Feljone g. ragma master's thesis

COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE
SECONDARY SCHOOLS IN SAN FERNANDO CITY, LA UNION:
BASIS FOR A TWO-PRONGED TRAINING PROGRAM

A Thesis
Presented to the Faculty
of the Graduate School
College of Teacher-Education
Saint Louis College
City of San Fernando (La Union)

In Partial Fulfillment of
the Requirements for the DEGREE
MASTER OF ARTS IN EDUCATION
MAJOR IN MATHEMATICS

By
FELJONE GALIMA RAGMA

February, 2011

INDORSEMENT
This

thesis,

TEACHERS

IN

FERNANDO

CITY,

entitled,

THE

―COMPETENCE

OF

PRIVATE SECONDARY

LA

UNION:

BASIS

FOR

MATHEMATICS

SCHOOLS
A

IN

SAN

TWO-PRONGED

TRAINING PROGRAM,‖ prepared and submitted by FELJONE GALIMA
RAGMA in partial fulfillment of the requirements for the degree of
MASTER OF ARTS IN EDUCATION MAJOR IN MATHEMATICS, has
been examined and is recommended for acceptance and approval for
ORAL EXAMINATION.
MR.GERARDO L. HOGGANG, MAMT
Adviser
This

is

to

certify

that

the

thesis

entitled,

―COMPETENCE

OF

MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS
IN SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED
TRAINING PROGRAM,” prepared and submitted by FELJONE GALIMA
RAGMA is recommended for ORAL EXAMINATION.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member

MARILOU R. ALMOJUELA, Ed.D
Member

Noted by:
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College

APPROVAL SHEET
Approved by the Committee on Oral Examination as PASSED with
a grade of 96% on February 18, 2011.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member

MARILOU R. ALMOJUELA, Ed.D
Member

ENGR. ANGELICA DOLORES, MATE-Math
CHED RO I Representative
Member
Accepted and approved in partial fulfillment of the requirements for
the

degree

of

MASTER

OF

ARTS

IN

EDUCATION

MAJOR

IN

MATHEMATICS.
Saint Louis College
This is to certify that FELJONE GALIMA RAGMA has completed
all academic requirements and PASSED the Comprehensive Examination
with a grade of 94% in May, 2010 for the degree of MASTER OF ARTS
IN EDUCATION MAJOR IN MATHEMATICS.

Saint Louis College

ACKNOWLEDGMENT
The researcher wishes to express his sincerest gratitude and warm
appreciation to the following persons who had contributed much in
helping him shape and reshape this valuable piece of work.
Mr. Gerry Hoggang, thesis adviser, for always giving necessary
suggestions to better this study.
Dr. Nora A. Oredina, chairwoman of the examiners, for her
valuable critique, and most especially, for inspiring the researcher to
pursue his Masterate degree.
Engineer Angelica Dolores, MATE-Math, CHED representative, for
her intellectual comments and recommendations.
Dr. Marilou R. Almojuela and Mrs. Edwina Manalang, panelists,
for their brilliant thoughts.
Dr. Jose P. Almeida, Mrs. Rica A. Perez, Mrs. Rosabel N. Aspiras
for validating the two sets of questionnaire.
Sr. Teresita A. Lara, Sr. Angelica Cruz, Mrs. Evangeline L.
Mangaoang, Mr. Danilo Romero, and Mrs. Loreta Cepriaso for validating
the two-pronged training program.
Principals, heads, teachers and students of the Private Secondary
Schools in the City Division of San Fernando, La Union for lending some
of their precious time in giving their responses to the questionnaires.

Mr. Amado I. Dumaguin, his former Mathematics Coordinator, for
always giving him inspiration and push; and for believing in the
researcher‘s capabilities.
Mr. & Mrs. Felipe and Norma Ragma, researcher‘s parents, for
always being there when the researcher needed some push.
And lastly, to God Almighty for giving the needed strength in the
pursuit of this endeavor.
F. G. R.

DEDICATION

To my Parents
Mr. & Mrs Felipe and Norma
Ragma
and
To my siblings
Darwin, Felinor and Nailyn
This humble work is a sign of my love to
you!
F.G.R.

THESIS ABSTRACT
TITLE: COMPETENCE OF MATHEMATICS TEACHERS IN THE
PRIVATE SECONDARY SCHOOLS IN SAN FERNANDO CITY,
LA UNION: BASIS FOR A TWO-PRONGED TRAINING
PROGRAM
Total Number of Pages: 230
AUTHOR: FELJONE G. RAGMA
ADVISER: MR. GERARDO L. HOGGANG, MAMT
TYPE OF DOCUMENT: Thesis
TYPE OF PUBLICATION: Unpublished
ACCREDITING INSTITUTION: Saint Louis College
City of San Fernando, La Union
CHED, Region I
Abstract:
The

study

aimed

at

determining

the

competence

level

of

mathematics teachers in the private secondary schools in San Fernando
City, La Union with the end goal of designing a validated two-pronged
training program.
Specifically, it looked into the profile of the mathematics teachers
along highest educational attainment, number of years in teaching
mathematics and number of mathematics trainings and seminars
attended; the level of competence of mathematics teachers along content

and instruction; the relationship between teacher‘s profile and content
competence, teacher‘s profile and instructional competence and content
and instructional competence; the major strengths and weaknesses of
the mathematics teachers along content and instruction and; the type
and validity of the training program.
The study is descriptive with two sets of questionnaire as the
primary data gathering instruments. It covered thirteen (13) private
secondary schools in San Fernando City, La Union with heads, faculty,
and students as respondents.
The study found out that all the mathematics teachers are licensed
and majority of them are pursuing graduate studies and had 0-5 years of
teaching experience; 84.62% had very inadequate and 15.39% had
slightly adequate attendance in seminars. It also found out that the
teachers‘ level of content competence was average with a mean rating of
16. They scored highest in conceptual and computational skills but
lowest in problem-solving skills. On the other hand, their level of
instructional competence was very good with a mean rating of 4.24. They
were rated highest in management skills but lowest in teaching skills.
Moreover, the study found that there is no significant difference in
the perceptions between students and teachers and between teachers
and heads but there is a significant difference in the perceptions between
students and heads. Also, there is no significant relationship between

profile and content competence and between content and instructional
competence. On the other hand, there is a significant relationship
between highest educational attainment and instructional competence;
but there is no significant relationship between number of years of
teaching and number of seminars attended to instructional competence.
The teachers‘ conceptual and computational skills are considered
as strengths. On the other hand, reasoning and problem-solving skills
are considered as weaknesses. All the other skills under teaching,
guidance, management and evaluation were considered strengths. The
weakness of Mathematics teachers along instructional competence was
on the quality of

utilization of information and communication

technology. In connection to the output of the study, the two-pronged
training program enhances the weaknesses and the sustainability of the
strengths. Its face and content validity was found high.
Based on the findings, the researcher concluded that the
mathematics teachers are all qualified in the teaching profession; they
are very young in the service and are exposed minimally to trainings and
seminars but they still perform well in their teaching; the teachers had
only average competence in terms of their content competence but were
perceived very skillful in teaching Mathematics.
Further, the heads rated instructional competence higher than the
students; but all the respondents considered the teachers very skillful in

teaching. Teachers who have higher educational attainment, number of
years in teaching and seminars do not have higher subject matter
competence and teachers who have higher educational attainment have
higher instructional competence; but, teachers who are more experienced
in teaching and have more seminars do not mean that they have higher
instructional competence than those who are younger and those who
have lesser seminars. It does not also mean that when a teacher has high
content competence, he has high instructional competence as well and
vice versa.
Further, teachers are not so skilled at analysis and problemsolving and they do not use ICT and other innovative instructional
technology much in their daily teachings but still have very good
teaching performance.
The validated two-pronged training program is timely for the new
and tenured teachers to update and upgrade their content and
instructional competence. Moreover, it is a helpful tool for them to
understand more their subject and know more about the ways on how to
present a subject matter, especially on the use of ICT.
Based on the conclusions, the researcher recommends that the
teachers should be encouraged to enroll in their graduate studies;
incentive scheme for outstanding performance should be devised by
administrators; teachers should always be sent to seminars and

workshops where their participation is necessary; teachers should use
ICT in their teaching and that the school has to provide such ICT
materials; a closer monitoring system has to be applied by the heads; the
proposed two-pronged training program for the Mathematics teachers
should be implemented in the private secondary schools in the City
Division of San Fernando, La Union; a study to determine the efficiency
or efficacy of the two-pronged training program should be undertaken;
and lastly, a parallel study should be undertaken in other subject areas
such as English and Science.

TABLE OF CONTENTS
Page
TITLE PAGE ………………………………………………………………

i

INDORSEMENT ………………………………………………………….

ii

APPROVAL SHEET ……………………………………………………...

iii

ACKNOWLEDGMENT …………………………………………………..

iv-v

DEDICATION ……………………………………………………………..

vi

THESIS ABSTRACT ……………………………………………………..

vii-xi

TABLE OF CONTENTS …………………………………………………

xii-xvii

LIST OF TABLES ………………………………………………………..

xviii –xix

FIGURE ……………………………………………………………………

xx

Chapter
1

The Problem ………………………………………………

1

Rationale …………………………………………….
Theoretical Framework …………………………..

7-14

Conceptual Framework ………………………….

15-17

Statement of the Problem ……………………….

19-20

Hypotheses…………………………………………

20-21

Scope and Delimitation …………………………

21-22

Importance of the Study ………………………..

22-23

Definition of Terms ………………………………..
2

1-7

23-26

Review of Related Literature …………………………

27

Profile of High School Mathematics Teachers ..

27

Highest Educational Attainment ……………….

