Chapter of mathematical thinking and problem solving

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of the Study

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Mathematics is
considered as one of the cornerstones of civilization. It is evident in all aspects
of societies and culture. It permeates all walks of life. It plays an important
role specifically in this age of scientific and technological advancement. In
this world of modern technology, no nation can survive economical without advanced
science which includes mathematics. We live in age where knowledge of
mathematics where is necessary for effective living and efficient practices of
almost every occupation. The government, through the school system encourages
the study of mathematics in order that these can keep pace with progress. In
fact, Mathematics enables other disciplines to advance the frontiers of
knowledge. Mathematics has indeed become an indispensible tool in the study of
courses, such as maritime education, information communication technology,
engineering, teacher education, and industrial technology. These courses, among
others, require a solid background and training in Mathematics; they require
literacy in Mathematics to enable college graduates to develop their critical
thinking and to use wide varieties of Mathematics methods in solving problems
when they join in workforce. ( Deauna, 1990).

In addition, Mathematics
plays an important role in man’s life. Sibayan (2003 ascited by Litong, et al.)
noted that Mathematics knowledge, adeptness and skills are basic ingredients
for a learned man because numbers are part of everyday life. Man finds
situations and many of the ordinary activities involve application of Mathematics.
The level of mathematical thinking and problem solving needed in every
workplace has increased seriously. In such a world, those who understand and
can do Mathematics will have opportunities that others do not. Therefore, the
quality of teaching and learning Mathematics has been of great challenge and
consider as the major concern of all educators.

According to Fisco
(1993), a math teacher who is creative, diligent, and resourceful should always
consider giving meaningful activities that easily captivate the attention,
curiosity, and sense of wonder of students. A mathematics teacher should realize
that the best lessons in life come from the actual experiences, so he must
develops activities in such a way that students would experience learning in a
more desirable manner. While the importance of Mathematics is acknowledged, at
the same time, the low quality of mathematics education in the country is
noted. It has been observed that many students are not quite interested in
mathematics for certain reasons; (1) some say it’s a boring subject; (2)
mathematics teachers accept only their own solution to math problems and do not
discuss other alternatives; (3) seemingly, some teachers cannot explain the
reason behind the errors in the math exercises; (4) students are simply not
interested to learn Mathematics because it is a complicated subject so they are
just contented with a passing mark;

(5) some claim that they do not have
adequate mathematics background in basic education; (6) many students are
simply too lazy, perhaps due to lack of proper motivation on the part of the
teacher, so they don’t exert effort to enhance their Mathematics skills to a
level proportionate to their capability;

(7) other students may have difficulty
coping with the medium of instruction; and (8) some have poor study habits.
(Navarrro, 1996)

At present, many of
the children of the lower class families and those of the middle class families
as well, do not get beyond high school. It is a fact that only a fraction of
the high school learners can go to college. For the majority of them secondary
education marks the end of their formal education. Thus Mathematics education
in the secondary level should aim at helping these people to be functional in Mathematics.
Functional knowledge in Mathematics should equip them for practical parenthood
and a vocational and technical job.

Instructional design
is an effective way to ease problems related to the quality of teaching and
learning Mathematics. Knowing the factors affecting Mathematics performance is
particularly important for making the best design decisions that will suit to the
K-12 curriculum (an educational system implemented last June 2011 by the
Department of Education (DepEd). “K” stands for Kindergarteen whereas “12”
represents the succeeding 12 years of basic education. This is an initiative
made by the government to ensure that every student is completely equipped with
enhanced basic life skills for lifelong learning and employment here and
abroad.)  The concern about Mathematics
achievement has been observed in the K-12 curriculum where Grade 11 and 12 have
it as one of their core subjects. The current debate among curriculum planners
is what students should learn to be successful in Mathematics. A central and
persisting issue is how to provide instructional environments, conditions,
methods, and solutions that achieve learning goals for learners with different
skills and ability levels. It is then important for educators to develop
instructional approaches and techniques to ensure that students become
successful learners.

Instructional alone
cannot produce better learning and achievement. The instructional designer must
know crucial barriers that affect student learning and build a bridge between
goals and students performance. The researcher have long been interested in
exploring the barriers that affect the teaching-learning process contributing
effectively to the performance  and
achievement of Senior High learners in Mathematics under the K-12 Curriculum.
These barriers are inside or outside school and effect student’s quality of
academic performance. Identifying these barriers will also help educators to
utilize limited resources including financial resources and time more
effectively. In an effort to understand the barriers associated with
mathematical achievement, the researcher will focus in many barriers such as
students personal barriers that includes students attitude, study habits,
school pressure and school satisfaction. These barriers that inhibit or prevent
the learners from participating in activities will affect their academic
performance. Learner’s engagement in Mathematics will depend in many motivating
factors as well as their confidence in their ability to succeed and their
emotional feeling toward the subject.

