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ONYISHI, EUGENIA UCHENNA PG/ M.ED/02/33085 EFFECT OF MIND MAPS ON STUDENTS’ INTEREST AND ACHIEVEMENT IN MEASURES OF CENTRAL TENDENCY IN MATHEMATICS Education A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTERS’ DEGREE IN MATHEMATICS EDUCATION TO THE DEPARTMENT OF SCIENCE EDUCATION Webmaster 2009 UNIVERSITY OF NIGERIA
Transcript of Education - University of Nigeria, Nsukka EUGENIA UCHE… · labour, and appreciate those values...
ONYISHI, EUGENIA UCHENNA
PG/ M.ED/02/33085
EFFECT OF MIND MAPS ON STUDENTS’ INTEREST AND ACHIEVEMENT IN
MEASURES OF CENTRAL TENDENCY IN MATHEMATICS
Education
A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE AWARD OF MASTERS’ DEGREE IN MATHEMATICS
EDUCATION TO THE DEPARTMENT OF SCIENCE EDUCATION
Webmaster
2009
UNIVERSITY OF NIGERIA
ii
EFFECT OF MIND MAPS ON STUDENTS’ INTEREST AND
ACHIEVEMENT IN MEASURES OF CENTRAL
TENDENCY IN MATHEMATICS
BY
ONYISHI, EUGENIA UCHENNA
PG/ M.ED/02/33085
DEPARTMENT OF SCIENCE EDUCATION
(MATHEMATICS EDUCATION)
UNIVERSITY OF NIGERIA, NSUKKA
APRIL, 2009.
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TITLE PAGE
EFFECT OF MIND MAPS ON STUDENTS’ INTEREST AND
ACHIEVEMENT IN MEASURES OF CENTRAL TENDENCY
IN MATHEMATICS
BY
ONYISHI, EUGENIA UCHENNA
PG/ M.ED/02/33085
A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE AWARD OF MASTERS’ DEGREE IN
MATHEMATICS EDUCATION TO THE DEPARTMENT OF
SCIENCE EDUCATION
UNIVERSITY OF NIGERIA, NSUKKA
APRIL, 2009.
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APPROVAL PAGE
This thesis has been approved for the Department of Science Education,
University of Nigeria, Nsukka
By
--------------------------------- ----------------------------------
Prof. (Mrs) U.N.V. Agwagah Dr. E.K.N Nwagu
Supervisor Head of Department
--------------------------------- -----------------------------------
External Examiner Internal Examiner
-----------------------------------------
Prof. G.C. Offorma
Dean of Faculty
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CERTIFICATION
Onyishi, Eugenia Uchenna, a post graduate students in the Department
of Science Education and with Registration number PG/M.ED/02/33085 has
satisfactorily completed the requirements for the course and research work for
the degree of master in Mathematics Education. 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.
-------------------------------------- -----------------------------------
Onyishi, Eugenia Uchenna Prof. (Mrs.)U.N.V. Agwagah
Student Supervisor
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DEDICATION
This work is dedicated to Almighty God who strengthened and sustained
me throughout the period of this work.
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ACKNOWLEDGEMENT
The researcher expresses her profound gratitude to the Almighty God for
his guidance, protection, sustenance and successfully bringing this work to an
end. The researcher lacks words to thank her supervisor Prof. (Mrs.) U.N.V.
Agwagah for her dedication, patience, motherly advice and inspiration that
made this work what it is. May God bless and reward you abundantly. In the
same vane, the researcher is also indebted to her husband Mr. B.S. Onyishi and
her children for their moral, financial supports and encouragement. Remain
blessed.
The researcher thanks Prof. A.A. Ali, Dr. K. O. Usman, Dr. F. A Okwor,
for their corrections and guidance which helped to sharpen this work during the
proposal stage. Worthy of note is Dr. J. J. Ugwuja, Prof. D. N. Ezeh for their
contributions, corrections and advice that led to the completion of this work.
The researcher cannot thank enough the principals, teachers and students whose
schools were used for the study. Their wonderful co-operation and assistance
during the field work is highly appreciated. She thanks her colleagues Mr. I.
Onyeabor, Mrs M. N. Nwoye, Mrs E.N. Onah, Mrs. M. N. Ukwungwu whose
useful advice and encouragement especially at difficult moments, led her on, to
the completion of this work. Finally to Miss B. Eze who produced this work, her
dedication and patience is highly appreciated. May God bless all of you
abundantly.
Onyishi, E.U.
Nsukka, 2009.
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TABLE OF CONTENTS
TITLE PAGE…………………………………………………………………........……….I
APPROVAL PAGE……………………………………………………………………….II
CERTIFICATION …………………………………………………………………............III
DEDICATION ……………………………………………………………………...........IV
ACKNOWLEDGEMENT…...……………………………………………………............V
TABLE OF CONTENTS …………………………...…………………………………...VI
LIST OF TABLES …………………………………………………………….................VIII
ABSTRACT ……………………………………………………………………………...IX
CHAPTER ONE: INTRODUCTION………………………..………………………….…..1
Background of the Study…………………………………………………………………1
Statement of the Problem………………………..…………………………………….10
Purpose of the Study ................................................................................................................ 23
Significance of the Study ......................................................................................................... 23
Scope of the Study ................................................................................................................... 25
Research Questions .................................................................................................................. 25
Research Hypotheses ............................................................................................................... 26
CHAPTER TWO: REVIEW OF LITERATURE………………………………………........27
Conceptual Framework ............................................................................................................ 28
Meaning and Uses of Mind Maps ............................................................................................ 28
Other Mathematical Maps, Distinctions and Similarities ........................................................ 32
Distinctions between Concept and Mind Maps ....................................................................... 34
Similarities between Concept and Mind Maps ........................................................................ 35
Teacher Factor and Students’ Achievement in Mathematics .................................................. 35
Interest in Mathematics and Other School Subjects ................................................................ 40
Theoretical Framework ............................................................................................................ 42
Theories underlying the use of Mind Maps in Teaching Mathematics ................................... 42
Empirical Studies ..................................................................................................................... 47
Studies on Interest and Academic Achievement ..................................................................... 49
Studies on Mind Map ............................................................................................................... 50
CHAPTER THREE:RESEARCH METHOD………………………………………………..53
Research Design....................................................................................................................... 53
Area of the Study ..................................................................................................................... 54
Population of the Study ............................................................................................................ 54
Sample and Sampling Technique............................................................................................. 54
Instruments for Data Collection ............................................................................................... 56
Validation of the Instruments................................................................................................... 58
Reliability of the Instruments................................................................................................... 59
Experimental Procedure ........................................................................................................... 60
Control of Extraneous Variables .............................................................................................. 60
Teacher Variables .................................................................................................................... 60
Training of Teachers ................................................................................................................ 61
Method of Data Analysis ......................................................................................................... 61
CHAPTER FOUR: RESULTS……………………………………………………………….62
Summary of Findings ............................................................................................................... 69
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CHAPTER FIVE: DISCUSSION, CONCLUSION, RECOMMENDATIONS AND SUMMAR 71
Conclusions from the Study ..................................................................................................... 75
Educational Implications of the Findings ................................................................................ 76
Recommendations .................................................................................................................... 77
Limitations of the Study........................................................................................................... 78
Suggestions for Further Research ............................................................................................ 78
Summary of the Study ............................................................................................................. 79
REFERENCES…………………………………………………………………………………….82
APPENDIXES……………………………………………………………………………………..89
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LIST OF TABLES
Tables Pages
1. The Junior Secondary Certificate Examination (JSCE)
results in mathematics from the year 2000-2005 ……………………….5
2. Design Format…………………………………………………………..42
3. The Sample of Junior Secondary One Students used for the Study…....44
4. Table of Specifications on Measures of Central Tendency for…………46
5. The Mean and Standard Deviation scores in Measures of Central
Tendency Achievement Test (MCTAT) of Subjects in the
Experimental and Control Groups……………………………………....51
6. Analysis of Covariance (ANCOVA) of Students Scores in
Measures of Central Tendency Achievement Test (MCTAT)................52
7. The Mean Achievement Scores and Standard Deviation of Male
and Female Subjects…………………………………………………….53
8. The Mean Interest Scores and Standard Deviation of Measures
of Central Tendency Interest Scale (MCTIS) Scores of Subjects……...55
9. Analysis of Covariance (ANCOVA) of Students’ Score in Measures
of Central Tendency Interest Scale (MCTIS)………………………....56
10. The Mean Interest Scores and Standard Deviation of Male and
Female subjects Taught with Mind Map Strategy…………………….. 57
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ABSTRACT
The purpose of this work was to investigate the effect of Mind Maps on
students’ interest and achievement in measures of central tendency. To
ascertain the effect of teaching method and gender on the learners’ interest
and achievement, four research questions and six null hypotheses guided
the study. The design used for the study was the quasi-experimental
design, specifically, the non equivalent pre-test, post-test control group
design. Three hundred and fifty Junior Secondary one students were
selected from four purposively sampled schools in Nsukka education zone.
Two intact classes were randomly drawn from each of the four schools.
Two instruments namely, the Measures of Central Tendency Achievement
Test (MCTAT) and the Measures of Central Tendency Interest Scale
(MCTIS) were developed and used for the study. Mean, standard deviation
and analysis of covariance ANCOVA were used to answer the research
questions and test the hypotheses. The study revealed that the use of Mind
Maps teaching strategy enhanced the achievements and interest of male
and female students. The study also indicated that though female students
were more interested, the male students performed higher in measures of
central tendency achievement test. However, the results also indicated that
the Mind Maps teaching strategy could be used effectively in teaching
both male and female students. It was recommended that mathematics
teachers should adopt Mind Map in teaching measures of central tendency
and other topics in mathematics.
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CHAPTER ONE
INTRODUCTION
Background of the Study
The broad aim of secondary education within the overall national
objectives is: Preparation for useful living within the society and preparation for
higher education. Specifically, the secondary education should: Provide an
increasing number of primary school pupils with the opportunity for education
of a higher quality irrespective of sex, or social, religious, and ethnic
background; diversify its curriculum to cater for the differences in talents,
opportunities and roles possessed by or open to students after their secondary
school course; equip students to live effectively in our modern age of science
and technology; develop and project Nigerian culture, art and language as well
as the world’s cultural heritage; raise a generation of people who can think for
themselves, respect the views and feelings of others, respect the dignity of
labour, and appreciate those values specified under our broad national aims, and
live as good citizens; foster Nigerian unity with an emphasis on the common
ties that unite us in our diversity; inspire its students with a desire for
achievement and self-improvement both at school and in later life (F.R.N.
2004).
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Mathematics according to Butler and Wren, (1951) can contribute to the
realization of the general aims of education and mathematics education in
particular by:
Developing habits of effective critical thinking. This means
developing logical reasoning both inductively and deductively;
Providing competence in the basic skills and understanding for dealing
with number and form;
Fostering the ability to communicate thought through symbolic
expressions;
Developing the ability to differentiate between relevant and irrelevant
data and to make relevant judgment though the discrimination of
values;
Developing intellectual independence and aesthetic appreciation and
expression;
Advancing the cultural heritage through its own total physical and
social structure.
The role of mathematics in the society has been variously recognized and
acknowledged as the key to the science and technology based courses, and as
useful to man in his daily living (Aminu, 1990). In support of this Ale, (1994)
stated that mathematics is the backbone of knowledge. Eguavon, (2002) also
remarked that mathematics is the pivot of all civilization and technology
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development. According to Dedron and Itard, (1974) mathematics arose from
the need for areas and volumes. Furthermore, Adegboye, (1999) described
mathematics as universal language of communication. It is proved to be the
sharpest tool through its application in different subjects and in every day life.
Mathematics helps to enumerate, calculate, measure, collate, group, analyze and
relate knowledge (Osafehinti, 1986). All these were signals given to
mathematics as a descriptions tool for sustainable development. Odo, (1990)
pointed out that mathematics is a model for thinking, developing scientific
structure, drawing conclusion as well as for solving problems. Perhaps it is
because of the importance of mathematics that the study has been made
compulsory in secondary schools.
In spite of the social, cultural and disciplinary values of mathematics
world wide, the annual WAEC examination results indicate poor performance
of students in senior secondary certificate examination (S.S.C.E) in mathematics
as many of the candidates scored zero or marks within zero range (Chief
Examiner’s Report, 1996-1998). Factors identified by the Chief Examiner’s
Report as being responsible for the poor performance include poor preparation
of students for the examination and failure to observe the rubrics. Furthermore,
Chief Examiners’ Report (2000) stated that many of the questions demanded
fundamental understanding of the subject. The questions were devoid of guess
work. The rubrics were clear and unambiguous, yet the candidates performed
poorly. One of the suggestions for remedy by the Chief Examiners’ Report was
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that teachers should emphasize to the students that the concepts of the senior
secondary school mathematics depend on their understanding of mathematics
concepts at the junior school level. Hence, students’ poor performance in
mathematics at a higher level is a reflection of a weak foundation in
mathematics at the lower level. In other words, performance at the higher level
depends on what is learned at the lower level.
However, from the Chief Examiners’ Report, (2002) the summary of
candidates’ weakness on the West African Senior Secondary Certificate
Examination (WASSCE) in Nigeria included reading median from ogive.
Again, the performance of the candidates did not improve significantly in 2003.
The difficulty level of the paper was of the required standard. The rubrics were
clear and unambiguous. A summary of candidates’ weakness include use of
histogram to estimate the mode (Chief Examiners’ Report 2003). Again
questions from measures of central tendency comes out every year at both
junior and senior secondary certificate examinations (J.S.C.E and S.S.C.E.)
respectively. Based on the continuous poor performance of students on median
and mode the researcher chose the topic. According to the secondary school
curriculum measures of central tendency (mean, median and mode) are first
taught in J.S.I.
