EZEH, Sussan Ijeoma PG/ Ph.D/06/40953

EZEH, Sussan Ijeoma

PG/ Ph.D/06/40953

PG/M. Sc/09/51723

EFFECT OF USING COMPUTER AS TUTOR AND TOOL ON

STUDENTS’ ACHIEVEMENT AND RETENTION IN

QUADRATIC EQUATION IN ENUGU STATE,

NIGERIA

SCIENCE EDUCATION

A THESIS SUBMITTED TO THE DEPARTMENT OF SCIENCE EDUCATION, FACULTY

OF EDUCATION, UNIVERSITY OF NIGERIA, NSUKKA

Webmaster

Digitally Signed by Webmaster‟s Name

DN : CN = Webmaster‟s name O= University of Nigeria, Nsukka

OU = Innovation Centre

OCTOBER, 2009

2

EFFECT OF USING COMPUTER AS TUTOR AND TOOL ON STUDENTS’ ACHIEVEMENT AND

RETENTION IN

QUADRATIC EQUATION IN ENUGU STATE,

NIGERIA

BY

EZEH, Sussan Ijeoma

PG/ Ph.D/06/40953

DEPARTMENT OF SCIENCE EDUCATION

UNIVERSITY OF NIGERIA, NSUKKA

SUPERVISOR: DR. K.O. USMAN

OCTOBER 2009.

i

Title Page

EFFECT OF USING COMPUTER AS TUTOR AND TOOL ON STUDENTS‟

ACHIEVEMENT AND RETENTION IN QUADRATIC EQUATION IN

ENUGU STATE, NIGERIA

BY

EZEH, Sussan Ijeoma

PG/ Ph.D/06/40953

A THESIS PRESENTED TO THE DEPARTMENT OF SCIENCE

EDUCATION IN FULFILLMENT OF THE REQUIREMENT

FOR THE AWARD OF DEGREE OF DOCTOR OF

PHILOSOPHY (Ph.D) IN MATHEMATICS

EDUCATION

UNIVERSITY OF NIGERIA, NSUKKA

OCTOBER 2009.

ii

Approval Page

This project has been approved for the Department of Science Education,

University of Nigeria, Nsukka.

By

----------------------------------- -----------------------------------

Dr. Usman K.O Supervisor Internal Examiner

--------------------------------- -----------------------------------

Dr. C. R Nwagbo Head of Department External Examiner

-------------------------------------

Prof. S.A. Ezeudu

Dean of Faculty

iii

Certification

EZEH, SUSSAN IJEOMA, a post graduate student in the Department of

Science Education, with Reg. No PG/Ph.D/06/40953, has satisfactorily

completed the requirements for the award of the degree of Doctor of Philosophy

in Mathematics Education. The work embodied in this thesis is original and has

not been submitted, in part or full, for any other certificate, Diploma or Degree

of this or any other University.

------------------------------------ -----------------------------------

EZEH, SUSSAN IJEOMA DR. USMAN, K.O

(Student) (Supervisor)

iv

Dedication

This work is dedicated to my husband and our five children for their

support, encouragement and understanding.

v

Acknowledgements

The researcher humbly expresses her profound gratitude to the Almighty

God, for His care, guidance, and mercy throughout the period of this work. The

researcher sincerely and earnestly expresses her appreciation to the supervisor,

Dr. K.O. Usman for his unquantifiable assistance, guidance, encouragement and

brotherly care. The researcher owes him more gratitude than can really be

expressed here. The researcher equally acknowledges the contributions,

encouragement and motherly advice of Prof. U.N.V. Agwagah. The researcher

also appreciates the encouragement and support of Prof. D.N. Ezeh, Dr. E.K.

Nwagu, Dr. Okwor and Dr. J.J. Ugwuja.

The researcher‟s special thanks goes to all the principals, teachers,

students, research assistants, cyber cafes and computer operators that were

involved in the course of completing this work. The Almighty God will provide

for you all abundantly.

Finally, the researcher expresses her deep appreciation to her mother,

husband, brothers, sisters, In-laws, children, friends, well wishers and

colleagues for their understanding, contributions, patience and prayers

throughout the duration of this study. May God reward all of you.