This study will also
anchor on the concepts that a student’s academic performance in Mathematics is
affected by barriers such as student’s attitude and study habits.

Attitude. A
student’s academic performance in mathematics is affected by various factors
–the student’s attitudes, among others. De Torre’s article (1987) claimed that
proper attitudes toward work and study contribute better performance in various
fields of endeavor.

et al. (1988) made a study on gender and achievement status difference in
learning factors among black high schools students. They found out that there
were significant differences between male and female students on students
attitudes toward their lessons.

similar study on the influence of study habits and attitudes on academic
performance revealed that attitudes of students toward school work affected
their academic performance (Ayson,1982).

(1985) made a study on the relationship of students’ attitudes towards their
academic performance in mathematics. He found out that there were significant
relationships between students’ attitudes towards school work and their
academic performance.

Study Habits. The
structural concept of habit as an enduring aspect of personality has been
popular in efforts to conceptualize what students are like in terms of their
academic performance.

like manner, Weinert and Kluwe’s article (1987) suggest that sound study skills
and habits involve adjusting practices to (1) difficulty of the materials; (2)
time available for studying; (3) what is already known about the material ; (4)
purpose and importance of assigned task/ lesson; and (5) standards to be met.

addition attitude towards school work and study habits are influenced by
different factors surrounding the learner. Learning is habit formation and can
be conditioned. Situation and connected response-reward and/ or satisfaction
reduce the need and hasten the learning or performance. Learning takes place
when any change in behavior occurs (Andres and Francisco, 1989).Learning need
to be organized in terms of the learners interest, abilities, and activities.
The learner should be made the starting point, the center of learning ( Kaplan
and Saccuzzo, 2001). It is the learner who determines both the quality and
quantity of learning. If the aim of a curriculum or an academic program is to
let the learners grow in terms of knowledge, habits, skills, abilities, and
attitudes, the original nature and experiences of the learner must be made as
the starting point in accomplishing such growth.

Being a mathematics
teacher, the researcher feels that she has an important role to assume. As a
result she is motivated to undertake this study focus in finding out the
existing barriers in teaching-learning process in mathematics subjects of the
Senior High School learners in Tubao District. The research questions will
reveal the major barriers in teaching-learning process of mathematics and
propose possible solutions in order to overcome the identified barriers. It is
hope that in the light of the findings of this research, Mathematics teachers
in Senior High School, as well as administrators, will enlightened and such a
thing may result to better mathematics instruction which produces more
competent learners who will eventually become more efficient and productive
citizens of the Republic.

of Mathematics and the ability to apply it are essential to be able to function
in and contribute to society. As valuable as the discipline, teachers observes
many discrepancies as to how students learn or fail basic Mathematics
processes. Barriers involving the students, teachers, or the environment
contribute to the inability of the students to use the basic principles of Mathematics
in the application of advance scientific thinking.

is in this light that the researcher hopes to give significant contribution to
the elements that comprise the academe. This study should be useful to the
parents, teachers, administrators and students themselves.

For the students and
parents the data   gathered regarding variables affecting mathematics
performance served as basis for remedial steps that took when the learners
shall have been enrolled in college. As for instance, if statistics will show
significant relationship between any of the identified variables and
performance in Mathematics, then the parents may already think of possible
remedial courses of action that is pursuance of a course that would entail only
few mathematics subjects.

This study had a two-fold
contribution to the administrators and teachers. First, it would serve as basis
for reinforcements of effective or ineffective teacher methodology in teaching
Mathematics. Since the study yielded significant relationships between
performance of students in mathematics and school-based variables particularly
on teaching –learning strategies, then the teacher should try to do remediation
that would involve those methods and strategies which are affecting students
performance in Mathematics. Secondly, the administration especially the
immediate supervisor can use the findings as justifications for sanctions
imposed on the teachers for improvement or maintenance of the teacher’s

It is also hope of
the researcher to contribute to the body of knowledge already existing which is
related to the area of the study.

study was limited only to Senior High School Learners in Tubao District,
School’s Division of La Union.     Determining
the barriers affecting the teaching- learning process in Mathematics of the
Senior High School Learners in Tubao District Schools Division of La Union was
the focus of this research. The information needed was gathered using the
checklist style research-made questionnaire. All information and conclusions
drawn from this study was obtained only to this particular group of students.

