitude that girls are not as
capable as boys in Mathematics and, therefore, no discrimination should be made
between them.









Piloten (1983) made a study on the difficulties and attitudes of fourth year high
school students regarding Mathematics and found that students had difficulty in
Arithmetic, Algebra, Geometry and Trigonometry because of the following reasons: the
students do not have enough textbooks; the students can not understand the teachers’
explanation; the teachers cover the lesson too fast; the students are not given the
opportunity to ask questions; and the teachers lack explanations.
Nevertheless, if the students are actively engaged in and enjoying classroom
activities it makes little differences if the teacher is lecturing, using discovery technique,
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or using small-group activities for independent study. Brophy and Good (1978) claimed
that what is important in maintaining classroom atmosphere is how the teacher manages
the classroom, especially how he keeps the class actively attentive to lessons and be
involved
in
productive
activities.


According to Jenson (1998), the best way to grow a better brain is through
challenging problem solving. This creates new dendritic connections that allow even
more connections. This is a result of spawning a dynamic philosophy referred to as
“constructivism”, which refers to students in constructing new knowledge. Barab and
Landa (1997) supported this by indicating that students must focus on problems worth
solving to increase their motivation and learning capacity. Austin, Hirstein and Walen
(1997) added that this results to greater intellectual curiosity, improved attitude towards
schooling, enhanced problem-solving skills, and higher achievement in college. One of
the best ways to promote problem solving is through an enriched environment that makes
connections among several disciplines (Wolf and Brandt, 1998).
Level of Competencies in Different
Areas in Mathematics

Carino (1992) cited statistics which showed that education in many places of the
world is in crisis. The said statistics revealed that millions of children and youth satisfy
the attendance requirement but do not acquire the essential knowledge and skills for
functional daily living.

“The foundation of every state is the education of its youth.” This is according to
former Philippine DepEd secretary Florencio Abad. who added that the failure of
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education represents the failure of society. Furthermore, he reported that there is a crisis
in Philippine education and said that the 2004 High School Readiness Test, only 0.64
percent scored 75 percent or better, that is, 8,000 students out of 1.2 million examinees.
In the latest Trends in International Mathematics and Science Study, out of 38 countries,
Philippines placed third to the last, that is 36th place in a field of 38¹.
Dyscalculia is one of the reasons why in the recent statistics found recently,
Philippines ranked 3rd from the bottom among 54 countries in the international
mathematics for 13-year-old children. The country ranked lowest in the Asian region for
the same test. Moreover, high school students answered only 50 percent of the national
achievement test. As a manifestation, the results of the Third International Mathematics
and Science Study-Report disclosed the dismal performance of students in the two
subjects as compared to their international counterpart. This study was released last
March 9, 2001².

Mapandol (1980) found that children are most deficient in solving problems
involving whole numbers and rational numbers, percentages and measurements and
applying principles, rules and generalizations in solving problems about perimeter and
area, and on making quantitative comparisons.

In the study made by Bawang (1995), she found cited Vergara’s study showing
that students were very weak in Mathematical computation skills, have difficulty in
interpretation are unable to understand the problems, and fail to represent the given facts
or conditions and unknown quantities and interpret verbal statements to mathematical
forms.
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These problems of students regarding numbers stem from memory deficit.
Memorization is necessary since mathematics requires a set of procedures that must be
followed in a sequential manner. Those experiencing difficulty remembering things will
have difficulty remembering order of operations to be followed or the specific sequence
of steps to be taken to solve mathematics problem. Also, it is observed that negative
experiences in the past are often due to lack of confidence and that a positive attitude
leads to a better performance.

The Philippines is trying to go beyond the horizon. One hundred Filipino
elementary pupils compete in the Philippine Elementary Mathematics International
Contest and Asian Inter-cities Teenagers Math Olympiad at Bohol Tropics Hotel,
Tagbilaran City, Bohol. These pupils underwent rigid training by the mathematics
trainers Guild of the Philippines. This was successfully done because of the donation
given by Jose Miguel Arroyo, husband of the President, which cost P1 million to stage
the contest and in cooperation with the Department of Science and Technology Education
Institute and the Department of Education

What subject matter should be taught and how long should a teacher teach it
affects the teaching-learning situation. The daily period in Mathematics in Grades I, II,
and III includes a study of the four fundamental operations, fractions, metric and local
measures, the use of money and their application to practical problems based on activities
of real life. In grades IV, V, and VI, the child is expected to conceptualize the meaning of
ratio and proportion, angles, plans, and spatial figures of scales, maps, and graphs.
Besides further development of the basic Mathematical skills, the child is expected to
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solve problems related to business and industrial activities in the community.
Vergara further added that the daily periods of 40-minutes in grades I to IV shall
be scheduled in the daily class program as one whole block. For example, 40 minutes, or
this may be divided into two periods, in grades I and II, a 20-minute period in the
morning, and a 20-minute period in the afternoon.
There are several problems encountered in teaching Mathematics that can be
attributed to different reasons. Computational weakness is one. Many students, despite a
good understanding of mathematical concepts, are inconsistent at computing. They make
errors because they misread signs or carry numbers incorrectly, or may not write
numerals clearly enough or in the correct column. These students often struggle specially
in primary school, where basic computation and “right answers” are stressed. Often they
end up in remedial classes, even though they might have a high potential for higher –level
Mathematical thinking.
Another one is the difficulty in transferring knowledge. One fairly common
difficulty experienced by people with Mathematical problems is the inability to easily
connect the abstract or conceptual aspects of Mathematics with reality. Understanding
what symbols represent in the physical world is important to how well and how easily a
child will remember a concept. The students, on the other hand, should develop making
connections. Some students have difficulty making meaningful connections within and
across mathematical experiences
For some students, a mathematical disability is driven by problems with language.
These children may also experience difficulty with reading, writing, and speaking, In
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mathematics, however, their language problem is confounded by the inherently difficult
terminology, some of which they hear nowhere outside of the mathematics classroom.
These students have difficulty understanding written or verbal directions or explanations,
and find word problems especially difficult to translate.
A far less common problem-and probably the most severe-is the inability to
effectively visualize mathematics concepts. Students who have this problem may be
unable to judge relative size among three dissimilar objects. This disorder has obvious
disadvantages, as it requires that a student rely almost entirely on rote memorization of
verbal or written descriptions of mathematics concepts that most people take for granted.
Some mathematical problems also require students to combine higher-order cognition
with perceptual skills; for instance, to determine what shape will result when a complex
3-D figure is rotated.
Moreover, Dela Cruz (1992) noted the following as causes of difficulties in
problem solving: physical and mental defects, reading and arithmetic vocabulary
interests, lack of variety in problem solving experience, lack of method of attacking the
problems, and lack of skills in fundamentals
Barsaga (1995), after identifying poverty as one of the major factors affecting the
teaching-learning process, professed that this is a closely related variable and that one
who is poor, for example, is likely to have parents who are poorly educated and illiterate
and with little interest in schooling. Since the family is poor, he is most likely to be relied
upon to help his parents do household chores and to engage in child labor in order to
augment the family’s income. He therefore absents from class more frequently than the
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other pupils who are better-off. Because of his irregular attendance in class, he is likely to
lag behind in academic achievement.
Another factor which might be attributed to performance of pupils in learning
Mathematics is teacher competence. A study made by Sta. Maria (1972) discovered that
elementary teachers were deficient in the following areas which are ranked according to
difficulty: graphing, mapping, scaling; numbers and numerals; addition and subtraction;
geometry; multiplication and division; ratio, proportion and percentage; and, set and set
operations.
In a separate survey on teachers competence in Iligan City by Sister Coronel
(1981), the president of the Mathematical Society of the Philippines, it was discovered
that the teacher-respondents perceived that the pre-service Mathematics teaching that
they acquired was inadequate for them to teach the subject with competence. They
indicated that insufficient preparation is due to inadequate Mathematics courses in the
pre-service training. Most schools offer only six units of Mathematics to prospective
elementary Mathematics teachers.
The results confirmed what has been believed all along in teaching that the
teacher is the key factor in student achievement. The study also revealed that those pupils
who behave well, showed positive values and were delegated with responsibilities,
achieved higher scores than those otherwise.
The study found that high-achieving schools were those whose teachers were
competent, had quality boardwork, could communicate and interact well with their
pupils, used many instructional aids, and were able to maintain a classroom atmosphere
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conducive to learning. Finally, the role of the library in complementing
classroomlearning cannot be overemphasized.
Relationship Between Variables


Aglano (2002), a Mathematics teacher at Benguet State University Laboratory
High school, Benguet, Philippines made a thesis on Mathematics anxiety and its
relationship to the profile of the University of Baguio Science High School students,
which gave a definite concept for teachers to efficiently deal with the difficulties and
anxieties of students in the subject. Recommendations included the incorporation in the
system of changes in Mathematics grading system by making oral participation 15
percent of the student’s grade instead of 10 percent. This motivated students to recite
more often, increasing interaction among students and teachers during class discussion.
Oasan (1983) conducted a study on the relationship between NCEE scores ratings
in College Algebra with freshmen college students from the University of Baguio as
subjects. It was found that: The male students excelled over the female students in two
areas of the NCEE, namely, reasoning ability and mathematical ability; the females
excelled over the males in verbal ability and reading comprehension; and , The
performance in high school Algebra affects the performance in NCEE in the area of
mathematical ability.

The study of Ramos (1983) pointed out that anxiety as well as emotional stability
and the attitudes of the pupils toward their teachers are the factors that significantly
influence academic achievement in Mathematics.
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Abubo (1989) found that the greatest factor which is significantly related to the
Mathematics achievement of students is professional qualities of teachers.

Pilar (1989) studied the determinants of academic performance of students in
Mathematics at Northwestern College, Laoag City and found that the number of
preparations and teaching experience of Mathematics teachers were included among the
variables with possible effects on the teaching of Mathematics. The respondents of the
study were the first and second year college students.

Dinamling (1990) pointed out, after conducting a study on the teaching of
elementary Mathematics, that the most serious problems encountered by Mathematics
teachers are poor computational skills of pupils and their limited vocabulary to
understand and analyze problems. These deficiencies of pupils were magnified among the
findings of Marrero (1989) in a study of remedial measures on problem solving in
Mathematics IV. Also magnified were the following factors that cause difficulties among
students in problem solving as perceived by their teachers: lack of knowledge of
mathematical terms, poor vocabulary, lack of interest in Mathematics, and students not
like their teachers.

Other Related Studies
According to Japan International Corporation Agency (JICA)³ expert and
Science-Mathematics Education Manpower Development Program (SMEMDP) team
leader Kenichi Huira, the students’ low achievement and lack of interest in Mathematics
are caused by the lack of motivation given to the students. He said that there is a need to

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reinforce the inner drive among students to strive for academic excellence if
industrialization is the aim of the country.

Although there are very many problems emerging in the educational system,
private sectors, companies, the government and non-government organizations are trying
to do some researches and new innovations with regard to strategies including the
integration of technology as a means of processing mathematics problems. In the
California High School Exit Exam, which consists of an English-language arts portion
and mathematics portion, students must pass both portions of the test to graduate from
California public high schools. The purpose for this kind of system is to look for the
growth rate of the 10th graders, said Greg Franklin, Director of Curriculum, Instruction
and Assessment for the Glendale United School District. In 2004, only 10th graders took
the test compared with this year, when 10th- and 11th- graders who did not pass the first
time took the test again. Franklin said that the focus on teaching the standards to all the
students and providing additional support and intervention to juniors and seniors who
have not passed yet. In addition, President George W. Bush passed a law in 2002 entitled
“The No Child Left Behind Act.” This is intended to create accountability for results, an
emphasis on doing what works based on scientific research; expanded parental options;
and local control and flexibility5.

Another country whose status was also changed since it was founded is China. It
made a great progress in mathematics, and made remarkable contributions in complex
function, finite element calculation and other fields. It took China 20 years to catch up
with the world. Although China still has a large gap with America, France, and Germany
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in mathematics , its strength is powerful. Chinese young contestants have successfully
won Olympics math gold medals. This happens maybe because 3-5 years old children go
to informal schools and learn how to count from 1-20 only, how to pronounce number
and how to locate it in the fingers as a means of simple perception. They use also toys in
play activities in order for the teachers to let the children have an idea or concept of
numbers. Mathematics is already taught at the beginning of the formal schooling in grade
1. As the pupil grows and goes to a higher level, numbers being learned also increase up
to 100. Higher mathematics like Geometry is in grade 4, and Algebra and Statistics are
taught in the middle school and high school. In the new century, China’s mathematics is
sure to get faster development. Both domestic and foreign scientists hold that China will
become a math power within five years. Contemporary Chinese mathematician Wu
Wenju said that in the information era, using computer to conduct all kinds of
complicated work instead of human brain is to input algorithm into computer and then
computer can automatically calculate according to algorithm4.