EZEH, SUSSAN IJEOMA

PG/ Ph.D/06/40953

viii

List of Tables

Tables Pages

1. An illustration of non-randomized pretest – posttest design………………..56

2. Classes used for the Study -------------------------------------------------------60

3. Mean Achievement Scores and Standard Deviation of Students who were

taught with computer and without computer ------------------------------------64

4. Mean Achievement scores and standard Deviation of students taught with

computer as tutor and as tool-------------------------------------------------------65

5. Mean Achievement Scores and standard Deviation of male and female

students who were taught with computer and without computer -------------67

6. Mean retention scores of students taught with computer and without

computer)----------------------------------------------------------------------------69

7. Mean retention score of students taught with computer as tutor and tool-----70

8. Mean retention scores and standard deviation of male and female students

who were taught with computer as tutor and as tool----------------------------71

9. ANCOVA table of students‟ Scores in the Quadratic Equation Retention

Test (QERT)--------------------------------------------------------------------------72

10 ANCOVA table of students who were taught with computer as tutor and as

tool on achievement)----------------------------------------------------------------73

11 ANCOVA Table of Students‟ Scores on Retention ---------------------------75

12. ANCOVA Table of Students who were taught with Computer as Tutor and

as Tool on Retention----------------------------------------------------------------76

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LIST OF APPENDIX

APPENDIX PAGES

A. Table of specification or Test blue Print………………………………………………..100

B. Lesson Notes…………………………………………………………………………....101

C. Teacher made Acheivement Test for Pretest and Postest………………………...……..126

D. Solution for the TMAT/Marking Scheme……………………………………………....135

E. Teacher made Acheivement Test for Retention………………………………………...136

F. Solution for the TMAT/Marking Scheme………………………………………………144

G. Validators‟ Letter……………………………………………………………………….145

H. Validators‟ Report………………………………………………………………………146

I. Scores for Multiple Choice Test using Kudar Richardson Formulae (K-R 20) to find

Internal Consistency……………………………………………………………………147

J(1). Eight Schools used for the Research…………………………………………………..149

J(2). Schools in Nsukka L.G.A. …………………………………………………………….150

K. To test for stability, Raw score method of Pearson product moment correlation coefficient is

used………………………………………………………………………………………...…….151

L. Options ……………………………………………………………………………………………153

x

Abstract

This study compared the effect of using computer as tutor and as tool on

students‟ achievement and retention in Quadratic Equation. The purpose of the

study was to ascertain the mode of computer usage that is more effective in

enhancing students‟ achievement and retention in quadratic equation. This study

was carried out in Nsukka Education zone of Enugu State. Nsukka Local

Government Area was purposively chosen because of the availability of

computers in schools. A sample of two hundred and seventy one (271) SSII

students was involved in the study. The design of this study was quasi-

experimental research design as there was no randomization of subjects into

classes. Intact classes were used. Six research questions and eight research

hypotheses guided the study. Research questions were answered using mean and

standard deviation while Analysis of Covariance (ANCOVA) was used in

testing the hypotheses at 0.05 level of significant. Results from the study

revealed that students who were taught quadratic equation with computer

achieved and retained higher than those taught without computer. Also students

who were taught quadratic equation with computer as tool achieved and retained

higher than those taught with computer as tutor. The study equally revealed no

significant difference in the mean achievement and retention scores of male and

female students. Some of the recommendations made include; that teachers

should pay more attention to using computer as tool instead of using it as tutor

for effective teaching and learning of mathematics.

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CHAPTER ONE

INTRODUCTION

Background of the Study

Mathematics has all through the years been an important subject both in

the role it plays in everyday activities and in its usefulness to other sciences.

Mathematics is a body of knowledge centred on concepts such as quantity,

structure, space, change and also the academic discipline that studies them

(Pierce, 2007) . Mathematics is further defined by Pierce as the science that

draws necessary conclusions. Other practitioners of mathematics such as

Sowmya (2005), maintains that mathematics is the science of pattern and highly

needed in everyday life. According to Agwagah (2008), mathematics is the

study of topics such as quantity, structure space and change. Carl Friedrich

Gauss known as the “prince of mathematicians” as cited in Wikipedia (2007),

also refers to mathematics as “the Queen of the sciences” and the bedrock of

other sciences. These definitions emphasize the importance of mathematics.

Mathematics is widely used through out the world, in human life and

many fields including Social Sciences, Natural Sciences, Engineering, Medicine

and Education. It is a vital tool in science, commerce and technology.