Table 1 below shows the failure rate of students in J.S.C.E results in
mathematics from the year 2000 to 2005. This poor performance as mentioned
earlier is carried forward to the senior secondary school level.
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Table 1: The Junior Secondary Certificate Examination (JSCE) results in
mathematics from the year 2000-2005
Year Schools % With Credit and Above % With Pass % Failure
2000 A
B
C
D
E
62
14
13 20
08
03
34
71
67
34
94
4
9
20
58
3
2001 A
B
C
D
E
35
07
03 08
71
14
61
76
59
29
86
4
17
38
-
-
2002 A
B
C
D
E
35
07
03 26
71
14
61
76
59
29
86
4
17
38
-
-
2003 A
B
C
D
E
28
04
06 13
07
22
31
82
85
93
74
41
14
9
-
4
17
17
2004 A
B
C
D
E
15
04
01 06
10
-
77
93
71
81
74
8
3
28
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2005 A
B
C
D
E
26
10
04 12
07
14
69
87
90
85
84
5
3
6
8
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Source: Post Primary Schools Management Board (PPSMB) Nsukka Zonal
Office
Table 1 shows that only 20% of the candidates scored credit and above on
the average for the five schools in the year 2000, 08% in 2001, 26% in 2002,
13% in 2003, 06% in 2004 and 12% in 2005.
Students’ poor performance in mathematics at the Junior school level as
reflected in table 1 above is carried forward to the senior school level. Teachers
are mostly blamed for students’ poor performance in mathematics for instance,
Agwagah, (1993) recognized that, the teaching of mathematics still follows the
traditional pattern which is identified to be ineffective and a major factor
responsible for the poor performance of students in mathematics. Adedayo,
(2001) stated that the problem of failure at the secondary school level has
always been attributed to teachers’ failure to use appropriate method of
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teaching. Obioma, (1984) also attributed pupils’ poor performance in
mathematics to be dependent on the teachers’ use of inappropriate methods of
teaching such as descriptive and lecture method. Consequently students loose
interest in learning.
When one is interested in an activity he is likely to achieve highly in that
activity. In other words interest is believed to be an important variable in
learning. According to Oxford Advanced Learners Dictionary, interest is
condition of wanting to know or learn about something or somebody. It is
quality that arouses concern or curiosity. However, interest to do something
implies giving ones attention to something because the person enjoys finding
out about it or doing it. When something is interesting, it attracts attention of
people because it is special and exciting. Okpara, (1985) asserted that although
pupils’ poor performance in school subjects may be related to their lack of
interest and commitment to their studies and inadequate support from their
parents and even the government, all that the teachers are used to, is the
conventional (talk or lecture, descriptive) methods rather than strategies that
involve pupils’ participation. Ammo, (2002) also relate the failure of students in
mathematics to the teachers’ incompetence or ineffectiveness and lack of
interest in the subject by the students.
According to Oyadiran, (1991) students display poor performance due to
lack of interest in the subject, inadequate preparation and failure to use
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instructional materials to teach mathematics, there is lack of consideration given
to materials like textbooks. Consequently students are scared of the subject.
Other factors identified by Amoo, (2001) that are responsible for
students’ poor performance in mathematics are the overloaded and unrealistic
nature of the curriculum, teacher “teach all” policy at primary and Pre-Primary
levels of education, delay in the payment of teachers’ salary, poor
environmental background which a child encounters before he leaves home for
his immediate environment, recruitment of unqualified mathematics teachers
and the societal call for certificate without proficiency lead students to cheat in
order to pass exanimation (that is through examination malpractice).
The question then is what is the way out? Identification of a problem they
say, is a step towards its solution. To the researcher, there is need to search for a
strategy where students must be given sufficient opportunity for creative
activity where each can bring out his own measure of talent and thereby display
his personality. This process might be enhanced by having the students in small
groups, to discuss about the concepts taught and connections to be drawn.
Consequently, the students develop awareness of his or her own knowledge
organization. Hence this study was motivated by the desire to adapt mind map
in the teaching of measures of central tendency in junior secondary schools.
Mind Map according to Wikipedia encyclopedia (1998) is a diagram used
to represent words, ideas, tasks or other items linked to and arranged radially
around a central key word or idea. It is used to generate, visualize, structure,
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classify ideas, and as an aid in study, organization, problem solving and
decision making.
Mind map according to Hugh, (2003) is a convenient graphical tool that
helps one think and learn by putting complex thoughts or interconnected ideas
into simpler forms or ideas. He concluded that mind map can be used to take
lecture notes, plan an essay / dissertation /thesis, outline a presentation /
seminar, revise a topic being studied, make notes from textbooks, summarize
articles / chapters, organize one’s thought about any topic (whether academic /
emotional / personal).
Mind map, or radiant thinking as it is sometimes called, is a fairly good
techniques that allows one to both brainstorm and structure his thoughts using
graphics, colours, and words in a free-ranging map (Kennedy, 1999).
Furthermore, Brinkmann, (2001) stated that mind map may show connections
between mathematics and the rest of the world. As a mind map is open for any
idea someone associates with the main topic, non mathematical concepts may
also be connected with a mathematical object. Thus it becomes obvious that
mathematics is not an isolated subject but is related to the most different areas
of “the rest of the world”.
The researcher defines mind map as a diagram used to develop and
organize information in such a way that the central (main) idea is in the centre
from these, other sub-ideas are developed and organized. Simply put, it is a
mnemonic technique for sorting out both simple and complicated ideas. In other
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words, the structure of a mind map allows one to organize hierarchically
mathematical knowledge.
The special structure of a mind map according to Hemmerich, (1994) has
an open structure, one may just let one’s thoughts flow, every produced idea
may be integrated in the mind map by relating it to already recorded ideas. Mind
maps drawn by students provide information about the students’ knowledge.
The student, in small groups, construct mind maps as by it students have to
discuss about the concepts to be used and the connection to be drawn. The
students’ growth in the understanding of a topic can be checked when asking
them to create a mind map. In other words, the connections students make as the
map is drawn enables the teacher to assess or evaluate their achievement. Each
mind map has a unique appearance and strong visual appeal. Thus, the learning
process is speeded up and information recalled faster.
From the foregoing, students achieve poorly in mathematics. The
researcher sees the need for a teaching strategy that will improve the
achievement of both male and female students in measures of central tendency.
Thus, the researcher investigated how the use of mind maps affect students’
performance in measures of central tendency in statistics.
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Statement of the Problem
Secondary education has been acknowledged as preparation of the child
for useful living within the society and preparation for higher education (F.R.N,
2004). Any inadequacies and deficiencies at that level are likely, to adversely
affect the childs’ learning at subsequent levels and living within the society.
Despite, this recognition accorded mathematics as the key to the science
and technology based courses, and useful to man in his daily living students still
perform poorly on the subject Aminu (1990). Research results reveal that the
methods presently in use by teachers of mathematic are the traditional, talk or
lecture rather then the strategies, that involve students’ participation (Agwagah
1993). Probably, the non-use of innovative methods that are problem solving
oriented such as concept maps, mind maps and so on could be the main cause of
poor performance of students in mathematics.
Mind maps however, has been used as an effective strategy in enhancing
students’ achievement both in mathematics and other subjects outside Nigeria
(Brnkmann, 2002). There is no evidence in literature of the use of mind maps in
the teaching of secondary school mathematics here in Nigeria. Therefore, the
problem of this study, put in question form is: to what extent will the use of
mind map positively affect male and female students’ achievement and interest
in measures of central tendency?
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Purpose of the Study
The general purpose of the study was to find out the effect of mind maps
on achievement and interest of junior secondary school students in measures of
central tendency.
The study specifically intended to:
1 Determine the effect of mind map on the achievement of students
taught measures of central tendency.
2 Determine the influence of gender on the achievement of students.
3 Determine the effect of mind map on interest of students in measures
of central tendency.
4 Determine the influence of gender on the interest of students in central
tendency.
5 Determine the interaction effect of method and gender on students’
achievement and interest in mathematics.
Significance of the Study
Evidence of poor achievement in mathematics especially in measures of
central tendency as a result of factors earlier highlighted is the motive behind
the present study to investigate the effect of mind maps on the achievement and
interest of secondary school students in measures of central tendency.
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Findings of the study would be of immense benefit to:
1 Secondary school teachers as they would acquire new instructional
strategy. This will make the teaching of mathematics more interesting and
thus improve teachers’ effectiveness. This could secure the attention of
the students in the course of instruction and therefore enhance greater
interest and learning of mathematics by students.
2 The results of the study could sensitize curriculum planners on the use of
mind map for teaching measures of central tendency.
3 The result of the study would make students have a better understanding
of the central tendency. Their involvement in creating mind maps might
generate interest and hence facilitate better achievement.
4 The result would furnish the teacher training institutions such as Institutes
of Education, Faculties of Education, and Colleges of Education with
useful methods, learning strategies and materials that are useable in
secondary schools since educational institutions organize in-service
(Sandwich) courses for secondary school teachers. Thus the in-service
trainers would acquire the knowledge and as well disseminate the
information.
5 The use of mind map would furnish the text book writers with additional
information and variety in the manner of presenting the mathematical
materials and instructions that will work in Nigerian school setting.
6 The result from this study might be introduced during workshops,
seminars and conferences. Supervisors and inspectors of education will
also benefit from such conference at the state and federal levels. This, it is
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hoped will ensure improvement in mathematics methodology in the
school to enhance achievement and to generate students’ interest in the
subject.
Scope of the Study
The study will be limited to junior secondary one (JSI) students in
Nsukka Local Government Area of Enugu State. The J.S.I students will be used
because measures of central tendency is contained in their curriculum. The topic
covered the following contents.
a. Mean as the average
b. Median as the middle number
c. Mode as the number with the highest frequency
d. Word problem on mean, median and mode
The topic will be used because it is one of the topics in mathematics that
students find difficult as highlighted earlier.
Research Questions
The research questions formulated to guide this study are as follows:
1. What are the mean achievement scores of students taught measures of
central tendency using mind maps method and those taught with
conventional method?
2. What are the mean achievement scores of male and female students
taught measures of central tendency with mind maps?
3. What are the mean interest scores of students taught central tendency
with mind map?
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4. What is the influence of gender on the mean interest scores of students
in central tendency when taught with mind maps?
Research Hypotheses
The following hypotheses were formulated to guide this study, and tested
at .05 level of significance.
H01: There is no significant difference in the mean achievement scores of
students taught central tendency using mind maps and those taught using
conventional method.
H02: There is no significant difference in the mean achievement scores of male
and female students in central tendency.
H03: There is no significant interaction effect of method and gender on the
mean achievement of students in measures of central tendency.
H04: There is no significant difference in the mean interest scores of students in
central tendency when taught with mind maps and those taught with
conventional method.
H05: There is no significant difference in the mean interest scores of male and
female students in central tendency.
H06: There is no significant interaction effect of method and gender on the
mean interest of students in measures of central tendency.
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CHAPTER TWO
REVIEW OF LITERATURE
The chapter presents a review of work related to this study under the
following headings:
1. Conceptual Framework
(a) Meaning and uses of mind maps.
(b) Other mathematical maps, distinctions and similarities.
(c) Teacher factor and students’ achievement in mathematics
(d) Interest in mathematics and other school subjects.
2. Theoretical Framework
(a) Theories underlying the use of mind maps in teaching
mathematics.
3. Empirical Studies
(a) Studies on gender as a factor in mathematics achievement
(b) Studies on mind mapping
(c) Studies on interest and academic achievement
4. Summary of Related Literature
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Conceptual Framework
Meaning and Uses of Mind Maps
Mind map was first developed by Tony Buzan, a mathematician,
psychologist and brain researcher, as a special technique for taking notes as
briefly as possible and also as interesting to the eye as possible. Mind maps
have, among other things, been used in education, but yet rarely in mathematics.
The method of mind mapping basically takes into account that the two halves of
the human brain are performing different tasks. While the left is mainly for
logic, word arithmetic, linearity sequences, analysis, lists, the right side of the
brain mainly performs tasks like multidimensionality, imagination, emotion,
colour, rhythm, shapes, geometry synthesis. Mind mapping uses both sides of
the brain, hence work together and thus increases productivity and memory
retention. Buzan (1991) claimed that the mind map is a vastly superior note
taking method because it’s “semi-hypnotic trace” state, is induced by the other
note forms. He also pointed out that mind map, utilizes the full range of left and
right human cortical skills, balance the brain, taps into the 99% of the unused
mental potential as well as intuition.
Mind map represents logical structures using an artistic spatial image that
the individual creates. Thus mind mapping connects imagination with structure
and pictures with logic (Svantesson, 1992) .
According to Entrekin (1992) mind map has unique appearance
and a strong visual appeal. Thus information may be memorized and recalled
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faster, the learning process is speeded up and structured information becomes
long living. She stated further that at the end of the teaching unit, the subject
matter of the treated topic can be repeated and structured by composing a mind
map; this mind map then serves as a good memorial summary. Several teachers
she said who introduced mind mapping in their mathematics lessons could
observe that some of their students began on their own initiative to construct
mind maps at home, especially when preparing for an examination, in order to
get a structured overview on the subject matter. In conclusion, she presented the
case of a teacher who told about a ten year old girl that proudly showed her a
mind map she had drawn as a decoration for her exercise book. The map
represented the contents of her exercise book in a structured way.
Brinkman, (2001) pointed out that mind map shows connections between
mathematics and the rest of the world. He stated further that mind map are not
obtained automatically. They are expected to think and argue within
mathematics. It is of need for teachers to give a respective hint when
introducing mind mapping in a class. Students often express their surprise that
they are allowed to insert non mathematical terms in their maps, but also their
good feelings when doing so. Mind map guidelines of packages available for
producing mind map according to Buzan (1991) are:
1. Start in the centre with an image of the topic, using at least three colours
2. Use images, symbols, codes and dimensions throughout your mind map.
3. Select key words and print using upper and lower case letters.
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4. Each word/image must be alone and sitting on its own line
5. The lines must be connected starting from the central image. The central
lines are thicker becoming thinner as they radiate out from the centre.
