1 EFFECTS OF INSTRUCTION IN METACOGNITIVE SKILLS ON MATHEMATICS SELF – EFFICACY BELIEF, INTEREST AND ACHIEVEMENT OF LOW – ACHIEVING STUDENTS IN SENIOR SECONDARY SCHOOLS BY YUNUSA UMARU PG/Ph.D/07/42658 A THESIS SUBMITTED TO THE DEPARTMENT OF EDUCATIONAL FOUNDATIONS, UNIVERSITY OF NIGERIA, NSUKKA, IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY IN EDUCATIONAL PSYCHOLOGY DEPARTMENT OF EDUCATIONAL FOUNDATIONS UNIVERSITY OF NIGERIA, NSUKKA SUPERVISOR: DR. UCHE N. EZE NOVEMBER, 2010
Transcript
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EFFECTS OF INSTRUCTION IN METACOGNITIVE SKILLS ON MATHEMATICS SELF – EFFICACY BELIEF, INTEREST AND
ACHIEVEMENT OF LOW – ACHIEVING STUDENTS IN SENIOR SECONDARY SCHOOLS
BY
YUNUSA UMARU PG/Ph.D/07/42658
A THESIS SUBMITTED TO THE DEPARTMENT OF EDUCATIONAL FOUNDATIONS, UNIVERSITY OF NIGERIA, NSUKKA, IN PARTIAL
FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY IN
EDUCATIONAL PSYCHOLOGY
DEPARTMENT OF EDUCATIONAL FOUNDATIONS UNIVERSITY OF NIGERIA, NSUKKA
SUPERVISOR: DR. UCHE N. EZE
NOVEMBER, 2010
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CERTIFICATION
YUNUSA UMARU, a postgraduate student in the Department of Educational
Foundations with registration number PG/Ph.D/07/42658 has satisfactorily
completed the requirements for the degree of Doctor of Philosophy in Educational
Psychology. The work embodied in this Thesis is original and has not been
submitted in part or full for any other diploma or degree of this or any other
University.
_________________ ____________
Yunusa, Umaru Supervisor
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APPROVAL PAGE
This thesis has been approved for the Department of Educational
_______________ _________________ External Examiner Head of Department
_______________ Dean of Faculty
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DEDICATION
This work is dedicated to Almighty Allah, the beneficent and the merciful
and to all my benefactors during the course of this programme, for their various
moral and financial supports.
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ACKNOWLEDGEMENTS
I wish to express my profound gratitude to my supervisor Dr. Uchenna Eze
who painstakingly scrutinized each stage of this work, making constructive
criticisms and giving helpful advice. His encouragement made this thesis a reality.
I also wish to thank him for analyzing all the data.
I owe a lot of thanks to Dr. Ngwoke D. U. who, in spite of his tight schedule,
made time to read through this work and effect some fundamental corrections. I am
grateful to Dr. Onuigbo, Liziana N. in a special way for necessary advice and
guidance to effect some corrections.
I wish to thank Dr. Uche Igbokwe, Professor U.N.V Agwagah and Professor
D. N. Eze, Dr. (Mrs.) Umeano E., Dr. Usman K. O. and Dr. R. E. Ozioko, Dr. (Mrs)
Ngozi M.E. Eze, Professor Ike Ifelunni and Mrs. Ngwoke Anthonia for their
contributions and useful criticism for validation of the instrument used for the
study.
I thank my research assistants, Mr. J. A. Ajani and Mallam Imran, and my
greeting go to Aisha A., Sanda, Eze Ovoko, Dr. Abolari, E. E. Yakubu, S. A.,
Ekele, C. E., Idris Akaba, and Ibrahim Ndawaka for their support. Thanks to Miss
Ngwu Mabel and Miss Blessing who helped in typing, formatting and printing the
work.
I am grateful to all members of D. C. P (Alhaji) Shuaibu Lawal Gambo
families and to all friends and well wishers and to my wife Maimunat, for her
patience and understanding through the period of this work. I remain grateful to
my father Alhaji Baba Isah Bida, and my mother Hajara Kaka Isah for their
encouragement and belief that I could make my dream come true.
Finally, I am grateful to God Almighty to whom all adoration belongs.
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TABLE OF CONTENTS
Title - - - - - - - - - - - i
Certification - - - - - - - - - ii
Approval - - - - - - - -- - - iii
Dedication - - - - - - - - - - iv
Acknowledgements - - - - - - - - v
Table of Contents - - - - - - - - vii
List of Tables - - - - - - - - - ix
List of Figures - - - - - - - - - x
List of Appendices - - - - - - - - xi
Abstract - - - - - - - - - - xii
CHAPTER ONE: INTRODUCTION: - - - - - - 1
Background of the Study - - - - - - - - 1
Statement of the Problem - - - - - - - - 10
Purpose of the Study - - - - - - - - - 11
Significance of the Study - - - - - - - - 11
Scope of the Study - - - - - - -- - - 14
Research Questions - - - - - - - - - 15
Hypotheses - - - - - - - - - - 16
CHAPTER TWO: LITERATURE REVIEW - - - - 17
The Concept of Metacognition - - - - - - - 18
The Concept of Metacognitive Skill - - - - - - 20
The Concept of Self-efficacy - - - - - - - 23
The Concept of Interest - - - - - - - - 24
The Concept of School Achievement - - - - - - 27
The Concept of Low Achieving - - - - - - 29
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Relationships among Metacognitive Skill, Self-efficacy Belief,
Interest and School Achievement - - - - - - 30
Theoretical Framework - - - - - - - - 32
Piagetian Theory of Cognitive Science - - - - - 32
Information Processing Theory - - - - - - - 35
Flavell’s Theory of Metacognitive Development - - - - - 42
Models of Instructions in Metacognition - - - - - - 45
Albert Bandura’s Social Cognitive Theory - - - - - - 47
Empirical Studies - - - - - - - - - 50
Studies on Metacognitive Skills and Mathematics Achievement - - 51
Studies on Perceived Self-efficacy and Achievement in Mathematics - 56
Studies on Interest and Achievement in Mathematics - - - - 58
Studies on Gender as a Factor in Mathematics Achievement - - 62
Summary of Review of Literature - - - - - - - 66
CHAPTER THREE: RESEARCH METHOD - - - - - 70
Design of the Study - - - - - - - - - 70
Area of the Study - - - - - - - - - - 71
Population of the Study - - - - - - - - - 71
Sample and Sampling Technique - - - - - - - 72
Instrument for the Study - - - - - - - 72
Treatment Procedure - - - - - - - - - 78
Method of Data Analysis - - - - - - - - 82
CHAPTER FOUR: RESULTS - - - - - - - 83
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CHAPTER FIVE: DISCUSSION OF FINDINGS, CONCLUSIONS, RECOMMENDATIONS AND SUMMARY - - 99 Discussion of Results - - - - - - - - 99
Conclusion - - - - - - - - - - 106
Educational Implications - - - - - - - - 107
Recommendations- - - - - - - - - 109
Limitation of the Study - - - - - - - - 110
Suggestion for Further Study - - - - - - - 111
Summary of the Study - - - - - - - - - 112
REFERENCES - - - - - - - - - - 116
APPENDICES - - - - - - - - - - 126
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LIST OF TABLES
Table Page
I. Quasi-Experimental Design - - - - - - - 70 II. The Blue Print for Developing the Mathematics Achievement Test (MAT) - - - - - - - - - 73 III. Pre-Test and Post-Test Means Scores and Standard Deviations on MAT of Low-Achieving Mathematics Students - - - 83 IV. Pretest-Posttest Mean Score and Standard Deviation of Mathematics Efficacy
Scale (MSES) - - - - - - - - 84 V. Pre-Test and Post Test Mean Score and Standard Deviation of Mathematics Interest Inventory MII - - - - - 85 VI. Summary of the 2 -Way Analysis of Covariance (ANCOVA) on the Low-
Achieving Mathematics Students on Mathematics Achievement Test - - - - - - - - - - - 86
VII. Summary of 2-Way Analysis of Covariance (ANCOVA) on the Low-
Achieving Mathematics Students on their Mathematics Self-efficacy Scale (MSES) - - - - - - - - - 87
VIII. Summary of 2-Way Analysis of Covariance (ANCOVA) on the Low-
Achieving Mathematics Students on their Mathematics Students on their Mathematics Interest Inventory (MII) - - - - - 88
IX. The Mean and Standard Deviation of the Students Score in the Pretest Posttest
in Treatment Group by Gender - - - - - - 90 X. Mean and Standard Deviation of the Students Scores in Post Test in
Mathematics Self-efficacy Score (MSES) (Treatment and Gender) Level 94 XI. Mean and Standard Deviation of the Students Score in Posttest in Mathematics
Interest Inventory (MII) (Treatment and Gender) Levels 95 XII. Mean and Standard Deviation of the Students Score in Posttest in a
Mathematics Achievement Test (MAT) (Treatment and Gender) Levels 96
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LIST OF FIGURES
Figures Page
I. Relationship among Metacognitive Skill, Self-efficacy Belief,
Interest and School Achievement- - - - - - 31
II. Flavell’s Model of Metacognition - - - - - 42
III. Problems Solving Models - - - - - - - 46
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LIST OF APPENDICES
Appendices Page A. Mathematics Achievement Test (MAT)- - - - - 126 B. Mathematics Self-efficacy Scale (MSES) - - - - 129 C. Mathematics Interest Inventory (MII) - - - - 130 D. Solution to Mathematics Achievement Test (MAT) - - - 131 E. Validation of Mathematics Achievement Test - - - 136 F. A Sample of Lesson Plan on Mathematics - - - - 137 G. Metacognitive Skill Training Programme (MTP) - - - 146 H. Conventional Training Programme (CTP) - - - - 152 I. Name and Address of School in Kabba-Educational Zone Kogi State Nigeria - - - - - - - - - - - 155
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ABSTRACT
The present study investigated the effect of instruction in meta-cognitive skills on
mathematic self-efficacy belief, interest and achievement of low-achieving
mathematics students in Kogi State, Nigeria. Three research questions and three
hypotheses were generated to guide the study. The design of the study was a quasi-
experimental non-randomized pretest-posttest-control-group design, involving one
experimental group and one control group. The sample consisted of 129 SSII low-
achieving mathematics students in four senior secondary schools. The instruments
used for the study were a researcher- made Mathematics Achievement Test,
Mathematics Self-efficacy Scale and Mathematics Interest Inventory which were
validated by experts and used for data collection. Mean, standard deviation, and
Analysis of Covariance (ANCOVA) were used to analyze the data collected. Major
findings of the study show that (I) Instructing students in metacognitive skills
significantly enhanced their self efficacy belief, interest and achievement in
mathematics, (II) The gender of the students was not a significant factor on their
mathematics achievement, self efficacy belief and interest, (III) There is no
significant interaction effect of gender and instruction in metacognitive skills on
the self –efficacy belief, interest and achievement of low – achieving students in
mathematics. Based on these findings, conclusions were drawn and the educational
implications were extensively discussed. Among the recommendations made were
that teachers should develop in students the skills in applying metacognitive
strategy in solving mathematical problems and that instruction in metacognitive
skills should be conducted involving male and female students since both gender
benefits from such.
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CHAPTER ONE
INTRODUCTION
Background to the Study
Higher order cognitive skills, such as ability to elaborate, synthesize,
analyzed, apply, and evaluate specific learning information are very necessary for
one to achieve academic success and adjustment in life. With the increasing
demand of an ever changing and challenging problem-ridden world, the least any
learner ought acquire from school is the ability to utilize an efficient thinking and
problem solving strategy to face the complex situation and challenges of everyday
life (Onu,2005). Higher order cognitive skills help learners to think more
effectively, manage conflict by themselves, engage in practical thought,
experiment, and question their own basic assumptions (Brown, 1997).
Mathematics is a core subject in the schools. It has been described as the key
that unlocks the mystery of the subjects that shape and enhance logical thinking
with its calculative inference and deductions (Exam Ethics Project, 2002).