According to China East Normal University Professor Zhu Zhiting’s report
(2002), on the functioning modes of information technology in classroom instruction:
Predictable, classroom instruction will still be a major form for school
education in a not-short future time. To improve classroom instruction with
support of information technology stands for a practical strategy for educational
reforms in school. There is a need for us to understand the functioning modes of
information technology in classroom instruction and thus we can select and make
use of technology reasonably and effectively. This article first identifies the
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orientation of instructional reforms in the classroom and creates an action space
concerning the use of technology to support this kind of reforms. Based on this,
an theoretical framework is a addressed to posit the functioning models of
information technology in classroom instruction, in which three modes are
suggested: enhancement, innovation, and training. A number of instructional
cases in relation to each modes are then studied in order to identify a set of sample
models for technology-supported classroom instruction. This article is ended with
our suggestions as to how different instructional models and technologies can be
integrated into classroom-based instructional process.
Chinese Math researcher, Wen Jie (2005), found that interest is the most active
factor for students in learning mathematics, and it is also the most positive factor for
learning other subject areas. To improve the student’s interest in learning math is the
teacher’s very important role.
According to Chinese Wen Xin Elementary School Grade I Mathematics teacher
Wu Guiti (2006), knowledge, concept and methods, must be practiced by the students in
actual activities. Learners in Mathematics will then understand and grasp the concept
while the teacher facilitates it. The actual experiences during the activities will lessen
dependence on the teachers.
China Guang Zhou City’s Secondary school teacher, Jia Guofu (2006), gave a
new Mathematics teaching process. The process is setting a set of questions, pre-test the
set of questions to the students, planning the curriculum program based from the
questions, carrying out the plan, summing up and re-planning for improvement
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His new Mathematics teaching process is intended to develop the student’s
ability; personality and moral character. Values is also integrated in the mathematics
curriculum as part of the process.
Conceptual Framework
The researcher used an observational-comparison approach and sampling
technique using questionnaire to gather information and data from the two schools being
studied and compared.
The general objective of mathematics in the elementary level as mentioned by
Salandanan et al. (1988) is…
to help the child compute and solve problems relating to occupations, business
practices, measurement, estimation, income and expenses, taxes, rental rates and
interest charges, gather and interpret data using graphing and scaling, and other
matters related to the problems of daily living.

They added that the foregoing general objective aims to develop in the elementary
school child the following knowledge/skills: the number relationship of facts and
processes, the meaning of the number facts and processes, and application of the number
facts and processes to life or lifelike situations.

To achieve the general objectives of a mathematics program they moreover gave
assumptions such as:
1. The teaching of mathematics should help the elementary school pupil to
develop clear concepts about numbers, numeral, mathematical operations, and the like,
for a clear understanding of simple number relationships contributes much towards the
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comprehension of the basic structure of mathematics;
2. Mathematics instruction should enable the children to master mathematical
knowledge. Modern mathematics in the elementary grades still emphasizes the mastery of
certain facts;
3. One of the major purposes of mathematics instruction is to arouse and develop
among children the appreciation for mathematics. This appreciation will make them
realize how mathematics can be used to solve their own daily problems.
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Independent Variables
Dependent Variables


1. Profile

1. Performance of pupils in
a. age
Mathematics

b. gender


c. parents’ occupation
2. Degree of Relationship between the

d. nationality
teacher’s socio-economic profile and

f. type of school
their:

a) extent of use of teaching methods
2. Teaching Approaches & methods
in teaching Mathematics
in Mathematics

b) teaching approach

c) extent of provision of activities to
3. Activities provided to students in

pupils in learning Mathematics
learning Mathematics
d) degree of needs in areas for


improvement in teaching Mathematics
4. Competencies in Mathematics



Moderate Variables
1. Extent of use of teaching methods / approaches
2. Extent of providing activities to pupils in learning
Mathematics
Figure 1. Paradigm of the study 29
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The independent variables that the researcher manipulated were the background
information about the pupils, teaching approaches and methods, activities provided to
students in learning mathematics, and competence in Mathematics.

Those variables considered to affect the independent and dependent variables were
related to the extent of use of teaching approaches and methods in Mathematics and
extent of providing activities to pupils in learning Mathematics.

Construed as the output variables are performance of pupils in Mathematics and
degree of relationship between: socio-economic profile of teachers and their teaching
approaches and methods; socio-economic profile of students and level of competencies;
teaching approaches used by teachers; extent of provision of activities in learning
Mathematics, and degree of needs for improving their teaching.

Definition of Terms
The following are terms operationally defined for common understanding.
Acquisition Phase. It refers to the phase of learning where students should attain
100% of the objectives. The end product is according to the learners.
Activity Method. It refers to the students are engaged in the activity to have a first
hand experience about the concept being learned.
Age. It refers to the respondents time from birth to the period of his study.
Assignment Method. It refers to the students are given interesting homework that
requires a little research or participation and assistance from family members.
Board work. It refers to activities such as solving problems using the blackboard.
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Competence. This refers to the mathematical competence of pupils based on their
ability to use the four fundamental operations dealing with whole numbers, fractions,
decimals and worded problems. This also includes mathematical competencies in dealing
with ratios, ratio and proportion, transforming a number to percent, identifying shapes of
objects, determining measurements of angles and areas of solid objects.
Deductive Method. It refers to the teacher begins teaching from a generalization
and subsequently gives examples and specific situations that are supportive of it.
Degree
of
Need.
This is referring to the areas where teachers need to further
improve their teaching in Mathematics. These are measured according to degree of need
using the scale ranging from very much needed to not needed.
Demonstration Method. It refers to the teacher shows a step by step presentation
through concrete actions and materials of which the students will observe.
Discussion Method. It refers to the students are guided to give a free exchange of
ideas about a particular topic.

Extent of provision of activities. This refers to the extent the learning activities are
provided to students to learn mathematics. This is measured using the scale that range from
Very much provided to not provided.
Gender. It refers to the respondents, either male or female.
Generalization phase. It refers to the phase of learning where students are exposed
to new problems to construct new ideas.
Grade level. It refers to the pupils grade.
Inductive method. It refers to the students are taught starting from the known to the
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unknown; from the specific to the general; from the particular to the universal; from simple
to complex; and from the concrete to the abstract.
Integrated Method. It refers to the teacher combines two or more subjects to explain
a main topic. One is a springboard and the other is the main topic. Other subject areas
could be supportive to the main topic.
Investigatory Method. It refers to the students are required to do an experiment,
conduct an investigation, try out different alternatives to solve a given problem.
Lecture Method. It refers to the students are provided with needed information by
factual presentation and textual explanation of a particular topic.
Maintenance Phase. It refers to the phase where students review their own learning.
Mastery Phase. It refers to the phase of learning where student manifests expected
behavior within a time frame.
Mathematics. It refers to the subject which deals with numbers and their properties,
relations, and combinations and spatial shapes and their structure and measurement:
Modular Method. It refers to the students are given a self-contained and
independent unit of instruction with specific objectives. The student is given an
opportunity to know the specific objectives and do the learning activities by following
specific procedures.
Parent’s Occupation. It refers to the respondent’s work of parents or parent’s job.
Performance . This is determined by the scores obtained by the student in a given
test. The performance is one of the factors used to describe the group of pupils, their
distribution and their characteristics as learners.
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Practice and Drill Method. It refers to the students are required to practice and
master important prerequisite skills necessary for the whole lesson. Constant review is
necessary.
Problem-solving Method. It refers to the teacher sets a good criteria for students to
come up with a solution.
Recitation Method. It refers to the students are made to focus on sets of questions
which are answered from reading books and other printed materials. They share their
insights and answers during the class session.
Reporting Method. It refers to the students are allowed to search for information
about a given topic and report it in class.
Self-pacing Method. It refers to the students’ individual differences are recognized
by giving the student the freedom to set his own schedule for learning and to monitor his
own progress while the teacher acts as a consultant.
Socio-economic profile. This includes the profile of teachers as well as pupils. The
teacher’s profile include the age, gender, educational attainment, salary and years in
service in teaching. While the pupils’ profile include their age, gender and parents’
occupation.
Teaching approach. This describes the viewpoint of the teacher described as
teaching goal, the nature of the teaching-learning process, role of the teacher and plan and
structure of the instruction.
Teaching method. This refers to a set of procedures which is done to achieve
certain specific aims of instruction. This is procedural in nature.
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Traditional Method. It refers to the teacher uses textbook learning, rote learning,
directed technique and memorization.
Type of school It refers to the administration of either public or private entities.

Hypotheses of the Study
The following hypotheses were put forward for testing:
1. The Mathematics teachers are significantly different in their extent of use of
the teaching approaches.
2. The Mathematics teachers significantly vary in the extent of providing
activities to pupils in learning Math.
3. The Mathematics teachers significantly different in their degree of need to
improve their teaching.
4. The grade VI pupils differ significantly in their competencies in
Mathematics along
a. Use of the four fundamental operations in whole numbers, fractions,
decimals and word problems
b. other areas in Elementary Mathematics
7. There is a significant relationship between the socio-economic profile of
teachers and
a. the extent of use of methods in teaching mathematics.
b. Teaching approach
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c. Extent of provision of activities in learning Mathematics
d. Needs for improving their teaching


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METHODOLOGY
Locale of the Study

The study was conducted at two selected public schools in La Trinidad, Benguet
and two selected public schools in Huai Hua of Hunan.
Chosen on the Philippines were Benguet State University Elementary Laboratory
School and La Trinidad Central School; and in China were Xing Guang Elementary
Laboratory School and Ying Feng Road Elementary School.

BSU is located at the heart of the municipality of La Trinidad. It is six kilometers
away from Baguio City and a gateway to the mountain provinces. It first opened its door
in 1916 as the La Trinidad Experimental Station. In 1946, it was called La Trinidad High
School. Four years later, the special and normal curricula were added to its Agricultural
Education Program. Later it became Mountain Nation Agricultural College (MNAC)
then changed to Mountain State Agricultural College (MSAC) through Republic Act
59223.

Sixteen years later, on January 12, 1986, former President Ferdinand E. Marcos
elevated the college to a state university by virtue of Presidential Decree 2010, thus it
became Benguet State University.

BSU is considered as one of the biggest learning institutions in the Cordillera
today. It has four levels of education, namely, elementary, secondary, tertiary, and
graduate schools.


The Elementary Laboratory School, formerly named Ilang Elementary School,
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was adopted into the institution in July 1979 as a part of the College of Teacher
Education. It used to be under the direct supervision of the Department of Education.

The current population of the BSU Elementary Laboratory School is 563 pupils. It
has 3 non-teaching staff and 15 teachers.
Huai Hua City is in the southwest of Hunan Province in China. Its area is 27,600
km and has a population of 4,800,000.
Xing Guang Elementary Laboratory School is located at the middle of Ying Feng
Dong Road Huai Hua City. It was built in 1982; the whole school area is 1.2 hectares.
The school has 26 sections from grades 1-6 and has 995 students this school year.
It has seven officers, 12 non-teaching staff, and 53 teachers. It is the first elementary
laboratory school in Huai Hua City since the New Chinese Political and Economic
System was reformed in 1980.
Ying Feng Road Elementary School is located at # 6 Yu Cai Alley of Ying Feng
Zhong Road Huai Hua City. It was built in 1975. The whole area of the school is
153,000m².
The school has 66 sections from grades 1-6 and has 2,967 pupils this school year.
It has 21 school officials and non-teaching staff, and 110 teachers. It is the key
elementary school in Huai Hua City. It is directly administered by the Department of
Education.
Respondents of the Study

This study used a total enumeration of the grade six pupils in Benguet State

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University Elementary Laboratory School; the grade six pupils in La Trinidad Central
School; the grade six pupils in Xing Guang Elementary Laboratory School; and the grade
six pupils in Ying Feng Road Elementary School who are currently enrolled for the
school year 2006-2007 as well as the Mathematics teachers.
There are 103 grade six pupils and eight Mathematics teachers in Benguet State
University Elementary Laboratory School; 225 grade six pupils and 20 Mathematics
teachers in La Trinidad Central School; 165 grade six pupils and 18 Mathematics
teachers in Xing Guang Elementary Laboratory School; and 492 grade six pupils and 40
Mathematics teachers in Ying Feng Road Elementary School.
The four schools were chosen because they have almost of the same economic
level and all are public elementary laboratory schools.
Table 1. Distribution of respondents
SCHOOL PUPIL
TEACHER

Benguet State University Elementary
100 7
Laboratory School
La Trinidad Central School
100 16
Xing Guang Elementary Laboratory School
100
8
Ying Feng Road Elementary School
100
10

Total
400
41


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Research Design
This study is basically a descriptive-survey research. This approach was used since the
researcher is interested in finding the extent of the level of Mathematics competencies
among grade six pupils in Xing Guang Elementary Laboratory School and Ying Feng
Road Elementary School in China and Benguet State University Elementary Laboratory
School and La Trinidad Central School in the Philippines. The researcher gathered the
data to find answers to the problems indicated in this study through questionnaires,
interviews and actual observation. Questionnaires were used to find out the profile of
grade six pupils. They were also used to determine the level of learning in Mathematics.
Interview and observation were used to determine the time spent for learning
Mathematics, the teaching approaches used by the teachers in teaching Mathematics, and
to identify the activities provided to pupils in learning Mathematical contents taught in
grade six.
Instrumentation


There were two sets of questionnaires which were answered by the grade six
pupils and the Mathematics teachers of the four schools. The teacher’s questionnaire
includes background in the profession, methods and approaches in actual teaching, and
personal opinion of what needs to be improved. The pupil’s questionnaire includes
background and a set of test in all areas of mathematics learned in grade VI.
Personal interviews to the pupils and teachers, and actual observation in their
classrooms were done to supplement the questionnaires.
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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42
Data Gathering


The researcher constructed the questionnaires to know the profile of the pupils
and identify their level of competency in the acquisition phase, mastery phase,
generalization phase and maintenance phase.

