TABLE OF CONTENTS
Page
TITLE PAGE I
APPROVAL PAGE II
CERTIFICATION III
DEDICATION IV
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES VIII
ABSTRACT IX
CHAPTER ONE: INTRODUCTION 1
Background of the Study 1
Statement of the Problem 8
Purpose of the Study 10
Significance of the Study 10
Scope of the Study 12
Research Questions 12
Research Hypotheses 13
CHAPTER TWO: REVIEW OF RELATED LITERATURE 14
Conceptual Framework 15
Theoretical Framework 29
Empirical Studies 35
Strategic interventions and Academic achievement,
by School Counsellors. 43
Summary of Literature Review 46
vii
CHAPTER THREE: RESEARCH METHODS 48
Design of the Study 48
Area of the Study 49
Population of the Study 49
Sample and Sampling Technique 50
Instrument for Data Collection 51
Validity of the Instruments 51
Reliability of the Instruments 52
Method of Data Collection 53
Method of Data Analysis 56
CHAPTER FOUR: PRESENTATION AND ANALYSIS OF DATA 58
Research Questions 58
Testing the Null Hypotheses 59
Summary of Findings 62
CHAPTER FIVE: DISCUSSION, CONCLUSION, AND
SUMMARY OF FINDINGS. 63
Discussions of the Findings 63
Conclusion 65
Implication of the Findings 66
Recommendations 67
Limitation of the Study 68
Suggestions for Further Studies 68
Summary 69
REFERENCES 71
APPENDICES 82
viii
LIST OF TABLE
Table Title
S/N
1 Detailed Distribution of Subjects 51
2. Pretest and post-test mean Differences on
Experimental and Control groups 58
3. Pretest and post test mean scores of male and
female in the experimental group 59
4. ANCOVA on the Pre and Post-test mean scores of
experimental and control groups 60
5. ANCOVA on the mean Achievement Scores of
Male and female students who received
cognitive restructuring 61
ix
ABSTRACT
This study was geared towards investigating the effects of
cognitive restructuring, in enhancing mathematics achievement of
adolescents in secondary schools in Oshimili South Local
Government Area. Two research questions and two null
hypotheses, guided the study. Quasi experimental research design
was adopted. The population used was four thousand and twenty
two students of the SSII class from Oshimili South Local
Government Area. Random sampling was used to compare two
boys schools and two girls schools for the study. Through
purposive sampling, 40 pupils with poor mathematics performance
from each of the four schools made up the final sample. A 50 item
researcher developed mathematics achievement test, validated by
three experts from Delta State University (D.E.L.S.U) and Nnamdi
Azikiwe University (N.A.U) was used to collect data. Data analysis
was done using mean, standard deviation, t-test and ANCOVA at
0.05 levels of significance. The findings of the investigation were
that:-Cognitive restructuring technique is effective in enhancing
students’ mathematics achievement and also females gained
higher mean achievement scores than their male counterparts
when cognitive restructuring technique is adopted. Based on the
findings of this study, necessary conclusions and
recommendations were also made. One of which is that learning of
specific restructuring technique should be incorporated as an
aspect of school curriculum.
1
CHAPTER ONE
INTRODUCTION
Background of the Study
Mathematics is a branch of knowledge dealing with measurements
numbers and quantities. It’s such an important subject that currently, it’s
been made compulsory for admitting candidates into all discipline in
tertiary institutions in Nigeria. Therefore, for students to achieve success
in their desired academic career, they are expected to pass the subject
properly with at least a credit pass.
According to Cohen, O’Donoghue & Fitzsimons (2000), mathematics is
the language of science, as a discipline. It is the pivot around which the
whole essence of living revolves. Again mathematics is viewed as the
basis for scientific and technological analysis. According to Gillings
(1982), for analysis of weather to be accurate, mathematical calculations
are necessary. Also Mckee (2002) opined that, every new body of
discovery is mathematical in form. This is because, variables such as
time and age, must be calculated mathematically, since it is concerned
with symbols and is necessary for any meaningful involvement in
modern civilization. This is why adolescents, who must fit positively into
society, are expected to understand the basic concepts and principles of
the subject mathematics by constantly practicing the rudimentary
2
concepts involving figures, particularly in the basic areas of factorization,
like and unlike terms, simultaneous equation, quadratic equation and
word problems in mathematics, as their usefulness is relevant in
everyday dealings.