Ikeriondu (2006), maintained that mathematics offers the experience needed to
develop ways of dealing with problems, not only at school but in all aspects of life.
Generally, mathematics is regarded as the key to success in the study of other
sciences and science related disciplines (Iwuoha, 1986).
Most universities in Nigeria insist on at least a pass in mathematics for any
course of study while a credit level pass is compulsory for any science related
course (JAMB 2006, 2007, 2008). However, it has been observed to be a subject
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that scares many candidates. The truth is that mathematics is a subject for all
because virtually everybody, be they traders or sportsmen or carpenters, tailors or
even farmers, make use of aspects of mathematics in their daily activities
(Ikeriondu, 2006). The study of mathematics permeates all fields of human
endeavour and has found a place in sciences, architecture, engineering, industries,
aeronautic /space science, navigation, survey, nuclear energy to mention but few
(Osuagwu, Anemelu,& Onyezili, 2000).
The challenge for schools is how to relate mathematics concepts and theories
to practical activities of daily life (Peter, 2000). Okeke, and Ochuba (1989),
Nwoke (1995) and Nateinyin (1995) observed that, the teachers’ teaching method
and mastery of the subject is the key determinant of students’ achievement. In spite
of teachers’ efforts to improve students’ mathematics achievement in Nigeria
especially in Kogi state, their learning outcomes have continued to be very low.
Evidence from the secondary school continuous assessment records in Kogi state
has shown a consistent failure rate in Mathematics for some years. (MOE Report,
2008) West Africa Examination Council (WAEC) Chief Examiner’s Report shows
evidence of poor mathematics achievement. For instance, in 2006, only 177, 800,
candidates representing 15% of the 1, 184,384, that sat for the examination
obtained credits in five subjects including, Mathematics. Similarly in 2007, only a
25% of the total population of 1, 275,330 candidates that sat for May/June WAEC
passed with credit in mathematics. According to the results announced by the West
African Examination Council (WAEC Chief Examiner Report, 2008), a total of
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325,754 candidates representing 25.54% of the population obtained credit and
above in English language, Mathematics and three other subjects. Also, 37,635
other candidates (2.95%) of the total figure obtained five credits and above in 5
subjects, but without English and Mathematics. Of that number, the council said
165, 994, (13.02%) were male candidates while 159,760 (12.52%) were female
candidates (WAEC Chief Exams Report 2006, 2007 and 2008). These are
indications of low mathematics achievement, which may be due to poor teaching
or lack of interest on the part of the candidates or the perceived phobia for the
subject (Exams Ethics Project, 2002).
The low-achieving mathematics students therefore, need special intervention
if they must record success in dealing with mathematical problems. Low
mathematics achievers are those students whose achievements are consistently
very low and who, in spite of efforts to cope, may be quite slow, confused and lack
confidence in themselves (Okebukola 1994). They are those whose achievements
are consistently below average, and who may have numerous aversions associated
with solving arithmetic related problems, (Montague, 1998). Such problems could
be attributed to a number of environmental factors such as peer group influence,
relationship with teachers, cultural factors and school factors (Obioma and Ohuche
1985, Okeke and Ochuba 1989).
Recent studies in Nigeria show that most learners do not have effective
strategy that could facilitate learning, including the learning of mathematics (Eze,
2003). Instead, they adopt rote learning methods which have been found to be
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ineffective for learning complex task (Eze, 2007). Many studies have been carried
out on the teaching strategies which were to be effective. They include the use of
advance organizers, concept mapping, and group activity strategies (Okebukola,
1994; and Idowu, 2002). These methods seem to be inadequate for teaching
Mathematics. Mathematics is a subject requiring problem solving and such
strategies as metacognitive learning strategy that will transfer the responsibility of
learning by developing in the learners self-regulating skills has been suggested to
thinking is the ability to distinguish between one’s perspective and some one
else perspective. The following telephone interaction between 4–years-old
Mary, who is at home, and her father, who is at work, typified Egocentric
thought: -
Father: Can Mary speak to mummy?
Mary: (Nods against silently)
Mary’s response is Egocentric in that she failed to consider her father‘s
perspective; she does not realize that he cannot see her nod (Santrock 2001).
Concrete operational stage (Elementary and early adolescence 6/7-11years).
This stage is characterized by conservation of numbers, length, liquid mass,
weight, area, colour and volume. Intelligence is more demonstrated through
logical and systematic manipulation of symbols related to concrete objects.
Operational thinking develops (mental actions that are reversible).
Egocentric thought diminishes.
Formal operational stage (Adolescence and adulthood 11+ years): In this
stage, intelligence is demonstrated through the logical use of symbols related
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to abstract concepts. Early in this period there is a return to egocentric
thought. This period coincides with the secondary school age of students in
Nigeria (Eke, 1992; Harbour-Peter’s 1999). Furthermore, the formal
operational stage was also characterized by logical reasoning from
hypothetical prepositions, evaluating hypothesis through testing all possible
conclusion, presenting reality as one alternative in an array of possibilities
and ability to think about thinking (metacognition) and use theories to guide
thought processes (Morgan, King, Weiz, and Schopler, 2004).
To the researcher, Piagetian theory of cognitive development is tangential to
this study. It explained the processes that deal with intellectual skills development.
The theory outlines the stages through which intellectual skills evolve. It
emphasize that ideal adult intellectual operation is characterize by capacity for
abstract reasoning, preoperational logic and reasoning. That is to say that students
at this stage can be taught a new kind of thinking, which is abstract, formal and
logical. Thinking symbolically at this stage is necessary if one should be able to
deal with problem solving in mathematics.
Information Processing Theory of Cognitive Development
The information process approach emphasizes that children manipulate
information, monitor it, and strategize about it. Central to this approach are the
processes of memory and thinking. According to the information–processing
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approach, children develop gradually as they increase in their knowledge and skills
for processing information (Stevenson, Hofer, and Rendel, 1999).
In the last two decades, the information – processing approach has spread
through the field of cognitive development. Its emergence is linked principally to
(a) the advancement in understanding of the way the nervous system works, and (b)
the development of Computer Based Systems, which stimulates a number of
human functions (Michel, 1990).
The metaphors established between the human brain and the computer is
useful in that mental operations are to some extent comparable to the working of a
computer since they both take in information (input function), perform operations
(throughput), and display result (output function). More generally, both human
beings and computers manipulate symbols and transform input into output (Michel
1990).
According to Michel (1990), the human processing system consists of four
major elements: (a) Sense organs, (b) Short-term memory (d) Long-term memory,
and (d) Muscle systems. The system also involves function and processes within
each element and the interactions among these elements.
The Sense Organs: such as eyes, ear, taste buds, pressure and pain nerves in
the skin receive impressions from the environment. They serve as input channels,
which gather information from the environment. Each sense organ is, however, a
very specialized instrument, attuned only to one type of stimulation. They gather
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impression in a selective way, filtering out much information and allowing some
environmental stimuli to enter the human processing system.
The Short-term Memory: Theories have labeled Short-term Memory, as
primary memory, active memory or working memory. Many people consider those
terms as being synonymous. The working memory’s primary function is to hold
limited amount of information for a very short period of time, evaluated at a few
seconds at role and functioning. This is explained by reviewing its 3 stages (Michel,
1990).
a) Sensory Memory: This is an unselective type of memory which holds for
only one or two seconds all stimuli that strike the particular sense organ
within a range of receptiveness. Labels applied to this early stage are iconic
memory, echoic memory, and tactile or hepatic memory.
b) Encoding: this term suggests that at this second stage of impressions stimuli
are recast into a form-manipulated and stored in long- term memory or else
they are lost. This stage lasts for one or two seconds and holds every little
capacity.
c) Semantic memory: At this point, the person compares the information of
stage (a) and (b) with some selected elements of long-term memory. It is a
stage of perceptual recognition during which the information is identified for
what it represents in terms of the person’s past experience or long memory.
It is believed that a mature adult can hold an average of seven chunks’ of
information at a time (Miller, 1984). A chunk is described as a portion of person’s
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knowledge base that is actually activated and deactivated as a unit (Kail and Binaz,
1985). Chunking could be described as a benefited organizational memory strategy
that involves grouping or packing information into higher order units that can be
remembered as single unit. Chunking works by making large amount of
information more manageable and more meaningful. For example, consider this
simple list of words hot, city, books, forget, former, smile. Try to hold these in
memory for a moment, and then write them down. If you recall all the six words,
you succeed in holding 34 letters in your memory. (Santrock, 2001).
Long term memory: Is a type of memory that holds enormous amount of
information for a long period of time in a relatively permanent fashion (Santrock,
2001). It has two principal functions
(a) Directing the operation of the entire processing system, and
(b) Storing information or coded material derived from the person’s past
encounters with the environment (Michel 1990). Coded material takes two main
forms: (i) episodic memories which are memory traces about single events from
the past involving specific person or object, and (ii) Semantic memories which
consist of more generalized instrument of thought, concept and processes which
are not limited to one place or time. Other elements, which also constitute the
anatomy of long-term memory, are goals, relationships, affects, and values. Goals
are motivational components, which stimulate the individual to focus attention
more on certain facets of the environment than others. Relationships are the
connections and rapports existing between one long-term memory and another.
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Affects are emotions, which are often associated with concepts, certain events and
relationship. Values are opinions about the desire, ability or priority, or goodness
of something. They too are associated with certain elements of the memory bank
(Michel, 1990).
A popular suggestion is that long-term memory is organized like a fishnet,
with each model representing an individual memory trace such as an events and
concepts. The strands lead to other events and concept. The links between some
nodes are stronger, meaning that linkages are more quickly and strongly
established between these memory traces than between other which represent more
distant association. However, such a component is inadequate for describing the
complex intricacies of human thoughts and the mechanisms of interaction between
short term and long-term memories (Anderson, 1983).
One of the most important interactions is that of matching the stimuli
received from the environment with the content of long-term memory. Thus, active
decision-making and problem solving are carried out through somatic short-term
memory and long-term memory during a flow of rapid transactions. Then the
person assigns a meaning’ from the long-term memory to each and recognizes
sensory encounter with the environment (Michel, 1990). The main ideas or
concepts are then stored in the memory bank. The results of the new encounter
may be similar to existing memory traces or may be new addition to the memory
traces. In some instances new memory traces are recorded in great detail and exact
phrasing; at other times they are not. In all cases, old coded traces influence how
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new experiences are constructed and stored. It may also happen that the new
experience considering the logical memory construction processes is fed by
peoples past and present experience in their memory banks. These coded traces and
their interactions with short-term memory make up the human processing system
(Michel, 1990).
Robert Siegler (1998) described three main characteristics of the information
processing approach:
Thinking: - In Siegler’s view, thinking is information processing. In this
regard, Siegler provides a broad perspective on thinking. He maintained that
when children perceive, encode, represent, and store information from the
world, they are engaging in thinking. Siegler believed that thinking is highly
flexible, which allows individuals to adapt and adjust to many changes in
circumstances, task requirements, and goals.
Changes Mechanism: Siegler maintained that there are four main
mechanisms that work together to create changes in children’s cognitive
skills: encoding, autoimmunization, strategy contraction, and generalization.
Encoding is the process by which information get into memory. Siegler
states that a key aspect of solving problems is to encode the relevant
information and ignore the irrelevant parts. The term automaticity refers to
the ability to process information with little or no effort. With age and
experience, information processing become increasingly automatic on many
task, allowing children to detect connections among ideas and events that
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they otherwise would miss. Hence automaticity is the ability to respond
quickly and effectively when mentally processing or physically performing a
task.
The third and fourth change mechanisms are strategy construction, and
generalization. Strategy construction involves the discovery of a new procedure for
processing information. Siegler says that children need to encode key information
about a problem and coordinate the information with relevant prior knowledge to
solve the problem. To fully benefit from a newly constructed strategy, children
need to generalize, or apply, it to other problem (transfer). Transfer occurs when
the child applies previous experience and knowledge to learning or problem
solving in a new situation.