The researcher also interviewed the grade six teachers of the given schools and
observed in their classes to determine the time allotted for learning Mathematics and the
methods used by the teachers, the activities they provided to their pupils, and the content
of their lessons.
To validate the content of the self-constructed questionnaires on the level of
competency of the pupils, the questionnaire was presented to a committee of authorities
and experts in the field of Mathematics and education for evaluation.

Statistical Treatment of Data

Collected data were categorized, tabulated, and analyzed with the use of
appropriate statistical tools. Descriptive statistics such as means, frequencies,
percentages, and Pearson-product-moment correlation coefficient were used to describe
the data.
Inferential statistics such as the One way and Two-way Analysis of Variance were
used to test the hypotheses of significant differences between and among variables. . The
t-test was used to test the significant relationship between variables tested in the study.
Comparisons were made at 0.05 level of significance.
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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RESULTS AND DISCUSSION


Profile of Respondents



The profile of respondents include a description of the socio-economic status of
Mathematics teachers which include their age, gender, highest educational attainment,
length of service in teaching and salary.

On the other hand, the profile of pupils include their age, gender and parents’
occupation.

Socio-economic Profile of Mathematics Teachers

Age. Table 2 and Figure 4 show the percent distribution of Mathematics teachers
according to their age. The Mathematics teachers from La Trinidad Central School range
in age from 21 to over 61 years; from State University Elementary Laboratory School
and Ying Feng Road Elementary School, 21 to 60 years; from Xing Guang Elementary
Laboratory School, 21 to 50 years.

La Trinidad Central School has the greatest distribution of teachers who range in
age from 21 to 30 years or 41 to 50 years. On the other hand, Xing Guang Elementary
Laboratory School has highest percent distribution of teachers who range in age from 31
to 40 years at BSU, Huai Hua Ying Feng Road Elementary School and Xing Guang
Elementary Laboratory School.

Overall, the great majority of Mathematics teachers are young , as indicated by
the highest percent distribution at 21 to 40 years in the four schools. However, on the

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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44
Table 2. Percent distribution of respondents according to age

SCHOOL N
AGE
(YR)
21- 30 31 –40 41-50
51-60
Over 61

BSU Elementary Laboratory School 7
28.57 57.14
14.28
0.00
0.00
La Trinidad Central School
16
37.50 6.25
25.00
18.75
12.50
Ying Feng Road Elementary School 10
30.00 40.00
20.00
10.00
0.00
Xing Guang Elementary Laboratory 8 12.50
62.50 25.00 0.00 0.00
School

AVERAGE 41
29.27
34.15
34.15
9.76
4.88

Legend: N- Total number of respondents

70
60
n
o
ti 50
u
i
b 40
i
str
30
t
D
en 20
r
c
e
P 10
0
21- 30
31 - 40
41 - 50
51 - 60
Age (Yr)
BSU
LTCS
YFRES
XGELS



Figure 4. Percent distribution of Mathematics teachers according to their age

average, the teachers teaching Mathematics are in their middle ages as shown by the
mean percent distribution of 34.15, at ages of 31 to 40 years or 41 to 50 years.
Gender. As gleaned in Table 3, the Mathematics teachers in all schools are
dominated by females, whose average percent mean is 75.61.
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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45
Table 3. Percent distribution of teacher- respondents according to gender

SCHOOL N
GENDER
Male Female

BSU Elementary Laboratory School
7
28.57
71.42
La Trinidad Central School
16
6.25
93.75
Ying Feng Road Elementary School
10
40.00
60.00
Xing Guang Elementary Laboratory School
8
37.50
62.50

TOTAL 41
24.39
75.61

Legend: N- Total number of respondents

100
N 90
I
O
80
BUT 70
60
STRI 50
40
30
20
PERCENT DI 10
0
BSU
LTCS
YFRES
XGELS
SCHOOL
MALE
FEMALE

Figure 5. Percent distribution of Mathematics teachers according to gender

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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46
It is noteworthy to cite that Mathematics teaching is gender sensitive as
manifested by the existence of many male teachers in three schools: Ying Feng Road
Elementary School, 40 percent; and Xing Guang Elementary Laboratory School, 37.50
percent; and BSU Elementary Laboratory School, 28.57 percent. In the case of La
Trinidad Central School, however, a few are male teachers, as indicated by a percentage
of 6.25.
Educational Attainment. Table 4 shows that a great majority of the teachers are
bachelor’s degree holders. However, only in BSU Elementary Laboratory School have
the a greater majority of the Mathematics teachers with master’s degree.

It appears that La Trinidad Central School does not implement the Civil Service
Rule providing a minimum requirement of Master’s degree for its employed teachers.
This finding jibes with the observation of Toledo (1982) that a great number of
Mathematics teachers have not advanced professionally.
Conversely, in the two schools in China, few Mathematics teachers are master’s
degree holders. This finding indicates having master’s degree is a minimum requirement
for employment in teaching.
As a whole, only La Trinidad Central School does not strictly implement the
minimum requirement for obtaining a master’s degree. Thus, it may be inferred that
professional development is not much emphasized in the school.

The foregoing findings would indicate significant contributions in the
improvement of the quality of the teachers that the system employs and this is confirmed

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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47
Table 4. Percent distribution of teacher respondents according to highest educational
Attainment

SCHOOL N
EDUCATIONAL ATTAINMENT


Bachelor’s
Master’s
Degree
Degree

BSU Elementary Laboratory School
7
42.86
57.14
La Trinidad Central School
16
100.00
0.00
Ying Feng Road Elementary School
10
80.00
20.00
Xing Guang Elementary Laboratory 8 87.50 12.50
School

TOTAL 41
82.93
17.07


120
N
I
O
100
UT
B
RI
80
T
S
DI
60
NT
40
RCE
E
P
20
0
BSU
LTCS
YFRES
XGELS
SCHOOL
Bachelor's
Master's

Figure 6. Percent distribution of Mathematics teachers according to highest educational
attainment

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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48
by Guerrero (1989). Tating (1993) cited that the teacher occupies a most important place
in modern society and that his knowledge of his field accompanied with experience,
prepares the pupils in meeting , Thus, one of the best measures of teachers, as found by
Lubrica (1996), is their academic and professional training.

Length of service. As gleaned in Table 5, the great majority of teachers have
taught Mathematics for 6 to 10 years. This is followed by those who have taught the
subject for less than six years and those who have taught it for over 20 years.
Specifically, the greatest percentage of teachers in La Trinidad Central School have
taught for 5 – 10 years; BSU-ELS, 6- 10 years; Xing Guang Elementary School, 11-15

Table 5. Percent distribution of teacher respondents according to length of service in
Teaching


SCHOOL
N
LENGTH OF SERVICE (YR)
0 – 5 6 – 10 11– 15 16-20
Over 20
years

BSU Elementary Laboratory School 7
14.28 71.43
0.00
14.28
0.00
La Trinidad Central School
16
37.50 18.75
0.00
18.75
25.00
Ying Feng Road Elementary School 10
10.00 20.00
30.00
30.00
10.00
Xing Guang Elementary Laboratory 8 0.00
12.50 50.00
25.00 12.50
School

TOTAL 41
29.27
36.58
13.79
14.63
9.76

Legend: N- Total number of respondents



Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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49
80
N
I
O 70
T
60
I
BU
R 50
T
I
S 40
D
T 30
EN 20
C
R 10
PE
0
0 - 5 yrs.
6 - 10Yrs.
11-15 yrs.
16-20yrs.
Over 20 yrs.
LENGTH OF SERVICE
BSU
LTCS
YFRES
XGELS

Figure 7. Percent distribution of Mathematics teachers according to length of service

years; and Ying Feng Road Elementary School, 16-20 years. At the same time, La
Trinidad Central School has the highest percentage of teachers who have taught the
subject for over 20 years.

Comparatively, Figure 6 shows that BSU Elementary School has the
highest number of teachers having the longest length of service, 6- 10 years. This finding
is supported by the age distribution (Table 2), which is likewise high.
Salary received. The salary received by teachers teaching Mathematics range
from PhP 8,000 to above PhP 18,000 (Table 6). But the four schools have varied percent
distribution. The teachers of BSU ELS range in salary from PhP 8,000 to PhP 16,000;
La Trinidad Central School, from PhP 8,000 to PhP 14,000; Yeng Feng Road Elementary
School, from PhP 8,000 to above PhP 18,000; and Xing Guang Elementary Laboratory
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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50
Table 6. Percent distribution of teacher- respondents according to salary




SALARY (PhP )
SCHOOL
N
8,000-
10,001-
12,001-
14,001-
16,001-
Above
10,000
12,000
14,000
16,000
18,000
18,000

BSU Elementary
7 14.28 57.14 14.28 14.28
0.00
0.00
Laboratory School
La Trinidad Central 16 56.25 31.25
12.50
0.00
0.00
0.00
School
Ying Feng Road
10 10.00 30.00
20.00
20.00
10.00
10.00
Elementary School
Xing Guang
8 12.50 37.50 25.00 12.50
12.50 0.00
Elementary
Laboratory School

TOTAL 41
29.27
36.58
17.07
9.76
4.88
2.44

Legend: N- Total number of respondents

80
n 70
t
i
o
u 60
r
i
b
BSU
50
i
st
LTCS
40
e D
YFRES
30
t
ag
XGELS
20
cen
er 10
P
0
8,000-
10,001-
12,001-
14,001-
16,001-
Above
10,000
12,000
14,000
16,000
18,000
18,000
SALARY (PhP)

Figure 8. Percent distribution of teacher-respondents according to salary

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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51
School, from PhP 8,000 to PhP 18,000. Comparatively, teachers from La Trinidad
Central School have the lowest salary range. Although 100 percent of its faculty have the
highest degree earned. Despite the differences in salary scale between China and
Philippines, the results would indicate the relevance of educational attainment, which is
compensated with salary increase.

The foregoing findings on socio-economic profile are related to the study
conducted by Lubrica (1996) indicating that for teachers to improve in their teaching,
they should have more academic and professional trainings in their field of specialization,
shall have more teaching experiences, and should participate more in seminars and
workshops relative to Mathematics.

Socio-economic Profile of Grade VI Pupils


The socio-economic profile of pupils include their age, gender and parents’
occupation. These data were used to describe the performance of the pupils as affected
by these variables.
Age
distribution. As gleaned in Table 7 and Figure 9, the majority of grade six
pupils range in age from 11 to 12 years. This finding indicates that these pupils have
been admitted in grade one at aged six or seven. This finding is in line with the
Department of Education Memorandum that mandates admission age be seven years.
Nevertheless, the memorandum allows those aged six to enter grade one. With those
admitted at an earlier age of five years, it is assumed that these children have entered pre-


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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52

Table 7. Frequency distribution of respondents according to age


SCHOOL AGE
(YR)
10
11
12
13
TOTAL

BSU Elementary Laboratory School
4
57
39
0
100
La Trinidad Central School
1
61
33
5
100
Ying Feng Road Elementary School
0
32
65
3
100
Xing Guang Elementary Laboratory School
0
44
49
7
100

TOTAL
5 194
147
15 361


70
60
n
o
ti 50
u
40
t
r
i
b
i
s
30
t D
20
r
cen
e
P 10
0
10
11
12
13
Age (Yr)
BSU
LTCS
YFRES
XGELS


Figure 9. Frequency distribution of student- respondents according to their age

school at 5 ½ years and have proven their acceptance in grade one having passed the
exams.
Likewise in China, the distribution shows an admission age of six and seven as
reflected by the frequency distribution.
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53
BSU Elementary school adheres to the Department of Education Memorandum
indicating an admission age of six. The three other schools admit pupils in grade one at
ages six to eight.
Gender. As gleaned in Table 8 and Figure 10, females dominate the males as
manifested in the consistent distribution among all the three schools. Conversely, in
Table 8. Frequency distribution of pupil- respondents according to gender


SCHOOL GENDER
Male
Female

BSU Elementary Laboratory School
43
57
La Trinidad Central School
46
54
Ying Feng Road Elementary School
53
47
Xing Guang Elementary Laboratory School
57
43



60
50
i
on
40
i
s
t
r
i
but
Male
30
y
D
Female
nc 20
e
que
FR 10
0
BSU
LTCS
YFRES
XGELS
School


Figure 10. Frequency distribution of pupil- respondents according to gender

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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54

Xing Guang Elementary Laboratory School, more males are found among the grade six
pupils with frequency distribution at 57 for males and 43 for females. However, the
distribution between males and females is not widespread as manifested by a small
difference.
Parents’
occupation. Table 9 reveals the distribution of pupil-respondents
according to occupation of both mother and father. The distribution shows that both
mother and father are working.