27-28

Number of Years in Teaching Mathematics ….

29-30

Number of Seminars Attended …………………..

30-31

Level of Content and Instructional Competence ..

31

Subject Matter/Content …………………………….

32-33

Teaching Skills ……………………………………….

33-37

Guidance Skills ………………………………………

37-39

Management Skills …………………………………..

39-40

Evaluation Skills ……………………………………..

40-42

Comparison in Perceived Instructional Competence
Among Respondent Groups …………………………

42-43

Relationship of Profile and Content
Competence ……………………………………………

43-46

Relationship of Profile and Instructional
Competence …………………………………………….

46-48

Relationship between Content and
Instructional Competence ………………………..

48-50

Strengths and Weaknesses in Teachers‘
Competence ………………………………………….
Training Programs …………………………………..
3

50-52
52-53

Research Methodology ……………………………………..

54

Research Design …………………………………….
Sources of Data ……………………………………..

54-55

Instrumentation and Data Collection ………….

56-58

Validity and Reliability of the Instrument …….

58-60

Tools for Data Analysis ……………………………

60-64

Data Categorization ………………………………..

64-66

Proposed Training Program ………………………

66

Validity of the Training Program ………………..
4

54

66-67

Presentation, Analysis and Interpretation of Data…

68

Profile of Mathematics Instructors ………………

68

Highest Educational Attainment …………….

68-70

Number of Years in Teaching Mathematics…

70-71

Number of Seminars Attended ………………..

71-72

Summary of the Profile of Mathematics Teachers.. 73-74
Level of Content Competence ……………………….. 74
Conceptual Skills ………………………………….

74-76

Analytical Skills ……………………………………

76-78

Computational Skills ……………………………… 78-79
Problem-Solving Skills ……………………………. 79-81
Summary of Level of Content Competence.……. 81-83
Level of Instructional Competence ………………………………. 83
Teaching Skills ………………………………………….

83-86

Substantiality of Teaching ……………………….

86-87

Quality of Teachers‘ Explanation ………………

87

Receptivity to Students‘ Ideas
And Contributions ………………………………….

87-88

Quality of Questioning Procedure ………………

88

Selection of Teaching Methods ………………….

88

Quality of Information and Communication
Technology Used …………………………………..

89

Guidance Skills ….……………………………………

89-90

Quality of Interaction with Students ………….

90-91

Quality of Student Activity ………………………

91

Management Skills …………………………………..

91

Atmosphere in the Classroom …………………..

91-93

Conduct and Return of Evaluation
Materials ……………………………………………
Evaluation Skills ……………………………………..
Quality of Appraisal Questions………………….

93-94
94
94-96

Quality of Assignment/Enrichment
Activities …………………………………………….

96

Quality of Appraising Students
Performance …………………………………………
Comparison in the Perceived Instructional

97

Competence of the Groups of Respondents
Students and Teachers……………………………

97-98

Students and Heads……………………………….

99-100

Heads and Teachers……………………………….

100-101

Summary of Level of Instructional Competence ………

102-105

Relationship between Profile and
Content Competence ……………………………………….

105-108

Relationship between Profile and
Instructional Competence …………………………………

108-111

Relationship between Content and
Instructional Competencies ……………………………..

111-113

Summary of Relationship…………………………………….

113-114

Strengths and Weaknesses along Content Competence… 115-116
Strengths and Weaknesses along
Instructional Competence…………………….

116-121

Teaching Skills……………………………………

121-122

Guidance Skills ………………………………….

122

Management Skills ………………………………

122

Evaluation Skills …………………………………

122-123

Proposed Two-Pronged Training Program ………………

123-129

Level of Validity of the Proposed …………………………..

129-13)

Two-Pronged Training Program ………………………….

131-140

Sample Flyer of the Two-Pronged Training Program………. 141
5

Summary, Conclusions and Recommendations ……. 142
Summary …………………………………………

142-144

Findings ……………………………………………

144-145

Conclusions……………………………………….

146-147

Recommendations ………………………………

147-149

BIBLIOGRAPHY………………………………………….

150-161

APPENDICES …………………………………………….

162-219

CURRICULUM VITAE…………………………………….

210-213

LIST OF TABLES

Table 1……………………………………………………………

56

Table 2……………………………………………………………

69

Table 3……………………………………………………………

71

Table 4……………………………………………………………

72

Table 5……………………………………………………………

73

Table 6……………………………………………………………

75

Table 7……………………………………………………………

77

Table 8……………………………………………………………

79

Table 9……………………………………………………………

80

Table 10…………………………………………………………

82

Table 11…………………………………………………………

84-86

Table 12…………………………………………………………

90

Table 13…………………………………………………………

92-93

Table 14…………………………………………………………

94-96

Table 15…………………………………………………………

98

Table 16…………………………………………………………

99

Table 17…………………………………………………………

101

Table 18…………………………………………………………

103-104

Table 19…………………………………………………………

106

Table 20…………………………………………………………

109

Table 21…………………………………………………………

112

Table 22…………………………………………………………

114

Table 23…………………………………………………………

116

Table 24…………………………………………………………

117-121

Table 25 ………………………………………………………..

129-130

FIGURE

Figure
1

Page
The Research Paradigm …………………………………..

18

Chapter 1
THE PROBLEM
Rationale
The tremendous task of education today, under the enormous
influx of technological advances and innovations, is still the development
of a learner into a whole person, a complete human being capable of
understanding his own complexity and his intricate society. The teacher,
who is in charge of this global task, needs to cope with the challenges of
the modern times. He has to be equipped with the resources vital in
arousing and sustaining students‘ interest, in facilitating the learning
process, and in evaluating the learning outcomes. He should be a master
of his craft and is genuinely concerned with the total growth and
development of his students (Clemente-Reyes 2002).
Quality education is first and foremost a function of instruction.
Thus, for education to attain and sustain its quality, it should be coupled
with the best preparation for excellent instruction. It is then emphasized
that to be an excellent high school teacher, one should both have full
command of the subject and full knowledge of the teaching-learning
process including course structure and examination system. The
teacher, therefore, should not only have mastery of the subject matter
but also an in-depth understanding of the mind set and standards of

students within the class (http://www.dooyoo.co.uk/discussion/whatqualities-make-an-excellent-teacher/1039890/).
It is irrefutable that secondary education plays an essential part in
every nation‘s educational system (Darling-Hammond 2008). One high
school subject highly supportive of this is Mathematics.
No one can question the role being played by Mathematics in
education. In fact, Mathematics is one of the basic tool subjects in
secondary education. As such, mathematics teachers contend that the
place

of

mathematics

in

the

basic

education

is

indispensable

(http://wiki.answers.com/Q/Why_is_Mathematics_Indispensable).

It

has

been felt that mathematics has both utilitarian and disciplinary uses
necessary for everyone. By the very nature of the discipline, its
application to both science and technology and to the human sciences is
easily recognized by the layman. The bricklayer, the carpenter, and the
nuclear

scientist

use

mathematics

of

varied

complexities

(www.eric.edu/practicalities_mathed). Thus, the role of mathematics in
the holistic formation of every learner is vital (Sumagaysay 2001).
It can be gleaned, therefore, that it is important for students to
develop their potentials and capacities in mathematics to the fullest in all
possible means. In doing this, a sound mathematics curriculum that
would provide each learner the necessary skills and competence in
mathematics is hence necessary. The 2010 Secondary Mathematics

Education Curriculum Guide explicitly presents the Mathematics
Curriculum framework:
The goal of basic education is functional literacy for
all. In line with this, the learner in Mathematics should
demonstrate core competencies such as problem solving,
communicating mathematically, reasoning mathematically
and making connections and representations.
These competencies are expected to be developed
using approaches as practical work/ outdoor activities,
mathematical investigations/games and puzzles, and the
use of ICT and integration with other disciplines.
With these contents in the Secondary Mathematics Framework,
quality secondary mathematics education, reflective in the best practices
in instruction, would also entail the use of effective approaches and
techniques of teaching, which would equip each learner the needed skills
and competencies. On top of it all, a competent mathematics teacher who
empowers learners to achieve the goals of mathematics education, and
who is efficient and effective in providing quality mathematics instruction
is imperative (Gonzalez 2000).
The

country‘s

vision

for

quality

education

with

focus

on

Mathematics Proficiency is undoubted. But, our country, of course, is
not relieved from the crises. In fact, Dr. Milagros Ibe of the University of
the Philippines said that the result of a survey on the competence of
Science and Mathematics teachers showed that majority of the teachers
are not qualified to teach the subjects. With this issue at hand, Ibe

remarked that it is easy to understand why the achievement of Filipino
Students in Science and Mathematics was dismally low (Lobo 2000). In
the 2000 issue of the Philippine Journal of Education as cited by Aspiras
(2004), Ibe supports her contention of the connection of teachers‘
competence and students‘ achievement. She stressed that Filipino
students suffer from poor thinking skills; they are only able to recall
concepts but for questions beyond that or which require multiple-step
problem solving, our students appeared to have been stumped. As a
result, math and science skills of students from 42 countries showed
that Filipino students are biting the dust of their global counterparts.
These ideas prompted former President and now Congresswoman Gloria
Macapagal-Arroyo (Educator‘s Journal, 2003). She stressed that in order
for Filipino students to be globally competitive, the national aims to
improve the country‘s educational standards and to upgrade teachers‘
competence have to be pushed (Educator‘s Journal, 2003). Despite these
aims, recent LET results revealed that majority of the secondary teacherexaminees are not qualified to teach. In April, 2010 the passing rate for
secondary teachers was only 23.32% and in September, 2010 the
passing rate was 25.86%. These rates reveal that teachers, though
possess the needed degree/s are not yet qualified to teach; thus, they are
not competent. However, Lee (2010) clarified that passing the test does
not guarantee content competence. This is because majority of the

passers have rates of 75-79%. He highlighted that rates such as these
reflect fair or if not, poor competence.
On

the

light

of

mathematics

teacher‘s

qualification

and

competence, issues arise, too. First, Lobo (2000), as cited by Oredina
(2006) reveals in his article that only 71% of the Mathematics Teachers
claim to have formal preparation in Mathematics. This means that 29%,
who are unqualified to teach mathematics, still teach the subject. In
addition, the Civil Service Commission (CSC) has ruled that the
Department of Education (DepEd) may hire and retain teachers even if
they had not yet registered with Professional Regulation Commission
(PRC) as mandated by Republic Act No.7836 (Educator‘s Journal 2003).
This further implies that a non-registered math teacher or a non-major is
teaching math. Another, teacher handling the same subjects or in the
same year level develops the idea and practice to be stagnant-an ordinary
lecturer in a classroom (Farol 2000). Furthermore, many graduates of
teacher-education institutions, though received formal education, are not
prepared to handle a class of learners (Adams 2002).