Self-modification: The importance of self-modification in processing
information is exemplified in metacognition, which means cognition about
cognition, or knowing about knowing (Flavell, 1999). It emphasizes
students’ self-awareness of their mental processes and how they can adapt
and manage their strategies during problem solving and thinking.
To the researcher, information processing theory is a clear prove to this
study. It emphasized that children manipulate information, monitor it and
strategize about it. Central to this approach are the presence of memory and
thinking. For instance, a student has to be genuinely interested in the task and
consciously activate the body of knowledge in the short-term memory through self-
modification or metacognition, which is a key variable to this study.
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Flavell’s Theory of Metacognitive Development
Flavell (1999) makes the first attempt to define the component of
metacognition by creating a model of cognitive monitoring/regulation. His
proposal includes four components (a) metacognitive knowledge, (b)
metacognitive experiences, (c) goals or tasks, (d) actions or strategies. A person’s
ability to control a wide variety of cognitive enterprises depends on the actions and
interactions among these components. Figure 2 shows the relations between them.
Fig. 2. Flavells Model of Metacognition
Metacognitive knowledge: is one’s knowledge about cognitive processes, a
personal perspective of one’s own cognitive ability as well as others. The statement
“I am good at arithmetics, but Baba knows more words than I do” is an example of
metacognitive knowledge. Flavell states that metacognitive knowledge consists
primarily of knowledge or beliefs about what factors or variables act and interact in
what ways to affect the course and outcome of cognitive enterprises (Flavell, 1979).
He also identifies three general categories of these factors the person variable, the
task variable and strategy variables.
Cognitive strategies
Metacognitive experiences
Metacognitive knowledge
Cognitive goals.
Task Person Strategy
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The person variable comprises everything that one can come to believe
about the nature of oneself and others as a cognitive processor. This variable
relates to knowledge and belief one has about differences between individual or
intra individual differences (for example, the realization that one is better at
calculating than at memorizing history).
As the name indicates, the task variable has in it the information available
and demands of the specific cognitive task the person is engaged at the moment. In
that category, we would find the understanding of what are the implication of the
way information is presented (for example, the task is well or poorly organized)
and the goal set (for example, recall the gist or recall the wording of a text) to the
path one will choose to manage the cognitive task in the best way to reach the goal
and how likely one is to do it successfully.
In the strategy variable,one’s find knowledge about which strategies are
likely to be effective for achieving sub-goals or goals in various cognitive tasks.
Flavells, as we remember, argues that metacognitive knowledge does not differ in
form and quality from other knowledge stored in long-term memory. As a
consequence, it can either be retrieved as a result of a deliberate and conscious
memory search, or it can be activated unintentionally and automatically by
retrieval cues in the task situation. The latter situation is the most common
metacognitive knowledge that can be used unconsciously. However, it may also
rise to consciousness and provide what he calls a metacognitive experience.
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Metacognitive Experience/Regulation of Cognition
Regulation of cognition refers to metacognitive activities that help
control one’s thinking or learning. Although a number of regulatory skills have
been described in the literature, three essential skills are included in all accounts:
planning, monitoring, and evaluation (Schraw, 2000).
Planning: Involves the selection of appropriate strategies and the allocation of
resources that affect performance. Examples include making predictions before
reading, strategy sequencing, allocating time or attention selectively before
beginning a task (Miller, 1985).
Monitoring: - refers to one’s on-line awareness of comprehension and task
performance. The ability to engage in periodic self-testing while learning, is a good
example of metacognition. Schraw (2000) found that adult’s ability to estimate
how well they would understand a passage prior to reading was related to
monitoring accuracy on a post-reading comprehension test.
Evaluation: - refers to appraising the products and regulatory processes of one’s
learning. Typical examples include re-evaluating one’s goal and conclusion.
The Goal or Tasks refer to the actual objectives of a cognitive endeavour, such as
reading and understanding a passage for an up coming quiz, which will trigger the
use of metacognitive knowledge and this will lead to new metacognitive
experiences.
Action or Strategies refer to the utilization of specific techniques that may assist
in achieving those goals. For example, metacognitive experience could be
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remembering that outlining the main idea of a passage on a previous occasion has
helped increase comprehension.
This model is important to define what metacognitive knowledge is and
what are the main factors that influences its content and development most.
To the researcher, Flavell theory of metacognition is tangential to this study.
It explains the processes that engendered metacognitive skills development. The
theory also outlines the various ways to acquire knowledge about cognitive
processes. It ensures that the learner will be able to construct meaning from
information. To accomplish this, the learner must be able to think about their
thought processes, identifying the learning skills that work best for them and
consciously manage how they learn. Development of metacognitive skills is the
key variable in this study.
The Model of Instruction in Metacognition
The model proposed by McLaughlin and Hollingsworth (2001) served as a
useful guide on how actual instruction in teaching metacognitive skill should
proceed.
58
Phase 1 Phase 2 Operationalization of Create problem solving situation Metacognitive skills Phase 3 Student solve problem Phase 8 Change Activities Phase 4 Effectiveness Phase 7 Reflection Phase 5 Interaction Phase 6 Transfer Fig. 3. Problems Solving Models
Source: Mc Laughlin and Hollingsworth (2001).
Figure 3 explains graphically the problem-solving model proposed by
McLaughlin and Hollingsworth (2001). This model was used as a guide by the
researcher to teach metacognitive skills in problem solving in mathematics.
According to the above proposed models, teaching metacognitive skills
requires that the instructor operationalises the concept of metacognition such as
awareness, planning, monitoring, reflection/regulating and evaluation. This is
59
followed by creation of problem situation requiring solution. Teachers create
problem for students to solve. Also in finding the answer or solving the essay type
questions, the students were given clear explanation by the teacher on the steps to
be used while trying to answer the questions such as, identifying the problem,
recognizing the problem, finding the answer, trying the solve the problem and
evaluating the answer obtained. For ensure effectiveness of using the model.
In addition, using the above proposed model, the students were allowed to
have peer interaction by comparing their work with each other with that of an
expert and this will allow transfers of learning set. Finally, Reflection which is the
process by which students assess their own level of understanding the problem
solving processes through revision of the past exercises. The students now gain
knowledge to actively solve problem on their own (independently).
Also from the findings of McLaughlin and Hollingsworth (2001), the control
groups were given instruction by the teacher in the traditional way that is largely
through chalk and talk exposition and note taking. Based on this study therefore,
the training programme was developed using this model approach.
Albert Bandura’s Social Cognitive Theory
The concept of self-efficacy is the focal point of Albert Bandura’s social
cognitive theory. By means of self-efficacy, individuals exercise control over their
thoughts, feelings and actions. Among the beliefs with which an individual
evaluates the control over his/her actions and environment, self-efficacy beliefs are
60
the most influential arbiter of human activity (Bandura, 1997; 2001). Self- efficacy
is the belief in one’s capabilities to organize and execute the course of action
required to produce a given attainment. It is constructed on the basis of the four
most influential sources: enactive attainment, vicarious experience, verbal
persuasions and physiological as well as emotional factors. Self-efficacy plays the
central role in the cognitive regulation of motivation because people regulate the
level and the distribution of effort they will expend in accordance with the effect
they are expecting from their actions (Ormrod, 2006).
Bandura (1997) postulated four principal sources of self- efficacy: mastery
experience, modeling or vicarious learning, verbal social persuasions and
physiological factors.
Experience: Mastery experience is the most important factor deciding a
persons’ self-efficacy- simply put success raises self-efficacy, failure lower it
(Bandura 2001).
Modeling/ Vicarious Experience: If they can do it, I can do it as well. This is
a process of comparison between a person and someone else. When people
see someone succeeding at something, their self-efficacy will increase; and
where they see people failing, their self-efficacy will decrease. This process is
more effectual where the person sees himself as similarly to his /her model. If
a peer who is perceived as having similar ability succeeds, this will likely
increase an observers’ self-efficacy. Although not as influential as past
61
experience, modeling is a powerful influence when a person is particularly not
sure of him/herself (Bandura, 1997, 1998, 2001, 2008.)
Social Persuasions: Social persuasions relate to encouragement/
discouragements. These can have a strong influence. Most people remember
times where something said to them significantly altered their confidence.
Where positive persuasions increase self-efficacy, negative persuasions
decrease it. It is generally easier to decrease someone’s self-efficacy than it is
to increase it (Bandura, 1998; Joanne and Shui-fong, 2008).
Physiological Factors: In unusual, stressful situation, a person commonly
exhibits signs of distress; shakes, aches and pains, fatigue, fear and nausea. A
person’s perceptions of these responses can markedly alter a person’s self-
efficacy. If a person gets butterflies in the stomach “before public speaking, a
person with low self-efficacy may take this as a sign of their own inability,
thus lowering their efficacy. A person with high self-efficacy is likely to
interpret such physiological signs as normal and unrelated to his/her actual
ability, which will continue to be seen as a disregard for trembling hands.
Thus, it is the person’s belief on the implications of the physiological response
that alters their self-efficacy, rather than the sheer power of the response
(Bandura, 1997, 2001; Baron, 2004; Banyard 2003).
School is a principal place where children develop the cognitive
competencies and acquire the knowledge and problem- solving skills essential for
participating effectively in the larger society. Here are knowledge and thinking
62
skills that are continually tested, evaluated and socially compared. As children
master their cognitive skills; they develop a growing sense of their intellectual
efficacy (Bandura, 1997). Students’ belief in their capabilities to master academic
activities affects their aspiration, their level of interest in academic activities, and
their academic accomplishment (Schunk, 1990).
Bandura (1997) maintained that an ideal school offers an excellent
opportunity for the development of self-efficacy. Consequently, educational
practice should reflect their reality. That is, materials and method should be
evaluated not only for academic skills and knowledge, but also for what they can
accomplish in enhancing students perception of themselves and social relationship.
For Bandura (1997), social cognitive learning means that information we
process from observing other people, things, and events influence the way we act.
To the researcher, Bandura social cognitive theory is related to this study. It
explained the various sources that influence social cognitive skill development.
The theory explained that social cognitive skills are important in the regulation of
academic work for social relationship. Development of self-efficacy is a dependent
variabled in this study.
Empirical Studies
A number of research studies have been conducted mainly in foreign
countries on training in the use of metacognitive skills on self-efficacy belief,
interest, and achievement of the low-achieving mathematics students in schools.
63
This study was review under the following sub-headings:
I. Studies on effect of Metacognitive skills and Mathematics Achievement
II. Studies on Self-Efficacy and Mathematics Achievements III. Studies on Interest and Mathematics Achievement
IV. Studies on Gender and Mathematics Achievement Studies on the Effect of Metacognitive Skills and Mathematics Achievement Mavareach and Amrany (2007), in their study on the effect of metacognitive
instruction on student mathematics achievement and regulation cognition. The
purpose of their study is two fold: (a) to examined the extent to which students
exposed to metacognitive instruction while preparing themselves to the
matriculation examination in mathematics attained higher level of mathematic
achievement than the counterpart who where not exposed to metacognitive
instruction, and (b) to examine different effects of metacognitive instruction on
two components of metacognitive knowledge about cognitive and regulation of
cognition. Participants were 61 Israeli high school students who studied four-point
credit on the matriculation examination in mathematic 31 students were exposed to
metacognitive instructions called improve (experimental group) and other 31
students studies with no explicit metacognitive guidance (control group). Three (3)
kinds of instrument were used: mathematics achievement test (MAT),
metacognitive awareness questionnaire, and interviews. The analysis includes both
quantitative and qualitative methods. The results indicated that improved students
64
outperformed their counterpart on mathematics achievement and regulation or
cognition, but not on knowledge about cognition.
Further more, during the matriculation examination, improved students
executed better kinds of cognitive regulation processes than the control group. The
control groups focused mainly on attempt to comprehend the problems. The
experimental groups try to make connection and reflect on the process and the
products. Given the findings of the processes on their study, one reasonable
conclusion is that students have to be trained to regulate their learning as shown in
this study.