A greater percentage of the pupils’ mothers and fathers are involved in blue collar
jobs than in white collar jobs. A greater number of unemployed mothers are observed in
BSU Elementary Laboratory School and La Trinidad Central School.

Table 9. Frequency distribution of respondents according to parents’ occupation

SCHOOL EMPLOYMENT

Unemployed
Blue
White
TOTAL
Collar Collar


Father 0 61
28
89
BSU Elementary Laboratory School
Mother 29 35
29 93

Father 3 75
14
92
La Trinidad Central School
Mother 32 43
12 87

Father 1 43
56
100
Ying Feng Road Elementary School
Mother 3 45
52
100

Father 0 39
61
100
Xing Guang Elementary Laboratory
Mother 7 42
51
100
School

TOTAL
75
384
251


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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55
80
70
n
i
o
60
ut
t
r
i
b
50
i
s
D
40
y
c
n
30
ue
q
20
e
Fr
10
0
BSU
LTCS
YFRES
XGELS
School
Unemployed
Blue Collar
White Collar



Figure 11. Frequency distribution of student-respondents according to the nature of
employment of their father.

60
n 50
io
40
t
r
i
but
Unemployed
i
s
D 30
Blue Collar
y
nc
White Collar
20
ue
q
r
e
F 10
0
BSU
LTCS
YFRES
XGELS
School


Figure 12. Frequency distribution of student-respondents according to the nature of
employment of their mother.


The foregoing results show that the pupils are economically sufficient in terms of
their support for schooling.

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56

Teaching Approach Used By Teachers
in Teaching Mathematics



Table 10 reveals the discovery, conceptual, process and unified approaches are
frequently used by teachers in teaching Mathematics. In BSU Elementary Laboratory
School, all the teaching approaches are frequently used, with the process approach having
the highest mean. This finding would indicate that the teachers focus more on the
development of the pupils’ skills and the determination of pupils’ weaknesses in their
skill formation. The pupils are also taught to learn to search for solutions of a problem
through exploration and evaluation and their previous learning is reinforced by their
Mathematics teachers.

Conversely, the other three schools most frequently use the unified approach.
This finding indicates that the teachers from La Trinidad Central School, Ying Feng Road
Elementary School and Xing Guang Elementary Laboratory School focus their teaching
on the presentation of content geared towards student vocabulary, which is expanded
through citation of relevant examples and concrete situations.

The use of the four approaches in teaching Mathematics is significantly different
among the teachers, as indicated by the computed value of 4.00 which is higher than
tabular value of 1.92. It may be inferred that varied use of teaching approaches in
teaching their students in Mathematics. The difference can be attributed to the fact that
the students have varied characteristics, motivation and abilities. These could be factors
affecting the instructional decision of teachers in designing their instructional program of
their pupils.
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Table 10. Teaching approach used by Mathematics Teachers


SCHOOL
APPROACH
BSUELS LCS YFRES XGELS OWM

• Discovery
3.46 3.40
3.38
3.39 3.41
• Conceptual
3.78 3.48
3.70
3.63 3.65
• Process
3.78 3.46
3.82
3.71 3.69
• Unified
3.71 3.59
3.85
3.80 3.74

OVERALL WEIGHTED MEAN
3.68
3.48
3.69
3.63
3.62
F(between teaching approach) = 4.00s F(0.05) = 1.92
F(between schools) = 5.67S F(0.05) = 2.84
Legend: s- significant

Statistical Limit Descriptive Value

Interpretation
3.26 – 4.00
Frequently utilized
76% - 90% used in most instruction
2.51 – 3.25
Often utilized

50% - 75 % used in instruction
1.76 – 2.50
Seldom utilized

less than 50% used in instruction
1.00 – 1.75
Not used

The four schools significantly differ in their use of the teaching approaches, as
revealed by the computed F-value of 4.00 being significantly higher than the tabular F-
value at 1.92. Furthermore, the overall weighted mean indicates that the teachers of
Yang Feng Road Elementary School have a significantly highest use of all the teaching
approaches as compared to the other three schools.
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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Instructional variety characterizes an effective teacher. As claimed by Levak et al.
(1993), flexibility allows teachers to utilize alternative approaches across disciplines,
instead of forcing connections where connections do not exist. Their use of alternative
approaches seems to engender success.

It is therefore inferred that teachers teaching Mathematics vary in their
instructional approaches, which may come in the form of variation in activities, learning
experiences and learning materials. However, this variation should be clearly employed
to make learning more meaningful.

As a whole, the hypothesis of significant difference in the frequency of use of the
teaching approaches by teachers is therefore accepted.

Teaching Methods Employed by Teachers
in Teaching Mathematics

As gleaned in Table 11, varied methods are used by teachers in teaching Mathematics
teacher from BSU Elementary Laboratory School frequently use lecture, discussion,
activity, inductive, deductive, recitation, integrated, problem-solving and assignment;
oftenly use investigatory, traditional, modular and practice and drill method; seldom use
reporting and self-pacing method. Although using varied activities in teaching
Mathematics, the teachers frequently use activity method, inductive method and problem-
solving method.
Conversely, the teachers of La Trinidad Central School frequently use lecture,
reporting, demonstration, activity, inductive, deductive, self-pacing, traditional,
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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Table 11. Teaching Methods used by teachers


SCHOOL
METHOD
BSU LTCS YFRES XGELS

The students are provided with needed information by factual presentation
3.43 3.50 3.56 3.12
and textual explanation of a particular topic (Lecture Method)
Students are guided to give a free exchange of ideas about a particular topic 3.43 3.25 3.78 3.62
(Discussion Method)
Students are allowed to search for information about a given topic and report 2.28 3.94 2.67 2.88
it in class (Reporting Method)
Teacher shows a step by step presentation through concrete actions and
2.73 3.67 3.56 3.38
materials of which the students will observe (Demonstration Method)
The students are engaged in the activity to have a first hand experience about 3.71 3.50 3.11 3.50
the concept being learned (Activity Method)
The students are taught starting from the known to the unknown; from the
3.71 3.69 3.67 3.75
specific to the general; from the particular to the universal; from simple to
complex; and from the concrete to the abstract (Inductive Method)
The teacher begins teaching from a generalization and subsequently gives
3.43 3.31 4.00 3.50
examples and specific situations that are supportive of it (Deductive Method)
Students are required to do an experiment, conduct an investigation, try out
3.14 3.19 3.22 3.38
different alternatives to solve a given problem (Investigatory Method)
Students’ individual differences are recognized by giving the student the
2.43 3.38 3.70 3.25
freedom to set his own schedule for earning and to monitor his own progress
while the teacher acts as a consultant (Self-pacing Method)
The teacher uses textbook learning, rote learning, directed technique’ and
2.57 3.44 4.00 3.88
memorization (Traditional Method)
The students are made to focus on sets of questions which are answered
3.43 3.44 3.56 3.25
from reading books and other printed materials. They share their insights
and answers during the class session. (Recitation Method)
Teacher combines two or more subjects to explain a main topic. One is a
3.57 3.19 3.78 3.50
springboard and the other is the main topic. Other subject areas could be
supportive to the main topic. (Integrated Method)
Teacher sets a good criteria for students to come up with a solution
3.71 3.25 4.00 4.00
(Problem-solving Method)
Students are given a self-contained and independent unit of instruction with
2.71 2.94 3.78 3.50
specific objectives. The student is given an opportunity to know the specific
objectives and do the learning activities by following specific procedures.
(Modular Method)
Students are given interesting homework that requires a little research or
3.28 3.69 4.00 3.88
participation and assistance from family members (Assignment Method)
Students are required to practice and master important prerequisite skills
3.14 3.69 4.00 4.00
necessary for the whole lesson. Constant review is necessary. (Practice and
Drill Method)

OVERALL WEIGHTED MEAN
3.17
3.38
3.65
3.52

F(between teaching methods) = 1.73ns F(0.05) = 1.92
F(between schools) = 6.361.73S F(0.05) = 2.84
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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60
Legend: ns- sot significant, s- significant
Statistical Limit Descriptive Value

Interpretation
3.26 – 4.00
Frequently utilized
76% - 90% Used in most instruction
2.51 – 3.25
Often utilized

50% - 75 % used in instruction
1.76 – 2.50
Seldom Utilized

less than 50% used in instruction
1.00 – 1.75
Not used
recitation, assignment and practice drill method; and oftenly use discussion,
investigatory, integrated, problem-solving, and modular. The results show that reporting
method is most frequently used and modular is least. This finding could be attributed to
the fact that pupils are made to work in pairs or groups and then made to report results
after the task is done, and that the teachers satisfy the required competencies prescribed
by the Philippine Elementary Competency standards.
On the other hand, teachers of the Ying Feng Road Elementary School have a
relatively higher frequency of use of all the identified methods. Seventy-six to 90 percent
of their instruction involves the use of lecture, discussion, demonstration, inductive
method, deductive method, self-pacing, traditional, recitation, integrated, problem-
solving, modular, assignment and practice and drill method. Some 50 to 75 percent of the
teachers’ instruction involves oftenly the use of reporting, activity and investigatory.
Such results would indicated a wide use of the methods for Mathematics instruction.
Lastly, most teachers of Xing Guang Elementary Laboratory School frequently
use more teaching methods; few seldom use them. Those claimed to be frequently used
are discussion, reporting, demonstration, activity, inductive, deductive, investigatory,
traditional, integrated, problem-solving , modular, assignment and practice and drill.
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Such results would show that teachers in Xing Guang give emphasis on those methods
that are frequently used in teaching Mathematics.

Despite the differences in means of frequency of use, the methods used are not
significantly different among teachers teaching Mathematics, As indicated by the
computed F-value of 1.73 and a tabular F-value of 1.92. This result implies that the
methods employed are applicable to teaching content and competencies in Mathematics.

Comparatively, the four schools significantly differ in their frequency of use of
the teaching methods. In BSU, consistently highest in frequency for activity are
inductive method and problem-solving. Reporting method is highest for La Trinidad
central; traditional method, problem solving, assignment and practice drill method for
Ying Feng Road Elementary School; and problem solving and practice and drill method
for Xing Guang Elementary Laboratory School. This difference implies that the schools
vary in the frequency of use of all the methods and that the type of school system differs
in terms of what the teachers and students could bring to the classroom. These
requirements include the nature of teachers, content and competencies to be taught in
Mathematics, location of the school and characteristics, motivation and abilities of
pupils entering the school system.

The above findings show how important the teacher’s competence in making the
pupils learn Mathematics through appropriate use of methods. Thus, as suggested by
Salandanan (1988), and methods must be appropriate for given behavioral objectives and
concepts. Meanwhile, Lardizabal et al (1991) stated that before taking up specific
techniques for organizing classroom activities, it is best to consider first the social needs
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of pupils in planning classroom experiences which can be expressed in terms of abilities
required to satisfy them. Practices have gradually replaced undesirable features of so-
called hearing procedures which is due in part to the gradual acceptance of the newer
philosophy of education.

Further, the use of methods characterizes effective teachers as possessing five key
behaviors which are related to lesson clarity, instructional variety, task orientation and
engagement in the learning process, and student success. Elliot et al. (2000) stated that a
teacher’s teaching techniques remain flexible during the presentation of the lesson. A
secondary Chinese school teacher, Guofu (2006), presented new Mathematics teaching
process relating to how a teacher structures his questions, carries out his instructional
plan and re-plans for instructional improvement. The teaching process should intend to
develop students’ ability as well as their personality. Valuing process in learning forms
part of the instructional component of curriculum development in Mathematics.