Further, the UP

Institute of Science and Mathematics Education also revealed that ―many
teachers at all levels do not have the content background required to
teach the subjects they are teaching‖. The survey revealed that only 41%
of mathematics teachers are qualified to teach the subject (Cayabyab
2010). With this reality, it is not surprising why students performed

poorly in Mathematics Achievement Test. This is stressed by Roldan
(2004) in her assertion that students‘ mathematics low performance is
reflective of the weak mathematics teachers‘ influence. Roldan (2004)
revealed that secondary teachers in Region I were proficient only in
concepts and computations but they were deficient in their skills in
problem-solving and the use of teaching strategies. Thus, mathematics
teachers frequently find themselves focusing on mechanics, the answerresulting procedures-without really teaching what mathematics is all
about-where it came from, how it was labored on, how ideals were
perceived, refined, and developed into useful theories-in brief, its social
and human relevance (Cayabyab,2010).
It was also disclosed by Bambico (2002) in her dissertation that
that majority of the mathematics teachers in Region I scored 17 out of 35
simple mathematics problems; and their instructional competence
ranged from 54.71% to 78.03% only. These ratings were emphasized to
be weaknesses and the major reasons why the passing rate of the region
in the NAT has not even reached 80% and up.
In the City Division of San Fernando, particularly in the Private
secondary schools, quality mathematics teaching had been given much
emphasis. Several seminars and training-workshops had been organized
to update and upgrade teachers‘ competence.

One most recent

Mathematics Seminar was organized by the Association of the Private

Schools last July, 2010. The seminar-workshop on Trends in Teaching
High School Mathematics was an aim to improve the students‘
mathematics performance in the 2009 National Achievement Test (NAT)
(Eligio 2010). The seminar was attended by mathematics teachers in the
Private Schools in La Union where the researcher served as the resource
speaker. This brought out that majority of the teachers could not fully
analyze problems in higher Mathematics such as Geometry and
Trigonometry despite the fact they have graduated with a Mathematics
degree. They were also found to be very young in the service and that
they tend to teach mathematics word problems using one approach.
Even though seminars and trainings were conducted, these only
lasted for few hours and had no follow-ups. Another, only a few are sent
by the participating schools to attend such endeavor.
It is then with these predicaments that the researcher embarked
on the idea to appraise and evaluate the competence of mathematics
teachers along content and instruction. The results, in turn, will be the
foundations of proposing a validated two-pronged training program for
the Mathematics teachers in the Private Secondary Schools of the City
Division of San Fernando for the academic year 2010-2011.
Theoretical Framework
To put this study in its theoretical framework, a discussion on the
competence theories, theories of teaching and learning, the best practices

and approaches of an effective teacher, and the concept of training are
presented. Several theories on learning are also included since teachers
are learners, too. They need to learn first the fundamentals, the
strategies and techniques before they can actually impart knowledge to
their students.
Mathematics involves learning simple skills, calculations, facts and
procedures where memory, most especially practice are the most
essential. It requires a high level of creative and analytic thinking. Thus,
mathematics teachers should know when and what concepts to teach,
when and why students are having difficulties, how to make concepts
meaningful, when and how to improve skills and how to stimulate
productive and creative thinking in order to fully analyze what they are
doing (Subala 2006).
Piaget (1964) opined that as a child acquires knowledge of the
environment, he or she develops mental structures called concepts.
Concepts are rules that describe properties of environment events and
their relations with other concepts. As applied to teachers, when teachers
get familiar with certain concepts and routines, they are able to master
the skills.
Dewey‘s (1896) notion of knowledge for teaching is one that
features inquiry with, and practice as the basis for professional judgment
grounded in both theoretical and practical knowledge. If teachers

investigate the effects of their teaching on student learning and if they
study what others have learned, they come to understand teaching to be
an interesting endeavor. They become sensitive to variation and more
aware of the different purposes and situations. They are assessed on
contingent knowledge to become more thoughtful decision-makers.
According to Thorndike (1926), learning becomes more effective
when one is ready for the activity, practices what he has learned and
enjoys the learning experience. As applied to teachers, they cannot teach
effectively if they have not learned sufficiently.
Thorndike‘s law of exercise states that the more frequently a
stimulus response connection occurs, the stronger association and
hence, the stronger learning. Practice without knowledge of results is not
nearly effective as when the consequences become known to the learner.
Further, concepts are the substance of mathematical knowledge.
Students can make sense of mathematcs only if they understand its
concepts and their meanings or interpretations. An understanding of
mathematical concepts involves around more than mere recall of
definitions and recognition of common examples. The assessment of
students‘ understanding of concepts should be sensitive to the
development nature of concept acquisition. (Arellano 2004)
Bruner‘s (1968) most famous statement is that, any subject can be
taught effectively in some intellectually honest form to any child at any

stage of development. He insisted that the final goal of teaching is to
promote the general understanding of the structure of a subject matter.
To learn and use mathematics requires a substantial mastery of
computation. To master a skill of computation requires constant
practice, repetition and drill. Computational skills are essential in order
to facilitate the learning of new math concepts, to promote productive
thinking in problem solving, research and other creative thinking
activities.
Mathematics teachers have always viewed problem solving as a
preferential objective of mathematics instruction (Subala 2006). It was
not until the National Council of Teachers of Mathematics (NCTM)
published its position paper that problem solving truly came of age. As
its very first recommendation, the council proposed that problem solving
be the focus of school mathematics and performance in problem solving
be the measure of the effectiveness of the personal and national position
of mathematical competence (Taback, 1998).
Bruner (1968) believed that intellectual development is innately
sequential,

moving

from

inactive

through

iconic

to

symbolic

representation. He felt it is highly probable that this is also the best
sequence for any subject to take. The extent to which an individual finds
it difficult to master a given subject depends largely on the sequence in
which the material is presented. Further, Bruner also asserted that

learning needs reinforcement. He explained that in order for an
individual to achieve mastery of a problem, feedback must be reviewed as
to how they are doing. The results must be learned at the very time an
individual is evaluating his/her performance.
The above theories suggest that problems and applications should
be used to introduce new mathematical content to help students develop
both their understanding of concepts and facility with procedures, and to
apply and review processes they have learned.
Besides his abilities and competence, a teacher who is tasked to
facilitate the teaching-learning process, also needs a set of teaching
theories. These theories, which are based on the teachers‘ understanding
of the learner and the educative process, become the bases of his ways
on how to influence his students to learn. The 2010 Secondary
Mathematics Curriculum provide the three most important theories.
These

are

Experiential

Learning

by

David

Kolb

and

Rogers,

Constructivism and Cooperative Learning.
Experiential Learning by Kolb and Rogers presents that significant
learning takes place when the subject matter is relevant to students‘
experience and is purposeful to their personal interest. This further
connotes that human beings have the natural tendencies to learn; as
such, the task of the teacher is just to facilitate learning. Facilitating
learning revolves around (1) setting a positive climate, (2) clarifying the

purpose of the learner, (3) organizing and making available learning
resources, (4) balancing intellectual and emotional components of
learning and (5) sharing feelings and thoughts with learners but not
dominating. Thus, Experiential learning substantiates the Principle of
Learning by doing (http://oprf.com/Rogers).
On the other hand, constructivism roots from the idea that ―one
only knows something if one can explain it‖. This idea was formalized by
Immanuel Kant, who asserted that students are not passive recepients of
information;

rather,

they

are

active

learners

(www.wikipedia.com/ImmanuelKant). A basic theoretical proposition of
constructivism is that the students are eager participant in the
acquisition of knowledge. So, in the constructivist room, the teacher
serves not as the authority, but the pathfinder of knowledge.
Cooperative Learning Theory by Johnson and Johnson, in
addition, holds that learning is significant when students work together
to accomplish a task. The cooperative tasks are designed to elicit positive
interactions, provide students with different opportunities, and make
students engage in learning. This theory suppports the MultipleIntelligence Theory by Gardner (Montealegre 2003).
The Mathematical Framework also necessitates integration. As
such, the Reflective Teaching Theory is vital. This theory is based on the
Ignatian Pedagogy asserting that teaching experience should include