Miles. Blum, Staats, and Dean (2003) in their study on the effect of
metacognitive skills on mathematics and computer science achievement on
students’ grades in college course investigated the effect of training in
metacognitive skills on mathematics achievement and computer science
application among the college students. Participants were 210 students in New
York High School. The Metacognitive Skills Inventory (MSI) was the instrument
used for the study. Lower scores on the inventory indicated lower levels of
metacognitive skills while higher score indicate high levels of metacognitive skills.
The findings of the study show that the MSI was a good predictor of the sample
exercised. Those groups expose to training on MS and CS performed better than
non – MS and CS students in the college.
Goldberg and Bush (2003), in their study on the effect of metacognitive
skills to improved 3rd graders in mathematics problem solving. The purposes of
65
their study were to (i) explore mathematical problem – solving and metacognitive
skills as developed by third-grade students prior to instruction in metacognition,
and (ii) examine the impact of year – long mathematics instruction that centre
explicitly on development of metacognition on the students growth in
metacognitive and problem – solving skills. The subjects were the entire 3rd –
grade population, 2 classes of eight and nine years old, in a rural school in
Kentucky. Each class had 21 students in the metacognitive class and 23 students in
the non – metacognitive class at the end of the school year. The instrument in their
study consist of (a) Strategies that focus on raising students of self-awareness on
their own thinking (b) strategies that focus on planning, monitoring and evaluation
within problem solving events are presented to those in experimental groups. The
non-metacognitive group was not exposed to those strategies. The analysis
revealed that students in the metacognitive class scored significantly higher (P<.05)
than students in the non-metacognitive class but the differences were not
significant in metacognitive skill of the 3rd grade students exposed to
metacognitive instruction than their counter part not exposes to.
A similar study by Panoura and Philippi (2006) on the measurement of
young pupils’ metacognitive ability in mathematics, the case of self-Representation
and self-evaluation, investigated the interaction between young pupil self-
Representation and self-evaluation in relation to their mathematic performance.
Data were collected from 126 children (about 8-11years old) in grade three through
five (37were 3rd grade 40 were 5th grade). A questionnaire was developed for
66
measuring pupil’s metacognitive ability. Their instrument consists of
metacognitive awareness inventory reflecting pupils’ perceived behavior during
problem solving activity. A-3 pairs of problems for which pupils had to evaluate
the difficulty of the tasks and the degree of their similarity were administered to
measure the subjects. The results of the study show that low achieving pupils
evaluation of the difficulty and the similarity of mathematics task were optimistic
rather than realistic. They appeared unaware of the ineffectiveness’ of any strategy
they may use. Learners who are skilled in metacognitive self-assessment are more
aware of their ability (more strategically thinking) and perform better than those
who are not aware of working on their own mental system.
Desoete (2008) examined the evaluation of metacognitive processes in
solving problem in mathematics to improve the learning process through
metacognition. A longitudinal study was conducted on 32 children in mathematical
skills in grade 3 and 4. Metacognitive skills were evaluated through teaching
ratings; thinks aloud protocol, prospective and respective child rating as well as
Evaluation and Prospective Assessment (EPA) were the instrument used. The
result reveals are useful to evaluate the metacognitive knowledge and belief of
young children. Teacher questionnaire were also found to have some value added
in the evaluation of metacognitive skills. The data show that metacognitive
skillfulness assessed by teacher rating accounted for 22.2% of the mathematics
performance.
67
Study conducted by Mevareach and Kramarski (2003) on the effect of
metacognitive training versus worked–out examples on student’s mathematics
reasoning examined two ways to structure groups’ interaction. One is based on
work out example (WE) and the other on metacognitive training (MT). The
objectives are two fold: (1) to investigate the effect of metacognitives training
versus worked-out examples on students’ mathematics achievement; Participants
were 122 eight grades Israel students who studied algebra in five heterogeneous
classrooms. 3 instruments were used to assess students’ mathematical achievement
a Pretest, immediate post test and a delayed post test. ANOVA was carried out to
the posttest scores. In addition, Chi Square and Mann-Whitney procedure were
used to analyse cooperative, cognitive and metacognitive behaviour. The result
indicated that students who were exposed to metacognitive training out performed
students who were exposed to work out example on both the immediate and delay
post test. Lower achievers gained more under the Metacognitive Training (MT)
than under the Workout Examples (WE) conditions.
Biryukov (2006) studied the effect of metacognitive skills on problem-
solving. Specifically the study investigated the metacognitive behaviours of
pedagogical college students during problem solving, assessed the importance of
metacognition for problem solving and to analyze the skills chosen for solving
combinatory problems, success, pitfall and typical errors. The study was conducted
with 48 first and second year pedagogical college students, using combinatory
problem in mathematics. Means and T-test Statistics were used to analyse the
68
result. All participants were asked to solve two combinatory problems that were
presented to them on a list of paper. The result of the analysis and comparism of
students’ reflective self-reports on metacognitive training of their problem solving
abilities in the two combinatory problems, shows that those exposed to
metacognitive experience outperform and do better than those that were not
exposed to during combinatory problem in mathematics. Only students who
perform both action, succeeded in solving the second problem.
The finding of the empirical research on metacognitive skills and
mathematics achievement is quite interesting as these strategies have been proved
to be successful with the sighted. However, there appear to be not much literature
in teaching the metacognitive skills of planning, monitoring, regulating, and
evaluation. In order to integrate them in problem solving among low achieving
mathematics students, as this seems to affect mathematics achievement adversely,
the students therefore, need to be trained on the new skills that can enhance the
achievement in mathematics and this is the main trust of this study.
Empirical Studies on Self-Efficacy and Mathematics Achievements
Chouinard and Roy (2008) undertook a study on the changes in high school
student’s competence belief, utility value and achievement goals in mathematics.
The study aimed to examine the hypothesis that there was a general breakdown of
students’ competence belief, utility value and achievement goals in mathematics
during adolescence. 1,130 participants from 18 secondary schools distributed in
69
two cohort in Canada. Attitudinal scales were used to measure competence believe,
utility value and achievement goal in mathematics. Hierarchical linear modeling
was used to analyze the data. The result of the findings shows that boys experience
a greater decrease over time in motivation in mathematics. Moreover girls show a
more positive attitude towards mathematics than boys at the old age.
The study conducted by Maria and George (2006) on mathematics self
efficacy and achievement in problem solving explored the relationship between
mathematics self-efficacy belief in problem solving and achievement. The sample
consisted of 238 fifth grade students (99 boys and 139 girls) from eleven classes,
from 6 rural and urban primary schools in Cyprus. Three questionnaires were
administered to the subjects during the academic year for measuring Self-Efficacy
(SE) and related constructs. The analysis of the data shows that most of the
subjects feel quite efficacious in mathematics. 38.5% of the subject have high and
32.5% extremely high SE believe, 22.4% neutral believe, and only 3.6% rated
themselves on the negative side of the scale. Comparism with their classmate’s
result shows that 16.8% are not good as majority of their class mates, 24.5% claim
that they are excellent students, while 37.4% said they are very good students in
mathematics.
Halon and Schneider (1999) in their study investigated a pilot intervention
designed to improve students’ mathematics proficiency through self-efficacy
training. First year college students participated in a five-week summer programme
that included whole class instruction, small group tutoring, and individual meeting
70
with instructional coordinators. The data from the SE training intervention were
analyzed using a hierarchical lineal model approach. Student achievement score on
a maths proficiency exam improved significantly as did their confidence levels
about passing their examination. Students who participated in the SE intervention
group out-performed students who were involved in the regular remedial classed.
Overall results demonstrate the positive role of believing in effort/competencies in
a given task.
Neilson (1996) study the psychometric data on the mathematics self-efficacy
skill. The purpose of his study was to examine the development and preliminary
psychometric data pertaining to a new skill designed to measure mathematics self-
efficacy at the level of domain corresponding. 302 of 9th and 10th grade student in
Australia from catholic and independent schools across the metropolitan
Melbourne and surrounding districts volunteered to participate in the study. There
were 163 females (54%) and 139 males. The instrument used for their study was
mathematics self-efficacy skill (MSES), using a 5 point likert type scale. Higher
scores indicated higher level of mathematics self-efficacy while lower scores
indicated lower level of mathematical self-efficacy. The resultant scores provide an
indication of student perceived competence for the content.
Empirical Studies on Interest and Mathematics Achievement
Hassan (1995) in his study investigated the factors affecting science interest
of secondary school students. The purpose of his study was to determine the
71
influence of some selected variables (instruction, student, home and society) on the
development of student interest in science. 4 hypotheses guided his study. For
instance there was no overall difference between student with high interest in
science and student with low interest in science on the following inner
multinational variable: The sample consisted of 340 eleventh grade science
students ranging from 16 to 19 students who were randomly selected from four
major secondary schools in Jordan. There were 166 boys and 174 girls in the
sample. Students interest in science were measured by a science interest scale
consisting of 40 traded statement. Data of the variables stated were collected from
all students in the sample by means of questionnaires consisting of personal
information questions, check list and written scale. Mean scores of both groups on
every variable were compilled using the positive test. The level of significance was
set as 05. The result of the findings was hypothesized that students with high
interest in science did not differ significantly (P< 0.5) from student with low
interest on a selected number of variables measured.
Ngwoke (2005) investigated the effect of cognitive and emotional interest
adjuncts on students’ comprehension of an instructional text. His study also
explored the interaction effect on interest adjunct and gender on students’
comprehension of an instructional text. Three null hypotheses guided his study.
Randomized post-test only control group design, was utilized to execute his study.
The sample of his study was 2002 undergraduate students randomly composed
from the University of Nigeria Nsukka. Students who registered for a faculty of
72
education course in the year 2002/2003 academic season. Subject in his study was
randomly assigned to two experimental groups and a control group. The control
group studied a 385 words instructional text while the experimental groups studied
the same text with 122 words interest segments added within the text. All subject
in his study attempted a 5 questions short essay-type comprehension test after
studying the text. The result of his study shows that no significant main effect due
to interest adjunct on students’ comprehension of an instructional text and the
interactional effect of interest adjunct and gender on students’ comprehension of
text was also not significant.
Minner and Lauri (2008) had a study on university students’ emotions,
interest and activities in Web-Base Learning Environment (WBLE). The purpose
of their study was to examine how emotion experienced while using a WBLE
student interest toward the course topic. Participants were 99 university students
who finished from the five web- based courses in University of Turku in Finland.
The findings show that the fluctuation of emotional reaction was positively
associated with both visible collaborative and invisible non-collaborative activities
in the WBLE Interest toward the web- based leaning was positively associated
with invisible activity. The result also demonstrated that student not participating
in the collaborative activities hard more negative emotional experiences during the
course than others students.
George (2006) studied interest and mathematics achievement in problem
solving approach. The purpose of his study was to explore the relationship between
73
interest and mathematics achievement in problem approach. 150 students (90 boys
and 60 girls) from six classes and from three primary school Cyprus were used.
Three scale were used to measure interest and mathematics achievement scale (i)
student were asked to locate their interest (i = association 11= real love, 6 =
neutral), (ii) consist of comic type pictures, each presenting persons with various
expression about mathematics. Specifically, their feelings toward the subject
appeared, in callouts (for example, ‘I hate mathematics’, ‘Every time do
mathematics’, ‘I want to scram!”). Students of course, were expected to choose the
picture reflecting feelings toward mathematics ranging from extreme negative to
extreme positive (for example, mathematics thrill me! It is my favorite lesson”!).
The analysis of the data revealed that a high proportion of student hold positive
interest toward mathematics task. The finding on the linear scale indicated that
50% adored mathematics, while 21.8% consider declared neutral, choosing the
middle scale only 10.1% to express negative attitudes, hate and dagust. The same
pattern of response also emerged from students feeling analysis.
The findings above are clearly proved when cited. However, none of these
studies investigated how interest has interacted with instructions in metacognitive
skills and mathematics achievement among low achieving mathematics students.