Extent of Provision of Activities
in Teaching Mathematics



Table 12 presents the activities provided to students in teaching Mathematics. As
shown, the teachers provide varied activities during the teaching learning process in
Mathematics. However, Yang Feng Road Elementary School provides most. Frequently
provision of activities in teaching Mathematics. Following in descending order of
frequency are Xing Guang Elementary Laboratory School, BSU Elementary Laboratory
School and La Trinidad Central School.
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Table 12. Extent of provision of activities in teaching Mathematics

SCHOOL
ACTIVITIES
BSU LCS
YFRES XGELS

Recitation 4.86
4.62
4.00
3.75
Problem-solving 4.28
4.12
5.00
4.62
Board Work
4.57
4.25
5.00
5.00
Assignment/homework 4.28
3.94
5.00
4.88
Quizzes 4.71
4.15
5.00
4.88
Tests/Examinations 4.28
3.87
5.00
4.75
Discussion with classmates
3.57
3.62
4.40
4.12
Solving through modules
4.00
3.69
4.40
4.12
Memorization/Rote learning
2.71
3.06
4.50
4.00
Drawing and paper cutting
3.57 3.39 4.30 3.25
Other activities
2.71
2.94 2.70 2.12

OVERALL WEIGHTED MEAN
3.96
3.78
4.48
4.13

F(between activities) = 10.60s F(0.05) = 2.16
F(between schools) = 6.47S F(0.05) = 2.92

Legend:
Statistical Limit Assigned Value
Description
4.21 – 5.00
5


Very frequently utilized
3.41 – 4.20
4 Frequently utilized
2.61 – 3.40
3 Moderately utilized
1.81 – 2.60
2 Seldom utilized
1.00 – 1.80 1


Not utilized

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The four schools significantly differ in the extent of providing activities in the
teaching of Mathematics, as indicated by a computed F-value of 6.88 which is
significantly higher than the tabular F-value of 2.96. The difference may be attributed to
the prescribed mathematical competencies intended to be learned by grade six pupils. In
the Philippines, BSU and La Trinidad Central School teachers are guided by the
Philippine Elementary Learning Competencies (PELC), which prescribes the minimum
content and competencies for learning Mathematics. The variation could likewise be
attributed to the differences in the educational systems between the Philippines and China
and the goals of the institutions.
On the other hand, the activities do not significantly vary among all the teachers
in terms of the extent of providing activities to pupils learning Mathematics. The extent
of provision of activities IS presented in decreasing mean values, as follows: board work,
quizzes, assignment/homework and problem-solving. Board-work, assignment/homework
and quizzes are activities provided in the mastery level of learning. Evaluation of
performance test and providing quizzes are the most convenient methods. The provision
of other activities, evidently is lowest in extent. Such as enrichment and enhancement of
learning.

The hypothesis of significant difference in the provision of activities among
Mathematics Teachers and among the four schools is therefore accepted,





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Table 13. Degree of need in identified areas to improve teaching Mathematics among
grade VI pupils.

AREA
BSU
LCS
YFRES XGELS OWM

Attendance to in-service trainings
3.28
3.12
2.60
3.25
3.06
Attendance to seminars
3.43
3.19
2.60
3.12
3.08
Making Modules
3.43
2.81
2.20
2.62
3.08
Upgrading of subject content
3.14
3.00
1.70
2.62
2.62
Conduct of action research
3.43 2.62 2.00
2.50
2.64
Update on current strategies
3.57
3.19
2.70
3.25
3.18
Improvise teaching aids
3.57
3.19
2.90
3.50
3.29
Use of modern technology
3.43
3.00
3.10
3.50
3.26
Increase in teaching time
2.71
2.88
1.30
1.25
2.04
Use of other textbooks
3.86
3.25
1.50
1.62
2.56

OVERALL WEIGHTED MEAN
3.39
3.02
2.26
2.72
2.85

F(between needs)
= 9.21s F(0.05) = 2.66
F(between schools) = 8.86S F(0.05) = 3.16

Legend: ns- sot significant, s- significant
Statistical Limit

Descriptive Value


3.26 – 4.00



Very much needed


2.51 – 3.25


Much needed



1.76 – 2.50


Needed



1.00 – 1.75


Not needed





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Perceived Degree of Needs in Specific Areas
in Teaching Mathematics


Table 13 presents the Mathematics teachers’ needs in improving the teaching of
Mathematics.

In the case of BSU Elementary Laboratory School, the teachers feel that to
improve their teaching in Mathematics they must attend in-service trainings and
seminars, make modules, conduct action research, update current strategies, improvise
teaching aids, use modern technology and use other textbooks. They also need much to
upgrade subject matter to increase teaching time. This finding implies that although
knowledgeable of the content, the teachers have inadequate skills in instructional
delivery and inadequate instructional materials.
The teachers in La Trinidad Central School have fewer needs to improve their teaching in
Mathematics than those in BSU, as indicated by the mean values reflecting a great need
of specified areas.

The same areas ae perceived as needs for improving teachers in their teaching of
Mathematics in Ying Feng Road Elementary School (YFRES). Those areas which are
much needed in improving the teachers are attending in-service training and seminars,
updating of current strategies and improvising teaching aids. A lesser degree of need to
improve the teacher is felt on making modules and conducting action research. The
teachers in the same school claim they have the content, enough textbooks and enough
time in teaching Mathematics implying that these are not priority areas for their
improvement. Overall, the teachers feel the need to improve their teaching of
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Mathematics.








Conversely, teachers of Xing Guang Elementary Laboratory School feel that they
need very much to improve in improvising their teaching aids and updating current
strategies in teaching, much need to improve themselves in their teaching by attending
training and seminars, making modules, upgrading subject matter, updating current
strategies, improvising teaching aids and using modern technology in teaching. They also
feel to a lesser degree the need to improve their means of conducting research. The
teachers claim that they do not need to increase their time in teaching and to use
textbook. This result implies that the teachers are adequate in their textbooks but need to
improve on other areas where priority is based on the degree of need.

The teachers significantly differ in areas where they need to improve their
instruction in Mathematics. Likewise, the schools vary significantly in the degree of
needs to improve their teachers along the specified areas. This finding implies that all the
teachers are not one in their perception and although they seek to improve in their
teaching of Mathematics. This is an indication that the teachers desire to become
effective and efficient in the identified areas. The difference in perceptions stem from the
governance of the school systems which differ from one another.

It is therefore inferred that the degree of needs for improving teaching along
specified areas is accepted for the schools and rejected according to needs.


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Performance of Grade VI Pupils in Mathematics


Table 14 reveals the performance of grade VI pupils coming from the four
schools. The data were generated from a test administered to the pupils. These are used to
support the foregoing discussions in identifying areas where the pupils are competent.

Pupils in Ying Feng Road Elementary School perform highest as evidenced by the
mean score of 28.83. This is followed in decreasing mean scores of 28.14, Xing Guang
Elementary School; 23.39 for La Trinidad Central School; and 21.13 for BSU Elementary
Laboratory School. Such results show that the pupils are proficient in Mathematics since
each mean score has surpassed the cut off score at 17.5.

However, only the pupils of La Trinidad Central School have a positive skewed
distribution which indicates that they are generally low performers in Mathematics
despite some pupils getting scores below the mean score. Such distribution show that
there are more low performing pupils than high performing ones.
Table 14. Performance of grade VI pupils in Mathematics


QUANTITAIVE MEASURE

OF PERFORMANCE
TYPE OF
SCHOOL
Mean
Median
Mode
DISTRIBUTION

BSU Elementary Laboratory School
21.13 20.78 21.5 Negatively
skewed
La Trinidad, Central School
23.39
24.5
22
Positvely skewed
Ying Feng Road Elementary School
28.83 28.5 27 Negatively
skewed
Xing Guang Elementary Laboratory
28.14 26.5 30 Positively
skewed
School


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On the other hand, the pupils from BSU, Ying Feng Road Elementary School and
Xing Guang Elementary Laboratory School are negatively skewed in their distribution.
The negative skewed distribution implies that a greater number of pupils perform higher
than the mean score of their respective group and that the three groups are composed of
high-performing pupils.

The differences in the mean performance of pupils may be attributed to the
provision of mathematical experiences of teachers suitable to the state of development of
their concept and the method of presentation by teachers to improve the pupils’ level of
thinking (Salandanan et al., 1988). Borich (1992) cited one attribute in Mathematics
learning and this is related to lesson clarity, which refers to how clear the teacher makes
his presentation to the class.

Bawang (1995) presented some problems encountered in teaching Mathematics.
The problems can be attributed to computational weakness among the pupils. Many
students, despite a good understanding of mathematical concepts, are poor of computing.

However, a Chinese Mathematics researcher, Wen Jie (2005), found that interest
is the most active factor in learning Mathematics and to improve it depends on the
teacher’s role. This suggestion was supported by Wu Guiti (2006) who repeated that the
teacher’s knowledge, concept and method, must be practiced by the students in actual
activities.


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Competencies of Grade Six Pupils in
Varied Areas in Mathematics


Table 15 and 16 reveal the performance of students in different areas in
Mathematics. These areas include using mathematical operations in whole numbers,
fractions, decimal numbers, and word problems; ratios, ratio and proportion, transforming
number to percent; identifying solid objects, measurements of angles of solid objects and
computing an area of solid objects.
Mathematical Operations

In mathematical operations in whole numbers (Table 13), the grade six pupils are
most competent in addition. A total of 191 out of 400 pupils coming from the four
schools excel in it. This is followed by subtraction, multiplication and division. The
pupils from BSU- Elementary Laboratory School, La Trinidad Central School and Ying
Feng Road Elementary School are consistently highest in their competency in addition
followed in decreasing distribution by subtraction, multiplication and division. On the
other hand, pupils of Xing Guang Elementary Laboratory School are competent in
subtraction followed by addition division and multiplication. The findings imply that the
grade VI pupils from different school significantly vary in competencies in using the four
fundamental operations in whole numbers.
Generally, all the pupils in the four schools do not significantly differ in their
competence in addition of whole numbers, subtraction, multiplication, and division.
Such results imply that although the pupils excel in mathematical operation of whole
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Table 15. Competencies of grade six pupils using the four fundamental operations in
Mathematics

SCHHOL
COMPETENCY BSU
LTCS
XING
GUANG
YING
FENG

1. Whole numbers




Addition
50
48
47
46
Subtraction
44
47
47
47
Multiplication
28
37
42
42
Division
21
14
41
43
F(between mathematical operation) = 5.09s F(0.05) = 3.86
F(between schools) = 1.46ns F(0.05) = 3.86
2. Fractions




Addition
36
34
43
44
Subtraction
36
18
44
42
Multiplication
35
35
72
78
Division
21
12
24
39
F(between mathematical operation) = 7.86s F(0.05) = 3.86
F(between schools) = 6.89S F(0.05) = 3.86
3. Decimal numbers




Addition
47
47
47
47
Subtraction
48
49
44
41
Multiplication
31
35
22
40
Division
21
15
36
41
F(between mathematical operation) = 5.58s F(0.05) = 3.86
F(between schools) = 0.46ns F(0.05) = 3.86
4. Word Problems




Addition
19
41
45
44
Subtraction
37
44
49
43
Multiplication
19
35
38
38
Division
37
45
46
45
F(between mathematical operation) =6.28s F(0.05) = 3.86
F(between schools) = 13.21S F(0.05) = 3.86
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numbers, they still need to improve further the competencies in mathematical operations
in Mathematics, as indicated by the mean distribution which is below 200. It may be
inferred that there is a need to improve the competencies of pupils using the four
fundamental operations in Mathematics. Some four schools are one in the distribution
along the four fundamental operations, the pupils do not significantly differ in their
competence along this area.

On the use of the four fundamental operations in Mathematics in fractions, pupils
are proficient in multiplication of fractions as compared to addition, subtraction and
division, as indicated by the mean frequency distribution below 200. This is observed to
be consistently highest in La Trinidad Central School, Xing Guang and Ying Feng
indicating their pupils to be proficient in multiplication followed by addition, subtraction
and division of fractions. Conversely, BSU pupils are competent but low in addition and
subtraction followed by multiplication and least for division. Only the pupils in Chinese
schools showed their proficiency in multiplication of fractions but they are consistently
low in all the other mathematical operation.

The competencies of grade six pupils in the use of the four fundamental
operations in fractions significantly vary, as indicated by the observed values, where the
computed f-values are significantly higher than the tabular F-values. Such results imply
that the pupils in BSU and La Trinidad Central School need to improve their competency
in using the four fundamental operations in Mathematics in fractions. In the two Chinese
\\
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schools, there is a need to improve the competencies of pupils in addition, subtraction and
division of fractions.

The pupils of the four schools do not significantly vary in their competencies in
the use of the four fundamental operations in decimal numbers. Although the distribution
is lower than the mean frequency distribution, BSU and La Trinidad Central School have
the highest in frequency of pupils competent in subtraction followed by those in addition,
multiplication and division. On the other hand, the highest frequency of pupils in Xing
Guang and Ying Feng is in addition followed by those in subtraction, multiplication and
division. Overall, the pupils of BSU and La Trinidad Central Schools perform best in
subtraction of decimal numbers and poor in division; whereas, the pupils of Xing Guang
and Ying Feng Elementary School perform best in addition and poor in division. The
schools vary significantly in terms of the competencies of pupils in the four schools.
Observation would also imply that the pupils are consistent in the area where they need to
improve their competencies.