interaction from the students, which calls the plan to implement
reflections that give birth to new insights, knowledge and enlightenment
regarding one‘s self based upon the content of teaching (Crudo 2005).
In addition, in her dissertation on Mathematics Education,
Cayabyab (2010) theorized a mathematics stepping-stone theory. She
stressed that in teaching mathematics, students should be taught that
every mistake, every fault, every difficulty encountered becomes a
stepping-stone to better and higher things. She added that in teaching
and learning mathematics,skills on patience and accuracy are developed.
When a teacher has finished teaching, he therefore administers
strategies for assessment and evaluation to gauge learning. The theory of
Evaluation by Burden and Byrd, as mentioned by Oredina (2006),
pointed out that frequent, continuous and impartial evaluation of
academic performance is vital not only for the growth of institution but
also for the growth of the individual. Evaluation would tell whether
improvement is necessary.
If a teacher wants to be the best teacher for her students, he
should not fail to upgrade and update himself. The concept of training
enters the scene. Training is the process of acquiring specific skills to
perform a better job. It helps people to become qualified and proficient in
doing some jobs (Fianza,2009). Usually, an organization facilitates the
employees‘ learning through training so that their modified behavior

contributes to the attainment of the organization‘s goals and objectives
(Oredina 2006).
Further, training is a complex activity and must be clearly
planned. Design and preparation of training course usually consume
more time than delivery of the material. Successful training requires
careful planning by the trainer. Planning helps the trainer/s determine
that the appropriate participants have been invited to the training course
and that the training is designed to meet their needs in an effective way.
Thus steps in planning for effective training program are a requisite.
According to the PDF article accessed from the internet, the parts of a
training program include objectives, content , materials or resources,
methods

or

procedures,

and

evaluation

strategy

(www.jifsan.umd.edu/pdf/gaps-en/VI-Effective-Training-Com.pdf).
The abovementioned instructional competency dimensions find its
essence in the general areas cited in the questionnare.These serve as the
building blocks in structuring this research.
Moreover, the theories in teaching and learning, practices and
approaches,

and

the

principles

in

teaching

mathematics

show

parallelism in each of the content of the instructional dimensions. These
may also serve in the formulation of the recommendations of the study.
The concept of training serves as the core idea in designing the
output of this pursuit.

Conceptual Framework
The task of a teacher is complex and many-sided and demands a
variety

of

human

abilities

and

competencies.

The

abilities

and

competencies of a teacher, according to Nava (1999), as cited by
Clemente (2002), are subject matter – mastery of content-specific
knowledge for the effective instruction,

classroom management –

creation of an environment conducive to learning, facilitation of learning
– implicit and explicit knowledge of various teaching strategies and
methods to attain instructional objectives, and diagnostic – knowledge of
class needs and goals, abilities and achievement levels, motives,
emotions, which influence instruction and learning. These competence
dimensions were also mentioned by Lardizabal (2001). According to her,
the four dimensions are teaching skills, guidance skills, management
skills, and evaluation skills.
Effective high school mathematics teaching, therefore, involves
mastery of the subject matter on the part of the teacher, understanding
students‘ differences, interest and background, skills in the use of
appropriate methods and techniques, appropriate assessment strategies
and flexibility and sensitivity to adopt to the needs of students. Thus, the
nature of the task of a teacher is not easy. This then implies that the
teacher has to improve if his vision of influencing students to learn is of
prime concern.

One of the most time-tested ways for continuing development of
the professional teachers is the training and in-service educational
program. Its rationale is to help teachers carry out their job better. The
outcome of a well-planned training program is manifested in an
environment

of

learning

suited

to

the

needs

of

the

children

(www.britannicaonlineencyclopedia/training). This then connotes that
when teachers improve for the better, students improve for the better,
too.
Boiser (2000) extends his idea that if one aspires to continue
teaching effectively, he needs to continue upgrading himself. He opines
that to upgrade necessitates reading professional references, enrolling in
advanced courses and attending trainings, conferences and workshops.
Additionally, Lapuz (2007),as cited by Bello (2009), stresses the need for
training and retraining if teachers really wanted to be competent.
It is in this light that the study is thought of, formulated and set
up. This conceptualization is logically designed in the research paradigm
in Figure 1. The paradigm made use of the Input-Throughput-Output
model. The input is composed of the profile of mathematics teachers
along highest educational attainment, number of years in teaching, and
number of trainings and seminars attended. Further, it also contains the
variables on the level of competence along content and instruction. These
variables are indeed necessary to determine how competent the

mathematics teachers in the Private Secondary Schools in the City
Division of San Fernando, La Union are.
The throughput incorporated the processes of analyzing and
interpreting the variables in the input- profile (highest educational
attainment, number of years in teaching, number of seminars attended);
level of competence along content and instruction; the comparison in the
perceived instructional competence among the three respondent groups;
the culled-out strengths and weaknesses,and tests of correlation between
profile and the levels of competence along content and instruction; and
the relationship between the levels of competence along content and
instruction. It also holds the process of conceptualizing and validating
the output of the study.
The output of the study, therefore, is a validated two-pronged
training program for mathematics teachers in the Private Secondary
Schools in the City Division of San Fernando, La Union for academic year
2010-2011.

Input

A. Profile of mathematics teachers
along:
1. Highest educational
attainment;
2. Number of years in teaching
math; and
3. Number of seminars and
trainings
B. Level of competence of
mathematics teachers along:
1. Content
a. conceptual skills
b. reasoning/analytical
skills
c. computational skills
d. problem-solving skills;
and
2. Instruction
a. Teaching/
Facilitating Skills;
b. Guidance Skills;
c. Management
Skills; and

Throughput

Output

A. Analysis and interpretation of:
1. Teachers’ profile
2. Level of competence along
content and instruction
2.1 Comparison in the
perceived instructional
competence among the
respondent groups
3. Relationship between
a. teachers’ profile and
level of competence
along content;
b. teachers’ profile and
level of competence
along instruction; and
c. teachers’
competencies along
content and instruction
4. Strengths and weaknesses
on the level of competence
B. Development of a Proposed
Two-Pronged Training
Program for Mathematics
Teachers
C. Validation of the TwoPronged
Training Program

d. Evaluation Skills
1. face
2. content

Fig. 1
Research Paradigm

A Validated TwoPronged
Training Program
for Mathematics
Teachers

Statement of the Problem
This study aims primarily to determine the level of competence of
mathematics teachers in the Private Secondary Schools in San Fernando for
the academic year 2010-2011 as basis for a validated two-pronged training

program. Specifically, it aims to answer the following questions:
1. What is the profile of the mathematics teachers along:
a. highest educational qualification;
b. number of years in teaching mathematics; and
c. number

of

mathematics

trainings

and

seminars

attended?
2. What is the level of competence of mathematics teachers along:
a. Content
a.1. Conceptual Skills
a.2. Reasoning/ Analytical Skills
a.3. Computational Skills
a.4. Problem-Solving Skills ; and
b. Instruction

b.1.Teaching Facilitating Skills
b.2. Guidance Skills
b.3. Management Skills
b.4. Evaluation Skills?

2.1 Is there a significant difference in the instructional competence
of the teachers as perceived by the students, heads and
teachers, themselves?
3. Is there a significant relationship between:
a. Teacher‘s profile and competence along content;
b. Teacher‘s profile and competence along instruction; and
c. Competence

along

content

and

competence

along

instruction?
4. What are the major strengths and weaknesses of the mathematics
teachers along:
a. Content; and
b. Instruction?
5. Based on the findings, what training program may be proposed to
enhance

the

content

and

instructional

competence

of

the

mathematics teachers?
5.1 What is the level of validity of the training program along:
a. face; and
b. content?
Hypotheses
The researcher is guided by the following hypotheses:
1. There is no significant difference in the perceived instructional
competence of the teachers among the three respondent groups.

2. There is no significant relationship existing between:
a. Teacher‘s profile and competence along content
b. Teachers‘s profile and competence along instruction
c. Competence along
Scope and Delimitation
The primary aim of this study is to determine the level of
competence of high school mathematics teachers in the Private Schools
of the City Division of San Fernando for the academic year 2010-2011.
The 13 (thirteen) schools include Brain and Heart Center (BHC), Saint
Louis College (SLC), Christ the King College (CKC), Gifted Learning
Center, MBC Lily Valley School, La Union Cultural Institute (LUCI), La
Union Colleges of Arts, Sciences and Nursing (LUCNAS),Union Christian
College (UCC), San Lorenzo Science High Schoool (SLSHS), National
College of Science and Technology(NCST), Central Ilocandia College of
Science and Technology (CICOSAT), Felkris Academy, and Diocesan
Seminary of the Heart of Jesus (DSHJ). Further, there are three (3)
respondent groups: the Mathematics teachers, the heads, and the
students. Each Mathematics teacher in the private schools of San
Fernando is evaluated by one of his/her classes.
Based on the identified strenghts and weaknesses on the level of
content and instructional competence of the mathematics teachers, a
proposed two-pronged training program is formulated. The proposed

training program will be administered to the Private Secondary Schools
in the City Division of San Fernando, La Union. Since it involves
logistics, the administrators of the Private Secondary Schools in the City
Division of San Fernando are asked to validate the proposed two-pronged
training program for teachers.
Importance of the Study
This piece of work will greatly benefit the administrators, heads,
teachers, students, the researcher and future researchers.
To school administrators of the Private Secondary Schools in the
City Division of San Fernando, this study will provide them with data
that can help them formulate the in-service training programs. Further,
they will also be guided in structuring the Faculty Development Program
that is aimed at intensifying and sustaining the skills of the teaching
workforce;
To the Mathematics heads of the City Division of San Fernando,
this study will give them insights about the competence of their teachers.
This will also provide them data in designing the Human Resources
Development Plan;
To Mathematics teachers, this study will give them baseline data of
their strenghts and weaknesses in content and instruction. The output of
the study, on the other hand, will make them more competent, prepared,
directed and helped in carrying out their noble tasks;

To students of the Private Secondary Schools in San Fernando City
Division, this study will lead them to a thoughtful understanding of
mathematics for they are handled by more competent teachers;
To the researcher, a Mathematics teacher and at the same time the
Subject Area Coordinator for Mathematics of Christ the King College, this
study will help him in improving his mathematics teachers‘ competence;
and
To future researchers, who will be interested to conduct similar
studies, this study will motivate them to pursue their research since this
study can be used as basis.
Definition of Terms
To

better

understand

this

research,

the

following

items

are

operationally defined:
Content Competence. This pertains to the subject matter knowledge of
the

Mathematics

Mathematics
Algebra,

teachers

subjects:

Geometry,

in

the

Elementary

Advanced

four

(4)

Algebra,

Algebra,

secondary

Intermediate

Trigonometry

&

Statistics. Further, this also gauges the cognitive skills in
Mathematics along conceptual, analytical, computational and
problem-sloving.