This study will therefore, be carried out to see the interaction effect of instructions
in metacognitive skills and interest among low achieving students.
74
Empirical Studies on Gender and Mathematics Achievement The influence of gender difference on students’ level of achievement has
been a matter of concern to science educators. Finley (1982) investigated the
science reading achievement and attitudes of students to passage reading. Five
hundred (500 respondents comprising 250 boys and girls were selected from
secondary schools in England, Sweden and U.S.A. and an achievement test was
administered to respondents and the data obtained were subjected to mean,
frequency and person product moment correlation coefficient statistics. Findings
revealed that boys performed better than girls. The study showed that gender
difference influence students achievement in science reading test.
Idowu (2002) worked on gender difference among Mathematic students in
the College of Education (Technical) Lafiagi. One hundred (100) students
comprising 50 male and 50 female were randomly chosen from pre – NCE students
result admitted between 1998 and 2000 academic sessions. The Pre – NCE results
of respondents were subjected to standard deviation and student t-test statistics.
Findings showed that there was a significant difference in the achievement of male
and female student in Mathematics.
Gray Bill (1990) studied the gender related difference of Adolescents in
problem – solving ability. The purpose of his study was to determined sex
difference in the transition from concrete to formal thinking level as defined by the
work of Piaget and Inhelder. It was hypothesized that sex differences in intellectual
development would become apparent in the transition from concrete to formal
75
operational stages, and that boys would become more successful than girls in
solving selected science problems. The subjects included for study were pairs of 9,
11, 13 and 15 years old boys and girls in senior secondary school in Newjersy.
Each subject was interviewed on each of the four problem selected. Interviews
were recorded on tape for later analysis. A spearman Rank other correlation Test
was used to compare the ratings of each subject. The result shows that girls differ
from boys in point at which they developed logical thinking abilities as defined by
Piaget and Inhelder and that boys scored as well as or better than girls on every
experiment at each age level except for the chemical combination results in the 9
years old female group.
Mboto and Bassey (2004) in their study investigated the influence of attitude
on gender with respect to performance in science, technology and mathematics
(STM). The population of the study was senior secondary schools two (SS II)
students of physics, chemistry and mathematics in Cross River State Nigeria. Out
of the total of 300 students from eight secondary schools in the area, only 240
students were used for the study. The random sampling technique was used to
obtain the sample. A face validated attitude 15 items inventory scale were used to
classify the subject with respect to positive and negative attitudes. Similarly,
careful prepared lesson notes were used to teach specific science, technology, and
mathematics topics for four weeks under homogeneous conditions using actual
subject teachers as trained assistants. The result of the study shows that attitude has
a significant influence on science, technology and mathematics on students, with a
76
much more facilitating influence on the female than the male. It is evident that
student with positive attitude toward a subject usually perform better than those
with a negative attitude.
David, Lay and Kay (1987) conducted a study on the effect of knowledge of
item arrangement, gender, and statistical and cognitive item difficulty on test
performance. The purpose of their study was to examine the effect of statistics and
cognitive level of difficulty and the effect of explicit learner knowledge on test
performance when gender of examinee is controlled. The subjects consisted of 155
students, enrolled in an undergraduate education course in Oklahoma State
University. There were 59 male and 96 female participant proportions, which
typified the make up of these classes. A 40 item multiple choice examinations was
developed for use in these study with test content drawn from the course textbook
and the test was designed to be a standardized mid term examination for their
multi-section course. Data were analysed using two 5 X 2 analysis of variance used
to examined the data; the second analysis used multivariate ANOVA. Examination
of the results indicated no significant differences for items order by gender by total,
F (2,235) = 0.27, P < 0.05, items order by gender, F (2,235) =1.49, P<0.05 or items
order by label, F(2,235)=0.08, P<0.05. A significant difference was found.
However, the findings of the study, show that female students performed at a
higher average level on the textbook ( =26.83) than did male ( =23.12) in
examination 1 while in experiment II, males score increased dramatically when
77
label were used. Certainly these results supported the continued inclusion of
gender as variable in future research.
Betiku (2002) in his study on differential performance of students in some
newly introduced topic in senior secondary school mathematics investigated the
performance of school certificate students in set and probability theories. The
subjects were 376 SS3 students (208 boys and 168 girls) distributed across four
randomly selected secondary schools in FCT Abuja. A 20 item multiple choice
questions on senior secondary certificate mathematics (Achievement Test in
Mathematics) was the major instrument used for the study. Data were analyzed
items by items and the t-test was employed to determine whether or not significant
difference could be detected among the variables under test. The findings of their
studies show that boys seem to perform better than girls, and the students in the
urban setting perform better than students in the rural setting, and the new methods
could not be conceptualized by the students in the rural setting.
In a similar development, Omirin (2005) undertook a study on sex and
course of study as predictor of academic performance of master degree students of
the university of Ado-Ekiti. He investigated the influence of admission
requirement such as sex and first-degree background of candidates on their
academic performance at the masters’ degree level. Two null hypotheses of
significance.; (i) there is no significant difference between the academic
performance of male and female masters students, (ii) first – degree background
will not significantly influence the academic performance of master degree
78
students. The study employed the expose – factor design, since the data collected
were already on ground without any manipulation. The data were the scores of the
master degree students who completed their programme between the year 2000 and
2002. The population consists of all the postgraduate students of the University of
Ado –Ekiti, Nigeria who graduated between the year 2000 and 2002. Sample of S1
students (28 in 2000; 12 in 2001; and 11 in 2002). The hypotheses were tested
using student’s t – test and analysis of variance respectively at 0.05 level of
significant. Finally the findings of his study revealed that there was no significant
difference between the performance of male and female students.
From the literature review it is evident that studies on gender as a factor in
mathematics achievement have focused on such variable as motivation, interest,
educational competence. None of these studies have investigated how gender has
interacted with instructions in metacognitive skills, self-efficacy belief, and interest
among low achieving mathematics students. This study will therefore, be carried
out to see the interaction effect of gender and instructions on metacognitive skills
on low-achieving mathematics students.
Summary of Literature Review The review of literature has enabled the researchers to provide useful and
clarifying information to the problem under study. From the review, basic concepts
such as metacognition (metacognition could be defined as the awareness of one’s
own mental abilities or understanding of one’s thought processes), metacognitives
79
skills, self-efficacy, interest, and school achievement as well as their relationships
were defined. In the review, metacognitive skills training assist efficient learners to
know precisely how to approach learning situation through effective skills of
directing and redirecting their cognitive and thinking processes.
In addition, from the review, Piagetian theory of intellectual development
was also mentioned and this includes sensori-motor, pre- operational, concrete
operational and formal / hypothetic –deductive operation. The formal operation
stage is characterized by capacity for abstract reasoning, prepositional logic, and
combining reasoning. Also according to his theory, it is clearly stated that it is
through the action of assimilation, accommodation, adaptation and self-regulation
that any individual intellectual steadily progresses from naïve infancy level to the
ideal adult level.
The information processing theory of cognitive development conceptualize
human intellectual function as a computer metaphor. Like the computer, human
intellectual performed input through input and output function. It stores symbol
and manipulates it to solve different kinds of problems. The information
processing theory, assume a set of three major component namely sensory register,
short time memory, and long time memory. It also has three main characteristic,
thinking, change mechanism (including, automation, strategies construction and
generalization), and self-modification (metacognition). Flavell model’s of
metacognitive development were also reviewed. Metacognition consists of both
metacognitive knowledge (knowledge of performances variable, task variable and
80
strategy variable), and metacognitive experience or regulation (planning,
monitoring, regulation, and evaluation).
Albert Banduras social cognitive theory was also reviewed. Four sources of
Data presented in Table 6 show that treatment as main factor had a
significant effect on the mathematics achievements of the students with low –
achieving in mathematics. The F–value of 159.402 was significant at .000. The
null hypothesis of no significant difference in the treatment group taught using
instruction in metacognitive skills and those in the control group was rejected. This
implied that those exposed to instruction in the treatment groups out performed
those who were not exposed to metacognitive skills instruction. The adjusted R
squared of .561 further suggested that 56% of the total variance on the dependent
99
measure was contributed by treatment using instruction in metacognitive skills.
These evidences showed that instruction in metacognitive skills was effective in
enhancing the mathematics achievement in the classroom.
Table 7: Summary of 2 – Way Analysis of Covariance (ANCOVA) on the Low – Achieving Mathematics Students on their Mathematics Self–Efficacy Scale (MSES)
Source Type III Sum
of Square df Mean
Square F Sig. Decision at
0.05 level Corrected Model
intercept
Pretest
Experimental
Gender
Experimental *Gender
Error
Total
Corrected Total
5699.314a
4030.119
1073.447
4410.000
21.5562
31.155
2843.492
215343.000
8542.806
4
1
1
1
1
1
124
129
128
1424.828
4030.119
1073.447
4410.000
21.5562
31.155
22.931
62.134
175.747
46.811
192.313
940
1.359
. 000
. 000
. 005
. 000
. 334
. 246
S
NS
NS
a. R Squared = .574 (Adjusted R Squared = .656)
The data in Table 7 above indicate the treatment as a main factor had
significant effect on students mathematics self – efficacy. This was because the F –
value of 192.213 in respect of the treatment group as main effect was shown to be
significant at .000 levels. This therefore, showed that 0.05 levels, the result implied
that training in metacognitive skills improved the mathematics efficacy of the low
achieving students significantly. Hence the null hypothesis of no significant
differences in the mathematic group was therefore rejected. The adjusted R
Squared of .66 further suggested that 66% of the total variance on the dependent
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measure was contributed by treatment using instruction in metacognitive skills.
These evidences showed that instruction in metceguitive skills was effective in
enhancing the mathematic efficacy of the students.
Table 8: Summary of 2 – Way Analysis of Covariance (ANCOVA) on the Low–Achieving Mathematics Students on their Mathematics Students on their Mathematics Interest Inventory (MII)
Source Type III Sum
of Square Df Mean
Square F Sig. Decision at
0.05 level Corrected Model
intercept
Pretest
Experimental
Gender
Experimental *Gender
Error
Total
Corrected Total
10278.706a
2282.132
539.045
8682.872
232.946
11.842
7853.387
334660.000
18132.093
4
1
1
1
1
1
124
129
128
2569.677
2282.132
539.045
8682.872
232.946
11.842
63.334
40.574
36.033
8.511
137.099
3.678
. 187
. 000
. 000
. 004
. 000
. 057
. 666
S
NS
NS
a. R Squared = .567 (Adjusted R Squared = .553)
The data presented in table 8 above showed that treatment group as main
factor had a significant effect on the mathematics interest inventory of the low -
achieving mathematics students. The F–value of 232.946 was significant at 0.000
levels and also at 0.005 levels of significance. This suggested that the null
hypothesis of no significant differences in the mathematics interest inventory of
students taught using instruction in metacognitive skills was rejected. In other
words, there was a significant difference in the students’ interest in mathematics of
the two groups in favor of those exposed to instruction in metacognitire skills. The
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Adjusted R squared of 0.553 further suggested that 55% of the total variance on the
dependent measure was contributed by treatment using instruction in
metacognitive skills. This evidence showed that instruction in metacognitive skills
was effective in enhancing the mathematics achievement and interest of the
students in treatment groups as compared to those.
Research Question Two
What is the influence of gender on (a) mathematics Achievement (b) self-
efficacy, (c) and interest of low- mathematics achieving student in senior
secondary school?