Framework and Conceptual Framework

study was subscribed to the Brunner’s (1996) theory of instruction. In this
theory, Brunner points out that a theory of instruction is a prescription of
rules for achieving knowledge or skills and providing techniques for measuring
or evaluating outcomes. This theory facilitates the researcher with the
barriers affecting the performance of mathematics in Senior High School in
Tubao.  Brunner, argues that a theory of
instruction is concerned with what one wishes to teach can best be learnt. He
specifies four salient features that the theory must embrace. These include:
predisposition to teach, a group of knowledge structure, hierarchy and
sequencing of content, and ability to reward and reinforce learning effects. These
teachers of mathematics need to be adapted at all these four constituents of
learning.  To Brunner (1996), with
sufficient understanding of the structure of a field of knowledge more advanced
concepts can be taught appropriately at much earlier ages. This is achieved by
planning and structuring learning experiences that arise the curiosity of the
learner. The theory further emphasizes that the experiences provided should
recognize the different levels of the learner’s thinking. Bruner says that it
is the responsibility of the teacher to identify the concepts that from the
basic structure of the subject, in this case barriers affecting the performance
in mathematics.  This theory was chosen
because it provides knowledge on how teachers of mathematics can develop
cognitive abilities of learners by preparation of instructional products and
processes. The theory further guides the teacher in structuring and sequencing
of learning activities, preparation before class instruction includes content
familiarization, lesson plan preparation and sourcing of instructional resources.

mathematics K-12 Curriculum is organized hierarchically and spirally. The
teacher therefore used this to make lesson preparation that were identified,
the pre-requisite concepts and those that we to come later. Since learning of
mathematics is an ongoing process of building on the previous, the sequencing
should be well-planned to create room for students to be rewarded and feel
motivated. This further resulted in more classroom interactions of the students
with resources teachers and amongst themselves. These variables explained are
represented in the conceptual framework.

is a conception by many that mathematics is a very difficult subject compared
with all the subjects offered in a certain school. Based on the results of the
many achievement or performance test given by the Department of Education
Division Office as well as the Regional Office, it has been proven that scores
in Mathematics are low. With this mathematics has become the most disliked
subject by most learners and even by some teachers. If only each one has
received a proper motivation on Mathematics, then its importance may be

have been very many studies made to update the areas of mathematics with the
aim to help and guide teachers to have better updated strategies and methods to
use in mathematics teaching. Likewise there are also some techniques and
methods which make mathematics functional. There are also some procedures and
methods suggested to improve the subject matter and give meaningful behavior on
the part of students.

regard to why most students get low scores in their achievement test, besides
teacher factor, there are other barriers which contribute to the failure of an
individual in any area or field of endeavor aside from teacher factor. These
barriers, such as study habit, sex, age, nutritional status, experience with
the physical world, and socio-economic status should not be underestimated.
Gregorio (1976) posits that learning is most potent when the school curriculum is
brought in harmony with the experiences, abilities, and needs of the students,
and when his environmental conditions are more advantageous. From this it can
be deduced that the nature of the learner is a function of the learning

Of The Study

these theories and concepts,the conceptual framework paradigm in Figure 1 shows
the relationship and flow of each variable in the study. The study was focus on
the Academic Performance in Mathematics of the Senior High School Learners in
Tubao District, Tubao La Union. Thus, the paradigm of the study shows the
relationship of input variables which contain learner’s profile in terms of (1)
personal, that includes age and sex and (2) academic that includes the learners
grade in General Mathematics. The extent of the student’s personal barriers in
terms of their attitude, study habit and school pressure and satisfaction was
also considered under input. While in the process contains the survey, data
gathering, data analysis, and data interpretation. Based on the research
results, action plan will be design which will serve as an output of the study.
These plans may, in-a-way will help the students to improve their performance
in mathematics and for the faculty development programs for the improvement of
the teaching- learning process in mathematics.





Learner’s Profile
    1.1 Personal Profile
           1.1.1 Age
           1.1.2 Sex
     1.2 Academic Profile
           – Grades in General Mathematics
Student-Related Barriers Affecting Learner’s Performance in Mathematics
2.1Student’s Attitude
2.2 Study Habit
2.3 School Pressure
2.4 School Satisfaction

action plan on teaching – learning process in Mathematics

Adaption and modification of the Questionnaire
Data Gathering
Data analysis
Data Interpretation







Faculty Development Programs for
the Improvement of the Teaching- Learning process in Mathematics
















of the Study


of the Problem

study was attempted to determine barriers affecting the Performance in
Mathematics of the Senior High School Learners at Tubao Distict, Division of La

this study sought to answer the following questions:

1. What is the profile of the students
in terms of the following:

Personal Profile



Academic Profile

in General Mathematics

1.3 Student- Related

1.3.1  Student’s

1.3.2 Study Habit

1.3.3 School Pressure

1.3.4 School Satisfaction

2. What is the level of performance in
Mathematics of the Grade 12 learners at Tubao District in General mathematics?

3. Are there significant relationships
between performance and students attitudes towards mathematics, study habit,
and school pressure and satisfaction?

4.  Based on the study, what action plan can be
evolve to enrich the teaching- learning process in Mathematics?


null hypotheses guided the researcher in this investigation. It was tested with
appropriate statistical formula to five (5) percent level of significance.

 There is no significant relationship between
mathematics performance of grade 12 learners and student- related barrier in terms
of the ff:

a. Students attitude
towards mathematics.

b. Study Habit

c. School Pressure

d. School

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