Analytical

Skills.

This

pertains

to

the

skills

on

comprehension that requires investigative inquiry and
logical reasoning.
Computational Skills. This pertains to the skills that involve
the fundamental mathematical operations.
Conceptual Skills. This pertains to the skills on learning facts
and simple recall.
Problem-Solving Skills. This pertains to the skills that
require multiple-step plan to come up with a decision
or a solution.
Instructional Competence. This is divided into four dimensions:
teaching/facilitating skills, management skills, guidance skills
and evaluation skills.
Evaluation

skills.

This

is

an

area

on

instructional

competence which includes quality of appraisal questions,
quality of assignment/enrichment activities, and quality of
appraising students‘ performance.
Guidance skills. This is an area on instructional competence
which includes quality of interaction and quality of
activity.

Management
competence

skills.

This

which

is

an

area

includes

on

instructional

atmosphere

in

the

classroom,and conduct and return of evaluation materials.
Teaching skills. This is an area on intsructional competence
which includes substantiality of teaching, quality of
teacher‘s explanation, receptivity to students‘ ideas and
contributions, quality of questioning procedure, selection
of teaching methods, and quality of information and
communication technology utilized.
Heads. This pertains to the principals, academic coordinators, subject
area coordinators and department heads.
Level of Competence. This pertains to the degree or extent of
attainment along content and instruction of the Mathematics
teachers.
Mathematics students. These are the students duly enrolled in a private
high school in San Fernando for the academic year 2010-2011.
Mathematics teachers. These are the teachers handling secondary
mathematics in the Private Secondary schools in San Fernando for
the academic year 2010-2011.
Private Secondary schools in San Fernando. These are the nongovernment schools owned by private institutions and individuals
where the three groups of respondents came from.

Profile. This contains the variables on highest educational attainment,
number of years in teaching, and

number of trainings and

seminars attended.
Highest educational attainment. This pertains to the highest
academic qualification of the

high school mathematics teachers

for the academic year 2010-2011.
Number of years in Teaching. This refers to the length of service
a mathematics teacher has in the academe.
Number of Seminars attended. This refers to the frequency of
trainings undergone by a Mathematics teacher for the past 2 years.
Strength. This term refers to a content competence rating of 17 and
above and to an instructional competence rating of 3.51 and
above.
Two-Pronged Training Program. This refers to an action plan devised in
the study to enhance the content and instructional competence of
mathematics teachers of the Private schools in the City Division of
San Fernando.
Weakness. This refers to a content competence rating of below 17 and an
instructional competence rating of below 3.51.

Chapter 2
REVIEW OF RELATED LITERATURE AND STUDIES
A summary of professional literature and studies related to the
present study are presented in this chapter. These helped strengthen the
framework of this study and substantiated its findings.
Profile of Secondary Mathematics Teachers
According to the Executive Summary on Teachers and Institution,
teacher qualifications matter (www.sec.dost.gov.ph). It is with this idea
that the areas on teacher‘s profile are established. The areas include
Highest Educational Attainment, Years in teaching Mathematics and
Numbers of Trainings and Seminars Attended.
Highest Educational Attainment
Republic Act 9293, an act amending section 26 of RA 7836 states
that no person shall engage in teaching or act as a professional teacher
whether in preschool, elementary or secondary level unless the person is
duly registered.
Fianza (2009) revealed in her study that majority of the
respondents possessed the required eligibility to teach secondary
mathematics since most of the teachers were LET/PBET passers and
degree holders of mathematics. She further stressed that 40 out of 56
respondents were bachelor‘s degree holders, 15 had master‘s degree and
1 had doctorate degree.

Bautista, as cited by Binay-an (2002), stressed that teachers, in
general, met the educational requirements in accordance with the Magna
Carta for Public School Teachers. She also stressed that teachers didn‘t
want to remain stagnant in their field.
Eslava (2001) found out that out of the 40 teacher-respondents in
the secondary schools in La Union, only 12 or 30% were AB/BS
graduates, 19 or 47.5% were AB/BS with MA/MS units, or 8 or 20%
were MA/MS graduates and 1 or 2.5 was a PhD/EdD graduate. It was
pointed out that the mathematics teachers value continuing education to
further equip themselves in the issues and concerns about teaching.
In the Education Journal of the District of Thailand year 2009, the
study of Dr. Naree Aware-Achwarin (2005) was noted. The findings of this
published study disclosed that most of the teachers (92.88%) held
bachelor‘s degree; very few teachers (6.23%) held master‘s degree or
higher degrees.
Rulloda (2000), as cited by Oyanda (2003), expressed that teachers
did not want to remain stagnant in their undergraduate degrees. They
endeavored to improve their competencies by updating and upgrading
themselves through the formal process. It was necessary for them to
elevate their professional outlook to make them effective and worthy
members of the profession.

Number of Years in Teaching Mathematics
In the revised guidelines of the appointment and promotions of
teaching and related teaching group (DepEd order No.66, s 2007)
teaching experience is one of the criteria. Thus, the more experienced a
faculty member is the more confident and effective he is in teaching. This
was confirmed and affirmed by the study of Aware-Achwarin (2005). She
stressed that most of the teachers (71.07%) had teaching experience of
more than 10 years.
However,

several

local

studies

ran

nonparallel

to

these

international findings. Oyanda (2003) revealed that 136 high school
Mathematics teachers taught for 5-9 years, 132 taught for 0-4 years and
only a few had 20 years or more teaching experience. This implied that
majority of the teacher-respondents were quite young in the service.
Fianza (2009) also revealed that 67% of her respondents were very
young in teaching high school geometry. These respondents are in the
teaching service for less than 4 years.
According to Laroco (2005), 10% of the Private High School
Mathematics teachers in Urdaneta had been teaching for 15-19 years.
30% had 5-9 years of teaching and majority (60%) had taught for 4
years. The same implication was revealed.
Yumul (2001) noted that the length of teaching experience was a
valid indicator of performance. This is also seconded by the study of

Mallare (2001) stating that teaching experience is the best predictor of
mathematics achievement. These assertions can be easily established
since teachers develop their effectiveness as they become aware and
more experienced in the realities and complexities of teaching.
Number of Seminars and Trainings Attended
As teachers become the 21st century teachers, they need to
continually update and upgrade themselves to serve the needs of the socalled digital learners. One way of doing this is through attending
mathematics seminars or trainings.
Oyanda (2003) revealed that 6 (six) had attended international
trainings and 45 had national trainings. However, 4 revealed that they
had not attended any training. It was pointed out that only a few went to
international seminars/in-service trainings due to financial reasons
including lack of sponsorship from the government and private sectors.
Laroco (2005) brought out that most of the teacher-respondents
only attended seminars within the division level. The 2nd was regional.
The 3rd was at school and 4th was at the national level. This was due also
to financial constraints.
Fianza (2009) divulged that more than fifty percent of the
respondents attended trainings on curriculum, teaching strategies,
management, and assessment methods/ tools. Less than fifty percent of

the respondents attended trainings on content in Geometry. These
seminars are based on school and local.
Cabusora

(2004)

unveiled

that

attendance

of

his

teacher-

respondents to seminars and trainings were mostly local and regional.
Oredina (2006) disclosed that the instructors have attended a few
trainings and seminars for professional development. With these,
majority of the teacher-respondents have ―very inadequate‖ participation
in seminars and training workshops. The reasons she stressed were
financial constraints, non-availability of the instructors due to school
commitments and the distance of the seminar venue.
Level of Content and Instructional Competence
The significant factor in achieving quality Secondary Mathematics
Education is teachers‘ competence along content and instruction. Diaz
(2002) supports this by expressing that to be a successful mathematics
teacher, one must be competent in math and in mathematics
instruction. Thus, the levels of competence along the two dimensions
show teachers‘ strengths and weaknesses that serve as basis to develop
and

actualize

activities

that

will

further

improve

and

enhance

competence. Mathematics teachers can therefore improve the ability of
their learners when they have very good content knowledge of their
subject area and at the same time sound instructional skills.

Subject Matter/ Content
Cabusora (2004) stressed that the first essential of effective
teaching is teacher‘s thorough grasp of the subject matter he teaches.
According to Toledo (1992) and Bagaforo (1998), as cited by Diaz
(2000), teachers, in general, felt moderately competent in their knowledge
and ability in mathematics. It was disclosed that the teachers still lack
the

knowledge

of

mathematics

subjects,

particularly

the

higher

mathematics. Thus, it was concluded that teachers did not possess math
competence at level adequate for teaching secondary mathematics. Diaz
(2000) also found out in her study that teachers were moderately
competent in their knowledge in mathematics.
Gundayao (2000) found in her study that the teachers teaching
secondary mathematics in the Province of Quirino had ―good‖ level of
proficiency in Algebra, ―poor‖ in Geometry and ―poor‖ in Trigonometry. In
general, the results were poor because the teachers lacked the
competence in analyzing high level of category in analyzing problems.
Subala (2006) found out in her study that the graduating math
majors of teacher-training institutions in Region I were moderately
competent in Basic Math, fairly competent in Algebra and Statistics and
poorly competent in Geometry and Trigonometry.