For this reason, the subject must be embraced by restructuring the
cognitive pattern of thinking in the adolescents, which society, peer
group, and adults have irrationally and erroneously misconstrued in the
adolescents’ mind, through what they say and how they react even when
the subject is merely mentioned.
Accordingly to Benson (2000), for transactions in relation to buying and
selling to succeed, ones cognitive abilities must be tuned to a point that
he understands some level of mathematical symbols and calculations.
This he believes will eliminate cheating amongst the parties involved, to
a large extent, which is why cognitive skills of students should be
sharpened through cognitive restructuring techniques to reduce or
eliminate the phobia associated with learning the fundamental
mathematical concepts, particularly in the adolescent age.
It’s as a result of the importance of mathematics that it has been made
one of the compulsory and pre-requisite subjects that science and arts
students must pass at the school certificate level in order to be admitted
into the University. This is one of the moves by the Federal Government
of Nigeria to make mathematics popular. Also with the inclusion of
3
scientific and technological development in the National Development
Plan, it becomes obvious that if mathematics achievement is not
enhanced among the adolescents in secondary schools using
appropriate cognitive restructuring techniques, national progress and
development would be adversely affected (Okoye, 2006).
As regards school subjects, the irrational belief that some school
subjects are difficult to comprehend begins to register in the adolescents’
subconscious, based on environmental and societal irrational beliefs.
Probably, this could be the reason why most students do not achieve the
desired pass in some dreaded school subjects like mathematics. Gal in
2000, emphasized that some contributory factors to students’ lack of
mathematics achievement are the students’ attitude towards the subject,
which is based on fear and the general impression created by the
society, who believe that mathematics is difficult to comprehend. Also,
the teacher’s method of teaching the subject content which seems to be
complex particularly if the subject is not taught with the right models.
This invariable affects the students level of achievement.
Even amongst the students’ gender, there still exists some level of
discrepancy in mathematics achievement. According to Davis (2001),
female students still have not attained mathematics equity as their male
counterparts in school because, the female students see the subject as
emotionally draining and cognitively difficult, coupled with the routinely
4
negative self- statements the female students make about mathematics
being a difficult subject to pass. He also attributes these lapses to some
parents’ negative attitude towards science inclined courses for their
daughters, a shortage of female mathematics teachers to serve as role
models, early marriage age for females and most especially the societal
discriminatory attitude in terms of job opportunities. These factors seem
to create a negative attitude amongst the female students thereby
inhibiting their enhancement, in mathematics performance.
Even amongst secondary school students however, the skills in
enhancing learning has been a major concern of many scholars,
particularly Guidance Counsellors, who seek diverse ways of enhancing
students’ level of achievement particularly in a core subject like
mathematics (Dossey & Usiskin, 2000). Students, according to Dahir
and Stone(2003), do not learn automatically, particularly in mathematics
and that they need guidance and direction before real interest is
developed in the subject, eventually leading to effective learning. Some
of the diverse ways sought by Guidance Counselors includes trying to
adopt the technique of cognitive restructuring to encourage the students
particularly the females, who have unconsciously developed a phobia for
the subject and to re-address their mind with positive statement such as,
“I will understand mathematics, if I practice the concepts regularly”.
5
Again, Mckee (2002), opines that there is growing evidence in the
importance of students’ negative attitude and belief about mathematics
and that, through various teaching and learning styles, adopted by
Guidance Counsellors to aid students understanding, by making the
students talking to themselves positively, the students’ positive attitude
and self esteem becomes actualized.
Cognitive restructuring is a type of therapeutic technique, which refutes
ones irrational ideas and replaces them with rational ones. Dibatolo,
Frost, Dixon and Almodorar (2001), defined Cognitive restructuring as
“employing self-statements, arguments and disputations to make the
client see irrationality in his or her behaviour and to be able to devise
positive alternative ways to such irrationality in case the urge arises in
the future”.