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Table 9: The Mean and Standard Deviation of the Students Score in the Pretest Posttest in Treatment Group by Gender
Dependent Variable
Gender of respondents Pre-test Posttest Mean gain score
9
(a)
Ach
ieve
men
t
Male Mean N Std. Deviation
16.5915 71
8.84562
37.9839 71
10.02211
21.40
Female Mean N Std. Deviation
18.8966 58
8.42039
39.3276 58
10.39802
20.42
Total Mean N Std. Deviation
17.6279 129
8.69992
38.5691 129
10.12473
20.87
9 (b
) Se
lf-ef
ficac
y
Male Mean N Std. Deviation
30.2676 71
7.58999
38.5070 71
8.10797
8.24
Female Mean N Std. Deviation
32.5862 58
5.99132
41.9138 58
7.91464
9.32
Total Mean N Std. Deviation
31.3101 128
6.98749
40.0388 129
8.16950
8.72
9
(c) I
nter
est Male Mean
N Std. Deviation
38.0141 71
4.93238
47.0845 71
11.64611
9.07
Female Mean N Std. Deviation
39.2069 58
4.94801
52.5345 58
11.61248
13.32
Total Mean N Std. Deviation
38.5504 129
4.95500
49.61248 129
11.90197
10.98
The data presented on Table 9 (a) above indicate that male students had a
mathematic achievement pretest mean achievement score of 16. 59 with a standard
deviation of 8.85 and a mathematic achievement posttest mean achievement score
of 37.99 with standard deviation of 10.02. The mean gain score of male students
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was 21. 40. The Female students had a mathematic achievement pretest mean score
of 18.90 with standard deviation of 8.42 and a posttest mean achievement score
and the standard deviation of 39.32 and 10.39 respectively. The mean gain score
for the female student was 20. 42. The standard deviations of 8.90 and 8.42 in the
post test achievement scores for male and female students respectively were not
much. However, the male students had more variation in scores from the mean
than their female counterpart.
In addition, the data presented on Table 9 (b) above indicate that male
students had a mathematics efficacy pretest mean score of 30.27 with a standard
deviation of 7.59 and a mathematics efficacy post test mean score of 38.51 with
standard deviation of 8.11. The mean gain score of male student was 8.24. The
female students had a mathematics efficacy pretest mean score of 32.59 with
standard deviation of 5.99 and a post test mean score of 41.91 and the standard
deviation of 7.91. The mean gain score for the female students was 9.32. The
standard deviation of 7.59 and 5.99 in the pretest and 8.11 and 7.91 in the post test
for male and female students respectively was not much. However, males had
more scores spread out from the mean than the females. The result in table 9 (b)
suggested that the female students showed better mathematics efficacy than the
males as indicated by the post test mean score of 41.91 in favor of female and
38.51 for the male. The females still gained more from the instruction in
metacognitive skills and indicated higher mathematics efficacy than their male
counterpart.
104
HO2: there are no significant differences on the influence of gender on
mathematics achievement, mathematics self efficacy, interest in mathematics
of low-achieving senior secondary school students as measured by the mean
scores on MAT, MSES and MII.
Furthermore, the data presented in Table 9 (c) above indicate that the male
students had a mathematics interest pretest mean score of 38.01 with a standard
deviation of 4.93 and a mathematics interest inventory post test mean score of
47.08 with standard deviation of 11.65. The mean gain score of male students was
9.l07 and the female students had a mathematics interest inventory pretest mean
score of 39.21 with standard deviation of 4.95 and a posttest mean score of 52.53
and the standard deviation of 11.61. The main gain score for the female students
was 13.32. The standard deviations of 4.93 and 4.94 in the pretest and 11.65 and
11. 61 in the posttest for male and female students respectively was not much.
However, female students had more spread out scores from the mean than the
males. The result in table 9 (c) suggested that the female students showed higher e
mathematic interest as indicated by the posttest mean score of 52.53 than the
males with mean score of 47.08.
A corresponding hypothesis raised to further address research question
three is HO2:
Result presented in Table 6 revealed that there was no significant difference
in the mean post achievement scores of male and female student in mathematic
achievement test (MAT). This was because the F-value of .879 in respect of gender
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as main effect was shown to be significant at .350. This indicated that at 0.05
levels, the F-value of .350 was not significant. The null hypothesis of no
significant influence of gender on mathematic achievement of the low-achieving
student therefore stands. This showed that the male students did not perform
significantly better than the female student in the mathematic achievement test.
Therefore, Gender was not a significant factor on the mathematics achievement
attained by the low achieving students and the null hypothesis is therefore, not
rejected
The result presented in the Table 7 also revealed that there was no
significant difference in the means post test response score of the male and female
student in mathematic self – efficacy. This was because the F – value of .940 with
respect to gender as main effect was shown to be significant at 334. This indicated
that 0.05 levels, the F-value of .940 was not significant. The null hypothesis of no
significant influence of gender on mathematics efficacy of the low – achieving
student therefore, stands. This showed that the male student did not perform
significantly better than the female students in the mathematics efficacy. Therefore,
gender was not a significant factor on the mathematic self–efficacy attained by the
low achieving student. The null hypothesis is therefore not rejected.
Result presented in Table 8 further reveal that there was no significant
difference in the mean posttest responses score of the male and female students in
mathematics interest inventory (MII). This was because the F – value of 3.678 in
respect of gender as main effect was shown to be significant at 0.057. This
106
indicated that at 0.05 levels, the f- value of 3.678 was not significant. The null
hypothesis of no significant influence of gender on mathematics interest of the
low – achieving students therefore, stands. Therefore, gender was not a significant
factor on the mathematics interest attained by the low achieving students. The null
hypothesis was therefore accepted.
Research Question Three
What will be the interaction of instruction in metacognitive skills and gender
on (a) mathematics achievement (b) mathematics self – efficacy and (c) interesting
mathematics students in senior secondary schools?
Table 10: Mean and Standard Deviation of the Students Score In Posttest in a Mathematic Achievement Test (MAT) (Treatment and Gender) Levels
Experimental Groups Gender of respondents
Mean Std. Deviation N
Treatment Male Females Total
45.35 47.73 46.06
5.07 5.30 5.17
31 33 64
Control Male Females Total
32.28 29.56 31.23
9.16 6.73 8.36
40 25 65
Further more, the results in Table 10 above indicated that male students
exposed to instruction in metacognitive skill had a posttest mean achievement
score of 45.35 with standard deviation of 5.07 as against their male counterpart in
the control group with a posttest mean achievement score of 32.28 with standard
deviation of 9.16. The difference in the posttest mean achievement scores of male
in the two groups was 13.07. Female students exposed to instruction in
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metacognitive skills had a higher post test mean achievement score of 46.73 with a
standard deviation of 5.30 as against the female counterpart in the control group
with a posttest mean achievement scores of 29.56 with a standard deviation of 6.73.
The differences in the posttest mean scores of females in the two groups is 17.17.
The results showed that male and female students in the treatment groups
performed better than males and females in the control groups.
Table 11: Mean and Standard Deviation of the Students Scores in Post Test in Mathematics Self–Efficacy Score (MSES) (Treatment and Gender) Level
Experimental Groups Gender of respondents
Mean Std. Deviation N
Treatment Male Females Total
44.90 47.03 46.00
2.700 2.83 2.95
31 33 64
Control Male Females Total
33.55 35.16 34.17
7.39 2.37 7.38
40 25 65
Result in table 11 indicate that the male students exposed to instruction in
metacognitive skills had a higher posttest mean MSES score of 44.90 and a
standard deviation of 2.700 as against males in control group with a posttest mean
score of 33.55 and a standard deviation of 7.39. The difference in the posttest
means score of male in the 2 group (treatment and control) was 11.35. Female
students exposed to instruction in metacognitive skills had a higher posttest mean
efficacy score of 47.03 and a standard deviation of 2.834 as against females in
control group with a posttest mean efficacy of 35.16 with a standard deviation of
7.39. The difference in the posttest mean efficacy score of the two female groups
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above is 11.87. This indicated that males and females in the treatment groups
performed better than males and females in the control group.
Table 12: Mean and Standard Deviation of the Students Score In Posttest in Mathematics Interest Inventory (MII) (Treatment and Gender) Levels:-
Experimental Groups Gender of respondents
Mean Std. Deviation N
Treatment Male Females Total
56.32 59.8 58.14
9.053 7.75 8.31
31 33 64
Control Male Females Total
39.92 42.88 41.06
7.75 8.89 8.27
40 25 65
Result in table 12 indicated that the male students exposed to instruction in
metacognitive skills had a higher posttest mean interest score of 56.32 with a
standard deviation of 9.053 as against the male counterpart in the control group
with a posttest mean interest score of 39.92 with standard deviation of 7.75. The
difference in the posttest mean interest score of male in the 2 group (Treatment and
control) was 16.40. Female students exposed to instruction in metacognitive skills
had a higher post test mean interest score of 59.85 with standard deviation of 7.28
as against the female counterpart in the control group with a posttest mean interest
score of 42.88 with standard deviation of 8.89. The difference in the posttest mean
interest score of female in the 2 groups (treatment and control) is 16.97. This also
indicated that males and females in the treatment groups performed better than
males and females in the control group.
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HO3: There is no significant interaction effect of instruction in metacognitive
skills and gender on (a) mathematics achievement, (b) mathematics self –
efficacy, and (c) interest on mathematics as measured by their mean score on
MAT, MSES and MII.
The interaction effect of gender and the metacognitive skills on the
mathematics achievement of low – achieving students as measured by their mean
score in mathematics achievement test was not significant at 0.05 levels. As shown
in Table 6, the observed f–value of 2.891 was significant at .092 but not significant
at 0.05 levels of significance. The null hypothesis of no significant interaction
between gender and instruction in metacognitive skills on mathematics
achievement test of the low – achieving students was therefore, accepted as the
difference was not significant.
The Interaction effect of gender and the metacognitive skills on mathematics
self–efficacy of low achieving students as measured by their mean score on MSES
was not significant at 0.05 levels. As shown in Table 7 the calculated f–value of
1.359 which is significant at .246 levels was not significant at .05 levels of
probability. The null hypothesis of no significant interaction between gender and
instruction in metacognitive skills on mathematics self – efficacy score of the
low – achieving students was therefore accepted.
The interaction effect of Gender and metacognitive skills on mathematics
interest of low – achieving students as measured by their mean score on MII was
not significant at 0.05 levels. As shown in Table 8, the observed f – value of .187
110
which was significant at .666 was not significant at .05 levels of probability. The
null hypothesis of no significant interaction between gender and instruction in
metacognitive skills on mathematics interest of the low achieving students was
therefore, accepted. This implies that both gender benefited from the metacognitive
instruction as the instruction is not biased by gender.
Summary of Results
Results presented in this chapter reveal the following:-
I. Instructing students in metacognitive skills has a facilitative effect on self-
efficacy belief, interest and achievement of low-achieving mathematics
students. Those exposed to instruction in metacognitive skills benefited
significantly higher than those not exposed as they showed better mathematics
self-efficacy, interest and achievement.
II. Gender has no significant influence on the mathematics achievement,
mathematics self-efficacy and interest of low-achieving mathematics students.
III. There is no significant interaction effect of gender and instruction in
metacognitive skills on mathematics self–efficacy belief, interest and
achievement of low – achieving mathematics students.
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CHAPTER FIVE
DISCUSSION OF RESULTS, CONCLUSIONS, RECOMMEDATIONS AND SUMMARY
This chapter focuses on the discussion of major findings of the study, their
educational implications and recommendations. Included in this chapter also are
the conclusions, suggestions for further study and summary of the study.
Discussion of Results
The findings of this study were discussed in line with the research questions
and hypotheses raised in the study.
a. Effect of instruction in metacognitive skills on Achievement in mathematics
of low-achieving mathematics students.
b. Effect of instruction in metacognitive skills on mathematics self-efficacy of
low-achieving mathematics students.
c. Effect of instruction in metacognitive skills on interest in mathematics of low-
achieving mathematics students.
d. Influence of gender on mathematics achievement of low-achieving
mathematics students.
e. Influence of gender on mathematics self-efficacy of low-achieving
mathematics students.
f. Influence of gender on interest in mathematics of low-achieving mathematics
students.
112
g. Interaction effect of instruction in metacognitive skills and gender on
mathematics achievements of low-achieving mathematics students.
h. Interaction effect of instruction in metacognitive skills and gender on
mathematics self-efficacy of low-achieving mathematics and,
i. Interaction effect of instruction in metacognitive skills and gender on interest
in mathematics of low-achieving mathematics students.