Roldan (2004) revealed that her respondents were Above Average in
Math I and II and average in Math III and Math IV. She concluded that
the conceptual skills of the mathematics teachers were very important
and teachers need to consistently update and upgrade their capabilities
to enable them to cope with the challenges of the new millennium. Thus,
teachers needed to improve their skills in the topics of a particular
subject found to be weaknesses.
Teaching or Facilitating Skills
The shift of the teacher‘s role as provider of knowledge to facilitator
of learning or pathfinder of knowledge calls for proper application of
teaching methods to make the learning experiences vital and relevant.
Thus, the effectiveness of teaching Mathematics relies to a great extent
not only upon the teachers‘ educational attainment or skills but also
upon his competence in the subject.
Laroco (2005) unveiled that teachers mostly relied on textbooks to
facilitate the teaching-learning process. She also cited Yumul (2001)
revealing that the adequate instructional materials were not highly
utilized.
Sameon (2002) found out in his study that the most pressing
problems encountered by the instructors were inadequate facilities and
equipment; inadequate knowledge of teaching strategies and approaches.

Likewise, Bello (2009) also divulged that her respondents were
capable in teaching but had not yet achieved the level of competence for
optimum effectiveness. She stressed that teachers have more to enhance
such as on educational technology, technology integration, professional
relationship, community linkages and collaboration.
Also,

according

to

the

monitoring

and

evaluation

of

the

implementation of the basic education curriculum, there were gross
inconsistencies between the kind of graduates/learners that the schools
desire to produce and the strategies they employ. Instruction was still
predominantly authoritative and text-book based, learning was usually
recipient and reproductive, supervision was commonly prescriptive and
directive; and assessment was focused more on judging rather than on
simproving performance.
The second finding was that teachers wanted to know more about
integrative teaching. Teachers did not feel confident to use the
approaches because of the limited knowledge to operationalize them in
terms of lesson planning, instructional materials development, subject
matter organization, presentation and evaluation. There were still many
teachers who do not have enough knowledge about the key concepts and
approaches. However, they were willing to learn how to be more effective
in facilitating the full development of the students‘ potentials and to be
facilitator of the integrative learning process.

Thirdly, teachers had limited knowledge of constructivism as a
learning process. Learning as a construction process and the learner as a
constructor of meaning is among the basic concepts of the BEC.
Although the concept was unfamiliar to many teachers, it was observable
in some classes where problem solving, inquiry, or discovery approaches
were being used.
Another finding of the team was that several factors constrained
teachers from playing their role as facilitators of the learning process.
The factors that inhibited teachers from playing the facilitators‘ role
effectively were students‘ English deficiency, overcrowded classes, and
insufficient supply of textbooks, prescriptive supervision and an
examination system that encourages authoritative teaching.
However, there were also findings which revealed positive results.
One was the study of Aware-Achwarin (2005) on Teacher Competence of
Teachers at Schools in the Three Southern Provinces of Thailand which
revealed that teachers‘ competence was at high level. The highest was on
―teachership‖.
The second was that of Villanueva (1999), as cited by Binay-an
(2002), which revealed that the instructional abilities of the teachers
were rated high along ability to explain correctly, having a good
command of the language and sufficient knowledge of the subject matter.

Further, the findings of Acantilado (2002) showed that the faculty
members of Tertiary Accredited Programs of SUCs in Region I were highly
competent. Another, Roldan (2004) cited Subala revealing that teacherrespondents were competent. This finding revealed that the instructors
could be proper sources of assistance and guidance to their students in
analyzing different mathematical problems. She stressed that the more
competent the instructors are the better is the result in terms of the
teaching-learning process.
Grouws and Cebulla (2002), as cited by Fianza (2009) mentioned
that research findings indicated that certain teaching strategies and
methods should be worth careful consideration as teachers strive to
improve their mathematics teaching practice. Teachers should use
textbooks as just one instructional tool among many rather than feel
duty-bound to go through the textbook as one section per day basis. As
technology is used in mathematics classroom, teacher must assign tasks
and responsibilities to students in such a way that they have active
learning experiences with technological tools employed.
Research then suggests that teachers should concentrate on giving
opportunities for all students to interact in problem-rich situations.
Teachers must encourage students to find own solution method and give
opportunities to share and compare their solution method and answer in
small groups. Such solutions were presented by Roldan (2004) as she

cited Diaz (2000). The solutions were: (1) the administration must hire
only competent Mathematics Teachers to teach the subject. This step is
supported by Rivera (2010) citing an article posted on www.eric.ed.gov
conveying that schools are hiring teachers who are competent since
students‘ attainment level is hoped to improve; (2) the administration
should also be fully aware of the importance of faculty development
through the pursuit of graduate courses and attendance to seminars and
in-service training, for such are essential to the teachers‘ professional
growth and development, particularly on effective teaching; (3) teachers
should strive to elevate their level of attitudes along concept and
mathematics from above average to higher level; (4) rigid annual
evaluation of teachers may also be of help for them to assess their
weaknesses, make improvements on such and maintain and sustain
their strengths; (5) moderately competent and competent teachers attend
Saturday and summer classes or workshops to be able to upgrade their
competence; and (6) teachers should be encouraged to attend seminars
and workshops particularly in Mathematics to update them with recent
trends and educational innovations.
Guidance Skills
Educational Guidance is the process of helping students to achieve
the self-understanding and self-direction necessary to make informed
choices and move toward personal goals (Microsoft ® Encarta ® 2009).

One of the innate tasks of a teacher is to promote learning. He
does this by guiding the learning process of students through planning
and organizing meaningful learning experiences, creating a desirable
learning environment, using a variety of instructional materials,
providing for individual differences and appraising students‘ growth and
development.
Diaz (2000) expressed in her study that a teacher who is the
facilitator of learning should also have special knowledge and skills in
guiding, directing and advising learners. She stressed that doing so gives
substance to teacher-students relationship. Thus, in this special task,
the teacher must possess knowledge and skills in assisting students in
their problems.
Graycochea (2000) revealed in his study that his teacherrespondents were highly competent in providing an environment
conducive to learning. This had been perceived by the teachers, students
and their heads.
The study of Oredina (2006) exposed that mathematics teachers‘
guidance skills were perceived as strengths. She emphasized that the
teacher-respondents were very good in directing, supervising and guiding
the

learning

process

by

providing

an

atmosphere

which

is

nonthreatening. Further, they were able to provide appropriate level and
needs of the students. In addition, they can direct the work of the
students properly.
Management Skills
The principle of a favorable learning environment is of universal
acceptance. To teach effectively is to manage class effectively, too. This
principle suggests that learning becomes interesting and enjoyable under
favorable working conditions. Good classroom practices; thus, enter the
scene.
Bueno (1999), as cited by Tabafunda (2005), asserts that a sound
classroom can be maintained by employing classroom management
practices. These practices are: (1) structuring the learning environment;
(2) religious preparation of lessons; and (3) maintenance of constructive
pupil-behavior correction. Thus, a successful teacher is one who can
evaluate situations and then apply appropriate styles to address such
situations. (http//www.classroom%20management.03-29-10)
One of the most difficult problems that confront teachers is to
manage classrooms. This is because one cannot fully learn the
techniques of proper management from books or from earning a
bachelor‘s degree.

Achwarin

(2005)

reveals

that

among

the

dimensions

of

instructional competence, classroom management was rated the lowest.
Olbinado (2007) in her study entitled, ―Enhancement Program for
Secondary Teachers who are Non-math Majors‖ revealed that the
teacher-respondents were good at classroom management. She stressed
that even though the teachers were not holders of mathematics degree,
they were good at managing classes since most of them were seasoned
teachers.
Oredina (2006) underscored that the teacher-respondents were
very good at guidance skills. This means that the teachers were highly
aware of the importance of extrinsic motivation and strengthen positive
attitudes such as giving commendations and approval.
Evaluation Skills
When a teacher finishes the course of the discussion, he
automatically administers the tools to assess learning. It is through
assessment that students‘ performance is monitored. The purpose of
evaluation is hence necessary.
According to Laroco (2005) there are four principles of educational
assessment. These are: (1) educational assessment always begins with
educational values and standards. Assessment is not an end in itself but
a vehicle for attaining educational goals; (2) educational assessment

works best when it accurately reflects the students‘ achievement/
attainment and understanding of educational goals and standards; (3)
educational assessment works best when it is ongoing, not episodic and
when varied measures are used; and (4) effective educational assessment
provides students with information (e.g. goals, standards, feedback) to
motivate and enable them to attain educational targets. Students should
be aware of what they are being assessed for and should also be given
information on what is needed to attain the expected outcomes.
Sameon (2002) revealed that his respondents perceived themselves
as very competent in assessment. He stressed that the teachers
understood the underlying theories and practices to improve students‘
performance.
Rivera and Sambrano (1999), as cited by Tabafunda (2005),
stressed that effective teaching should be coupled with the art of
questioning. Good questions served as essential in developing students‘
ability to define and exercise judgments.
Oredina (2006) found out in her study that the teacherrespondents were perceived ―very good‖ in evaluation and assessment.
She revealed that along the four competence dimensions, the skill on
evaluation had the highest rating. This means that the respondents were

highly capable in formulating questions with the purpose of developing
critical thinking; mathematics teachers were competent in providing
reasonable, appropriate, practical and challenging enrichment activities
to substantiate what had been taken in class.
Comparison in the Perceived Instructional Competence Among the
Groups of Respondents
According

to

the

article

accessed

from

http://en.wikipedia.org/wiki/individual_differences_psychology,

―Every

man is in certain respect (1) like all other men, (2) like some other men
and (3) like no other men‖. Thus, two contrasting ideas are revealed –
individual similarities and differences. This means that any two
individuals may have same perceptions at a time; but they may also have
opposing perceptions at another time. The adage, ―Everyone experiences
different time and space than everyone else but can still find
commonalities at a certain time in space with everyone else‖ supports
this

thoughts

and

contentions

very

well

(http.//www.newton.dep.anl.gov/askasci/gen06/gen06327.htm).
Commonalities among perceptions exist because there is a
common code (shared representations) for perceptions and actions. This
is

contained

in

the

Common

Coding

(www.en/wikipedia.org/wiki/common_coding_theory).