According to Iji (2007), mathematics provides an important key to

understanding of the world. In the areas of buying and selling, communication,

timing, measurement, moulding, recording among others, the importance is

highly acknowledged. Mathematics is one of the core subjects in both junior and

senior secondary school curricula in Nigeria, which justifies its recognition as

1

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being essential in the development of technological advancement in Nigeria.

The Nigerian Federal Government made mathematics compulsory and one of

the core subjects in both primary and secondary schools because of its

usefulness (Federal Republic of Nigeria, 2004). Some of the roles of

mathematics according to Nurudeen (2007), include: its ability to enhance the

thinking capabilities of individuals by making them to be more creative,

reasonable, rational as well as imaginative. There is no school curriculum or a

national development planning which does not take cognizance of the

usefulness and development in school mathematics.

From the National Curriculum for senior secondary schools, mathematics

is divided into six sections which include: Number and Numeration; Algebraic

processes; mensuration; plane geometry; Trigonometry, statistics and

probability. The focus of this study is on Algebraic processes. This is because

reports have shown that Algebra occupies a major content in school

mathematics and students perform poorly in Algebra (WAEC Chief Examiner

Report, 2004). Algebra is a branch of mathematics of Arabian origin. It is a

generalization and extension of arithmetic in which symbols are employed to

denote operations and letters to represent number and quantity (Wikipedia,

2007). Algebra is an aspect of mathematics that opens students mind to critical

thinking. According to Michael (2002), Algebra is an aspect of mathematics

which every individual must know, as it is a gate way to other areas of

mathematics, yet many students struggle with Algebra and are left behind

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because they find it difficult to understand. It is the importance of Algebra that

makes it to be in almost all the classes in the National Mathematics Curriculum.

Algebra involves solving equations, graphing linear, simultaneous linear and

quadratic equations (Federal Ministry of Education, 2009). These areas have the

potential to open students‟ mind towards different styles of thinking and

understanding. It is good for students to know the basic fundamentals in

Algebra so as to meet up with the challenges of other areas of mathematics.

Wikipedia stated forms of algebraic equations as follows: Linear

equation, Simple and Simultaneous equations, Quadratic Equations, Cubic

Equations and Exponential Equations. Quadratic equation is a major topic in

SSII mathematics curriculum and also appears in West African School

Certificate Examination (WASCE) and National Examination Council of

Nigeria (NECO) Certificate Examinations. According to WAEC Chief

Examiner‟s report (2006), quadratic equation is among the areas students avoid

attempting questions on while those who dare to, perform poorly. The report

further indicated that most candidates ended up completing the table of values

but were not able to plot the correct graph or to read off the roots of the

equation. Some students do not like solving algebraic problems as they look at

algebra as difficult and abstract. According to Adedayo (2001), the problem of

failure at this level has always been attributed to teacher‟s failure to use

appropriate method of teaching and teachers lack of knowledge of technological

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innovations in the society. Hence a better teaching of the concept was

suggested.

Harbor-peter (1999) was of the opinion that poor method of teaching and

lack of basic knowledge are responsible for the observed poor performance of

students in secondary school mathematics. Michael (2002) also noted that poor

textbooks and lack of computer technology in schools are also responsible for

poor performance of students in mathematics. Mansil and Wiln (1998) are of the

opinion that lack of knowledge and unavailability of computers are responsible

for poor performance of students in mathematics. They suggested that teachers

be sent on in-service training and re-training so as to meet up with the

technological challenges in the society and also improve students‟ achievement

in mathematics.

The attempt to take care of poor achievement of students in mathematics

inspired some researchers to use computer technology in the classroom. Such

researchers include Hannafin and Saverge (1993), Adeniyi (1997), Barabara,

Ford and MaryAnn (1998), Mansil and Wiln, (1998), Odogwu (1999) and

Ifeakor (2005). Mansil and Wiln (1998) observed that learners are happier when

they engage in mathematics with a sense of personal accessibility, coalescence

and application rather than just a body of knowledge and skill. Odogwu (1999)

in his own view noted that the computer in teaching creates room for self-

checking and that the visual pictures enhance visualization and sensory

perception. The computer has the property of being patient and does not care

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how often the user makes mistakes. Wikipedia itemized the advantages of using

computers as follows:

Learner Autonomy: This indicates that the learner can work

at his own pace. The learner can spend more time on those

topics that are causing difficulty. Privacy: many learners feel

shy in the classroom for fear of making mistakes and being

the object of ridicule. Feedback: The computer can give

feedback to each individual at the touch of a button. Thus

learners can test their knowledge and learn from their

mistakes; Motivation: The computer motivates learners to

learn; Access to Information: Computer can provide more

information to learners when linked to other sites like

electronic dictionaries, detailed screens and net; Interactivity:

Computers promote interactivity among students. Learners

have to interact with the computer and cannot hide behind

their classmates. This indicates that if the learner does

nothing, nothing happens; and Repetition: The computer gives

room for constant repetition until a concept is mastered

(Wikipedia, 2007;2).