6. Make the lines the same length as the word/image
7. Use colours-your own code-throughout the mind map
8. Develop your own personal style of mind mapping
9. Use emphasis and show associations in your mind map
10. Keep the Mind Map clear by using radial hierarchy, numerical order or
outlines to embrace your branches. Mind maps can be drawn by hand
during a lesson or a meeting or can be more sophisticated in quality.
It is a shame that perfectly good teaching tools are
constantly being justified with hokum references to
neuroscience. I mind mapped this article before writing it. It
would be interesting to find out whether regular readers
notice any rinse in quantity (Philip, 2006, P.8).
Mind mapping is easy. To construct a mind map, draw something in the
middle of your paper. Do not go too near the sides so as to have space to spread
out thoughts. Draw six multicoloured lines out from the centre and a picture at
the end of each line that is related to the central image. The lines should be
airily, there is no room for the rule in the realm of the creative. Finally, write
key words in the upper or lower case of the curly lines. You have now drawn a
mind map and are now ready to rule the world (Philip, 2006).
Mind Maps according to Buzan, (1991) have all the seductiveness of popular
science. When we have mastered them, we feel as if we are in possession of a
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precious secret known only to the select few million who have purchased a
book by their progenitor. He continued mind maps “help make your life easier
and more successful”. Using images taps into the brain’s key tool for storing
memory, and that the process of creating a mind map uses both hemispheres.
Mind maps bring out the staffroom cynic in all of us he concluded.
The educationist Lan in his book Essential motivation in the classroom as
pointed out by (Philip, 2006), revealed the story of a school in which revision
notes were all in the form of mind maps. Come exam time, teachers erected a
giant white screen and asked students to project their recollections of their
revision notes not to it. Needless to say, everyone got an “A” and world peace
was finally achieved. As visual tools, mind maps have brilliant applications for
display work. They appear to be more cognitive than colouring in a poster. And
the researcher thinks it beyond doubt, that using images help students to recall.
Uses of Mind Maps
Mind maps have many applications in personal, family, educational, and
business stations, including note taking, brainstorming (wherein ideas are
inserted into the map radically around the centre node, without the implicit
prioritization that comes from hierarchy or sequential arrangements, and
wherein grouping and organizing is reserved for later stages), summarizing,
revising and general clarifying of thoughts for example, one could listen to a
lecture and take down notes using mind maps for the most important points or
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key words. One can also use mind maps as a mnemonic technique or to sort out
a complicated idea. Mind maps are also promoted as a way to collaborate in
colour pen creativity sessions. One can find the perfect lover, combat bullying,
persuade clients, develop intuitive powers, create global harmony, and tap the
deeper levels of consciousness by using mind map techniques. Manager and
students find the techniques of mind mapping to be useful, being better able to
retain information and ideas than by using traditional “Linear” note taking
methods. Mind maps can be drawn by hand for example during meeting or
lecture (Buzan, 1991). Thus mind map if effectively implemented can be of
much help to mathematical instruction.
Other Mathematical Maps, Distinctions and Similarities
There are many types of maps, other than mind map, which can be utilized
in mathematics instructions some of them as enumerated by Williams, (2002)
include concept map, topic map and cognitive map. These he said can be used
effectively to organize large amounts of information, combining spatial
organization and dynamic hierarchical structuring.
Concept mapping is a technique for visualizing the relationships between
different concepts. A concept map is a diagram showing relationships between
concepts. Concepts are connected with labelled arrows, in a downward
branching hierarchical structure. The relationship between concepts is
articulated in linking phrases for example “gives rise to”, “results in”, “is
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required by”, or “contribute to”. The technique of concept mapping was
developed as a way to increase meaningful learning in the sciences. Concept
maps can be used to stimulate the generation of ideas, and are believed to aid
creativity. For example, concept mapping is sometimes used for brain-storming.
Although they are often personalized and idiosyncratic. Concept maps can be
used to communicate complex ideas (Novak, 1990).
Topic maps are standard for the representation and interchange of
knowledge, with an emphasis on finding information. The standard is formally
known as ISO/IEC/13250:2003. A topic map can represent information using
topic (representing any concept, from people, countries and organizations to
software modules, individual files and events), associations and occurrences.
They are similar to semantic networks. In loose usage all those concepts are
often used synonymously, though only topic maps are standardized. Topics
associations and occurrences can be typed, but the types must be defined by the
creator of the topic maps, and is known as the ontology of the topic map. There
are also additional features, such as merging and scope. The concept of merging
and identity allows automated integration of topic maps from diverse sources
into a coherent new topic map. A format called linear topic map notation
(LTM) serves as a kind of shorthand for writing topic map in plan text editors
(LUTZ 2003).
Tolman (1984), defined cognitive map, mental maps, cognitive models, or
mental models as a type of mental processing, cognition, composed of a series
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of psychological transformations, by which an individual can acquire, code,
store, recall and decode information about the relative locations and attributes
of phenomena in their everyday or metaphorical spatial environment. Cognitive
maps are used to structure and store spatial knowledge, allowing the “mind’s
eye” to visualize images in order to reduce cognitive load, and enhance recall
and learning of information. He concluded that cognitive maps may also be
represented and assessed on paper or screen through various practical methods
such as a concept map, sketch map, spider diagram, or any variety of spatial
representation.
Distinctions between Concept and Mind Maps
Mind map is based on radial hierarchies and tree structures whereas concept
map is based on connections between concepts. Mind mapping starts off with a
central (main) idea in the centre of the paper with sub-ideas radiating outward
on lines (lines may be straight or curved); while concepts are connected in a
downward branching hierarchical structure in concept mapping. Whereas mind
mapping is open for any idea one associates with the main topic, in other words,
it reflects what one thinks. Concepts mapping is a system view of the
relationship between different concepts. Another contrast between concept
mapping and mind mapping is the speed and spontaneity when a mind map is
created. Mind map can be draw by hand with little discussion and one’s own
personal style of mind mapping while it takes a longer period of discussion to
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reach agreement about a concept map. The use of colours in mind mapping
makes it attractive with a strong visual appeal that enhances memory, whereas
in concept mapping colours are not used. Mind maps are based on separated
focused topics, while concept maps encourage one to label the connections one
makes between nodes (Buzan 1997; Novak, 1990 and Hugh, 2003).
Similarities between Concept and Mind Maps
Both maps are pedagogical tools for mathematics education and are used for
building structure. Concept and mind maps have been found to enhance
meaningful learning while enabling the potential as a true cognitive, initiative,
spatial and metaphorical mapping. Both maps are used for note taking,
summarizing, revising, brainstorming and general clarification of thoughts.
These tools can be used effectively to organize large amounts of information,
combining spatial organization, dynamic hierarchical structuring and node
folding (Buzan, 1997; Hugh, 2003 and Novak, 1990).
Teacher Factor and Students’ Achievement in Mathematics
There has always been a growing concern about poor achievement in
mathematics. Okolo, (2004) stated that mathematics education in Enugu State is
at crisis point. He in the analysis of senior school certificate result for the past
years revealed that only nine (9) out of one hundred (100) students in
mathematics qualified for admission into the sciences in our tertiary institutions.
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This poor performance is traceable to poor teaching methods adopted by
teachers as most of them teach the way they were taught. He concluded that if
this problem is not addressed, it may spell doom for our state.
This poor performance and sorry situation of mathematics education in
Nigeria is best observed from the West African Examinations Council (WAEC)
annual report (1996-1998 and 2002). The percentage of students who failed
mathematics each year outnumbered the percentage who are successful. This
situation in turn will affect student’s enrollment in mathematics and
mathematics related courses in tertiary institutions as well as nation’s scientific
and technological development. Cliffiths and Howson (1994) argued that no
matter how carefully structured a new course is or how brilliantly the various
educational media have been exploited, the success or failure of any innovation
hinges on the reception and flexibility of the classroom teacher. It is observed
that most teachers are ineffective. While acknowledging the vital role of
education in nation building and development, the National policy on education
(FRN 2004) stated that “no education system can rise above the quality of its
teachers”. When teachers are effective the quality education is ensured.
According to Agwagah, (1993) the teaching of mathematics today still follows
traditional pattern which is identified to be ineffective and a major factor
responsible for the poor performance of students in mathematics.
Sobel (1998) while commenting on the jobs description for teachers
summarized it as follows:
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Teachers must know the stuff. They must know the pupils
whom they are stuffing. And above all they must know
how to stuff them artistically.
Consequently, the way the teacher translates curriculum into knowledge for
assimilation by students is very important. Alio (1997) observed that teachers’
non utilization of the necessary techniques in teaching mathematical problem
solving is another contributing factor to the student’s poor performance.
Students performance is poor not only because it is difficult to understand
mathematics but because many teachers handle it perfunctorily. In other words,
teachers’ presentation of mathematics as collection of formulae to be
memorized will only discourage students from taking the subject. In support of
the above assertion. Adepoju, (1991) noted that lessons are not properly taught,
sometimes the teachers are too fast not minding whether students understood
the contents or not. There is also lack of continuity whereby one topic links
another and the prior knowledge are used for new situations.
Part of the observed teachers’ ineffectiveness lies with the methods which
they employ in teaching. Some of these methods include those that lower rather
than boost the morale of learners (Orji, 1984), lecture and descriptive methods
which result in learners’ lack of interest and poor achievement (Obioma, 1985).
According to Obodo, (1997) many of the professional teachers do not use
appropriate methods and teaching aids in the classroom. Some he stated use
sterile and uninspiring methods. Teachers give little or no consideration to the
psychology of the learner who may require concrete realities. Mathematics
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instruction is hardly related to real life situations even when it is obvious to do
it with little or no efforts. These aggregate the shape the students’ perception of
mathematics as difficult, abstract and uninteresting hence leads to poor
performance in mathematics. If this problem is not addressed, it may affect the
technological development of this country Nigeria. The problem lies more with
the teachers and the practices at the secondary school level of education as
pointed out earlier. In support of the above assertion, Familoye and Darico
(1996) pointed out the disadvantages of using lecture method by the teacher as
follows:
It is teacher-centred
Lack of participation by students set in boredom
It hardly caters for individual differences
The students initiative is not always taken into consideration
This then implies that students will not understand the topics covered and as
such lead to failure. Onyemerekeya (1998) stressed that if lecture method is
developed in a logical manner and with interest-catching devices, it can arouse
and sustain students’ interest. Similarly mind mapping strategy is effective in
arousing the interest of the learners.
All these blames on the teacher are in line with Cockeroft’s (1982) assertion
that, there is no area of knowledge where a teacher has more influence over the
attitudes as well as the understanding of pupils rather than his professional life.
A teacher of mathematics may influence for good or ill the attitude of
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mathematics of thousand young people and decisively affect many of their
career choices. It is therefore necessary that mathematics should not only be
taught to all pupils, but also well taught. All pupils should have the opportunity
of studying mathematics in the company of enthusiastic and well qualified
mathematics teachers.
Habor-Peters (2002) in support of this assertion explained that teachers’
competence in mathematics content is related to students’ achievement and
interest in mathematics learning. She pointed out that a competent mathematics
teacher teaches with confidence and commands the admiration of his/her
students. According to her, various structures must be properly put in place
(instructional strategies and materials and so on) since mathematics students of
today will become mathematics teachers of tomorrow, they need to be attracted
to learn and study mathematics.
From my teaching experience there is low achievement of secondary school
students in mathematics and mathematics-related disciplines. They practice or
learn other subjects more than mathematics although mathematics is made
compulsory for them. Consequently they perform poorly in mathematics
examinations, both internally and externally. Hence there is need to use
instructional materials, teaching methods and teaching strategies that can
generate (arouse) and sustain interest in teaching/learning of mathematics
especially measurers of central tendency. Teaching method is a procedure,
means of communicating, conveying, inculcating, ideas, skills and values
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implied in the aims and objectives of education (Onyemerekeya, 1998).
According to Obodo (1990), a teaching strategy is a set of unique activities
which a teacher employs to implement a particular teaching method. A teaching
strategy may be applicable to many instructional methods.
However, mind map teaching strategy leads to meaningful learning as
students are actively involved in the process of construction and showing
relationships between concepts.
Interest in Mathematics and Other School Subjects
It is assumed that the use of mind maps as stipulated in this study will
increase the level of interest in secondary school students in mathematics.
Interest has been seen as preferences for particular types of activities or
tendencies to seek and participate in certain activities (Agwagah 1993).
Interests in students according to Nwagu, (1992), are not innate but learnt. In
other words, teachers are advised to provide meaningful and interesting
activities to students. Harbor-Peters (2002), asserts that the teacher should make
their lesson objectives practical, meaningful, palatable and interesting to the
students. This they do by explaining the activities that interest students
especially in mathematics. This is because students’ interest can influence how
well they learn and what they learn.
Suydan and Weaver (1975), wrote “teachers and other mathematics
educators believe that children learn more effectively when they will achieve
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better in mathematics if they like the subject. In other words, interest produces
efforts, efforts increase interest and a combination of the two usually results in
success.
The researcher sees interest as wanting to be associated with something. It is
quality that increases relationship with something or somebody. Hence if
somebody is interested in something he’/she will likely achieve higher in that
thing.
Balogun (1997), stated that poor facilities for teaching, failure by teachers
to use instructional materials, poor teaching methods such as direct
dissemination of information method make students loose interest thus perform
poorly in mathematics.
Farrant, (1980) observed that affective leaning has to do with feelings and
values and therefore, influences our attitude and personalities our attitudes and
personalities. On gaining interest in what is to be learned, he said, “you can lead
a horse to the water but you cannot make him drink”. In support of the above
assertion, Obodo (1990) explained that teachers’ and students’ lack of interest
are among the factors that influence achievement in mathematics.