Effect of Instruction in Metacognitive Skills on Achievement in Mathematics of Low-achieving Mathematics Students The results of this study show that instruction in metacognitive skills
enhanced the mathematics achievement of the low-achieving mathematics
students. From the result, the group that used metacognitive skills of planning,
monitoring, regulation/ reflection and evaluation performed significantly better in
the selected mathematics concepts than the control group. The finding of this
study was in line with the findings of Mavareach and Amrany (2007), Goldberg
and Bush (2003), Panoura and Phillip (2006), and Mavaeach and Kramaski (2003)
who found that students who were exposed to metacognitive training out
performed those who were not. The findings of this study suggest that good
learners engage in the process of assessing the quality of their work based on
evidence and set criteria. They get involved in active self-appraisal and
management of their thought. These are attributes of metacognitive skills.
As students monitor their own learning they learn to check their own
responses and become aware of errors or answers that do not fit. Instruction in
113
metacognitive skills could have permitted the low-achieving students to gain
control of their learning activities and were therefore able to learn, the processes
in mathematics problem solving.
Effect of Instruction in Metacognitive Skills on Mathematics Self-Efficacy of Low-Achieving Mathematics Students The results of this study show that instruction in metacognitive skills
facilitates mathematics self-efficacy beliefs of the low-achieving mathematics
students. The study further shows that students in the treatment group who
received instruction in planning, monitoring, regulation/ reflection and evaluation
had a significantly higher mathematics self-efficacy than those in the control
group. The findings of this study may be explained in line with the study of
Maria and George (2006), Halon and Schneider (1999), Nalson and More (2003)
who found that students exposed to training in metacognitive skills manifest
higher sense of efficiency and appeared to be more competent in the subject
taught than those in the conventional classroom.
The instruction in metacognitive skills which helped the students ensure
ownership of their learning processes could have been the reason for the higher
self-efficacy demonstrated by those in the treatment condition.
Effects of Instruction in Metacognitive Skills on Interest of Low-Achieving Mathematics Students The results of this study show that instruction in metacognitive skill
enhanced the interest in mathematics of the low-achieving mathematics students.
Those in the treatment group who received instruction in planning, monitoring,
114
regulation/reflection and evaluation had a significantly higher in interest in
mathematics than those in the control group.
The finding of this study is in line with the findings of George (2006),
Miner and Lauri (2008) who found that students developed more competence in
subject that they are interested. Thus the interest students showed in an
activity/area of knowledge predicts how much they would attend to it; and how
well they process, comprehend and remember it (Deci, 1992 and Stipek, 1996).
Instruction in metacognitive skills could have been the reason for the higher
interest in mathematics as demonstrated by those in treatment condition.
The Influence of Gender on Mathematics Achievement of Low-achieving Mathematics Students The result of this study showed that male and female students in the
treatment groups performed better than their counterparts in the control group. The
findings were in agreement with the studies conducted by David, Lay and Kay
(1987) which shows that there was no significant difference in Mathematics
achievement between male and female students taught using learning skills.
These findings however, contradicted some earlier findings which projected
the view that gender was a significant factor in mathematics achievement. (Finley,
1982; Idowu, 2002; Graybills 1990 and Mboto and Bassey, 2004). Their results
favoured males scoring higher in mathematics achievement test than their female
counterpart. The finding of this study could be interpreted in line with the finding
of Omirin (2005) who stated that gender had no direct effect on mathematics
115
achievement. The point however, was that being a boy or a girls as shown by
Omirin, did not have direct effect on mathematics achievement. Instead there were
other factors which were central to the mathematics achievement. The major factor
which could have enhanced the interest of the students could have been instruction
in metacognitive skills which ensured students active participation in the learning
process. Students’ interests are usually aroused when they are actively involved in
the process of learning.
The Influence of Gender on Mathematics self-Efficacy belief of Low-achieving Mathematics Students Similarly, the finding of this study showed that the male students did not
perform significantly better than the female students in the mathematics efficacy.
Gender, was therefore, not a significant factor on the self-efficacy belief of low-
achieving mathematics students.
The finding were in agreement with earlier finding of Maria and George
(2006), Nelson (1996) which showed that there was no significant differences
between boys and girls in mathematics efficacy and maintained that students who
participated in Self-Efficacy intervention group out performed students who were
involved in the regular remedial classes. The involvement of both boys and girls in
the metacognitive instruction could have enhanced both gender interest in
mathematics and subsequently increased their achievement in mathematics.
116
The Influence of Gender on Interest in Mathematics of Low-achieving Students This study also showed that the male student did not show significantly
better interest in mathematics than the female students. Therefore gender was not a
significant factor on the mathematics interest attained by the low-achieving
mathematics students. This finding is also supported by the study by George (2006)
which noted that sex differences diminished when more favourable task condition
that promote positive interest toward mathematics tasks accomplishment are
presented. The findings of this study show that the socio cultural factors which
create gender differences in task accomplishment are removed when equal
opportunities are created for both boys and girls. The equal involvement of boys
and girls in the metacognitive skills instruction could have resulted in the non
significant difference in their mathematics interest.
Interaction Effects of Instruction in Metacognitive Skills and Gender on Mathematics Achievement of Low-Achieving Mathematics Students The result showed that male and females in the treatment group performed
better than males and females students in the control groups.
Moreover, the interaction effect of gender and instruction in metacognitive
skills on mathematics achievement of low-achieving students as measured by their
mean score in mathematics was not significant. The null hypotheses of no
significant interaction in metacognitive skills on mathematics achievement of the
low-achieving students was therefore, rejected. This finding was in line with the
finding of Mavareach and Kramaski (2006) which showed that the interaction
117
effect instruction in learning strategy and gender on mathematics achievement was
insignificant. This indicated that the relative effect of instruction in metacognitive
skills and achievement was also consistent across the two levels of gender,
suggesting that both the male and female students benefited significantly from the
metacognitive skills taught. This further suggests that the gender differences in
task performance could be attributed to socio-cultural factors which create
stereotypes and gender roles for works. Thus, when the same opportunities for task
performance usually mathematics task performance is presented both males and
females benefit irrespective of their sex.
Interaction Effect of Instruction in Metacognitive Skills and Gender on Mathematics self-Efficacy of Low-Achieving Students Furthermore, this study further indicated that males and females in the
treatment group showed better mathematics self-efficacy than the males and
females in the control group. The interaction effect of gender in metacognitive
skills and mathematics self-efficacy of low-achieving mathematics students as
measured by their mean score on mathematics interest was not significant.
The findings also supported the result of similar study by Eze (2003). In the
study, Eze found no significant interaction effect between instructions in
elaborative interrogative strategy and gender. In this study, the findings indicate
that both gender benefited almost equally from the metacognitive skills instruction.
This implies that the contribution of gender on the effect of treatment on the
dependent measures was not significant.
118
Interaction Effect of Instruction in Metacognitive Skills and Gender on Interest in Mathematics of Low-Achieving Students Also this study indicated that male and females in the treatment groups
performed better than male and female in the control group. However the
interaction effect of gender and the metacognitive skills on interest in mathematics
of low-achieving students as measured by their mean score on mathematics interest
was not significant. The null hypothesis of no significant interaction between
gender and instruction in metacognitive skills on interest in mathematics of the
low-achieving students was therefore accepted. This indicated that the relative
effect of instruction in metacognitive skills and interest was consistent across the
two level of gender suggesting that both male and female low-achieving
mathematics students benefited significantly from the skills taught.
Conclusion
From the findings and discussion of the study, the following conclusions are
made:-
1. Instruction in metacognitive skills helps to facilitate mathematics self-
efficacy belief, interest and achievement of low-achieving mathematics
students. There was a significant difference in mathematics achievement;
mathematics efficacy and interest in mathematics mean scores of the
treatment and control group.
119
2. Gender had no significant influence in the mathematics achievement, self
efficacy and interest of low- achieving mathematics students.
3. The interaction effect of instruction in metacognitive skills and gender on
mathematics efficacy, interest and achievement of low-achieving
mathematics students was not significant.
Education Implication
From the findings, one can deduce some important educational implication
for teachers, curriculum developers, students, authors and institutions. The study
provides an empirical evidence of the effectiveness of instruction in metacognitive
skills on self- efficacy interest and achievement of low- achieving mathematics
students. Since the type of learning skills which the student employs effects his
achievement in mathematics, it is not just enough to provide students with low-
achievers with instruction in learning skills, such students must be exposed to
learning skills such as planning, monitoring, regulating and evaluation that
promote higher order thinking processes and problem-solving approach in
mathematics. The result of the study shows that students can use instruction in
meta-cognitive skills to great advantage. For this reason, educational curriculum
planners may need to modify secondary school curriculum to include learning
through the application of meta-cognitive skills to promote self-efficacy, interest
and achievement in mathematics. These modifications imply that teacher training
120
courses may be revisited. Teachers need to have adequate knowledge of the skills
in order to teach the students who will be committed to their care.
The serving teachers many need to be sensitized on the effectiveness of
instruction in metacognitive skills, and these teachers may need to undergo
workshops and seminars in order to update their knowledge of those skills as the
most successful way to teach mathematics using models of instruction in meta-
cognitive skills. They should also be provided with orientation and awareness of
instruction in which the skills can be used.
Textbook writers should also provide new books for both teachers and
students that will include the learning instruction in meta-cognitive skills which
students can employ. It is assumed that those new skills, because of their efficiency
at the secondary school level, could be introduced at the primary school level. For
this purpose, textbook writers should provide texts that will incorporate those skills
to cater for both primary and secondary school levels of education.
Instruction in meta-cognitive skills would promote independent and self
regulated learning activities. In today’s world which thrives on information, the
low-achieving students who are well trained in the use of instruction in meta-
cognitive skills are better positioned to manage information themselves. The
results show that both the male and female student benefited from the strategy.
Those learning strategies should, therefore be taught in all schools where students
with low-achieving are common. Teachers should regularly model these skills,
121
monitor students’ use of these skills and encourage students to use them in their
learning episode/situation.
The result has also shown that instruction in meta-cognitive skills on self
efficacy beliefs, interest and achievement would make students become aware of
what and how to learn. These results also show that these skills could be taught.
The teachers’ role is, therefore, to make low-achieving students develop this type
of awareness so that they can learn to control their taught processes.
Recommendations
On the basis of the findings of this study, the following recommendations
have been made:
(a) Teachers should ensure that low-achieving mathematics students are
exposed to instruction in metacognitive skills to equip them with learning
skills relevant for solving mathematical problems.
(b) Researches on meta-cognitive learning skills should be sponsored by
government and non- governmental organizations to provide opportunities
for learners to know more about metacognitive learning approaches that will
help achieve their learning goals.
(c) Professional bodies likes STAN, MAN and others should seek ways of
integrating the funding of similar studies for science education and other
related arts subjects.
122
(d) Seminars, conferences and workshops should be organized on the theme:
meta-cogitation. Such seminars and workshops would provide opportunities
to examine critically the concept, procedure, and application of meta-
cognitive approaches in learning.
(e) Schools should learn to make learning students –centred and not teacher
centered. They should ensure that students are actively involved in the
learning activity by ensuring their active participation and their lessons
should be organized in such away that students can bring their own related
experiences to bear on the lesson and ask questions, make predictions and
examine their own answers in order to be actively involved in the learning
processes.
Limitation of the Study
- It is important to state that although the sample used was small, it is not less
true that this is a frequent situation in many low- achieving research studies.
The small size could have affected the result slightly.
- The use of regular mathematics teachers in the sample schools to teach the
content areas required for the study would have introduced teacher bias. This
situation may have introduced some extraneous factors in training conditions
across the four schools and also between the treatment and control
conditions.
123
- The conclusion and generalization of the study could be limited by the
adoption of a quasi-experimental design. Attempts were made to control
extraneous variables that could affect the result of the study however a true
experimental design would have ensured a more generalisable result, but it
was not possible in the study.