According to Odogwu (1999), a student/learner can continue interacting

with the computer until a concept is mastered. Ede and Aduwa (2007) noted that

the computer is capable of activating the senses of sight, hearing and touch of

the user. This indicates that the computer has the capacity to provide higher

interactive potential for users to develop their individual intellect and creative

abilities.

According to Taylor (1980), and Usman (2002), computer can be used in

teaching mathematics in three ways namely: As tutor, tool and tutee. As a tutor,

the computer acts as tutor by performing a teaching role. The student is tutored

by the computer to increase their skills and knowledge. This application is often

referred to as Computer Based Instruction (CBI), Computer Assisted Instruction

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(CAI) or Computer – Assisted learning (CAL). The general process is as

follows: Presentation of information, students‟ response, evaluation of the

students‟ response by the computer, and determination of what to do next.

According to Timothy, Donald, James and James (2006), Tutorial

applications involve:

(1) Embedded questions where students must take an active role by

answering embedded questions.

(2) Branching: Computer tutorials can automatically branch. That is, adjust

content presentation according to learner‟s responses to the embedded

questions. Remediation or advancement can be built in to meet the needs

of individual learners.

(3) Dynamic presentation: The computer can present information

dynamically, such as by highlighting attention or by depicting processes

using animated graphics. Or employ audio and video.

(4) Record Keeping: Computer tutorials can automatically maintain

students‟ records which informs students of their progress. In addition,

you can check the records to ensure that students are progressing

satisfactorily. In using computer as a tutor, the computer acts as a

teacher; teaching students like a human tutor.

Apart from using computer as a tutor computer could be used as a tool.

According to Gilberte & Hanneborne (2000), in using computer as a tool, the

computer could be used to register the activities of the students in log files, and

xvii

also to explore the possibilities of computer-based materials for differentiation

and individualization. Applying computer as a tool can help develop higher

order thinking, creativity and research skills thereby enhancing learning.

According to Taylor (1980), in using computer as a tool, the computer becomes

an instructional material similar to a pencil, typewriter, microscope, slide rule or

drafting table. With the computer, students can calculate numbers with great

speed and accuracy, especially in algebra, statistics and Geometry. Timothy,

Donald, James and James (2006) noted that computer could be used as a tool for

calculation, conducting research and for data analysis especially the statistical

package for social sciences (SPSS) which provides students more practice in

less time as it removes the burden of computing away from them.

Schwyten (1991) in his own view outlined five processing functions of

the computer when used as a tool. They are: Tools for mathematical

exploration; Tools for developing conceptual fluency: Tools for learning

problem-Solving methods; Tools for integrating different mathematical

representation; and Tools for learning how to learn. In using computer as a tool,

it helps the teacher in teaching and acts as an instructional material.

Computer Algebra Application Software (CAAS) is one of the soft wares

that applies computer as a tool and can demonstrate how computer could be

used as a tool for solving mathematical problems because of its computational

powers. CAAS software can manipulate symbolic expressions or equations, find

exact values for functions or equations and graph functions and also plot

xviii

relations. What many students had to do by hand, students today can use CAAS

software to do the symbolic manipulations (Heid, 1995). In doing so, computer

is used as instructional material.

The use of instructional material according to Obodo (2004) adds

enrichment, broadens the mathematical background of the students and

stimulates curiosity in new ideas. The importance of instructional material in

teaching is numerous. One of which is that it helps the teacher to communicate

ideas; it provides discovery activities for the student. It equally adds reality to

learning. It makes real, abstract concepts. According to Dike (2002),

instructional materials are resources which a class teacher can use in teaching in

order to make the content of his lesson understandable to the learner. The

computer being used as instructional material will enhance students‟

understanding of mathematical concept; keep students busy and active in the

class. It equally stimulates the imagination of students and gives room for

effective retention of mathematics concepts.