Mcmulin (2005) affirms that, human beings are generally rational, but
that they can develop irrational beliefs and neurotic behaviour as a result
of biological and social forces, through imitation of what people around
them regard as acceptable societal norms, which sometimes are
irrational thoughts. He further states that, as children develop into
adolescence, they tend to accept unconsciously, these irrational beliefs.
This invariably affects the psyche of the growing child, particularly
students who are prone to all sorts of forces, based on peer pressure
and societal beliefs passed on to the children. This is the basic reason
6
why students’ school performance particularly in mathematics has been
adversely affected in some regions in Nigeria, such as the Oshimili
South Local Government Area of Delta State.
According to Gargus (2002), when adolescents encourage themselves
with positive self-talk, on issues or areas that have been a burden to
them, they tend to increase their level of determination to succeed, in
that particular area of interest. This helps the adolescent to attain the
aspired level to achieve success.
Achievement according to Dahir & Stone (2003) is a common life
experience, which is obtained by the acquisition of skills and using these
acquired skills to the best of the individual’s abilities and capabilities, so
as to enhance his/her performance in life. In the words of Bandura
(1997), people’s personal expectations for achievement play an
important role in enhancing their desire to succeed. For instance, if you
believe that your effort at studying will lead to a good grade in your
examination, you will be motivated to study. This belief helps to mobilize
the individuals’ energy in performing a lot better. This is why students,
who constantly solve mathematics problems, with a mind-set to achieve
success in the subject, always excel.
According to Mangal (1998), when ones’ achievement in a desired field
is attained, life is fulfilling. The desire to achieve success he believes is
as basic and natural as other biological needs, such as Oxygen, which is
7
essential for survival as well as psychosocial needs, which an individual
requires for self-actualization. In the same vein, (Darling-Hammond,
2000) is of the opinion that, the desire to achieve success helps people
to succeed, particularly in their area of interest. This desire to achieve
becomes realistic when rational thinking is adopted by the individual,
through the cognitively restructuring of their thought pattern.
Meichenbaum (1977) adopted rational thinking to teach poor achievers,
to see if they could become more effective achievers, through cognitive
restructuring techniques. In his findings, he concluded that cognitive
restructuring is an appropriate technique that could be used to
encourage poor achievers.
This is also why cognitive restructuring technique, is adopted amongst
students whose mathematics achievement level has been declining
consistently over the years, to see if their level of understanding the
subject could be upgraded to a standard that will give them the
confidence they desire to be successful and the positive self belief to
write examinations into the tertiary institutions. However Davis (2001)
believes that, the imbibed phobia for mathematics sometimes affects
students’ level of performance, to higher achievement levels, even when
it is obvious that a good grasp of the subject would enable them gain
admission into higher educational bodies.
8
Inspite of its importance, students still perceived the subject with phobic
tendencies which is why the researcher decided to research on it since
there has been no known study by the researcher, which directly dealt
with enhancing mathematics achievement in adolescents, using
cognitive restructuring in the Oshimili South L.G.A of the Delta State of
Nigeria. Being a Guidance Counsellor, such information is considered
necessary to enable Guidance Counsellors give needed help to students
in their subsequent mathematics achievement. Based on this
background, the present research was committed to finding the effects of
cognitive restructuring technique in enhancing mathematics
achievement, amongst adolescents in the Oshimili South Local
Government Area of Delta State.
Statement of the Problem
A lot of families in Delta State have been known to have excelled
academically in the past such as the Ofilis, Azinges and the Obanyas.
Presently however, poor academic performance amongst students
particularly in mathematics, in the Oshimili South Local Government
Area of Delta State, over the years has made many students drop-out of
school, particularly the female students. This is because, the students
perceive the subject as very difficult to understand, compared to other
subjects. Therefore, the required credit needed in the subject which is a
compulsory prerequisite to gaining admission into any Nigerian tertiary
institution is not achieved by the student.
9
Even when students are aware that mathematics is a core subject and
that it has become part of our everyday life, which cannot be avoided,
the students still generate a high level of anxiety for the subject to the
extent that they run away from mathematics lessons. According to
Brigman & Goodman (2001), students’ negative attitude to mathematics
leads them to develop a lack of self-confidence in themselves and lack
of enthusiasm.