However, an individual is normally actively involved in an activity of
interest. It is therefore, pertinent to note that any attempt to tackle the problem
of poor performance in mathematics will be a failure if students’ interest is not
taken into consideration.
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Waston as sited in Okpara (1995) emphasized the need of training teachers
on the use of interesting methods and instructional materials. This need among
others have led the researcher to introduce mind maps in the instructional
procedure of measures of central tendency in the junior secondary school one.
Perhaps, this will improve students’ interest and achievement in mathematics.
Theoretical Framework
Theories underlying the use of Mind Maps in Teaching Mathematics
This study is anchored to two schools of thoughts. One is the Piaget’s
theory of learning and the other in the constructivist theory. The basic concepts
emanating from these theories that are useful to this study are principles for
building cognitive structures, co-operative learning and peer learning.
Piaget’s theory is based on the idea that the developing child builds
cognitive structure. In other words, mental “map”, schemes or networked
concepts for understanding and responding to physical experiences within his or
her environment. Piaget further attested that a child’s cognitive structure
increases in sophistication with development, moving from a few innate reflexes
such as crying and sucking to highly complex mental activities (Satterly, 1987).
Piaget’s theory identifies four developmental stages and the processes by
which children progress through them. The four stages are:
1. Sensorimotor state (birth-2years old) – The child, through physical
interaction with his or her environment, builds a set of concepts about
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reality and how it works. This is the stage where a child does not
know that physical objects remain in existence even when out of sight
(object permanence).
2. Preoperational stage (ages 2-7) – The child is not yet able to
conceptualize abstractly and needs concrete physical situations
3. Concrete operations stage (ages7-11) - As physical experience
accumulates, the child starts conceptualize, creating logical structures
that explain his or her physical experiences. Abstract problems solving
is also possible at this stage. For example, arithmetic equations can be
solved with numbers, not just with objects.
4. Formal operations (beginning at ages 11 - 15)- By this point, the
child’s cognitive structures are like those of an adult and include
conceptual reasoning (Satterly, 1987).
Piaget outlined several principles for building cognitive structures.
During all development stages, the child experiences his or her environment
using whatever maps he or she has constructed so far. If the experiences is a
repeated one, it fits easily or is assimilated into the child’s cognitive structure so
that he or she maintains mental : equilibrium” . If the experience is different or
new, the child loses equilibrium, and alters his or her cognitive structure to
accommodate the new conditions. This way, the child erects more and more
adequate cognitive structures.
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Wood (1998), stated that for Piaget’s theory to impact learning, educators
must plan a developmentally appropriate curriculum that enhances their
students’ logical and conceptual growth. In other words the planning of
mathematics curricula in the different levels of education should be sequential
from simple to complex. The topics should however have linking experiences.
On instructions he pointed out that teachers should ensure that a child has
mastered all the experiences necessary for mastering a mathematical concept
before introducing a new mathematical concept.
Adler, (1971) on the influence of Piaget’s theory on mathematics
teaching and learning pointed out that mathematics teachers can help the child
to overcome errors in his thinking by providing him with experiences which
will expose the child to errors. The teacher then indicates ways of correcting
such errors. In order to encourage mental growth of children he stated, the
experience of seeing things from varied perspectives is very necessary. The
mathematics teacher to enhance this should use different teaching methods.
Then for the child to learn effectively, he must be an active participant in
mathematical activities. Opportunities should be created for the child to be less
and less depended on the physical action until the action is completely
internalized as mental operation. To bridge the gap between perception and the
formation of mental image, the mathematics teacher should reinforce the
developing mental image with frequent use of perceptual data.
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On the other hand constructivist theory has the same view with Piaget
about the learner constructing knowledge based on his prior experience.
Constructivist epistemology essentially holds that the scientific knowledge are
personally constructed and reconstructed by the learner based on his prior
experience. Stofflet (1994) pointed out that what a student learns results from
the interaction between what is brought to the learning situation (by the learner)
and what is experienced in it. Constructivism holds the view that the learner is
creative, dynamic and has a free will. He is seen as the controller of his
environment.
According to Johnnason (1991) an individual’s knowledge is a function
of one’s prior experience, mental structures, and beliefs that are used to interpret
objects and events. The assumptions of the constructivists are:
Knowledge is constructed from experience.
Learning is a personal interpretation of the world.
Learning is an active process in which meaning is developed on the basis
of experience.
Conceptual growth comes from the negotiation of meaning, the sharing of
multiple perspectives and the changing of our internal representations
through collaborative learning.
Learning should be situated in realistic settings, testing should be
integrated with the task and not separately (Merill 1991).
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Constructivist approach added Cohern, (1996) views the teachers’ role in
the class as not to dispense knowledge but to provide students with
opportunities and incentives to build on. Teacher is a guide and learners are
“sense-maker”.
Driver, (1989) stated that teachers are co-coordinators, facilitators, recourse
advisers, tutors or coaches. Teachers he said are to introduce new ideas
necessary for that situation. Students are to listen and diagnose the ways in
which the instructional activities are being framed and then interpret the
information for further action. Teaching from this perspective is also a learning
process for the teacher.
Cohern, (1996) further stated that the content is not pre-specified,
direction is determined by the learner and assessment is subjective because it
does not depend on specific quantitative criteria, but rather the process and self-
evaluation of the learner. Evaluation here is based on notes, early drafts and not
final products. The learner is able to interpret multiple realities and deal with
real life situations. The learner he concluded can apply his/her knowledge in
solving problems in a novel situation.
From constructivists view how one arrives at a particular answer and not
the retrieval of an objectively true solution is what is important. Cohern (1991)
argued that learning requires self-regulation and the building of conceptual
structures through reflection and abstraction; that the focus of instruction is
content development and deep understanding rather than behaviours or skills as
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goal of instruction. Students’ errors are seen in a positive light and as a means
of gaining insight into how they are organizing their experiential world.
From the above expositions, one finds Piaget’s theory of learning and
constructivists’ theory strong bases for understanding the use of mind maps for
instruction. Major Piaget’s and constructivist theories of learning such as
knowledge being personally constructed by the learner based on his prior
experiences, active participation (involvement) of the learner, co-operative
learning, self-correction as discussed here are reflected in mind maps.
Empirical Studies
Studies on Gender as a Factor in Mathematics Achievement
Gender is a very important variable in the study of mathematics and
measure of central tendency in particular. Difference in academic achievement
due to gender has caused a lot of concern to educationists Hacker (1992), stated
that human beings are like “blank slate” at birth upon which social living is
written. He further observed that males are superiors in visio-spatial tasks while
females are superior in verbal performance.
Lassa (1995), revealed that the content of the curriculum for females are
made up of subjects like needlework, home management, nutrition, domestic
science and so on. This is to prepare them for their future roles as mothers and
house wives.
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Okoye (1987), stated that gender differences in mathematics achievement
are not due to intelligence make-ups of the male and female students. Rather,
the individual’s cultural and social environment account for the differences in
performances.
However, research findings on academic achievement due to gender are
contradictory. Barrack (1980), revealed that female students achieved
significantly higher than that of their female counterparts in mathematics.
Agwagah (1993), confirming Barrack’s view in her study to determine the
effect of instruction in mathematics reading on students’ achievement, found
that female students perform better than their male counterparts. She attributed
the result to the females’ higher ability in reading comprehension as being
responsible for the superior performance.
Furthermore, while Okeke (1990), Ezeugo and Agwagah (2000) found
significant gender differences in achievement in favour of female students,
Aiyedum (2000), pointed out that the cognitive power necessary for
mathematical ability correlates with general intelligence in which no consistent
sex differences were found. Agreeing with this view Akintola and Popoola
(2004), stated that gender has no significant effect on students’ performance in
mathematics of junior secondary school.
From research finding, it appears that gender issue on achievement is
inconclusive. This study therefore, intends to determine the effect of mind maps
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on the achievement and interest of male and female students in measures of
central tendency.
Studies on Interest and Academic Achievement
Interest has earlier been defined and found to be a strong factor in
teaching and learning of mathematics and other related subject areas. There is
evidence of poor performance of students in mathematics, measures of central
tendency inclusive (Chief Examiners’ Report 2002, 2003). It is therefore
necessary to teach measures of central tendency in order to enhance the
achievement of students.
Researches have been carried out to determine the effect of interest in
mathematics achievement. For instance, Okoli (1995), in an experimental study
sought to examine the effect of cooperative and competitive learning styles on
achievement and interest in biology of senior secondary school students. 360
senior secondary school two biology students randomly drawn from six
secondary schools in Onitsha urban area of Anambra State were used for the
study. All students in each group were pre and post tested using a 30-items
selected biology concepts achievement test. It was found that the co-operative
and competitive learning styles significantly enhanced students achievement
and interest in biology than the conventional style.
Ozofor (2001), in another study to determine the effect of two modes of
computer aided instruction on students’ achievement and interest in statistics
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and probability. The result revealed that students perform better and become
more interested in tackling mathematical problems when drill, and practice
method of computer assisted instruction was used in teaching.
Also, Agwagah (1993), in her study on instruction in mathematics
reading as a factor in students achievement and interest in word problem-
solving found that instruction in mathematics reading greatly enhanced
students’ achievement and interest in Algebra. Lack of interest in mathematics
results in poor performance of students. Instructional techniques adopted by
mathematics teachers can affect interest positively or negatively (Agwagah,
1994).
Although a number of studies on interest and academic achievement have
been reviewed, it can be seen that none of the studies were carried out on mind
map teaching strategy. Would the mind map strategy enhance the achievement
and interest of students in measures of central tendency?
Studies on Mind Map
A lot of studies have been carried out on mind maps. The few which are
relevant to this study include the following:
Entrekin (1992), in her study discovered that mind maps are very
effective in introducing new concepts in mathematics classes. According to her,
the new concept on the chalkboard or transparency and later forms an extended
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mind map. This visual representation she said, serves to help students relate
unknown concepts to known concepts.
Again, Hemmerich (1994), in another study on the efficacy of mind map,
revealed that students were encouraged to create both a pre and a post – unit
mind map which was used to check the students’ growth in the understanding of
a topic. The result revealed that mind maps can be used as memory aid for
students, summarize the ideas of several students and a very fruitful way of
action.
Further more, Brinkmann (2001), in study using mind map strategy
discovered that mind map is open for any idea one associates with the main
topic, non-mathematical concepts may be connected with a mathematical object.
Hence Mind map shows connection between mathematics and the rest of the
world. Students are expected to think and argue within mathematics. Students
express their surprise, that they are allowed to insert nonmathematical concepts
and their good feelings in their maps. The use of mind mapping learning
strategy was motivating and students manifested great interest in the class.
A study carried out by Farrand, Hussain and Hannessy (2002), found that
the mind map technique had a limited but significant impact on recall only, in
under graduate students. A 10% increase over baseline for a 600 – word text
only. As compared to another method a 6% increase over baseline for the same
number.
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Still a research carried out by Brinkmann (2003), in using mind map
strategy found that during the learning process, the human brain primarily
remembers:
1. Items from the beginning of the learning period.
2. Items from the end of the learning period.
3. Items that are associated with ideas or patterns already stored, or
linked to other aspects of what is being learned.
4. Items that are emphasized as being in some way outstanding or
unique.
5. Items that appeal particularly strongly to one of the five senses (or
sometimes to the sense of humour!)
6. Items that, for some reason, are of particular interest to the learner.
Mind map has been found to empower students in developing self
confidence which will in turn lead to better achievement in mathematics.
Summary of Related Literature
Evidence from the studies reviewed; reveal that mind map is quite an
effective learning strategy. None of the studies highlighted took place in
Nigeria. The researcher therefore would want to determine whether mind map
strategy will be effective in the teaching and learning of mathematics in Nigeria
setting (Classroom).
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CHAPTER THREE
RESEARCH METHOD
This chapter presents the research design, area of the study, population of
the study, sample and sampling technique, instruments for data collection,
validation of the instruments, reliability of the instruments, experimental
procedure and method of data analysis.
Research Design
The design of this study is the quasi-experimental design; specifically, the
non-equivalent pre-test, post-test control group design. This design was adopted
because the experiment was carried out in intact classes (Ali, 1996). Intact
classes was used to avoid disruption of normal classes. Thus, there will be no
randomization of students into treatment and control groups as this would
disrupt school organization. The researcher will manipulate the independent
variable; that is teaching strategy and observe the effect on the dependent
variables, that is achievement and interest.
TABLE 2: Design Format
Group Pre-Test Research
Condition
Post-Test
Experimental
Group
Yc X Yb
Control
Group
Yc -X Yb
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Where Yc = Pretest for both experimental and control groups
Yb = Post-test for both experimental and control groups
X = Treatment given to the experimental group
-X = Treatment given to the control group
Area of the Study
The study was carried out in Nsukka Local Government Area of Enugu
State, Nigeria. There are thirty (30) secondary schools in Nsukka education
zone.
The choice of this zone was based on the fact that the researcher is
familiar with the schools location, hence makes it easier for effective
supervision and monitoring of the study.
Population of the Study
The population of the study includes all the junior secondary one (J. S.
I.) students in the thirty (30) secondary schools in Nsukka Local Government
Area of Enugu State. The J.S.I students was used because it is at this level that
the content (measures of central tendency) is first introduced.
Sample and Sampling Technique
The sample for this study is made up of three hundred and fifty (350)
J.S.I students who were drawn from four (4) schools. Sampling was done in
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stages; therefore multi-stage sampling procedure was employed. Firstly,
purposive sampling technique was used to select four secondary schools from
Nsukka Local Government Area. Random sampling technique was used to
select two streams of J.S.I classes from the four schools..