In as much as efforts are being made to enhance students‟ achievement

in mathematics, it is equally important to consider students‟ ability to retain

what they have learnt. Retention is remembering what you have learnt after a

period of time (Ogbonna, 2007). Retention is an important variable in learning

especially in mathematics. This is because achievement lasts only when students

are able to retain what they have learnt. A student that learns a concept easily

and forgets will not perform well in mathematics. Inability to remember what

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one has learnt is regarded as a loss of memory. This according to Langer (1997)

is failure to remember the past.

Many researchers have in the past carried out studies on retention in one

field or the other. Some of these are: Iji (2003), Micheal (2002), Madu (2004)

and Ogbonna (2007). They all viewed retention as important in sustenance of

achievement. This is because if a student achieved high in a post test and when

a retention test comes, that student performs poorly, it is an indication that, the

student did not register the concept in the long term memory. It is therefore

necessary to search for a better strategy that will make students retain what they

have learnt in mathematics.

The likely existence of gender disparity in mathematics continues to give,

much concern to researchers, educators and mathematicians within and outside

Nigeria. This is because it is not clear which gender performs better than the

other in mathematics. Some researchers like Alio and Harbor-Peters (2000),

Ezugo and Agwagah (2000) have it that males perform better than females in

mathematics while others like Ezeh (2005) and Ogbonna (2007) found that

females perform better. Etukodo (2002) and Micheal (2002), recorded no

significant difference between male and female students achievement in

mathematics

There seem not to be any agreement yet among researchers on which

group performs better than the other. Since the computer has been recognized as

a machine that does not recognize gender, but only keeps to instruction, it will

xx

be necessary to find out if using the computer as tool and as tutor will record

any gender difference in mathematics achievement.

It is known that people have used computers as tutor and as tool, but it is

pertinent to compare the use of computer as tutor and as tool to see the mode

that is more effective for a better teaching and learning of mathematics.

Statement of the Problem

Poor achievement of students and lack of retention in mathematics is a

known fact and of great concern to educators, researchers and mathematicians.

Researchers are making great effort to see if there will be improvement on

students‟ achievement and retention in mathematics by adopting various

methods of teaching mathematics. Their aim of using various methods is

because poor method of teaching mathematics has been identified as one of the

reasons for poor achievement of students in mathematics. Students equally

perform poorly in quadratic equation. There are problems associated with

solving quadratic equations like unable to find factors, wrong units, incorrect

value of constants, and reading of scales incorrectly and finally the abstract

nature of quadratic equation that brings confusion to quadratic expressions. It is

in an attempt to remedy the situation that made researchers to suggest the use of

methods like- inquiry method, delayed formalization, expository, laboratory and

computer in teaching quadratic equation and other areas of mathematics. The

use of computer in teaching could be as a tutor, tool or tutee. These modes have

xxi

been identified as the various modes of using computer in teaching mathematics

Usman (2002), but the mode that is more effective in teaching and learning of

mathematics especially quadratic equation is yet to be ascertained which calls

for this study.

Researchers have equally used computer both as a tutor and as a tool, but

none has compared the modes to identify the one that is more effective in

teaching and learning of Algebraic processes. Hence this study tries to

investigate the problems:

1. How would the use of computer enhance students‟ achievement and

retention in quadratic equation?

2. How would the use of computer as tutor and tool affect male and

female students‟ achievement and retention in quadratic equation?

Purpose of the Study

The purpose of this study is to compare the effectiveness of computer as

tutor and as tool on male and female students‟ achievement and retention in

quadratic equation. Specifically to:

1. Compare the effectiveness of using computer and not using computer

in learning quadratic equation.

2. Compare the effectiveness of using computer as tutor and as tool in

learning quadratic equation.

xxii

3. Find out the mode that enabled student to retain more of what they

have learnt

4. Ascertain whether the modes have any effect on male and female

students‟ achievement and retention.

Significance of the Study

This study focuses on comparing two modes of using computer in

mathematics instruction: Computer as tutor and as tool. It is hoped that this

study will enable the mathematics teachers identify the mode of computer to use

in teaching students for effective teaching and learning. Apart from adding to

the number of instructional strategies at their disposal, it might make the

teaching of quadratic equation more enjoyable and hence improve achievement.