In solving problems using the four fundamental operations, the BSU pupils are
consistent in their distribution, indicating that they excel better in word problems that are
related to subtraction and division and low in addition and multiplication. Similarly
pupils of Xing Guang and La Trinidad Central fare better in subtraction followed in
decreasing order by division, addition and multiplication. The pupils of Ying Feng fare
best in division followed by addition, subtraction and multiplication. The pupils the
pupils fare significantly better in subtraction and division in the use of the four
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fundamental operations in Mathematics in word problems as compared to subtraction
and addition. Problem solving, according to Jenson (1998), is one best way to grow a
better brain since this involves analysis and application of concepts. Ausrin et al (1997)
concluded that problem solving results to greater intellectual curiosity.

Generally, the pupils in the four schools do not fare well in Mathematics as seen
from their frequency distribution, which is below the mean distribution of 50 per area.
The same finding was reported by Mapandol (1980): that children are most deficient in
solving problems that involve whole numbers and rational numbers, percentages and
measurements and that apply principles, rules and generalizations about perimeter and
area. Piloten (1983) suggested that the difficulties in Mathematics is attributed to how a
teacher maintains a classroom atmosphere that is conducive to learning and this can be
seen through the classroom management capabilities of teachers. Other attributes are
related to classroom inadequacies in the school system such as lack of textbooks and the
lack of students’ comprehension of the teacher’s explanation due to unclear presentations
Barab and Landa (1997)

The foregoing findings can be attributed to the task orientation and engagement
in learning process. As stated by Elliot et al. (2000), when students’ academic learning
time is increased, their achievement improves. With improvement, students understand
and correctly complete their work.

Overall, it is inferred that the pupils are competent in the use of the four
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fundamental operations in all areas but non competent in the use of whole numbers and
word problems.
Competencies of Grade VI Pupils
in other Areas

Table 16 shows that the pupils are significantly competent in transforming a
number to percent. They are likewise competent in other areas, which, however, are
below the acceptable mean frequency of 200 . these other areas include ratios, identifying
measurement of angles, identifying solid objects, computing area of solid objects, other
mathematical activities and ratio and proportion.

That the competencies of pupils along the varied areas are significantly differ,
implies that they are proficient in transforming a number to a percent but not in other
areas. Conversely, the schools significantly differ in the competencies of their pupils,
where Ying Feng Road Elementary School is observed to be significantly highest in
competency followed by Xing Guang, La Trinidad Central School and BSU Elementary
Laboratory School. Manifestations of these are observed in the total frequency
distributions of 307, 301, 253 and 209 respectively.

In a study, Mandali (1979) identified several factors that play significant roles in
the achievement of students in Mathematics. Some of those identified by Santos (1980)
were lack of textbooks, lack of intensive drill work, absence of remedial teaching, lack of
interest of teacher and inability of students to comprehend and understand the different
problems in Mathematics.

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Table 16. Competencies of grade six pupils in learning other areas in Mathematics

SCHOOL
COMPETENCY
BSU
LTCS
XING GUANG
YING FENG
TOTAL

Ratio 48
30
48
50
176
Ratio and Proportion
19
36
34
34
123
Transforming a number to percent
47
48
65
61
221
Identifying a solid object
28
35
40
38
141
Identifying measurement of an
31 34
45
44 154
angle
Computing an area of a solid 16 35
38
40 129
object
TOTAL
189
218
270 267

F(between area of competence) =10.60s F(0.05) = 2.16
F(between schools) = 6.47S F(0.05) = 2.92


Relationship Between Socio-economic Profile
of Teachers and Selected Variables


Table 17 reveals the factors affecting the teaching practice of mathematics
teachers in terms of the extent of use of teaching approaches and methods, provision of
activities to pupils in learning Mathematics and degree of need to improve teaching in
Mathematics.
Age is significantly and negatively relates to the use of methods, teaching
approach and provision of activities. This finding indicates that the younger the teacher

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Table 17. Relationship between characteristics of Mathematics teachers and some
selected variables



SCHOOL
VARIABLE
CHARACTERISTIC
BSU LTCS YFRES XGES


Age
-0.84S -0.90S -0.69S -0.90S

Gender
1.00S 1.00S 1.00S 1.00S
Extent of use of
Teaching Method
Years in service
0.00 0.73s 0.62s 0.70
Highest Educational
-0.93S -0.87S -0.84S -0.88S
Attainment
Salary
0.69 -0.89S -0.79S -0.71S

Gender
-1.00S 1.00S 1.00S -1.00S

Provision of
Years in service
-0.49 -0.13 0.67S
0.74S
Activities
Highest Educational
-0.80 -0.87S -0.84S -0.83S
Attainment
Salary
-0.32 -0.89S -0.64 -0.61

Age
-0.96S -0.17 -0.29 -0.81S
Degree of need to
improve teaching
Gender
-1.00S -1.00S -1.00S -1.00S
Years in service
-0.86S -0.02 -0.43
0.88

Age
-0.76S -0.86S -0.67S -0.85S

Extent of use of Gender
1.00S
1.00S
-1.00S
1.00S
Teaching Method
Years in service
-0.58S -0.06S -0.63
0.77S
Highest Educational
-0.87S -0.87S -0.82S -0.80S
Attainment
Salary
-0.77S -0.88S -0.78S -0.57


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the higher the extent of use of methods and approach and provision of activities in
Mathematics. It is therefore inferred from the results that age is a factor in determining
the performance of teachers through use of teaching methods and approach and provision
of activities. Similarly, age is significant and negatively related to the areas of needs by
teachers in improving their teaching in Mathematics in BSU and Xing Guang Elementary
Laboratory School but not significantly related to those of teachers in La Trinidad Central
School and Ying Feng Road Elementary School. Gender is negatively and significantly
related to the use of methods and approaches, provision of activities and areas needed to
improve teaching of teachers. This finding means that female teachers have a higher
extent of use of teaching method and approaches, provide more activities for learning and
have a higher degree of need in improving their teaching in Mathematics than male
teachers. Gender therefore affects teaching in terms of the aforementioned aspects. Such
findings contradict the observation of Santos (1980) that sex does not affect learning, but
corroborate the finding of Sorenson (1979) that sex is not a factor that determines the the
differences in performance of learners in Mathematics.
Years in service is significantly and negatively related to frequency of use of
teaching methods and approaches in LTCS and BSU; activities in YFRES and XGES;
and degree of need in improving teaching Mathematics in BSU and XG Elementary
School. The relationship indicates that those who are younger in service in the
aforementioned schools have a higher extent of use of teaching methods and approach
and provision of activities and higher degree of need in improving their teaching.

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Furthermore, the younger teachers are more efficient in teaching and feel they to grow to
become effective teachers as manifested by their need of improving their teaching.
Conversely, salary is a significant factor in the use of teaching approaches for all
the schools involved in the study, and is significantly related to the use of methods for all
the three schools except for BSU. In other words, those receiving lower salaries have a
higher extent in the use of teaching methods and approaches and provision of activities
because they are challenged to do better if they wish to be promoted.
Obtaining higher education significantly affects the teachers’ extent of use of
methods and approach in teaching and provision of activities, especially the younger
teachers with only a bachelor’s degree.
Generally, factors such as age, gender, educational attainment and salary
significantly affect the use of teaching and approaches, provision of activities in teaching
Mathematics and the need of improving their teaching the subject.


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SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

Summary

This study was conducted with the intent to compare the status of teaching
Mathematics in selected schools in the Philippines and China. Specifically, the study
aimed to determine the socio-economic profile of Mathematics teachers and grade VI
pupils in the selected schools; to evaluate the extent of use of teaching approaches and
methods in Mathematics; to determine the extent of providing activities to pupils in
learning Mathematics; to identify the area of need of teachers to improve their teaching
Mathematics; to determine the performance of students in Mathematics; to identify the
specific area in Mathematics that the grade VI pupils are competent in; and to determine
the relationship between the socio-economic profile of teachers and the extent of use of
methods in teaching mathematics, teaching approach, extent of provision of activities in
learning Mathematics, and degree of needs for improving their teaching.
The respondents of the study were taken from selected schools of La Trinidad,
Benguet and Huai Hua City in China. Those schools selected as site of the study include
BSU-Elementary Laboratory School, La Trinidad Central School, Ying Feng Road
Elementary School and Xing Guang Elementary Laboratory School. A total enumeration
of all Mathematics teachers teaching in the schools were drawn as teacher-respondents
while 100 grade VI pupils were drawn as student-respondents. A descriptive survey was
used in the study and a test was structured for gathering data about the performance and
competencies of grade VI pupils.
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81
The salient findings are the following:


1. The great majority of Mathematics teachers range in age from, 21 to 40 years in
the four schools. The teachers are dominantly females. Almost all of them are bachelor’s
degree holders, and have been teaching for six to ten years. Their salary range from PhP
8,000 to above PhP 18,000.

2. The grade six pupils range in age from 11 to 12 years. Females dominate the
males in the four schools . Most of their parents have blue or white collar job.

3. The teaching approaches frequently used are discovery, conceptual, process
and unified. The process and conceptual approach is most frequently at BSU, an the
unified approach is frequently used in the other three schools.
4. Varied teaching methods are used by teachers in teaching Mathematics. Most
frequently used at BSU Elementary Laboratory School are activity method, inductive
method and problem-solving method; at La Trinidad Central School are discussion,
investigatory, integrated, problem-solving, and modular; at Ying Feng Road Elementary
School are reporting, activity and investigatory; and at Xing Guang Elementary
Laboratory School are those methods which are frequently of use in teaching
Mathematics.

5. The teachers provide varied activities during the teaching learning process in
Mathematics. However, Ying Feng Road Elementary School (YFRES) showed a very
frequent provision of the activities in teaching Mathematics. The leading activity is

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82
practice and drill, followed by giving quizzes. The use of traditional form of evaluation
through a pencil-and-paper test is very common to all teachers.

6. The Mathematics teachers of BSU Elementary Laboratory School feel that to
improve their teaching in Mathematics, they should attend in-service trainings and
seminars, make modules, conduct action research, update current strategies, improvise
teaching aids, use modern technology and use other textbooks.
Those in La Trinidad Central School feel that they have fewer needs to improve their
teaching in Mathematics. Those in Yin Feng Road Elementary School feel that they need
to attend in-service training and seminars, update of current strategies and improvise
teaching aids. Those in Xing Guang Elementary Laboratory School feel the need to
improve teaching aids and update current strategies in teaching.

7. The pupils in Ying Feng Road Elementary School have the highest
performance in Mathematics, followed by those at Xing Guang Elementary Laboratory
School, La Trinidad Central School and BSU Elementary Laboratory School. La Trinidad
Central School have more low performing pupils. Conversely, BSU Elementary
Laboratory School, Ying Feng Road Elementary School and Xing Guang Elementary
Laboratory School have high performing group of pupils. The pupils are competent in
addition of whole numbers and decimal numbers, and least competent in division of
whole number. In using the same mathematical operation in fractions, all the pupils are
most proficient in multiplication and least proficient for division. In using the
fundamental operations in word problems, the pupils are more competent in solving
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83
problems using subtraction and division than in using addition and multiplication. The
pupils are proficient in transforming a number to percent and have shown competence in
all the other areas but have not surpassed the acceptable criterion.

8. Age significantly and negatively relates to the use of methods, teaching
approach and provision of activities; and gender significantly and negatively relates to the
use of methods and approaches, provision of activities and areas needed to improve
teaching of teachers. Years in service significantly and negatively relates to frequency of
use of teaching methods and approaches in LTCS and BSU, activities in YFRES and
XGELS; and degree of need in improving teaching Mathematics in BSU and XG
Elementary Laboratory School.
Educational qualification significantly affects the teachers’ extent of use of
methods and approach in teaching and provision of activities. Salary significantly relates
to use of methods and approaches in some schools except for BSU.

Conclusion


Based on the results, the following conclusions are drawn:

1. All the teaching approaches are used in teaching Mathematics but the schools
significantly vary in the extent of use of the teaching approaches used in teaching
Mathematics. Most applicable among teachers is the use of unified approach where they
use the student vocabulary in the presentation of a topic in Mathematics. Relevant and
concrete examples are needed in the teaching of Mathematics.

2. The teachers do not significantly vary in the extent of use of the teaching
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84
methods in Mathematics. Differences in the extent of use of the method is likewise
observed among the four schools.

The teachers are proficient in the use of the methods except for reporting. This
shows that teachers promote the collaborative or cooperative learning in Mathematics.

3. Enhancement activities are provided but not frequently. Mastery learning is not
much an emphasized in the teaching of Mathematics in the two schools in Mathematics
as manifested by the low extent of providing the activity.

4. There is a need to increase more time for teachers to spend in classroom
teaching for Mathematics. Textbooks are scarce and teachers lack research skills in all
schools.

5. There is a need for pupils in all the schools to enhance their competencies using
the four fundamental operations in Mathematics and other areas of learning. Age, gender,
highest educational attainment and salary received by teachers are significantly and
negatively related to the extent of use of teaching methods and approaches and provision
of activities to pupils in learning Mathematics.