TABLE 3: The Sample of J.S.I Students used for the Study
Schools
used for
the Study
Experimental
Group
Control Group
No of
Males
No of
Females
No of
Males
No of
Females
Total
A 30 - 30 - 60
B - 50 - 50 100
C 32 20 25 23 100
D 18 30 15 27 90
Total 80 100 70 100 350
For the experimental (treatment) group 80 males and 100 females a total
of 180 J.S.I students were used for the study. On the other hand, for the control
group, 70 males and 100 females were used for the study. For each school
sampled, two intact classes were randomly assigned experimental and control
groups. The treatment group was exposed to mind map strategy while the
control group was exposed to conventional teaching method based on
conventional approach.
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Instruments for Data Collection
Two instruments namely Measures of Central Tendency Achievement
Test (MCTAT) and Measures of Central Tendency Interest Scale (MCTIS) were
used for data collection by the researcher. MCTAT was used as achievement
test to measure students’ performance in measures of central tendency. It
consisted of 20 multiple choice items with four (4) options. The items were
selected from the content which included, meaning of mean, median and mode,
computing the mean, computing the median and computing the mode. In
constructing MCTAT, the researcher prepared a table of specification to serve
as a guide for the test development. The construction of the table of
specification was guided by the guidelines in the schools’ curriculum for J.S.I.
The table of specification (test blueprint) was subdivided into content dimension
and ability process dimension as shown in table 4.
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TABLE 4: The Table of Specifications on Measures of Central Tendency
for J.S.I
CONTENT
DIMENSION
ABILITY PROCESS DIMENSION
Topics Percentage
%
Lower
Cognitive
Processes
Higher
Thinking
Processes
Total
Meaning of mean,
median and mode
25 4(1, 2, 3, 4) 1 (17) 5
Computing the
mean
25 3(5, 6, 7) 2 (8, 18) 5
Computing the
median
25 3 (9, 10, 11) 2 (12, 19) 5
Computing the
mode
25 3 (13, 14, 15) 2 (16, 20) 5
Total 100 13 7 20
Content dimension contain the units that was taught in this study while
the ability process dimension was subdivided into lower cognitive and higher
thinking processes. The MCTAT was used for both pretest and posttest. In order
to minimize pretest sensitization, MCTAT was collected back from the students
after pretest and properly guided to prevent using it for revision by the students.
The researcher also prepared two sets of lesson plans for teaching the units set
out for the study. One set of the lesson plans was written based on mind map
strategy in teaching measures of central tendency for the experimental groups.
The other was written based on conventional approach in teaching measures of
central tendency for the control groups. It followed the same procedures as
treatment group except that it has no elements of mind maps.
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The Measure of Central Tendency Interest Scale (MCTIS) was used for
assessing students’ interest in measures of central tendency. This scale consisted
of 20 items. Each item was rated on a 4 – point scale with the following
response: A Strongly Agree, B. Agree, C. Disagree, D. Strongly Disagree.
Some items (1, 3, 5, 6, 8, 9, 11, 13, 15, 17, 19) were positively cued while
others (2, 4, 7, 10, 12, 14, 16, 18, 20) were negatively cued. To score the
positively cued items, the response (A) has 4 points, (B) has 3 points, (C) has 2
points and (D) has 1 point. On the other hand, to score the negatively cued
items, the response A, B, C and D has the points 1, 2, 3 and 4 respectively.
Validation of the Instruments
The instruments MCTAT and MCTIS were validated by experts in
mathematics education and measurement and evaluation. The validation of
MCTAT took the following procedure: The table of specification was face
validated by two experts from measurement and evaluation and two from
mathematics education at the University of Nigeria, Nsukka. The content
validation of MCTAT was accomplished by making sure that the test items
reflected the specification on the test blueprint. These experts were requested to
judge the suitability of the test items, check plausibility of the distractors, choice
of appropriate alternatives for the multiple choice questions, language level and
clarity of the items. Their comments were used to produce the final instrument
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which contains 20 test items (see appendix C). Two experts also validated the
lesson plans.
The MCTIS was validated by two experts from measurement and
evaluation and mathematics education respectively. They were requested to
validate the instrument based on clarity of the statement, language level of the
statement and appropriateness of the statements. After validation of MCTIS,
only 20 items of the interest scale remained to be used for the study (see
appendix D)
Reliability of the Instruments
The researcher used two intact classes of J.S.I. students from a school in
Nsukka Local Government Area to trial test the instruments MCTAT and
MCTIS. The school was not part of the experimental school. The trial testing
enabled the researcher to determine the actual time for the test. In other words,
the time taken by the first and last subjects to complete the test during the trial
testing were recorded and averaged. The scores obtained from trial testing were
used to determine the internal consistency of MCTAT using Kuder Richardson
formula 20 (K-R20). This fomular was used because the test items were of
different difficulty index. The internal consistency reliability coefficient of
MCTAT was 0.81 (see appendix K for computation).
The data collected from trial testing were used to determine the internal
consistency of MCTIS using Cronback Alpha ( ). The formula was used
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because the items were not dichotomously scored. The reliability coefficient
was found to be 0.88 (see appendix L for computation).
Experimental Procedure
The researcher trained the regular graduate mathematics education
teachers in each of the four (4) schools used for the study as research assistants.
The training was of two different sessions – one for the treatment group and the
other for the control group.
Control of Extraneous Variables
To avoid experimenter’s bias, the students were taught by their regular
mathematics teachers. The researcher will not be personally involved in
administering the research conditions.
Teacher Variables
In order to control this variable and enhance a uniform standard in
conducting of the treatment, the researcher prepared lesson plans covering the
unit of study for the teachers that will participate in the study. The teachers were
trained for one week, during which the lesson plans and research conditions
were discussed.
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Training of Teachers
The objectives of the training were to enable the teachers acquire the
competencies for implementing the experimental conditions. The researcher
trained them on the procedures of mind map for the experimental group and the
use of conventional method for the control group, review of lesson plans
prepared by the researcher, familiarization with the content and activities of
students in learning the unit of instruction.
Method of Data Analysis
The data collected were analysed as follows: Research questions were
answered using mean and standard deviation. Hypotheses were tested using
analysis of covariance (ANOCVA) at P <. 05 using pretest as covariate.
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CHAPTER FOUR
RESULTS
The results of the study are organized in accordance with the research
questions and hypotheses of the study.
Research Question 1
What are the mean achievement scores of students taught measures of
central tendency using mind maps method and those taught with conventional
method?
Table 5: The Mean and Standard Deviation scores in Measures of Central
Tendency Achievement Test (MCTAT) of Subjects in the
Experimental and Control Groups
Group
No of
Subject
Pre MCTAT Post MCTAT
Mean SD Mean SD
Control Group 170 18.14 10.28 42.74 10.55
Experimental
Group
180 17.35 10.21 63.61 15.86
Table 5 shows that the mean achievement score of the control group in
the pre MCTAT was 18.14 with standard deviation of 10.28 while that of the
experimental group was 17.35 with standard deviation of 10.21. In the post
MCTAT, the mean achievement score for the control group was 42.74 with
standard deviation of 10.55 while the mean for the experimental group was
63.61 and standard deviation of 15.86.
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Hypothesis 1
H01: There is no significant difference in the mean achievement scores of
students taught central tendency using mind maps and those taught using
conventional method
Table 6: Analysis of Covariance (ANCOVA) of Students Scores in
Measures of Central Tendency Achievement Test (MCTAT)
Source of
Variation
Sum of
Squares
DF Mean
Square
F Significance
of F
Decision
at .05 level
Pre-tests 966.626 1 966.626 5.316 .022 S
Main Effects 36774.212 2 18387.106 101.117 .000 S
Method 36658.162 1 36658.162 201.596 .000 S
Gender 19.873 1 19.873 .109 .741 NS
Method x Gender 84.321 1 84.321 .464 .496 NS
Explained 39222.591 4 9805.648 53.925 .000 S
Residual 62734.624 345 181.839
Total 101957.214 349 292.141
S = Significant at .05 level.
NS = Not Significant at .05 level.
The results in table 6 indicate that teaching method as a main effect on
students achievement in measures of central tendency is significant. This is
because the probability value of .000 at which this main effect is shown to be
significant is lower than the value of .05 at which its is being tested. Thus, the
null hypothesis of no statistically significant effect is rejected at .05 level of
significance.
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Research Question 2
What are the mean achievement scores of male and female students
taught measures of central tendency with mind maps?
Table 7: The Mean Achievement Scores and Standard Deviation of Male
and Female Subjects
Group
Type of Test
Male Female
Mean
SD
Mean
SD
Control
Group
Pre MCTAT
Post MCTAT
18.45
43.12
9.29
10.63
17.83
42.41
9.18
10.48
Experimental
Group
Pre MCTAT
Post MCTAT
17.64
54.30
9.11
17.99
17.06
52.85
9.09
16.41
Table 7 shows that the mean pre MCTAT score of male subjects in the
experimental group is 17.64 with standard deviation of 9.11 while that of the
female is 17.06 and 9.09 respectively. The male subjects in the experimental
group obtained a higher mean achievement score of 54.30 with standard
deviation of 17.99 in the post MCTAT compared with their female counterparts
in the experimental group with a mean achievement score of 52.85 and standard
deviation of 16.41.
Hypotheses 2
H02: There is no significant difference in the mean achievement scores of male
and female students in central tendency.
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Results from table 6 reveal that gender as a main effect on students’
achievement in measures of central tendency is not significant. This is because
the probability value of .741 at which this main effect is shown to be significant
is higher than the level of .05 at which it is being tested. This implies that no
significant difference exists in the mean achievement scores of male and female
subjects due to the mind map teaching strategy.
Hypothesis 3
H03: There is no significant interaction effect of method and gender on the
mean achievement of students in measures of central tendency.
Results from table 6 show that the interaction effects of method and
gender on students’ mean achievement score in measures of central tendency is
not significant. This is because the probability value of .496 at which the
interaction effect of teaching method and gender on students’ achievement score
in central tendency is shown to be significant is higher than the level of .05 at
which it is being tested. This implies that there is no significant interaction
between mind map and gender on students’ achievement in measures of central
tendency.
Research Question 3
What are the mean interest scores of students taught central tendency
with mind maps and those taught with conventional method?
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Table 8: The Mean Interest Scores and Standard Deviation of Measures of
Central Tendency Interest Scale (MCTIS) Scores of Subjects
Group
No of
Subject
Pre MCTIS Post MCTIS
Mean SD Mean SD
Control Group 170 43.59 4.21 47.44 4.61
Experimental
Group
180 43.37 4.07 52.68 4.85
In table 8, the mean interest score of the control group in the pre MCTIS
was 43.59 with standard deviation of 4.21 while that of the experimental group
was 43.37 with standard deviation of 4.07. In the post MCTIS, the mean interest
score of 52.68 with a standard deviation of 4.85 in the experimental group was
higher than that of the control group which had a mean interest score of 47.44
with a standard deviation of 4.61.
Hypothesis 4
HO4: There is no significant difference in the mean interests scores of students
in central tendency when taught with mind maps and those taught with
conventional method.
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Table 9: Analysis of Covariance (ANCOVA) of Students’ Score in
Measures of Central Tendency Interest Scale (MCTIS)
Source of
Variation
Sum of
Squares
DF Mean
Square
F Significance
of F
Decision at
.05 level
Pre-tests
76.576
1
76.576
3.485
.063
NS
Main Effects 2168.563 2 1084.281 49.343 .000 S
Method 2165.092 1 2165,092 98.528 .000 S
Gender 14.439 1 14.439 .657 .418 NS
Method x Gender 140.679 1 140.679 6.402 .012 S
Explained 2632.787 4 658.197 29.953 ,000 S
Residual 7581.167 345 21.974
Total 10213.954 349 29.266
S = Significant at .05 level.
NS = Not significant at .05 level.
The results in table 9 show that teaching method as a main effect on
students’ interest in measures of central tendency is significant. This is because
the probability value of .000 at which this main effect is shown to be significant
is lower than the level of .05 at which it is being tested. Thus, the null
hypothesis of no statistically significant effect is rejected at .05 level of
significance.
Research Question 4
What is the influence of gender on the mean interest scores of students in
central tendency when taught with mind map?
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Table 10: The Mean Interest Scores and Standard Deviation of Male and
Female subjects Taught with Mind Map Strategy
Group
Type of Test Male Female
Mean SD Mean SD
Control Group Pre MCTIS
Post MCTIS
43.20
47.60
4.10
5.02
43.96
48.23
4.31
4.20
Experimental Group Pre MCTIS
Post MCTIS
43.09
49.93
4.02
6.08
43.64
50.29
4.11
4.86
Table 10 shows the mean pre MCTIS score of 43.64 and standard
deviation of 4.11 for female subjects in the experimental group while the mean
and standard deviation scores of their male experimental group counterparts
were 43.09 and 4.02 respectively. In the post MCTIS, the mean interest score of
50.29 and a standard deviation of 4.68 for female subjects in the experimental
group is higher than that of their male experimental group counterparts who had
a mean interest score of 49.93 and standard deviation of 6.08.
Hypothesis 5
HO5: There is no significant difference in the mean interest scores of male and
female students in central tendency.
The results in table 9 show that gender as a main effect on students’
interest in central tendency is not significant. This is because the probability
value of .418 at which this main effect is shown to be significant is higher than
the level of .05 at which it is being tested. Hence the null hypothesis which
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states that gender does not statistically effect students’ mean interest score in
central tendency is accepted.
Hypothesis 6
HO6: There is no significant interaction effect of method and gender on the
mean interest of students in measures of central tendency.
The results in table 9 show that the interaction effect of teaching methods
and gender on students’ mean interest score in central tendency is significant.
This is because the probability value of .012 at which the interaction effect of
mind map instructional strategy and gender on interest in central tendency is
shown to be significant is lower than the level of .05 at which it is being tested.
Summary of Findings
The analyses of data revealed the following:
1. Mind map instructional strategy has statistically significant effect on
students’ achievement in central tendency
2. Gender had no statistically significant effect on students’
achievements when taught with mind map.