Suggestion for Future Research
In the light of the finding of the present study, the following are
recommended for future research.
I. The present study used SSII student in senior secondary schools where students
with low- achieving are trained. Future studies can improve on this by using
larger student population and by including other low- achieving students in
college, polytechnic or even primary school pupils so as to allow for
generalization to include students of different ages.
II. The study only investigated the effects of an immediate post test, without
looking at the effect in a transfer situation. Future research could be conducted
to describe any transfer effect on students’ use of in metacognitive skills in a
transfer situation.
III. For further researcher, it is recommended that:
a) Other mediation factors such as location of schools, home background,
and age of students (other than ability and gender) which could account
124
for the differential effects of instruction in meta-cognitive skills on self
efficacy belief, interest and achievement be studied
b) Replication of the present study in Nigeria using other science and art
related courses such as Physic, Chemistry History and Economics,
IV. Further research could be conducted on the effect of instruction in
metacognitive skills on the specific areas apart from mathematics using
different types of subject and a variety of learning context.
Summary of the Study
There are students who learn fast and easily and there are also children who
have difficulties in learning. Students who have difficulties in learning can be
found in every subject particularly in mathematics, which may be due partly to
mathematics phobia (fear of the subject, fear of certification, examination/ test)
poor teaching methods, incompetence on the part of teachers or students
themselves. This may lead to low- achievement in mathematics. Consequently, this
study sought to explore the effect of instruction in metacognitive skills on self-
efficacy belief, interest and achievement of low- achieving mathematics students in
senior secondary schools in the area.
To guide this study, the following research questions were posed.
I. What are the differences in the mean score on (a) mathematics achievement test
(MAT), (b) mathematics self- efficacy scale (MSES) and (c) mathematics
125
interest inventory (MII) of students exposed to instruction in metacognitive
skills differ from those who were not exposed?
II. What is the influence of gender on (a) mathematics achievement (b)
mathematics self-efficacy belief and (c) interest of in mathematics low-
achieving senior secondary school students?
III. What is the interaction of instruction in metacognitive skills and gender on (a)
mathematics achievement (b) mathematics self-efficacy belief and (c) interest
of in mathematics low- achieving students in senior secondary schools?
To answer these research questions, the following hypothesis were postulated
and tested at 0.05 levels of significance.
I. Instruction in metacognitive skills have no significant effect on students (a)
mathematics achievement (b) mathematics self-efficacy belief and (c) interest
of in mathematics measured by their mean score on MAT, MSES and MII.
II. There is no significance deference on the influence of gender on (a)
mathematics achievement (b) mathematics self-efficacy belief and (c) interest
of in mathematics of senior secondary school students as measured by their
mean score on MAT, MSES and MII.
III. There is no significant interaction effect of instruction in metacognitive skills
and gender on (a) mathematics achievement (b) mathematics self-efficacy
belief and (c) interest of in mathematics of senior secondary school as
measured by their mean scores on MAT, MSES and MII.
126
The empirical studies reviewed were mainly carried out in foreign countries
and most of the studies were done among primary grade pupils. The findings of the
studies indicate that instruction in use of metacognitive skills have positive effect
on Mathematics self-efficacy beliefs; interest and achievement. The major problem
as is evident from the literature is that this study is yet to be carried out in Nigeria.
Therefore, there is the need for the study in our environment. It is the bid to fill the
missing link that motivated this study.
The research design used in the study was a quasi-experimental non-
randomized pretest and post test control group design involving two treatment
groups and two control groups. A total of 129 SS II students in the four senior
secondary schools where there is high record of low-achieving students in Kogi
State were used for the study. The schools were randomly assigned to treatment
and control schools.
The instruments used for the study was a researcher constructed mathematic
Achievement test (MAT), mathematics self-efficacy scale (MSES) and
mathematics interest inventory (MII) which were developed and validated by
experts. An internal consistency reliability coefficient was determined for the
Mathematics Achievement Test using Cronbach alpha statistics and an estimated
value of 0.92 was obtained. The internal consistency reliability coefficient for the
Mathematics Self-Efficacy Scale, and Mathematics Interest Inventory were
determined using Cronbach Alpha and an estimated value of 0.88 and 0.92 were
obtained respectively.
127
Measures were taken to control extraneous variables. A pretest of the
Mathematics Achievement test as well as Mathematics Self-Efficacy Scale and
Mathematics Interest Inventory were administered before the treatment began and
the programme lasted for 6 weeks after which the MAT, MSES and MII were re-
administered. The data collected were analyzed using mean and standard deviation.
Analysis of Covariance (ANCOVA) was used to test the hypotheses at 0.05 levels
of significance
Results of the study showed that
I. Instructing students in metacognitive skills has a facilitative effect on self-
efficacy belief, interest and achievement of low-achieving mathematics
students. Those exposed to instruction in metacognitive skills benefited
significantly higher than those not exposed as they showed better
mathematics self-efficacy, interest and achievement.
II. Gender has no significant influence on the mathematics achievement,
mathematics self-efficacy and interest of low-achieving mathematics
students.
III. There is no significant interaction effect of gender and instruction in
metacognitive skills on mathematics self–efficacy belief, interest and
achievement of low – achieving mathematics students.
The findings of the study were extensively discussed; their educational
implications and recommendations were highlighted. Suggestions for further
research and limitations of the study were also given.
128
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138
APPENDIX A
MATHEMATICS ACHIEVEMENT TEST (MAT)
Instruction
Answer all Questions
In Each question, all necessary details of working including rough work
must be shown with the answer.
Give answers as according to data and tables allowed.
Use of graph paper and non-programmable and cordless calculator is
allowed
1. A die is rolled once. What is the probability of obtaining a prime number or a
number greater than 5?
2. If a number is selected at a random from a set B, (2,3,5 and 9), what is the
probability that the number is prime?
3 A box contains 5 red, 3green and 4blue balls. A boy is allowed to take away
two balls from the box. Use this information to answer Questions 3 and 4.
What is the probability that the two balls are red?
4. What is the probability that one is green and the other is blue?
5. Evaluate log28
log2(1/4). 6. Evaluate log105 +log1020?
7. Evaluate log10√35 +log10√2- log10√7
8. Simplify the following; (a) log38 (b) log16
0.25
139
9. Amos, is 5 years older than his sister Ekene. If the product of their age is
66years, find their ages?
10. A man is four times as old as his son. The difference between their ages is
36years. Find the sum of their ages.
11. When 189 is subtracted from five times a certain number, the result is equal to
one half of the original number. Find the number.
12. The sum of two numbers is 8, their product is 15. Find the numbers?
13. The table below shows the marks obtained by 40 pupils in a mathematics test.
Marks
No. of pupils
0-9 10-19 20-29 30-39 40-49 50-59
4 5 6 12 8 5
Draw a histogram for the mark distribution.
14. Find the median of the following numbers: 2.64, 2.50, 2.72, 2.91and 2.35?
15. Calculate the standard deviation of the numbers 2,5,6,4 and 8?
16. What is the mode of the numbers 8,10,9,9,10,8,11,8,10,9,8 and 14
17. Table below shows the numbers of students in each age group in a class;
Age years Frequency
16 17 18 19 9 11 11 5
A student is chosen at random from the class; what is the probability that the age of
the student is (i) 16 years (ii) under18 years (iii) not 19 years?
18. Simplify, without using mathematical tables.
log10(30/16) – 2log10
(5/9) + log10(400/243) ?
140
19. Demola is two years older than Deji and Tobi is half of Demola’s age.
The sum of their ages is 23. How old is Deji.
20. The marks obtained by 40 students in an examination are as follows;-
85 77 67 74 77 78 79 89 85 90
78 73 86 83 91 74 84 81 83 75
77 70 81 69 75 63 76 87 61 78
69 96 65 80 84 80 77 74 88 72
(a) Copy and complete the table for the distribution using the above data.
Class boundaries Tally Frequency
59.5-64.5
64.5-69.5
69.5-74.5
74.5-79.5
79.5-84.5
84.5-89.5
89.5-94.5
94.5-99.5
(b) Draw a histogram to represent the distribution.
(c) Using your histogram, estimate the modal mark?
141
APPENDIX B
MATHEMATICS SELF-EFFICACY SCALE (MSES)
Mark (√) for Very High Extent (VHE), Higher Extent (HE), Moderate
Extent (ME), and Low Extent (LE)
S/N Sample Statement Responses
VHE HE ME LE
1. I am one of the best students in mathematics.
2. I believe that I have a lot of weakness in mathematics.
3. Compared to others students I am a weak student in mathematics.
4. Mathematics is not one of my strength.
5. I usually could help my classmates, when they ask me for help in problem solving.
6. I could usually solve any mathematical problem.
7. I do not feel sure about my self in mathematics problem solving.
8. When I start solving a mathematical problem, I usually feel that I would not manage to get a solution.
9. I can easily solve two – step problems.
10. I have difficulties in solving one step – problems.
11. I have confidence in my ability to do school work in mathematics.
12. I have all the skills needed to do very well at school mathematics
13. I have the ability to successfully perform well in school examination in mathematics
14. I have no confidence in performing well in school Mathematics examination.
142
APPENDIX C
MATHEMATICS INTEREST INVENTORY (MII)
Mark (√) for Very High Extent (VHE), Higher Extent (HE), Moderate Extent (ME),
and Low Extent (LE)
The following motivate my interest towards Mathematics
S/N
Sample Statement
Responses VHE HE ME LE
1 1 Like Mathematics
2 1 want to be a mathematician
3 Most of my classmates are members of mathematics clubs. 4 1 desire to study in mathematics to become an engineer;
scientist, Teacher and accountant.
5 Mathematics is boring 6 1 would not study mathematics if it were optional.
7 Mathematics thrills me! Its my favourite subject. 8 1 get anxious when doing mathematics
9 I do not like school mathematics
10 I detest mathematics and avoid it all the times
11 I enjoy the struggle to solve a mathematics problem
12 I like problem-solving
13 I am not motivated to work vend hard on mathematics independently
14 Mathematics is one of my most dreaded subject
15 Mathematics make me feel incompetence
16 I am unease and get phobic when solving task involving mathematics.
17 I am interested in acquiring further knowledge of mathematics
18 Whenever the mathematics teacher enters the classroom, I develop fear and ran away until the period is over.
143
APPENDIX D
SOLUTION TO MATHEMATICS ACHIEVEMENT TEST (MAT) Solutions to Mathematics
Achievement Test (MAT) Allocation of marks
Solutions calculation 1 Let A be set of prime numbers
A={2,3,5} And B set of number greater than 5 B={6}. A and B are mutually exclusive :·Probability Of A = 3/6 Prob. Of B = 1/6 :· The Prob. Of Obtaining A Or B = 3/6 + 1/6 = 3+1 = 4/6 6 = 2/3 Ans.
2 Prob.= No Of Reg. Outcome No Of Possible Outcome :· A = {2,4,6,8} B= {2,3,5,9} Prob. Prime No M Set B Are 2,3,5 No of prime number is 3 .. Therefore, prob. of prime number = ¾
Log2 8 = log 23
Log2 (1/4) log2 4 -1
= 3log22 log22 -2
= 3log22 2log22 -2
=3/-2
3 log10 5 + log1020
= log10 (5x20) = log10100 = log10102
= 2log1010
=2x1 =2 Ans
___
144
4 Son’s age = x Man’s age = 4x 4x – x = 36 3x = 36 x = 36/3 x=12 sum of their ages = 4x + x = 5 Therefore 5(12) = 60yrs
5 Let the number to be x 5 time the number = 5x 5x – 189 = 1½ of x 5x – 198 = 3x/2 5x – 189 = 3/2 xX 5x – 189 = 3x/2
6 Multiply both sides by 2 2(5x – 189) = 3x 10x – 378 = 3x Collect like terms 10x-3x = 378 7x = 378 X = 378/7 X = 54