On

Theory
the

other

hand, differences exist because of different status of people, needs,

personalities, and beliefs. Further, individuals differ in terms of
perception

because

of

selective

perception

(www.ask.com/questions_about_selective_perception).
The aforecited thoughts are revealed in a study published in the
web revealing that there is a significant difference in the perceptions
along skills between the teachers and managers/heads. This is due to
the observation that when one holds a position, he has a certain degree
of confidence. He is sure of his capabilities and enjoys certain status
higher than others.
This can be supported through the educational thought presented
by Johnson (2010) on administrative support and cordial teacherstudent relationships. He stresses that these educational principles
integrate the concepts on backing-up, lending hands and sharing
appreciation.
Relationship of Profile and Level of Competence along Content
A teacher cannot share what he does not have. He has to be a
subject matter expert when he intends to instill lasting thoughts in the
minds of his learners.
Several articles posted on the World Wide Web implicitly and
explicitly cite the relationship between profile variables along highest

educational attainment, teaching experiences and number of seminars
attended and subject matter competence.
One article contends that subject matter/ content knowledge is
rooted from teaching experiences and the number of degrees a teacher
holds.

(http://doconnor.edublogs.org/finding-e-learning-and-online-

teaching-jobs/)
Another supports this thought by mentioning that subject matter
competence can be attained and maintained through continuing
professional education. It also extended that teachers who are subject
matter expert are the ones who have stayed in service for quite some
time. (jobs.stanlake.co.uk/recruiter/users/jobs.php?id=22).
A published research on Teacher Certification was also accessed.
The study revealed that teachers who had certification, longer years of
professional service and more frequencies of degrees show subject matter
competence (http://www.sedl.org/pubs/policyresearch/resources/ARA2004.pdf).
Another web article reveals that instructor-led training workshops
also

enhance

subject

(http://doconnor.edublogs.org)

matter

expertise

and

skills.

A national study on teaching expertise, though in the HEIs, by
Clemente-Reyes (2002) expresses that subject matter expertise is gained
through

possessing

educational

achievements,

gaining

years

of

professional teaching service and attending training. She mentioned that
earning a bachelors‘ degree was not sufficient; thus, recommending for
continuing professional education since majority of the teacher experts
were masters degree holders or even doctorate degree holders. Also,
when a teacher is exposed in the teaching profession, he is likely to
expand his horizons in his field; thus, contributing to teaching expertise.
Lastly, she asserted that training helped a lot in gaining additional input.
Such input met or not met by teachers in her formal education can affect
his content knowledge.
Further , the Australian Government commissioned the Australian
Council for Educational Research (2001) to conduct an investigation of
effective mathematics teaching and learning in Australian secondary
schools. The research revealed that teacher knowledge and educational
background is positively, but weakly related to teacher effectiveness. The
more this education has to do with mathematical content and pedagogy,
the more likely it is that teachers will be effective.
Keneddy (2001) also wrote in her article that a prospective teacher
majoring a subject like mathematics or science does not guarantee that

teachers will have the kind of subject matter knowledge they need for
teaching. She further stressed that college-level professional subjects do
not address the most fundamental concepts in disciplines. Instead,
professors provide massive quantities of information, with little attention
given to significance or fundamentals on how to deal with teaching.
Relationship of Profile and Level of Competence along Instruction
Teaching is a systematic presentation of facts, skills and
techniques. It needs certain competencies in order to teach effectively.
One way of assuring this is having a degree in education or any related
degrees. If a teacher wishes to teach in secondary, a field of specialization
is required in order to teach more competently. But having a degree does
not guarantee that one can teach well, he needs constant upgrading of
what he knows.
The study of Estoesta (1999), as cited by Fianza (2009) reveals that
there was a strong relationship between educational attainment and
teaching experiences to instructional competence. She stressed that the
teachers who had higher educational attainment and teaching experience
had high performance rating, thus higher competence. This study is
seconded by the study of Sameon (2002). According to him, teaching
competence is highly correlated to highest educational attainment and
teaching experience.

These findings were also supported by the international study of
Achwarin (2005) arguing that teachers‘ qualification is positively and
significantly related to teachers‘ competence.
Binay-an (2002) extended that length of service and number of
seminars and trainings were significantly related to competence.
Davis (2000), as cited by Binay-an (2002), claimed that teachers
who are younger in the service are more likely to possess greater
competence since they have greater inquisitive mind and zest for
teaching. However, this was not in congruence to the study of Laroco
(2005) claiming that teachers who had longer years in service are in
better position to adjust themselves to different classroom situations;
thus, they are more competent. She concluded that teaching experiences
add to the teaching competence.
Oredina (2006) accentuated that highest educational attainment is
significantly correlated to teaching skills but not significantly correlated
to guidance, management and evaluation skills. She also extended that
number of years in teaching, performance rating and number of
seminars attended are not significantly correlated to the four core
dimensions of instructional competence. These imply that teacher with
higher performance rating, with more number of years of teaching and
seminars were not necessarily more competent than those with less.

Soria (1995), as cited by Laroco (2005), found out that there was
no significant relationship between highest educational attainment and
number of years in teaching and their professional proficiency.
Parrochas (1998) also supported this contention, as cited by
Laroco (2005), by claiming that there is no significant relationship
between highest educational attainment of teachers and mastery level of
pupils.
Relationship of Subject Matter and Instructional Competence
Global goals of education stress the connection between how
teachers let the students know and what the teachers actually know.
Some of these goals are (1) all children should be taught by teachers who
have the knowledge, skills, and commitment to teach children well; (2)
for all teachers to have access to high-quality professional development;
and (3) for teachers and principals to be hired and retained based on
their ability to meet professional standards of practice. It is only with
these clearly stated and directed goals that teaching-learning process will
be meaningful.
Leinhardt, as cited by Subala (2006), disclosed that teaching
practices were often considered as one of the reasons why American
students were not currently demonstrating top achievement in science
and mathematics. He further stressed that teacher‘s knowledge of the
subject

matter

necessarily

influenced

their

classroom

practices.

Moreover,

linkages

between

teacher‘s

personal

knowledge

and

instructional activity had proven elusive despite the considerable level of
concern expressed regarding low levels of mathematics and science
knowledge possessed by pre and in-service teachers.
Binay-an

(2002),

in

her

study,

―Determinants

of

Teaching

Performance‖, pointed out that subject matter expertise is significantly
related to teaching expertise. He made use of the adage, ―One can‘t give
what he does not have‖ to substantiate this.
Cabusora (2004) asserted that subject matter expertise and
exemplary instruction are significantly correlated. He stressed that when
teachers have thorough grasp of the teaching-learning process, they are
likely to perform in instruction.
Diaz (2000) also stressed that teachers who are competent in
instruction are the ones who are competent in their field of expertise.
In the study of Dr. Flordeliza Clemente-Reyes (2002) on ―Unveiling
Teaching Expertise: A showcase of 69 Outstanding Teachers in the
Philippines‖, it was revealed that subject matter expertise was a
contributory factor to teaching expertise. It was stressed that mastery of
content-specific knowledge and the organization of this knowledge affect
effective instruction. If the teachers were not experts in their field, it is
unlikely for them to possess teaching expertise

An international study was cited by an article posted on the
Harvard Educational Review. This study was by Reynolds (1999). In the
study, he exposed that subject matter expertise was not contributory to
success in teaching. With these she expanded the meaning of subject
matter expertise to include an awareness of that expertise as learned.
(http://www.hepg.org/her/abstract/164).

Strengths and Weaknesses in Teachers’ Competence
The teacher is always confronted with different challenges that he
needs to face. Challenges of a teacher might be extrinsic or intrinsic.
Teachers might encounter problems on students‘ population, sizes of
classroom and the like. It can also be that a teacher finds preparing for
a class meaningless. These challenges are undoubted to be contributory
to the teacher‘s success in teaching.
Ordas (2000), as cited by Olbinado (2007), disclosed that schools
were not only faced with great lack of teachers; but with the massive
deficiency in qualified and competent teachers. She further stressed that
teacher training was deficient in terms of frequency and accessibility for
teachers.
Roldan (2004) concluded that secondary mathematics teachers in
Region I were proficient in concept and computations but they were
deficient in their skills in problem-solving and the use of teaching
strategies.

Oyando (2003) revealed in her investigation that teachers were
highly competent in basic mathematics; but were moderately competent
in higher mathematics.
Almeida (1998) and Diaz (1998) revealed that their respondents, in
separate studies, have moderate competence in their field. Diaz (1998)
added that mathematical analysis was wanting.
Verceles (2009) revealed that the use of calculators, especially
computers were all weaknesses. Lecture method was very dominant.
Nuesca (2006) indicated that Philippine Instruction is highly
teacher-centered. She supported this by enumerating the three most
common methods used by Filipino teachers: lecture, discussion and
demonstration.
Fianza (2009) disclosed that math instruction is often approached
in terms of stating and emphasizing rules- the ―tell, show and do‖ model.
Graycochea
teaching
technique;

were

(2000)

somewhat

motivational

revealed
serious.
strategies

that

problems

on

She

stressed

that

and

management

mathematics
questioning
were

the

contributory factors in this finding.
Cristobal (2004) found out that Instructors of Lorma Colleges
exhibited

capabilities

along

teaching

procedure,

substantiality

of

teaching and evaluation. The only expressed need is in the use of varied
instructional materials.