3. The interaction effect of teaching strategy and gender on students’
achievement in central tendency is not statistically significant. This
implies that mind map strategy is found viable in teaching
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mathematics and can be used for teaching both male and female
students.
4. The effect of mind map on students’ interest in measures of central
tendency is significant.
5. Gender does not significantly influence students’ interest when taught
with mind maps.
6. The interaction effect of teaching strategy and gender on students’
interest in central tendency is statistically significant.
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CHAPTER FIVE
DISCUSSION, CONCLUSION, RECOMMENDATIONS AND
SUMMARY
This chapter consists of the discussion, conclusion and implications of the
findings of the study. The recommendations, limitations and suggestions for
further research have also been made.
Discussion of Findings
The findings of this study revealed that mind map teaching strategy had
significant effect on students’ achievement in measures of central tendency. The
experimental group had higher mean achievement score (63.61) than their
control group counterpart (42.74) as shown in table 5. Results in table 6 further
confirmed this finding by indicating statistically significant effect of mind map
on students’ achievement in measures of central tendency. The observed
probability value of .000 which was significant at .05 level of significance
testifies to the result. This implies that the efficacy of mind map teaching
strategy is higher and more positive in enhancing and facilitating students’
achievement in measures of central tendency than the conventional method.
The finding of this study is in agreement with (Buzan, 1991; Kennedy,
1999; Hugh, 2003 and Philip 2006) which states that mind map teaching
strategy enhanced better achievement in the learners. However, the researcher’s
findings disagree with the findings of Presley, Vanetten, Yokoi, Freebern and
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VanMeter (1998) that learners tended to learn far better by focusing on the
content of learning material rather than worrying over any particular method.
In spite of this controversy, it is obvious from the findings of the present
study that the mind map teaching strategy is more efficacious than the
conventional method in enhancing students’ achievement in measures of central
tendency in mathematics. This could be attributed to the fact that the mind map
instructional strategy is child-centered and activity-based as against the teacher-
centered nature.
The results presented revealed that male students had higher mean
achievement score of 54.30 than their female counterparts with mean score of
52.85 as shown in table 7. This was further confirmed by the result in table 6
where gender had no statistically significant effect on students’ achievement in
central tendency. Although this finding is in contrast to that of Agwagah (1993)
and Kurumeh (2004) it is however in agreement with that of Akintola and
Popoola (2004) that gender have no significant effect on students’ performance
in mathematics. In other words, for enhanced achievement in mathematics
emphasis should be on teaching strategy and not on gender. This is very crucial
since all categories of students are expected to benefit from this teaching
strategy. In support of this finding Aiyedum (2000) states that cognitive power
necessary for mathematical ability correlates with general intelligence and not
on any particular sex. Results in table 6 further confirm this finding by
indicating the non presence of statistically significant interaction effect between
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the two variables (method and gender) on achievement in central tendency. The
observed probability value of .496 which was not significant at .05 level of
significance, affirms such a result. In other words, results of this study have
shown that students’ performance in central tendency is not necessarily a
function of teaching strategy and gender interaction effect. The findings of this
study have also provided evidence that students’ performance in central
tendency is dependent on teaching strategy irrespective of sex.
The finding of this study also revealed that the experimental group
enhanced greater and higher interest (52.44) as in table 8. This implies that the
students taught with mind map teaching strategy developed more interest than
their control group counterparts. This was further confirmed by the results in
table 9 where interest as a main effect indicated a probability value of .000 at
.05 level of significance. This implies that interest is a significant factor in
students’ achievement in measures of central tendency.
This result is in line with the findings of Hemmerich, Lim and Neel
(1994) who found that students not only developed an awareness of the
knowledge organization they had, but also an awareness of missing links
between isolated concepts they knew were belonging to the map topics as they
are in small groups construct mind map. Thus, students who were not good in
mathematics benefited from their group members. It engineered and stimulated
their interest thereby evoking greater understanding and higher achievement in
measure of central tendency. The reason for this highly generated interest could
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be as a result of active participation of the students, co-operative learning and
self correction. This type of lesson leads to creativity. This erased the
abstractness and monotony normally experienced in a mathematics classroom
setting. In other words, the students’ activity-based approach in the teaching of
mathematic are more likely to improve their interest in the subject than those
taught with the conventional approach. The adoption of this mode of teaching
in schools will no doubt develop in the students’ necessary skills and
enthusiasm for realizing enhanced achievement in mathematics and other
related science subjects.
A closer look at the results of this study in table 10 reveal that male and
female students obtained almost equal mean interest scores of 49.93 and 50.29
respectively in mathematics. This finding was further confirmed by the data in
table 9 which show that gender as a main effect has no significant effect on
students’ interest in mathematics. The observed probability value of .418 which
is not significant at .05 level of significance testifies to the result. This implies
that a student with higher achievement may not necessarily possess a higher
level of interest in mathematics. This finding is not in agreement with Agwagah,
(1993) that there is a strong relationship between genders and interest in school
subjects. Hence, irrespective of one’s gender there is need for fundamental
knowledge of the subject matter.
However, there was a significant interaction effect between the interest of
students and gender. The observed probability value of .012 in table 9 which is
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lower than the .05 significance level testifies to this result. Thus, students’
interest in mathematics has been boosted on account of the mind map teaching
strategy than the conventional group.
Conclusions from the Study
Based on the findings and discussion of this study, the following
conclusions were made:
1. The mind map teaching strategy stimulated and fostered students’
achievement and interest more positively than the conventional
method used in teaching their counterparts measures of central
tendency.
2. Gender does not have influence on mind map teaching strategy as
regards achievement and interest in measures of central tendency.
3. There is no significant interaction effect between teaching method and
gender on achievement in measures of central tendency.
4. There is significant interaction effect between method and gender on
students’ interest in measures of central tendency.
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Educational Implications of the Findings
The findings of this study have some important educational implications.
These implications as they relate to the teachers, students, policy makers and
textbooks authors are highlighted below.
The fact that mind map teaching strategy is a new innovation, it implies
that teachers will be exposed to variety of strategies to make use of during their
lessons. Since mind map is activity oriented it suggest that as students engage in
creating mind map, their interest could be aroused and sustained. Their
involvement in creating mind map could also evoke greater understanding and
higher achievement in measures of central tendency.
The non presence of significant interaction effect between teaching
method and gender implies that mind map teaching strategy could be used
effectively in teaching both male and female students. The use of mind map
could furnish textbook writers, ministry of education, National Mathematical
Centre (NMC) Abuja, faculty of education and various institutions involved in
training of teachers with additional information and variety in the manner of
presenting the mathematical material. The implication in that there could be
improvement in mathematics methodology in our schools which in turn could
enhance achievement in the subject.
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Recommendations
Based on the findings of this study, the researcher made the following
recommendations.
1. Teachers should adapt mind map teaching strategy in our school
system. However, mind map will help to make mathematics gain
popularity, capture the interest of the learners and challenge their
intellect and make the content more interesting in terms of basic
instructional approaches.
2. Government should make provision for in service training of theirs
teachers. This will help to enhance their competence especially in the
choice and use of the various teaching strategies.
3. Since mind map strategy is a new innovation in teaching learning
process, the federal government, the National Mathematical Centre
(NMC) Abuja and relevant professional bodies should include it as
one of their topics to be discussed during workshops organized for
teachers and professionals. Such innovations will help to make the
lessons more stimulating and interesting to the learner.
4. Authors of mathematics textbooks should write their texts to be child
centered and activity oriented as in mind map. This will help to
generate interest in learning of mathematics, which is said to be “the
key of all sciences”.
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Limitations of the Study
1. In spite of the use of some control measures, subject interaction may
have been possible since the two groups of students (male and female)
were both in the same school. This interaction may have likely
affected the results of the study.
2. Complete randomization was not possible because of the use of intact
classes. This may have affected the results of this study.
3. The regular mathematics teachers used as research assistants for the
study were considered in terms of qualification. Other factors such as
personality, tribe, age and classroom environment could also have
affected the results of the study.
4. The use of same achievement test for both pretest and posttest without
disguise may have affected the result of the study.
Suggestions for Further Research
Based on the scope, findings and limitations of the study, the following
suggestions for further studies are made.
1. This study can be replicated.
2. Parallel study could be conducted which would include other topics in
mathematics such as construction, graph, bearing and longitude and
latitude.
3. Effects of mind maps teaching strategy on variables other than
achievement and interest can be explored.
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Summary of the Study
There is a growing concern in Nigeria over the decline in students
performance in mathematics especially at the secondary school level of
education. This situation calls for immediate attention. Research efforts have
revealed that the persistent poor achievement and low interest of students in
mathematics and other science subjects emanate from the inappropriate teaching
strategies adopted by the teachers besides other factors. It has been suggested
that the inappropriate strategies if addressed, will go a long way to improving
students’ achievement and interest in the school subjects. This study however
revealed that mind map has been found to be an effective strategy in enhancing
students interest and achievement.
The design used for the study was the non-equivalent control group
Quasi-experimental design A total of 350 JSI students randomly drawn from
four (4) schools in Nsukka Education Zone were used for the study. In each of
the four purposively sampled schools, two intact classes were randomly drawn
from each of the four schools. Four intact classes were assigned to experimental
group while the remaining four intact classes were assigned to control group. In
each of the sampled schools, one experimental teacher taught both the
experimental and control groups of students. The students in both groups were
pre and post tested. Measures were taken to control possible extraneous variable
capable of affecting the validity of the study.
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To ascertain the interaction effect of teaching methods and gender on the
learner’s interest and achievement in measures of central tendency, four (4)
research questions were formulated and six (6 ) hypotheses tested at .05 level of
significance.
Two instruments namely, the Measures of Central Tendency
Achievement Test (MCTAT) and Measures of Central Tendency Interest Scale
(MCTIS) were developed and used for the study. Reliability coefficient of 0.81
was established for MCTAT while internal consistency reliability of 0.88 were
established for the MCTIS.
The data generated from the study were analyzed using a 2-way analysis
of covariance technique (teaching method X gender) in which the pre-treatment
scores of the two dependent variables examined in the study served as
covariates. The result showed that:
1. Teaching methods have statistically significant effect on studeents’
achievement in measures of central tendency.
2. Gender does not have statistically significant effect on students’
achievement in measures of central tendency.
3. There is no significant interaction effect between teaching methods
and gender on students’ achievement in measures of central tendency.
4. Teaching methods have significant effect on students’ interest in
measures of central tendency.
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5. Gender does not have significant effect on students’ interest in
measures of central tendency.
6. There is significant interaction effect between teaching methods and
gender on students’ interest in measures of central tendency. The
researcher strongly recommended that mind map teaching strategy be
adopted in our school system. Teachers be trained on the importance
and effective use of this strategy. Replication of the study was
suggested.
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APPENDIX A1
FIGURE SHOWING, MIND MAP ON MEAN
CHILDREN SHARE
DIVIDE SUM BY NUMBER
MEAN
SHARING
LOVE IN
SUM THE NUMBERS
CALLED AVERAGE
STUDENTS SHARE
IN THE SCHOOL
IN THE FAMILY
HALF-WAY
SYMBOLIZED X
ADDING NUMBERS IS X
n
xX
90
90
APPENDIX A2
MIND MAP SHOWING MEDIAN
MEDIAN
ONE NUMBER
TRUE FOR ODD
FOR EVEN NUMBERS
PICK TWO NUMBERS
DIVIDE BY TWO
THE MIDDLE NUMBER
ARRANGE IN ORDER
ASCENDING OR
DESCENDING
MEDIAN
CENTRE
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APPENDIX A3
MIND MAP SHOWING MODE
HIGHEST FREQUENCY
MODE
OCCURS MOST
MATHEMATICIANS
MOST RESPECTED
APPEAR MOST
TWO NUMBERS
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92
APPENDIX B
LIST OF SCHOOLS USED FOR THE STUDY
School A: S.T.C. Nsukka
School B: Q.R.S.S Nsukka
School C: Model Secondary School Nsukka
School D: C. S.S. Umabor
School E: C.S.S. Eha Ndiagu.
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APPENDIX C
MEASURES OF CENTRAL TENDENCY
ACHIEVEMENT TEST (MCTAT) FOR JS I STUDENTS
Name: ……………………………….. Male: …………………………...
School: ……………………………… Female: ………………………..
Time: 11/2hours
Instruction: Answer all questions. Identify the correct option lettered A-D for
each question
1. What position is an average in a set of data?
A. Middle B. First C. Last D. Odd
2. The number that is connected with highest frequency occurrence is?
A. Mode B. Mean C. Median D. frequency.
3. Name the average that is shown by putting the data in a frequency table
form.
A. Median B. Mean C. Frequency D. Mode
4. What is the general name representing set of scores in a given data?
A. Mode B. Average C. Mean D. Median
5. Calculate the mean of the set of numbers 2,10,1,5,7.
A. 3 B. 5 C. 4 D. 2
6. What is the mean of 3,6,4,5,7?
A. 5 B. 15C. 10 D. 8
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94
7. Three students scored 58, 67 and 55 in a mathematics test. Find the mean
score. A. 67 B. 58 C. 60 D. 55.
8. The costs of items bought from a super market were N33.50, N7.48,
N16.72, N40.56, N20.44 and N15.70. Find the mean cost of items.
A. N20.4 B. N21.5 C. N22.4 D N30.5
9. Find the median of 5,5,6,3,11,7,2.
A. 3 B. 9 C. 11 D. 5
10. Find the median of the ages of 9 students given as 17, 13, 12, 25, 19, 22,
27, 15, 12.
A. 17, B. 19 C. 25 D. 22.
11. Find the median of: 268, 372, 157, 749, 630, 492, 222.
A. 740 B. 372 C. 157 D. 630
12. Find the median of 4.33, 4.34, 6.72 D. 3.86, 4.50, 4.93, 5.06, 3.11.
A. 3.86 B. 4.50, C. 6.72, D. 4.42.
Find the mode of the following numbers:
13. 4.5, 4.8, 4.8, 4.9, 5.3, 5.3, 5.3.