It will also be useful to programmers and software designers to understand the

appropriate way to programme for effective teaching and learning.

To states and federal ministries of education the results of this study

might provide information with which they can organize seminars, conferences

and workshops for mathematics teachers. Such in-service training programme

will furnish teachers with necessary knowledge on the use of computers for

effective teaching and learning and thus promote the use of technology.

To students, the result of this study will help them use computer software

for a better understanding and achievement in quadratic equation. It will equally

expose them to the various ways of using computer in teaching quadratic

xxiii

equation and also inculcate the habit of individualization and interactivity

prevalent in using computer in teaching.

To policy makers, the result of the study will enable them make policies

on acquiring computers for schools in order to improve the level and relevance

of learning. It will equally enable them make policies on the use of instructional

materials in teaching quadratic equation and more so in using computer as

instructional material to augment teachers‟ effort. Curriculum planners should

include computer education in secondary school curriculum so that student

should learn about the use of computer.

Finally, the result of this study will provide empirical evidence of the

mode that enabled students achieve and retain higher in Algebra and so should

form a basis for further research by researchers.

Scope of the Study

This study is delimited to comparing the effectiveness of using computer

and not using computer in teaching and learning of quadratic equation. Also, the

effectiveness of using computer as tutor and as tool in teaching and learning of

quadratic equations. Only Senior Secondary Two (SS11), students were used for

the study. This is because students in this class are not beginners in Algebra and

will be able to understand quadratic equations when software is used. Those in

SS1 are beginners and so may be thrown off with the use of computers as they

have not learnt the basics of Algebra. To those in SS111, using computers may

xxiv

distract them as they are already busy with their final examination and may not

have time for drill and practice or any further demonstrations. The contents to

be covered are the four methods of solving a quadratic equation which include

factorization, completing the square, formulae and graphing.

Research Questions

1. What are the mean achievement scores of students who were taught with

computer and those who were taught without computer?

2. What are the mean achievement scores of students who were taught with

computer as tutor and those who were taught with computer as tool?

3. What are the mean achievement scores of male and female students who

were taught with computer as tutor and those who were taught with

computer as tool?

4. What are the mean retention scores of students who were taught with


5. What are the mean retention scores of students who were taught with


6. What are the mean retention scores of male and female students who

were taught with computer as tutor and those who were taught with

computer as tool?

xxv

Research Hypotheses

HO1: There is no significant difference between the mean achievement scores

of students who were taught with computer and those who were taught

without computer.

H02: There is no significant difference between the mean achievement scores

of students who were taught with computer as tutor and those who were

taught with computer as tool.


of male and female students‟ who were taught with computer as tutor and

those who were taught with computer as tool.

H04: There is no significant difference between the mean retention scores of

students who were taught with computer and those who were taught

without computer.


students who were taught with computer as tutor and those who were

taught with computer as tool.


male and female students who were taught with computer as tutor and

those who were taught with computer as tool.

H07: There is no significant interaction effect between the modes and gender

on retention scores of male and female students who were taught with

computer as tutor and those who were taught with computer as tool.

H08: There is no significant interaction effect between the modes and gender

on retention.

xxvi

CHAPTER TWO

LITERATURE REVIEW

This chapter presents the report of the literature reviewed for the study.

The review was organized under the following sub-headings: Conceptual frame

work, Theoretical Framework and Empirical Studies.

Conceptual Framework

Under this section, the following sub themes were discussed:

Poor achievement of students in mathematics;

Concepts in Algebra;

Issues on Retention;

Computer and learning of mathematics;

Gender and Mathematics achievement.

Theoretical Framework

Skinner‟s theory of linear programming

Crowder‟s theory of branching programming

Piaget‟s cognitive theory of constructivism

Empirical Studies

Under this section, the following sub themes were discussed:

Studies on male and female students‟ achievement and retention in

mathematics;

Studies on the effect of modes on achievement and retention.

Summary of the Literature Review

16

xxvii

Conceptual Framework

Poor Achievement of Students in Mathematics

For many years now, there have been a lot of hues and cries about poor

achievement of students in mathematics (Ozofor, 2001). This poor performance

was clearly stated in WAEC chief examiners report of 2006 and 2007, showing

that students performed poorly in mathematics over the years. Poor achievement

of students in mathematics is attributed to poor method of teaching, lack of

retention, lack of good and experienced teachers, lack of interest and non

challant attitude of teachers to teaching (Obodo, 1990, Harbor-Peter, 2001,

Micheal, 2002, Kurumeh, 2004, and Ezeh, 2005). These researchers are of the

opinion that mathematics today still follows traditional pattern which is

identified to be ineffective and a major factor responsible for poor performance

of students in mathematics.

