# Chapter of mathematical thinking and problem solving

Chapter

1

THE

PROBLEM

Background

of the Study

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.

Haynes,

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.

A

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).

Abenes

(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.

In

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.

In

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.

Knowledge

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.

It

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

performance.

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.

This

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.

Theoretical

Framework and Conceptual Framework

This

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.

The

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.

There

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

appreciated.

There

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.

With

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

process.

Paradigm

Of The Study

Along

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.

INPUT

1.

Learner’s Profile

1.1 Personal Profile

1.1.1 Age

1.1.2 Sex

1.2 Academic Profile

– Grades in General Mathematics

2.

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

Research

Output

An

action plan on teaching – learning process in Mathematics

OUTPUT

1.

Adaption and modification of the Questionnaire

2.

Data Gathering

3.

Data analysis

4.

Data Interpretation

Research

Outcome

Faculty Development Programs for

the Improvement of the Teaching- Learning process in Mathematics

Figure

1

Paradigm

of the Study

Statement

of the Problem

This

study was attempted to determine barriers affecting the Performance in

Mathematics of the Senior High School Learners at Tubao Distict, Division of La

Union.

Specifically

this study sought to answer the following questions:

1. What is the profile of the students

in terms of the following:

1.1

Personal Profile

1.1.1

Age

1.1.2

Sex

1.2

Academic Profile

Grade

in General Mathematics

1.3 Student- Related

Barrier

1.3.1 Student’s

Attitude

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

The

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

Satisfaction