A. 4.8 B. 4.9 C. 5.3 D. 4.5
14. 15,18,14,15,13,15,10,11
A. 15 B. 14 C. 13 D. 10
15. 380, 70
0, 61
0, 42
0, 610, 75
0.
A. 700 B. 61
0 C. 42
0 D. 75
0.
95
95
The staff attendance per week in classes in a certain school is shown
below
Class 1 2 3 4 5
No. of teachers 23 31 15 12 9
16. Which Class had the highest staff attendance per week?
A. 31 B. 5 C. 9 D. 2
17. What is the total number of teachers that attended classes per a week?
A. 90 B. 15 C. 31 D. 5
Score 6 7 8 9 10 11
Frequency 2 1 2 3 2 5
The table above represents the score of students in mathematics class.
18. Find the mean
A. 8.5 B. 7 C. 8.16 D. 15
19. Find the median
A. 7 B. 9 C. 15 D. 11
20. Find the mode
A. 11 B. 7 C. 5 D. 3
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96
APPENDIX C1
SCORING GUIDE FOR 20 ITEMS IN MCTAT
1. A Middle
2. A Mode
3. D Mode
4. B Average
5. B 5
6. A 5
7. C 60
8. C N22.4
9. D 5
10. A 17
11. B 372
12. D 4.42
13. C 5.3
14. A 15
15. B 61
16. D 2
17. A 90
18. C 8.16
19. B 9
20. A 11
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APPENDIX D
MEASURES OF CENTRAL TENDENCY
INTEREST SCALE (MCTIS) FOR J.S. 1 STUDENTS
Name of Student: …………………………… Male: ……………………..
Name of School: ……………………………. Female: …………………..
Time: 11/2 hours
Instruction:
Read the statements carefully and tick against each number the point that
expresses your feeling about the topic. The 4 points scale are: (A) Strongly
Agree (B) Agree (C) Disagree (D) Strongly Disagree
Now complete the following
S/N Questions SA A D SD
1. Solving problems in measures of central tendency is good
2. I will avoid questions on mean, median and mode during
examination
3. I spend my free time solving problems on mean, median
and mode
4. I spend my time talking and sleeping during lessons on
measures of central tendency.
5. I like doing assignment on mean, median and mode
6. Doing assignment on mean, median and mode is interesting
7. I do not ask questions during measures of central tendency
lesson.
8. I like answering questions during measures of central
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98
tendency lesson.
9. I like participating in workshops on measures of central
tendency.
10. I hate discussing problems on measures of central tendency
11. I am happy whenever I solve problems on measures of
central tendency.
12. I am always late for lessons whenever we are solving
problems on measures of central tendency
13. I am always happy when ever I see the mathematics
teacher that taught me mean, median and mode
14. I hate the teacher that taught me mean, median and mode
15. I always do corrections to the home work I failed in
measures of central tendency
16. When I fail questions on mean, median and mode, I make
no effort to get it
17. Solving problems on measures of central tendency makes
me to think creatively.
18. Solving problems on measures of central tendency makes
me dull.
19. I encourage other students to study topics on mean, median
and mode.
20. I do not enjoy the type of mathematics taught in measures
of central tendency.
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99
APPENDIX E
DAY 1
LESSON NOTE FOR EXPERIMENTAL GROUP
Subject: Mathematics
Class: J.S.I
Average Age: 12 years
Duration: 40 minutes
Topic: How to find the mean, (a measure of central tendency).
Instructional Objectives: At the end of the lesson, the students should be able
to:
(i) List the three measures of averages
(ii) Calculate the mean of a given set of numbers
Instructional Materials: New general and MAN mathematics for J.S.I., Mind
map showing the mean, marker of different colours.
Entry Behaviour: Students are expected to be able to add and divide numbers.
Entry Behaviour Test: Add 2, 5 and 3 oranges and divide the sum between the
class prefect and the assistant prefect. What is each person’s share?
100
100
Instructional procedure
Content
Development
Teacher’s Activities Student’s Activities Instructional
Strategy
Set Induction The teacher divides the
students into groups.
The teacher explains
that when we have a
set of examination test
scores, 16, 12, 6, 18, 8,
we can find a single
value that could be
used to stand for all
the scores. The teacher
provides opportunity
for them to discuss
among themselves.
The teacher asks them
to give the single or
representative value
for scores. The teacher
guides them to
discover the answer
Students discuss among
themselves in their
different groups. The
students also give the
representative value for
scores as the average
Explanation
Meaning of
mean
The teacher asks them
what the measure of
averages is. The
teacher again asks
them to obtain the ages
of their group
members. Find the
They give the answer,
mean, median and mode.
Students find the ages of
their group members. Add
their ages and divide by
the number of students in
their groups respectively.
Questioning,
Problem
solving,
discovery,
approach
101
101
sum of their ages.
Then divide this sum
by the total number of
students in their group.
What is the answer?
What is this type of
average called? How
did you get it? The
teacher gives the
formula, n
xX
. The
teacher lists scores in
their mathematics test
as; 3,5,6,6,5,8,7,2,8.
Write down the
numbers and how
many times each of
them occur. The
teacher asks them the
meaning of frequency.
They give the type of
average as mean.
Sum of numbers in the set
number in the set (n)
The students write the
numbers and the number
of times each number
occurs. That is,
X 2 3 5 6 7 8
F 1 1 2 3 1 2
Students answer that
frequency is the number of
times a number occurs.
Mind
mapping on
mean
Ask students to write
the main idea (mean)
in the centre of their
papers for each group.
List the ideas
associated with the
mean. Use the ideas to
form branches with the
use of markers. The
Listen and ask questions.
They begin with mean at
the centre; with marker
they use the ideas
associated with the mean
to form branches. Students
compare their mind maps
with the mind map on
mean presented by the
Explanation,
guided
discovery.
102
102
teacher show the
students the validated
map on mean (see
appendix A1)
teacher.
Evaluation Calculate the mean of
the following sets of
numbers.
(a) 1,8,6,8,7
(b) N60, N70, N70,
N90 and N120. Goes
round to supervise and
mark their books
Student solve the
questions given by the
teacher
Questioning
103
103
APPENDIX F
DAY 2
LESSON NOTE FOR EXPERIMENTAL GROUP
Subject: Mathematics
Class: J.S.I
Average Age: 12years
Duration: 40 minutes
Topic: Median and mode
Instructional Objectives: At the end of the lesson, the students should be able
to:
(i) Obtain the median of a given set of numbers.
(ii) Obtain the mode of a given set of numbers.
Instructional Materials: New general and MAN Mathematics for J.S.I.,
Marker of different colours, mind map on median and mode
Entry Behaviour: Students are expected to be able to identify the middle of
something; the most frequent occurring observation.
Entry Behaviour Test: Who is sitting at the middle in the first, second, third
rows and so on? Which teacher teaches you most often?
104
104
Content
Development
Teacher’s Activities Student’s Activities Instructional
Strategy
Set Induction The teacher divides
students into groups. Asks
them to arrange their ages
in ascending order. What
is the middle age in the
different groups? Which
age appeared most often?
What are they called?
Students elicit their ages
and arrange them in
ascending order. They say
the middle and the most
occurred ages. They give
the name as median and
mode respectively.
Explanation
and
questioning
Meaning of
median and
mode
The teacher tells them to
count the arranged ages
and indicate groups
whose ages are odd or
even. For the group age
that is even, take the two
middle numbers add them
and divide by two. The
teacher explains that
median is the middle
number when the
numbers are arranged and
when there are two
numbers at the middle,
one should add them and
divide by two (average).
The teacher also asks
them to say which age
They indicate in their
groups, odd and even
numbers. Students add the
two middle numbers, two
middle numbers, divide by
two and give the answer
listen and ask questions.
They say the ages that
occurred most in their
various groups.
The students prepare
frequency table on their
books. That is
X 1 2 3 4 5
F 2 3 2 1 1
Questioning
Deductive
and inductive
reasoning
Guided
discovery
Use of
examples
105
105
appeared most in their
groups?
The teacher gives the
students the score of 9
students in a test as
follows; 2,1,1,2,2,5,3,4,3
asks them to prepare a
frequency table, tells
them to find the median
and the mode.
Median = 2
Mode = 2
Mind Maps
on Median
and Mode
Ask students to start at the
centre of their papers.
Write the topic (Median)
at the centre and use ideas
related to the topic to
make branches. Again
write (Mode) at the centre
and use related ideas to
make branches. Then
presents the validated
Mind maps (see Appendix
A2 and A3).
Listen to the teacher, draw
their maps and ask
questions for clarity. Then
general discussion in the
class, compare with the
validated mind maps on
median and mode
Problem
solving and
guided
discovery.
Use of
example
Evaluation Ask students to solve the
following from MAN
mathematics for J.S.I Ex
22b No 1
Ex 22b No 2
Goes round to supervise
and mark their work.
Students solve the questions
given by the teacher.
Questioning
106
106
APPENDIX G
DAY 1
LESSON NOTE FOR CONTROL GROUP
Subject: Mathematics
Class: J.S.I
Average Age: 12 years
Duration: 40 minutes
Topic: How to find the mean measure (a measure of central
tendency)
Instructional Objectives: At the end of the lesson, the students should be able
to:
(i) List the three measures of averages
(ii) Calculate the mean of a given set of numbers.
Instructional Materials: New General and MAN Mathematics for J.S.I,
Entry Behaviour: Students are expected to be able to add and divide numbers.
Entry Behaviour Test: Add 2.5 and 3 oranges and divide the sum between the
class prefect and the assistant prefect. What is each person’s
share?
107
107
Instructional Procedure
Content
Development
Teacher’s Activities Student’s Activities Instructional
Strategy
Set Induction The teacher divides the
students into groups.
The teacher explains
that when we have a
set of examination test
scores, 16, 12, 6, 18, 8,
we can find a single
value that could be
used to stand for all
the scores. The teacher
provides opportunity
for them to discuss
among themselves.
The teacher asks them
to give the single or
representative value
for scores. The teacher
guides them to
discover the answer
Students discuss among
themselves in their
different groups. The
students also give the
representative value for
scores as the average
Explanation
Meaning of
mean
The teacher asks them
what the measure of
averages is. The
teacher again asks
them to obtain the ages
of their group
members. Find the
They give the answer,
mean, median and mode.
Students find the ages of
their group members. Add
their ages and divide by
the number of students in
their groups respectively.
Questioning,
Problem
solving,
discovery,
approach
108
108
sum of their ages.
Then divide this sum
by the total number of
students in their group.
What is the answer?
What is this type of
average called? How
did you get it? The
teacher gives the
formula, n
xX
. The
teacher lists scores in
their mathematics test
as; 3,5,6,6,5,8,7,2,8.
Write down the
numbers and how
many times each of
them occur. The
teacher asks them the
meaning of frequency.
They give the type of
average as mean.
Sum of numbers in the set
number in the set (n)
The students write the
numbers and the number
of times each number
occurs. That is,
X 2 3 5 6 7 8
F 1 1 2 3 1 2
Students answer that
frequency is the number of
times a number occurs.
Evaluation Calculate the mean of
the following sets of
numbers.
(a) 1,8,6,8,7
(b) N60, N70, N70,
N90 and N120. Goes
round to supervise and
mark their books
Student solve the
questions given by the
teacher
Questioning
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APPENDIX H
DAY 1
LESSON NOTE FOR CONTROL GROUP
Subject: Mathematics
Class: J.S.I
Average Age: 12 years
Duration: 40 minutes
Topic: How to find the mean measure (a measure of central
tendency)
Instructional Objectives: At the end of the lesson, the students should be able
to:
(i) List the three measures of averages
(ii) Calculate the mean of a given set of numbers.
Instructional Materials: New General and MAN Mathematics for J.S.I,
Entry Behaviour: Students are expected to be able to add and divide numbers.
Entry Behaviour Test: Add 2.5 and 3 oranges and divide the sum between the
class prefect and the assistant prefect. What is each person’s
share?
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Instructional Procedure
Content
Development
Teacher’s Activities Student’s Activities Instructional
Strategy
Set Induction The teacher divides
students into groups. Asks
them to arrange their ages
in ascending order. What
is the middle age in the
different groups? Which
age appeared most often?
What are they called?
Students elicit their ages
and arrange them in
ascending order. They say
the middle and the most
occurred ages. They give
the name as median and
mode respectively.
Explanation
and
questioning
Meaning of
median and
mode
The teacher tells them to
count the arranged ages
and indicate groups
whose ages are odd or
even. For the group age
that is even, take the two
middle numbers add them
and divide by two. The
teacher explains that
median is the middle
number when the
numbers are arranged and
when there are two
numbers at the middle,
one should add them and
divide by two (average).
The teacher also asks
them to say which age
They indicate in their
groups, odd and even
numbers. Students add the
two middle numbers, two
middle numbers, divide by
two and give the answer
listen and ask questions.
They say the ages that
occurred most in their
various groups.
The students prepare
frequency table on their
books. That is
X 1 2 3 4 5
F 2 3 2 1 1
Questioning
Deductive
and inductive
reasoning
Guided
discovery
Use of
examples
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111
appeared most in their
groups?
The teacher gives the
students the score of 9
students in a test as
follows; 2,1,1,2,2,5,3,4,3
asks them to prepare a
frequency table, tells
them to find the median
and the mode.
Median = 2
Mode = 2
Evaluation Ask students to solve the
following from MAN
mathematics for J.S.I Ex
22b No 1
Ex 22b No 2
Goes round to supervise
and mark their work.
Students solve the questions
given by the teacher.