In the process, career interest becomes jeopardized and the end result
is lack of enthusiasm and low self esteem.
Obanya (2002) believes that, poor performance trend in mathematics in
a student, could lead to the student developing an unconscious fear for
the subject, which could invariably hamper anticipated optimal
achievement level in the pursuit of academic excellence of the student.
As a result of the obvious effect of this mathematics phobia in students
and adolescents in general, it becomes necessary to find out why this
trend consistently exists amongst students. Also, since the primary
source of problem associated with poor performance in mathematics has
been identified to be fear and irrational thought of the subject, it
becomes necessary that a technique that tends to restructure the
students cognition be used.
It is against this background that the study asks, what is the effect of
Cognitive Restructuring in enhancing mathematics achievement of
students in Delta State?
10
The Purpose of the Study:
The purpose of the study is to determine the effects of Cognitive
Restructuring technique in enhancing mathematics achievement of
students in Oshimili South Local Government Area of Delta State.
In specific terms, the study seeks to:-
1. Determine the effects of cognitive restructuring in improving
students’ mathematics achievement.
2. Determine the effects of cognitive restructuring in pre and posttest
scores performance of students, in respect to their gender.
Significance of the Study:
The findings of this study will be of immense importance to the end users
when eventually published. Such end users includes: Teachers,
students, Guidance Counsellors, the school and future researchers.
These findings it’s expected, will yield data that would confirm, support
or reject the theories of achievement as they relate to cognitive
restructuring which holds that, peoples’ achievement goals affect their
achievement related attitude and behaviours .
The outcome of the study will offer useful framework for teachers who
are both planners and decision makers in the classroom, so that while
teaching the students, the technique of cognitive restructuring would be
inculcated in the scheme of work to help the students understand the
topic.
11
It is hoped that teachers would become aware of the necessary and
relevant cognitive restructuring techniques, which would be useful in
teaching mathematics.
Through these findings, students it is hoped will become aware of
necessary relevant cognitive restructuring techniques, which will be very
useful for them. Moreover, no educational guidance of secondary school
students will ever be complete without the guidance counsellors giving
them hints on how to improve on their academic achievement.
The result of this study also, will be of relevance to school guidance
counsellors, who will encourage students during counselling sessions,
with techniques such as self monitoring, positive self statements,
thought stopping and systematic desensitization so that the students will
adopt these skills to enhance themselves to improve their studies.
The school authority, it is hoped will use the findings of the study to
assess the extent of utilization of vital cognitive restructuring techniques
by teachers and know how lack of utilization of these techniques would
affect students’ mathematics achievement. Such an assessment, will
guide the school in its future use.
Finally, it is hoped that the study will be of immense benefit to
researchers, for future research information. This is because; the
findings are expected to prepare grounds for future researches and raise
questions for investigation. For instance, how would cognitive
12
restructuring technique, be used to enhance academic performance of
mathematics students so they become better achievers in the subject?
Scope of the Study:
The study was delimited to Senior Secondary School (S.S.11) students
in Oshimili South Local Government Area in the Delta State.
The study also covered the effect of cognitive restructuring in
mathematics problems in like and unlike terms, factorization, quadratic
equation, simultaneous equation and performance in word problems in
algebra. Another variable discussed included gender, as it relates to
cognitive restructuring skills and academic achievement.
Research Questions:
The following research questions guided the study:
1. What are the mean achievement scores of students who were
exposed to cognitive restructuring and those who were not
exposed?
2. What is the difference in pre and post test scores of male and
female students who are exposed to cognitive restructuring
techniques?
13
Research Hypotheses:
The following Null Hypotheses (Ho) were tested in the study, P (0.05)
level of significance.
Ho1 The effects of cognitive restructuring in enhancing students’
achievement in mathematics will not be significant in the
experimental group when compared with the achievement of the
students’ in the control group.
Ho2 The effects of cognitive restructuring in enhancing students’
achievement in mathematics will not differ significantly due to their
gender.
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