Recommendations


Based on the findings and conclusions, the following are recommended:

1. There is a need to improve the mathematical competencies of the grade VI
pupils. This can be done by improving performance of teachers through the use of
teaching methods and approaches.

2. Provision of trainings to upgrade the content and skills of teachers should be
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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85
addressed. While technology is one of the needs identified, teachers should be trained on
the appropriate use of instructional media including technology.

3. The different phases of learning should be emphasized in teaching. A
relearning process through in-service training is recommended where teachers should
explore other approaches in teaching mathematics to grade VI pupils.

4. Instructional planning and designing among Mathematics teachers should
include lesson clarity, instructional variety, task orientation and engagement in the
learning process.

5. Further study is recommended to find out other factors affecting performance
of teachers in Mathematics and the learning of pupils.




Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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LITERATURE CITED

ABUBO, E. P. 1989. The Pupils Factors in the Mathematics Achievement of First year

College students of Don Mariano Memorial State University. Unpublished thesis,

Don Mariano Memorial State University, College of Arts and Sciences, Agoo, La

Union.

AGLANO, A. M. 2002. Competencies of Students in Mathematics, Unpublished MA
thesis. Benguet State University, la Trinidad, Benguet.
ALCORN, M.1964. Better teaching in secondary school. New York: Holt, Rinehart and
Winston, Inc.

ALKEN, L.T. 1970. Attitudes Toward Mathematics. Review of Educational Research.

AUSTIN, ET AL. 1997. Effects of Thematically Integrated Mathematics Instruction on
Students of Mexican Descent. Journal of Educational Research. 88(5), 290-300.


BARAB & LANDA. 1997. Collaboration Among Teachers, Researchers and In-Service
Trainers to develop an Integrated Science Curriculum. Journal of Curriculum
Studies. 30(6), 661- 676.

BAWANG, R. G. 1995. Difficulties in Elementary Mathematics of Grade Six Graduates
Enrolled in State Universities and Colleges in the Cordillera Administrative
Region. Unpublished PhD thesis, Benguet State Univeristy, La Trinidad, Benguet.

BERLINER, B. C. 1988. As cited by ELLIOT, S. N. et al. 2000. Educational Psychology:
Effective Teaching, Effective Learning, 3rd Edition. Singapore: McGraw Hill
Companies, Inc.
BORICH, G. 1992. As cited by Elliot, S.N. et al. 2000. Educational Psychology:

Effective Teaching, Effective Learning, 3rd Edition. Singapore: McGraw Hill
Companies,
Inc.

BUSH, G.W. 2001. The No Child Left Behind Act. United States of America: American

Board For Certification of Teacher Excellence. P. 6.
CARINO, I. D. 1992. Will Education Succeed?. Manila: Department of Education

Culture and Sports. pp. 79-86.

CAET, J. D. 1979. An Appraisal of Elementary Mathematics Teachers in the Division of

Pagadian City. Unpublished Ma thesis. Bukidnon State College, Bukidnon.
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

---

87

DRAKE, S.M. 1998. Creating Integrated Curriculum: Proven ways to Increase Student

Learning. Thousand Oaks, C.A. Corwin Press.
DANTIS, S. A. 1982. Interrelationship of Academic Achievement Ability in

Mathematics Sex, Attitudes Toward Mathematics of Fourth Year High School

Students of Three Private Sectarian School in San Jose, Occidental, Mindoro,

1970-1971, Unpublished MA thesis. Centro Escolar University, Manila.

DELA, CRUZ de la, Pancho. 1992. Mathematical difficulties encountered by students of

accelerated Christian education schools, Baguio City, 1991-92. Unpublished

MA thesis, Baguio Central University, Baguio City.

DINAMLING, M. M. 1990. Mathematical Difficulties Encountered by the Students of

Accelerated Christian Education. Unpublished MA thesis. Baguio Central

University, Baguio City.

EDCOM, 1992. Point of View. Philippine Journal of Education.

ELLIOT, T.S. ET AL. 2000. Educational Psychology: Effective Teaching, Effective

Learning, 3rd Edition. Singapore: McGraw Hill Companies, Inc.

FRANKLIN, G. 2004. Curriculum, Instruction and Assessment: A Report. United States

of America: Glendale United School District.

GUERRERO, J. 1989. Te need for a revitalized teacher education. Diliman,Quezon City:
National Bookstore Inc.

HUIRA, K. 2006. Science and Mathematics Education Manpower Development Annual
Report. Philippines: Japan International Agency, University of the Philippines,
Diliman, Quezon City.

JIA, GUO FU (August 11, 2006), A New Mathematics Teaching Process. Unpublished

by Guang Zhou City 86th secondary school teacher.

BALINO, J.V. 1998. Selected Predictors of Performance of Students in Mathematics at

the cordillera Career Development College.

KASER, J. S. 1999. Enhancing Program Quality in Science and Mathematics. California:

Corwin Press, Inc.

KLEIN, J.T. 1996. Crossing Boundaries: Knowledge, Disciplinaries, and Inter-
disciplinaries. Charlottesville and London: U of Virginia Press.

Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

---

88

JENSON, J.R. 1998. Integrating Science, Mathematics, and technology in Middle Schoo

Technology-Rich Environments: ‘A Study of Implementation and Change’.
School Science and Mathematics. 100(1),27-35.

LARDIZABAL,A.,et al., 1991. Principles and Methods of Teaching. Phoenix Publishing

House Inc., Quezon City, Philippines

LEVAK, et al. 1993. ‘ Global Connections’, Educational Leadership. 51(1), 73-75.

LUBRICA, P.A. 1996. The Teaching of Science and Technology in the Secondary
School of Cordillera Administrative Region. Unpublished Doctorate Dissertation.
La Trinidad, Benguet

MADALI, E. L. 1979. Guidance in the School. Quezon City: R. P. Garcia Publishing Co.


MAPANDOL, P. M., 1980. Causes of Low Performance of Grade Six Pupils in

Mathematics in Bauko District, division of Mountain Province, Unpublished MA

thesis, Baguio Central University, Baguio City.

MARRERO, E.L. 1989. Remedial Measures on Problem-solving in Mathematics IV in

the Public Secondary School in Benguet. Unpublished MA thesis. Baguio Central

University, Baguio City.

MAZON, T. C. 1982. A Study of the Difficulties of Grade VI Pupils in Problem-solving
in Arithmetic in the Province of La Union. Unpublished MA thesis. Northern
Educational Institute, Dagupan City.

OASAN, N. D. 1983. The relationship Between the NCEE Scores of the University of
Baguio College Freshmen and Their Ratings in College Algebra. Unpublished
MA thesis. University of Baguio, Baguio City.

OCAMPO, V. 1987. The performance aoooraised system for teachers as implementaed
by the division of Benguet. Unpublished PhD disseration, Saint Louis
University, Baguio City.

PILAR, E. C. 1989. Determinants of Academic Performance in Mathematics.

Unpublished MA thesis. Northwestern College, Laoag City.

PILOTEN, P. V. 1983. Difficulties and Attitudes of Fourth Year High School Students
Regarding Mathematics. Unpublished MA thesis. Baguio Central University,
Baguio City.


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

---

89

RAMOS, Z. J. 1983. Factors Influencing Academic Achievement in Mathematics of

Grade VI Pupils ar Araulli Lyceum, Cabanatuan City. Unpublished MA thesis.

Araulo Lyceum, Cabanatuan City.

SALANDANAN, G, et al. 1988. The Teaching of Science, and Health, Mathematics, and
Home Economics, and Practical Arts. Teaching Strategies III. Philippine
Association for Teacher Education. Katha Publishing Co., Inc. Quezon City.

SALAMONIS, B. L. 1970. Methods and Materials in Today’s High School’ . New York:

Van ROstrand Reinhold.

SAMBRANO, G. and RIVERA, F. 1982. Toward Effective Teaching. Quezon City:

Golden Art Publishing Crop.

SANTOS, A. A. 1980. A Comparative Study of the Mathematical Ability of Boys and
Girls. Unpublished MA thesis. Abad Santos Educational Institution, Manila. P. V.

SERION, J.R. 1980. Our Contemporary Mathematics Program, New Thrusts in Philippine

Education. Current Events Digest Inc.



SORENSON, S. J. 1979. Psychology in Education. New York: Addison-Wesley.
STA.

TATING, A. Y. 1993. UNESCO’S Role in teacher development. The Modem teacher.

TOLEDO, M. 1982. In-service Training needs perceived by Mathematics Teachers of

Mountain State Agricultural College. Unpublished MA thesis , University of the

Philippines, Diliman, Quezon City.

WEN, J. 2005. How to Improve The Students Interest in Learning Mathematics. Chines

Mathe Research. China.

WU GUITI’s (2006), Impress Math and Experience Math. Unpublished report by Wen

Xin Elementary School Grade I Mathematics Teacher.

YI MING (2005), How to Develop the Student Interest in Learning Math. Unpublished

Master Thesis. East of China Normal University.

Zhu, Z. 2002. Functioning Modes of Information Technology in Classroom Instruction:

A report. China: East Normal University.


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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90
1. http://www.English.people.com.cn/English
2. http://www.weordstatting.com/onfo/teach/sample/resume.com
3. http://www.amth.about.com/cs/reference/a/discalcula.htm
4. http://www.pep.com
5. http://www.goal.com
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
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APPENDICES

APPROVAL LETTER
Republic of the Philippines
College of teacher Education
BENGUET STATE UNIVERSITY
La Trinidad, Benguet

August 4, 2006
ELADIO O. LAPICTO, Ed.D.
Prinicipal
Elementary Laboratory School
Benguet State University
La Trinidad, Benguet
Dear Sir,

The undersigned is taking up Master of Arts and Education, major in Educational
Administration and Supervision at the Benguet State University and at present
conducting a research study titled “LEVEL OF MATHEMATICS COMPETENCIES
AMONG GRADE VI PUPILS IN SELECTED SCHOOLS OF LA TRINIDAD,
BENGUET, PHILIPPINES AND HUAI HUA CITY, HUAN, CHINA: A
COMPARATIVE STUDY” in partial fulfillment of the requirements for the degree.
Related to this, may I request that I will be allowed to conduct my research in
your Department. Rest assured that the information supplied will be treated
confidentially.

Thank you very much.


Sincerely yours,




(Sgd) WUZHEN SHU








Researcher
Noted by:

(Sgd) PERCYVERANDA A. LUBRICA, PhD. (Sgd)TESSIE M. MERESTELA, D. Agr.
Adviser
Graduate School Dean


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Republic of the Philippines
College of Teacher Education
BENGUET STATE UNIVERSITY
La Trinidad, Benguet

August 4, 2006
ANDRES L. PAWID
Principal
La Trinidad Central School
Poblacion, La Trinidad, Benguet


Dear Sir,

The undersigned is taking up Master of Arts and Education, major in Educational
Administration and Supervision at the Benguet State University and at present
conducting a research study titled “LEVEL OF MATHEMATICS COMPETENCIES
AMONG GRADE VI PUPILS IN SELECTED SCHOOLS OF LA TRINIDAD,
BENGUET, PHILIPPINES AND HUAI HUA CITY, HUAN, CHINA: A
COMPARATIVE STUDY” in partial fulfillment of the requirements for the degree.
Related to this, may I request that I will be allowed to conduct my research in
your Department. Rest assured that the information supplied will be treated
confidentially.


Thank you very much.

Sincerely yours,




(Sgd) WUZHEN SHU









Researcher
Noted by:

(Sgd) PERCYVERANDA A. LUBRICA, PhD. (Sgd)TESSIE M. MERESTELA, D. Agr.
Adviser
Graduate School Dean


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95
TEACHER’S QUESTIONNAIRE
I. Please provide the necessary information as indicated.

Name (optional): ___________________
Date:________________

Age: ___________ Gender: ____Male ____Female
Nationality: ____________ Cultural/ Ethnic Background: ______________
Highest educational attainment: ____________________________________
Number of years in teaching Mathematics: ___________________________
Range of salary: Please check.
P8,000-P10,000 ___ P10,001-P12,000___ P12,001-P14,000 ___
P41,001-P16,000___ P16,001-P18,000___ more than P18,000___
II. Directions: The following are approaches employed in teaching Mathematics.
Please put a check mark under the appropriate column using the
following
scales.