Questioning
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112
APPENDIX I
INITIAL DRAFT OF MEASURES OF CENTRAL TENDENCY
ACHIEVEMENT TEST (MCTAT) FOR J.S.I. STUDENTS
1. What position is an Average in a set of data?
(a) Middle (b) First (c) Last (d) Dodd.
2. Which average is clearly seen when arranging data in order of
magnitude?
(a) Mode (b) Mean (c) Median (d) Average
3. What are the other 3 names of average? (a) Centre, Middle, Mean
(b) Mean, Median, Mode (c) Median, Centre, Mode
4. Are the mean, the mode and the median the same? (a) No (b) Yes
5. Why is 12 the median of the data 16, 12, 6, 18, 8? (a)Smallest No
(b) Highest No (c) Middle No (d) Second No
6. What is the general name representing set of scores in a given data? (a)
Mode (b) Average (c) Mean (d) Median
7. Calculate the mean of the set of numbers 2, 10, 1, 5, 7. (a) 3. (b) 5 (c) 4
(d) 2
8. The mean of 3, 6, 4, 5, 7 can be calculated as what? (a) 5 (b) 15 (c) 10 (d)
8.
9. Three students scored 58, 67 and 55 in a mathematics test. Find the mean
score. (a) 67 (b) 58 (c) 60 (d) 55
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10. The cost of items bought from a super market were N33.50, N 7.48, N
16.72, N4056, N20.44 and N15.70. Find the mean cost of items. (a) N20.
4 (b) N21.5 (c) N22.4 (d) N30.5
11. Find the median of 5, 5, 6, 3, 11, 7, 2. (a) 3 (b) 9 (c) 11 (d) 5.
12. Find the median of the ages of 9 students given as 17, 13, 12, 25, 19, 22,
27, 15, 12. (a) 17 (b) 19 (c) 25 (d) 22
13. The median of 268, 372, 157, 749, 630, 492, 222 is given as: (a) 740 (b)
372 (c) 157 (d) 630
14. Find the median of 4.33, 4.34, 6.72, 3.86, 4.50, 4.93, 5.06, 3.11. (a) 3.86
(b) 4.50 (c) 6.72 (d) 4.42
15. Find the mode of the following numbers: 4.5, 4.8, 4.9, 5.3, 5.3, 5.3. (a)
4.8 (b) 4.9 (c) 5.3 (d) 4.5
16. 15, 18, 14, 15, 10, 11. (a) 15 (b) 14 (c) 13 (d) 10
17. 380, 70
0, 61
0, 42
0, 61
0, 75
0. (a) 70
0 (b)61
0 (c) 42
0 (d) 75
0.
The Staff Attendance per Week in Classes in a Certain School is shown
below
Class 1 2 3 4 5
No of Teachers 23 31 15 12 9
18. Which class had the highest staff attendance per week? (a) 31 (b) 5 (c) 9
(d) 2
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19. What is the total number of teachers that attended classes per a week? (a)
90 (b) 15 (c) 9 (d) 2.
Score 6 7 8 9 10 11
Frequency 2 1 2 3 2 5
The Table above Represents the Score of Students in Mathematics Class
20. Find the mean. (a) 8.5 (b) 7 (c) 8.16 (d) 15
21. Find the median. (a) 7 (b) 9 (c) 15 (d) 11.
22. Find the mode. (a) 11 (b) 7 (c) 5 (d) 3
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APPENDIX J
COMMENTS FROM THE VALIDATORS OF THE RESEARCH
INSTRUMENTS
The instrument validators offered the following comments, corrections
and advice.
(A) Measures of Central Tendency Achievement Test (MCTAT)
Some stems were reformed better understanding by students eg No 6
reads, the mean of 3, 6, 4, 5, 7 can be calculated as what? Reads what
is the mean of 3, 6, 4, 5, 7?
The distractors were to be arranged in such as way that no matter how
the students solve the questions, they must get an answer that is
among the distractors.
Some comments were on grouping questions in higher thinking and
lower order questions in the items.
The instruction formerly read identify the correct option lettered A-D.
For each question write on the answer sheet the letter that bears the
same answer as the option you have chosen. Now it reads identify the
correct option lettered A-D for each question. Understanding.
Some questions were dropped entirely from the initial draft eg 3, 4 and
5.
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116
(B) Measures of Central Tendency Interest Scale (MCTIS)
The validators comment were thus.
Include negative items for a check
Some items were dropped e.g I like to be a maths teacher. Reason was
that the item may not actually indicate interest. I enjoy teaching my
young ones mathematics. Reason the respondent is a student and not a
teacher. Teaching is detested by students. I hope to offer mathematics
in Senior Secondary Classes. The Comment was that students can
offer mathematics not because they are interested but because it is a
compulsory subject.
(c) Lesson Plans
Comment include
The topic in the lesson plan now reads. How to find the mean ( a
measure of central tendency). Instead of Measures of averages, Mean.
The initial lesson plan did not include frequency table to reflect the
items MCTAT.
(D) Table of Specification
To change from higher order and lower order questions to higher thinking
and lower cognitive processes.
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APPENDIX K
COMPUTATION OF THE RELIABILITY OF MCTAT USING K-
R 20
S/N No. of
passes
No. of
failures
Proportion
that passed (p)
Proportion
that failed (q)
p.q
1. 18 2 90 .10 .09
2. 10 10 .50 .50 .25
3. 16 4 .80 .20 .16
4. 17 3 .85 .15 .13
5. 14 6 .70 .30 .21
6. 17 3 .86 .15 .13
7. 12 8 .60 .40 .24
8. 9 11 .45 .55 .25
9. 17 3 .85 .15 .13
10. 18 2 .90 .10 .09
11. 16 4 .80 .20 .16
12. 15 5 .75 .25 .19
13. 12 8 .60 .40 .24
14. 16 4 .80 .20 .24
15. 13 7 .65 .35 .23
16. 14 6 .70 .30 .21
17. 8 12 .40 .60 .24
18. 9 11 .45 .55 .23
19. 11 9 .55 .45 .25
20. 16 4 .80 .20 .16
∑pq = 3.75
2
1
2
1
1119
20
S
pqSR
Where R11 = K – R reliability coefficient
n = the number of items in the test
p= proportion of individuals who passed each item
q= proportion of individuals who failed each item
∑ = summation of
S12 = variance of the total score on the test.
81.0)774.0(05.1
61.16
86.12
19
2011
R
118
118
APPENDIX L
.88.0,84.005.1,16.0105.1,18.92
60.141
19
20,1
1 2
2
1
1
T
n
i V
V
n
n
S/N ITEM NUMBER
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1 4 3 4 3 4 4 1 4 3 1 3 4 2 3 1 2 3 3 2 4 58
2 4 4 4 4 3 3 4 3 3 4 3 3 4 3 4 4 3 3 4 3 70
3 3 3 2 2 3 2 2 3 3 4 3 1 4 1 4 3 2 2 4 1 52
4 3 3 4 3 3 3 4 3 3 3 3 4 3 4 3 3 3 3 3 4 65
5 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 4 4 4 4 4 77
6 2 4 3 3 4 3 2 3 2 4 2 3 3 3 4 1 3 4 4 3 60
7 3 4 3 3 3 4 3 2 3 2 3 1 1 3 2 3 2 3 3 1 50
8 4 3 4 4 4 3 3 4 3 4 3 4 4 3 4 3 4 3 4 4 72
9 3 3 3 2 3 3 2 3 3 2 2 3 3 1 2 2 2 2 2 3 48
10 4 4 4 3 4 1 3 1 3 4 1 3 3 4 4 4 4 4 3 3 64
11 4 4 3 4 3 4 4 4 3 2 4 3 3 4 2 3 4 3 4 3 68
12 1 4 3 1 3 4 1 4 1 3 4 3 3 4 3 3 1 3 3 3 55
13 4 3 4 4 3 3 4 4 4 3 3 4 4 3 4 4 4 4 4 3 74
14 4 4 2 4 3 4 4 2 4 4 4 2 3 3 4 3 4 3 2 4 66
15 3 2 3 2 3 2 2 3 3 2 2 3 2 3 2 2 3 2 3 2 50
16 3 4 3 4 4 4 4 3 3 3 3 3 4 3 3 3 3 4 4 70
17 4 2 2 2 2 4 4 3 4 3 4 3 4 2 4 4 3 4 2 4 63
18 3 3 4 3 3 3 3 2 2 2 2 2 2 3 2 2 2 2 3 2 51
19 2 1 1 1 1 3 4 3 3 4 3 3 4 3 3 3 3 3 4 4 67
20 3 2 2 2 2 3 2 3 2 2 3 3 3 1 3 2 3 3 2 3 49
21 4 4 4 4 4 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 78
22 3 3 3 3 3 2 3 3 3 2 2 3 2 3 3 3 3 3 3 3 55
SD 0.83 .072 0.77 0.92 0.73 0.83 1.04 0.81 0.76 0.93 0.84 0.87 0.86 0.97 0.92 0.84 0.84 0.68 0.81 0.94 X = 61.90
V12 0.68 0.51 0.59 0.85 0.54 0.69 1.09 0.66 0.57 0.86 0.71 0.76 0.75 0.95 0.84 0.71 0.84 0.46 0.66 0.88 SD = 9.60
∑V12
= 14.60 VT2 = 92.18
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119
APPENDIX M
EXPERTS’ VETTING
Department of Science Education,
University of Nigeria,
Nsukka
Dear Prof/Dr/ Mr/Mrs
--------------------------
--------------------------
VETTING AND FACE VALIDATION OF ACHIEVEMENT TEST IN
MATHEMATICS
Kindly help validate these instrument to enable me carry on my research
work. The validation will be of two phases, face and content validation.
(A) Face Validation of:
1. Test Blueprint
2. MCTAT
3. MCTIS
4. Marking guide
(B) Content validation of MCTAT using test blueprint. Criteria for face validation
is based on:
1. Relevance
2. Suitability of the test items
3. Plausibility of distractors
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120
4. Choice of appropriate alternatives for multiple choice questions.
5. Language Level and clarity of the items.
Enclosed Herewith are
(1) MCTAT
(2) MCTIS
(3) Research questions
(4) Research hypotheses
(5) Marking guide
(6) Test blueprint.
Thanks for co-operation.
Yours faithfully,
Onyishi, E.U.
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121
APPENDIX N
APPLICATION FOR PERMISSION
Science Education Department,
University of Nigeria,
Nsukka
16th November, 2007
The Principal,
-----------------------
-----------------------
Sir/Mrs,
PERMISSION TO CARRY OUT AN EXPERIMENT
I hereby request to carry out an experiment with the junior secondary one
(JSI) students in your school.
I am a post graduate student of the University of Nigeria Nsukka Studying
Mathematics Education.
This research work is aimed at improving teaching and learning of
mathematics in our schools. It is purely for research purpose and not for public use.
If permitted, the experiment will last for four weeks.
Thanks for co-operation.
Yours faithfully,
Onyishi, E.U.
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TABLE OF CONTENTS
TITLE PAGE………………………………………………………………………………........…I
APPROVAL PAGE……………………………………………………………………………….II
CERTIFICATION ……………………………………………………………………………....III
DEDICATION …………………………………………………………………………………...IV
ACKNOWLEDGEMENT………………………………………………………………………...V
TABLE OF CONTENTS ………………………………………………………………………..VI
LIST OF TABLES ……………………………………………………………………….........VIII
ABSTRACT ……………………………………………………………………………………...IX
CHAPTER ONE: INTRODUCTION……………………………………..………………………..1
Background of the Study………………………………………………………………………1
Statement of the Problem…………………………………………………………………….10
Purpose of the Study ................................................................................................................ 23
Significance of the Study ......................................................................................................... 23
Scope of the Study ................................................................................................................... 25
Research Questions .................................................................................................................. 25
Research Hypotheses ............................................................................................................... 26
CHAPTER TWO: REVIEW OF LITERATURE ............................................................................ 27
Conceptual Framework ............................................................................................................ 28
Meaning and Uses of Mind Maps ............................................................................................ 28
Other Mathematical Maps, Distinctions and Similarities ........................................................ 32
Distinctions between Concept and Mind Maps ....................................................................... 34
Similarities between Concept and Mind Maps ........................................................................ 35
Teacher Factor and Students’ Achievement in Mathematics .................................................. 35
Interest in Mathematics and Other School Subjects ................................................................ 40
Theoretical Framework ............................................................................................................ 42
Theories underlying the use of Mind Maps in Teaching Mathematics ................................... 42
Empirical Studies ..................................................................................................................... 47
Studies on Interest and Academic Achievement ..................................................................... 49
Studies on Mind Map ............................................................................................................... 50
CHAPTER THREE:RESEARCH METHOD ................................................................................. 53
Research Design ...................................................................................................................... 53
Area of the Study ..................................................................................................................... 54
Population of the Study............................................................................................................ 54
Sample and Sampling Technique ............................................................................................ 54
Instruments for Data Collection ............................................................................................... 56
Validation of the Instruments .................................................................................................. 58
Reliability of the Instruments .................................................................................................. 59
Experimental Procedure ........................................................................................................... 60
Control of Extraneous Variables.............................................................................................. 60
Teacher Variables .................................................................................................................... 60
Training of Teachers ................................................................................................................ 61
Method of Data Analysis ......................................................................................................... 61
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CHAPTER FOUR: RESULTS ........................................................................................................ 62
Summary of Findings............................................................................................................... 69
CHAPTER FIVE: DISCUSSION, CONCLUSION, RECOMMENDATIONS AND SUMMAR..71
Conclusions from the Study ..................................................................................................... 75
Educational Implications of the Findings ................................................................................ 76
Recommendations .................................................................................................................... 77
Limitations of the Study .......................................................................................................... 78
Suggestions for Further Research ............................................................................................ 78
Summary of the Study ............................................................................................................. 79
REFERENCES ................................................................................................................................ 82
APPENDIXES ................................................................................................................................. 89