Roldan (2004) exposed that the secondary mathematics teachers in
Region I were deficient in the use of teaching strategies. Binay-an (2002)
supported this finding when she exposed that her respondents were not
so competent in using methods and approaches.
Alano (2003) of the Philippine Normal University mentioned that
studies showed that almost half of the teachers teaching the core
subjects have computer units, but only a few among them use such for
classroom instruction.
Oredina (2006) in her dissertation revealed that teacher‘s level of
instructional competence was very good. The evaluation skills were rated
highest while their teaching skills were the lowest.
Two-Pronged Training Programs
To be a successful math teacher, one needs to continually upgrade
himself. With this belief, the Congressional Commission in Education, as
cited by Olbinado (2007), recommended that a periodic assessment of
training needs of school teachers in both public and private schools is
imperative.
Eslava

(2001)

pointed

out

that

attending

service

trainings

enhances, with no doubt, the professional qualities of teachers. Laroco
(2005) added this thought expressing that when teachers wanted to
continue improving on their teaching performance, they needed to
undergo necessary training.

Cristobal (2004) claimed that while training remains only one of a
number of alternative approaches towards human resource development,
it remains to be the most utilized instrument for the development of
adults, professionals and paraprofessionals alike in a wide variety of
specific areas.
Fianza (2009) believed that training is a very good approach to staff
development.

She

opined

that

quality

instruction,

especially

in

mathematics, can be attained and delivered through enhancing teachers‘
competence.
Roldan (2004) claimed that training should be of prime concern
when quality of education is of prime concern, too. Such training has to
be done before any plan for assigning longer period to the teaching of
Mathematics is implemented.
Lastly, Oredina (2006) discoursed that training allows teachers to
show and share ideas, ask questions, make decisions and share personal
experiences in teaching Mathematics. She stated that this program will
make teachers change their traditional method of teaching to that of a
facilitator of learning.

Chapter 3
RESEARCH METHODOLOGY
This chapter presents, incorporates and discusses the research
design, the sources of data, instrumentation, procedure and the tools for
data analysis.
Research Design
The descriptive method of investigation was used in the study. This
design aims at gathering data about the existing conditions. Calmorin
(2005) describes descriptive design as a method that involves the
collection of data to test hypothesis or to answer questions regarding the
present status of a certain study. Further, Deauna (2003) defines such
design as one that includes all studies that purport to present facts
concerning the nature and status of anything.
Since the comparison on the perceptions of the respondents along
instructional competence and the relationship of the data on the
teachers‘ profile, content and instructional competence were established,
the descriptive-comparative and the descriptive-correlational methods
were employed, respectively.
Sources of Data
The population of this study is composed of three (3) groups of
respondents: (1) heads, (2) High school mathematics teachers in the

Private City schools of San Fernando (3) high school mathematics
students for the academic year 2010-2011.
All the heads with the mathematics teachers were considered. For
the students, one-third of the class population was considered. This is
equivalent to thirty- three and one-third percent (33 1/3 %) of the total
number of students in a class. According to Gay, as mentioned by
Oredina (2006), ten percent (10%) of the population is an acceptable
sample but twenty percent (20%) is required from a small population.
However, to make the findings of this study more reliable and acceptable,
the researcher preferred to implement the statistical idea that the bigger
the sample, the more valid are the results.
The total population of three hundred and fifty-seven (357)
constituted the respondents of this study, broken down as follows: three
hundred eighteen (318) students, twenty six (26) teachers and thirteen
(13) heads. Substitute teachers or on-leave teachers are not considered
as respondents of the study.

Table 1 shows the distribution of the

number of specified respondents from the thirteen (13) Private Secondary
Schools of the City Division of San Fernando, La Union for the academic
year 2010-2011.

Table 1
Distribution of Respondents

SCHOOLS
Brain and Heart of a Christian (BHC)
Central Ilocandia Institute of Technology
(CICOSAT)
Christ the King College (CKC)
Diocesan Seminary of the Heart of Jesus
(DSHJ)
Felkris Academy
Gifted Learning Center (GLC)
La Union Cultural Institute (LUCI)
La Union Colleges of Nursing, Arts and
Sciences (LUCNAS)
MBC Lily Valley School
National College of Science and Technology
(NCST)
Saint Louis College (SLC)
San Lorenzo Science School (SLSS)
Union Christian College (UCC)
TOTAL

Number of
Students Teachers Heads
33
2
1
20
2
1
75
3

5
1

1
1

8
7
14
7

1
1
2
1

1
1
1
1

7
7

1
1

1
1

90
11
24
318

6
1
2
26

1
1
1
13

Instrumentation and Data Collection
To gather the data essential to the realization of this study, two
sets of data gathering instrument were utilized. One was a 60-point
researcher-made mathematics competence test for mathematics teachers
whose content was based on the 2010 Secondary Mathematics
Curriculum. The other is a questionnaire-checklist, the key instrument
in obtaining the data in evaluating the instructional competence of high
school mathematics teachers in the Private Secondary Schools.

The mathematics competence test is divided into 4 areas of
Secondary Mathematics (Elementary Algebra, Intermediate Algebra,
Geometry, Advanced Algebra, Trigonometry and Statistics). Each area
includes 15 questions; each question corresponds to one (1) point.
Further, it was made following the Bloom‘s Taxonomy of Cognitive Skills
for Mathematics (Conceptual, Reasoning/Analytical, Computational, and
Problem-Solving). (Please see appended Table of Specifications)
On

the

other

hand,

such

questionnaire

on

instructional

competence was composed of two parts: Part I elicited the profile of the
mathematics teachers along the highest educational attainment, years of
teaching mathematics and number of mathematics trainings and
seminars attended; Part II, on the other hand, drew out the level of
instructional

competence

skills/facilitating

skills,

along

the

management

four
skills,

areas
guidance

─

teaching

skills,

and

evaluation skills. The statements in the questionnaire for studentrespondents were rephrased in such a way that these are parallel to the
statements in the questionnaires for teachers and heads. This rewording
ensured that the student-respondents clearly understood the details for
assessment.
Each of the teacher-respondent took the mathematics competence
test not exceeding one hour or sixty (60) minutes in one sitting/ session.
The administration of the test was conducted during their free periods,

lunch breaks, and after the class hours as agreed upon by the researcher
and the teacher-respondents, themselves. Such being the case, the
researcher took him almost 2 months to gather the required data. Also,
each teacher was evaluated by his/ her students in one of his/her
classes, heads and himself.
With the permission of the school heads of the thirteen private
secondary schools, copies of the two sets of instrument were given to the
respondents to accomplish. In the mathematics competence test,
teachers were not allowed to use calculators. This was made sure by the
researcher during his proctoring of tests. The fully accomplished
questionnaires were retrieved personally by the researcher.
Validity and Reliability
The mathematics competence test was a researcher-made test
whose content was based on the 2010 UBD-Secondary Education
Curriculum. The questionnaire-checklist, on the other hand, was a
combination of the FAPE Performance Evaluation Tool, Institutional
Supervisory Instrument of Christ the King College and the questionnairechecklist utilized by Oredina (2006) in her study, ―Mathematics
Instruction in the HEIs in La Union: Basis for a Training Program‖. Since
the key instruments were based on several manuscripts, their validity
and

reliability

were

established.

The

Education

Supervisor

for

Mathematics; a Master Teacher II of La Union National High School; the

Academic Coordinator of Christ the King College and the members of the
reading committee served as the validators of the two sets of
questionnaires. The computed validity rating for the Mathematics
competency

test was

4.63,

which means

that

the Mathematics

competency test is of very high validity. On the other hand, the computed
validity rating for the Instructional competence test was 4.71 indicating a
very high validity, too. Further, all the suggestions cited by the validators
were incorporated, especially on the competence test where the radical
symbols and fractional bars have to be encoded using the equation editor
to

avoid

unnecessary

misconception.

Conversely,

their

internal

consistency or reliability was determined using the Kuder-Richardson 21
formula. The first one was used to get the reliability of the content
competence test while the second was used to get the reliability of the
instructional competence checklist.

The formulas are (Monzon-Ybanez

2002):
𝐾𝑅21 =

𝑘
𝑘−1

1−

𝑥 𝑘−𝑥
𝑘𝜎 2

where:
k = number of items
𝑥 = mean of the distribution
𝜎 2 = the sample variance of the distribution
or

(Garett 1966): 𝐾𝑅21 =

[𝑛𝜎 2 −𝑀(𝑛 −𝑀)]
𝑡
(𝑛−1)(𝜎 2 )
𝑡

where:
n = product of the number of items in the test and the highest
scale
𝜎 2 = variance
𝑡
𝑀 = mean

Through

the

assistance

of

the

Education

Supervisor

for

Mathematics, Dr. Jose P. Almeida, a dry run of the questionnaires was
administered to 20 students, 5 mathematics teachers and 1 Mathematics
head of La Union National High School. The mathematics competence
test had a reliability coefficient of 0.93, denoting that the competence test
was very highly reliable. Alternatively, the questionnaire checklist was
found to have very high reliability having a computed coefficient of 0.96.
Tools for Data Analysis
The data which were gathered, collated and tabulated were
subjected for analysis and interpretation using the appropriate statistical
tools. The raw data were tallied and presented in tables for easier
understanding.
For problem 1, frequency counts and rates were used to determine
the status of the profile of the respondents along highest educational

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