4 – Frequently utilized (76% - 90% Used in most instruction)

3 - Often utilized (50% - 75 % used in instruction)

2 – Seldom Utilized (less than 50% used in instruction)

1 – Not used




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TEACHING
APPROACH
4 3 2 1
1. Stress on the learning of concepts theories, principles and
____ ____ ___ ___
content through discovery.
2. Finding of the unknown including all forms of obtaining
____ ____ ___ ___
knowledge by use of one’s own mind
3. Deriving a concept or principle using mental processes
____ ____ ___ ___
4. The instruction is designed to make the students discover
____ ____ ___ ___
rules or principles in math.
5. The lesson is designed such that the students are taught the ____ ____ ___ ___
concepts leading them to discover rules or principles.
6. The students are taught the content from simple to complex.
____ ____ ___ ___
7. The students are guided to organize their data from simplified ____ ____ ___ ___
to complex level in the form of graphing, tables, diagrams
and figures.
8. The students are taught where knowledge is the main concern ____ ____ ___ ___
of the teacher.
9. The student are taught focusing on the development of their ____ ____ ___ ___
skills
10. The teacher is able to determine the weaknesses of the
____ ____ ___ ___
student in their skill formation.
11. The teacher questions more and tells less.
____ ____ ___ ___
12. The student is made to learn in search of truth information
____ ____ ___ ___
or knowledge.
13. The student is taught to search for the solution of a problem ____ ____ ___ ___
through exploration and evaluation.
14. Teacher reinforces previous learning.
____ ____ ___ ___
15. Presentation of topic of subject is geared to student
____ ____ ___ ___
vocabulary level.
16. Knowledge is expanded through citation of relevant
____ ____ ___ ___
example and concrete situation.
17. Others (please specify)







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III. Directions: The following are methods used in teaching Mathematics.
Please put a check mark under the appropriate column using the
following scales.

4 – Frequently utilized ( 76% - 90% Used in most instruction)

3 - Often utilized (50% - 75 % used in instruction)

2 – Seldom Utilized (less than 50% used in instruction)

1 – Not used

TEACHING
METHOD
4 3 2 1
1. The students are provided with needed information by




factual presentation and textual explanation of a particular
____ ____ ___ ___
topic (Lecture Method)
2. Students are guided to give a free exchange of ideas about a




particular topic (Discussion Method)
____ ____ ___ ___
3. Students are allowed to search for information about a




given topic and report it in class (Reporting Method)
____ ____ ___ ___
4. Teacher shows a step by step presentation through concrete




actions and materials of which the students will observe
____ ____ ___ ___
(Demonstration Method)
5. The students are engaged in the activity to have a first hand




experience about the concept being learned (Activity
____ ____ ___ ___
Method)
6. The students are taught starting from the known to the




unknown; from the specific to the general; from the
____ ____ ___ ___
particular to the universal; from simple to complex; and
from the concrete to the abs
tract (Inductive Method)
7. The teacher begins teaching from a generalization and




subsequently gives examples and specific situations that are ____ ____ ___ ___
supportive of it (Deductive Method)
8. Students are required to do an experiment, conduct an




investigation, try out different alternatives to solve a given
____ ____ ___ ___
problem (Investigatory Method)
9. Students’ individual differences are recognized by giving




the student the freedom to set his own schedule for
____ ____ ___ ___
learning and to monitor his own progress while the teacher
acts as a consultant (Self-pacing Method)
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98


10. The teacher uses textbook learning, rote learning, directed
____ ____ ___ ___
technique’ and memorization (Traditional Method)
11. The students are made to focus on sets of questions which




are answered from reading books and other printed
____ ____ ___ ___
materials. They share their insights and answers during
the class session. (Recitation Method)
12. Teacher combines two or more subjects to explain a main




topic. One is a springboard and the other is the main




topic. Other subject areas could be supportive to the main
topic. (Integrated Method)
____ ____ ___ ___
13. Teacher sets a good criteria for students to come up with a
____ ____ ___ ___
solution (Problem-solving Method)
14. Students are given a self-contained and independent unit




of instruction with specific objectives. The student is




given an opportunity to know the specific objectives and
do the learning activities by following specific
____ ____ ___ ___
procedures. (Modular Method)
15. Students are given interesting homework that requires a




little research or participation and assistance from family
____ ____ ___ ___
members (Assignment Method)
16. Students are required to practice and master important




prerequisite skills necessary for the whole lesson.
____ ____ ___ ___
Constant review is necessary. (Practice and Drill Method)
17. Others (please specify)




________________________________________
____ ____ ___ ___
________________________________________
____ ____ ___ ___






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IV. What are the activities provided in learning Mathematics? Please Check:

Scale: 5- Very Frequently Utilized
4
-
Frequently
Utilized
3
-Moderately
Utilized
2
-
Seldom
Utilized
1-
Not
Utilized
(5)
(4)
(3)
(2)
(1)
a.
Recitation
___
___
___
___
___
b.
Problem-solving


___ ___ ___ ___ ___
c.
Board
work
___
___
___
___
___
d.
Assignment/
homework

___ ___ ___ ___ ___
e.
Quizzes
___
___
___
___
___
f.
Tests/
examinations



___ ___ ___ ___ ___
g.
Discussion
with
classmates


___ ___ ___ ___ ___
h.
Discussion
with
teacher

___ ___ ___ ___ ___
i.
Solving
modules


___ ___ ___ ___ ___
j. Memorization ___
___
___
___
___
h. Drawing & paper cutting ___
___
___
___
___
i. Others (please specify)


___
___
___
___
___


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100
V. Please check the areas that needed Improvement.
Scale 4- very much needed
3- much needed
2- needed
1- not needed

(4)
(3)
(2)
(1)
a. attendance to in-service training ___
___
___
___
b. attendance to seminars ___
___
___
___


c. making modules
___
___
___
___


d. upgrade subject content
___
___
___
___


e. conduct action research
___
___
___
___


f. learn current teaching strategies ___
___
___
___


g. improvise teaching aids ___
___
___
___


h. include modern technology ___
___
___
___


i. addition teaching time ___
___
___
___


j. availability of appropriate textbooks ___
___
___
___


k. others (please specify) ___
___
___
___










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101
PUPIL’S QUESTIONNAIRE

I. Please provide the necessary information as indicated
Name (optional): ___________________

Date:________________

Gender: ____Male ____Female Age: ________________

Cultural/ Ethnic Background: _______________Nationality: ___________
Parent’s Occupation:
Father’s Occupation: ________________
Mother’s Occupation: _______________

II. Instruction: The following are mathematical problems. Please circle the correct
answer.
A. Mathematical Equations on Whole Numbers, Fractions and decimals.

1. 6,387 + 2,339 =
a. 8,726 b. 8,716 c. 8,626 d. not given

2. 762 + 219 =
a. 1,081 b. 981 c. 971 d. not given
3. ⅞+⅝+⅜+⅛=
a. 1⅞ b. 1⅜ c. 2 d. 2⅛
4. 1⅔+¾+¼=
a. 2 b. 2⅔ c. 1¼ d. 2½

5. 0.75
+0.1391


a. 0.9891 b. 0.8891 c. .01466 d. 0.1371
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102
6. 4.5980
+ 7.8165



a. 12.4045 b. 12.4145 c. 11.4145 d. 12.3145
7. 8 754 935 - 1 320 412 =
a. 7,434,523 b. 7,434,423 c. 7,424,523 d. not given
8. __– 3/10=5
a. 8/10 b. ⅔ c. 53/10 d. not given
9. 0.704
-0.019

a. 0.795 b. 0.685 c. 0.785 d. not given
10. 9.57128
-2.89340


a. 6.85788 b. 6.58778 c. 6.86788 d. not given
11. 493 202

X 87


a. 42,908,574 b. 42,908,476 c. 42,907,574 d. not given


12. 6 138 76
X 354


a. 217,312,114

c. 217,213,104
b. 217,312,104

d. not given


13. 1/9 x 3 =




a. 3/27 b. ⅓ c. 3 d. not given


14. 9 ⅓ x 30=


a. 300 b. 372 c. 280. d. not given



Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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103
15. 0.976 x 6.9 =

a. 7 b. 6 c. 10 d. not given


16. 182 ÷ 40 =




a. 4.55 b. 40.55 c. 4.5 d. not given


17. 1⅓÷ 7=

a. 7⅓ b. ⅞ c. ¾ d. not given


18. 234.6 ÷10 =


a. 2346.0 b. 0.2346 c. 2.346 d. not given
B. Ratio:
19. Given the illustration, which gives the correct ratio?







a. 3:4 b. 5:6 c. 4:3 d. not given
20. Given the illustration, which gives the correct ratio?






a. 7:8 b. 6:5 c. 6:4 d. 4:6


C. Ratio and Proportion:

21. 0.75= %=
12


a. 75 & 9 b. 25 & 10 c. 0.75 & 100 d. not given
22. 0.50 = ( ) %=( ) :14


a. 20 & 14 b. 0.5 & 7 c. 50 & 7 d. not given


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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104
D. Percentage


1. ½




a. 20% b. 40% c. 50% d. not given
2. ¼


a. 20% b. 25% c. 50 d. not given

3. ⅜


a. 30%. b. 37.5% c. 68% d. not given


E. Geometry
1. What kind of triangle is this?
a. right triangle b. equilateral triangle
c. Scalene triangle d. Isosceles triangle


2. What is the measure of the angle?

A
a. 180° b. 90° c. 45° d. not given
B
C

3. The quadrilateral b=46cm, h=34cm. what is the area of the
quadrilateral?

b a. 80cm² b.1564cm²
h
c. 782cm² d. not given





Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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105
4. What is the area of the triangle? (a=12cm b=12cm)


c
a. 24cm² b. 72cm²
a
c. 144cm² d. not given
5. Which polygon is a trapezoid?
b


a b c d







F. Problem Solving：

1. Alan ordered a model car hit for $27.98, a model boat kit for $22.79,
and a model airplane kit for $30. What was the total amount of his
order?
a. $79.67 b. $51.07 c. $80.77 d. not given
2. A lager theater has enough seats for 1,050 people. If 875 people attend
a show, how many empty seats are there?
a. 285 b. 175 c. 185 d. not given
3. Marco plans to take a 2-hour typing lesson 3 days a week. He will take
the lessons for 12 weeks. How many hours of lessons will he take in all?
a. 36 b. 84 c. 72 d. not given
3. What is the quotient when 35.46 is divided by 3?
a. 12 b. 32.46 c. 11.82 d. not given
Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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BIOGRAPHICAL SKETCH

Wuzhen Shu was born in Huai Hua City, Hu Nan Province, China on January 19,
1975. She is the fifth out of six children in her family.
She finished her elementary education at Tian Wan Central Elementary School in
July 1989. She finished her Middle School Education at Tian Wan Middle School in July
1992 and her high school at Chen Xi No. 2 Secondary School in July 1995. She received
her college degree of Bachelor of Science in Elementary Education at Hu Nan Teachers
University in July 1998. She finished a second degree, Business Administration, from the
International Studies Institute, Zhong Jiang Branch, Nan Jing City, Jiang Su Province,
China in March 2004.
She taught Chinese Language to grade I-IV pupils. She stopped teaching and was
employed at Guangzhou Television Station in the Editorial office as a TV play editor.
She spent time to learn how to work well in this job. She learned the art of dealing with
clients and shots advertisements, etc. After three months of hard work, she earned her
first advertisement. The proceeds of the advertisements went to the education of poor
children. She loves to do a kind of job that could help others in need.
She finished her degree in Master of Arts in Education major in Educational
Administration and Supervision at Benguet State University, La Trinidad, Benguet,
Philippines.


Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and
Huai Hua City, Hunan, China: A Comparative Study / Wuzhen Shu. 2006

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Document Outline

• Teaching Mathematics Among Selected Public Schools In La Trinidad, Benguet, Philippines and Huai Hua City, Hunan, China: A Comparative Study
  • BIBLIOGRAPHY
  • ABSTRACT
  • TABLE OF CONTENTS
  • INTRODUCTION
    • Background of the Study
    • Statement of the Problem
    • Objectives of the Study
    • Importance of the Study
    • Scope and Delimitation of the Study
  • REVIEW OF LITERATURE
    • Professional Profile of Teachers
    • Profile of Pupils
    • Teaching Approaches / Methods
    • Learning Activities in Mathematics
    • Level of Competencies in DifferentAreas in Mathematics
    • Relationship Between Variables
    • Other Related Studies
    • Conceptual Framework
    • Paradigm of the study
    • Definition of Terms
    • Hypotheses of the Study
  • METHODOLOGY
    • Locale of the Study
    • Respondents of the Study
    • Research Design
    • Instrumentation
    • Data Gathering
    • Statistical Treatment of Data
  • RESULTS AND DISCUSSION
    • Socio-economic Profile of Mathematics Teachers
    • Socio-economic Profile of Grade VI Pupils
    • Teaching Approach Used By Teachersin Teaching Mathematics
    • Teaching Methods Employed by Teachersin Teaching Mathematics
    • Extent of Provision of Activitiesin Teaching Mathematics
    • Perceived Degree of Needs in Specific Areasin Teaching Mathematics
    • Performance of Grade VI Pupils in Mathematics
    • Competencies of Grade Six Pupils inVaried Areas in Mathematics
    • Competencies of Grade VI Pupilsin other Areas
    • Relationship Between Socio-economic Profileof Teachers and Selected Variables
  • SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
    • Summary
    • Conclusion
    • Recommendations
  • LITERATURE CITED
  • APPENDICES
  • BIOGRAPHICAL SKETCH

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