Many researchers have made effort to develop strategies to improve on

the poor achievement of students in mathematics. Such strategies among others

include Target task approach used by Harbor-Peters (1999), Concept map by

Ezugo and Agwagah, (2000), Ethno-mathematics by Kurumeh (2004), CAI by

Ozofor, (2001), delayed formalization approach by Ezeh, (2005), and Computer

use by Micheal (2002). All these were in an attempt to improve on students‟

achievement in mathematics.

xxviii

However, none of these strategies tried to compare the effectiveness of

computer as tutor and as tool on students‟ achievement in mathematics and so

calls for the need for this present study.

Concepts in Algebra

Algebra is a branch of mathematics of Arabian origin which may be

characterized as generalization and extensions of Arithmetic in which symbols

are employed to denote operations and letters to represent numbers and quantity

(Wikipedia, 2007). Algebra as a generalization and extension of Arithmetic was

classified as;

Elementary algebra, where properties of operations on the real number

system are recorded, symbols are used as “place holders” to denote

constants and variables, and the rules governing mathematical

expressions and equations involving these symbols are studied.

Abstract algebra, where algebraic structures such as groups, rings and

fields are axiomatically defined and investigated.

Specific properties of vector spaces are studied in linear algebra.

Universal algebra, where those properties common to all algebraic

structures are studied.

Computer algebra, where algorithms for the symbolic manipulation of

mathematical objects are collected (Wikipedia, 2007).

xxix

Wikipedia further listed the following forms of algebra:

Linear equations

Simultaneous equations.

Quadratic equations

Cubic equations

Exponential equations

Algebra as stated in the National Mathematics Curriculum for Senior Secondary

Schools involves solving equations, graphing linear, simultaneous and quadratic

equations.

Solving Equations: Equations in Algebraic processes involve; linear equation,

simultaneous linear equations and quadratic equations. These equations though

related have various ways of being solved, but the interest of this work is on

quadratic equation. A quadratic equation is an equation where the highest power

of x is x2. Quadratic equations are written in the form y = ax

2 + bx + c where a,

is the coefficient of x squared, b the coefficient of x and c the constant for a ≠O.

As stated in the New General Mathematics for West Africa (SS11) by Cannon

and Smith (2001), the various ways of solving a quadratic equation are:

(1) Factorization Method

(2) Completing the Square

(3) Use of Formulae

(4) Graph Method.

xxx

Factorization Method

According to Wikipedia (2007), trinomials are algebraic expressions

consisting of three unlike terms, such as x2 + 3x + 2. They can be factored using

the “foil” technique where the expression is factored by using two sets of

parentheses, each consisting of two terms. The first, outside, inside and last

numbers of both sets multiplied together and added equal the trinomial.

For example x2 + 5x + 6 is equivalent to (x + 3)(x + 2). Explained as:

First (x times x) + outside (x times 2) + Inside (3 times x) + last (3 times 2) =

the trinomial (x2 + 5x + 6). The last numbers in each set of parenthesis have

another relationship which is: When multiplied together, they always equal the

last number (3 times 2 equals 6), and when added, they equal the coefficient of

the variable (3 plus 2 equals 5). The basic idea behind factorization is that if the

coefficient of x2 is unit, then find two numbers which when you multiply, will

give the constant and when added will give the coefficient of x. For example x2

+ 3x + 2 = 0. First find two numbers which when multiplied will be equal to 2

but when added will be equal to 3. The numbers are 2 and 1 which are the

factors. Addition of 2 and 1 equals the coefficient of x which is 3. Therefore

(x + 2)(x + 1) = x2 + 3x +2.

But if the coefficient of x2 is not unit, then multiply the constant with the

coefficient. Example: 2x2 + 11x + 12 = 0. The coefficient of x

2 is 2, then 2 x 12

= 24. Factors of 24 that will be equal to11 when added are 8 and 3.

Therefore (2x2+8x) + (3x + 12) = 0

xxxi

2x (x + 4) + 3 (x + 4) = 0

Which implies that (2x + 3)(x + 4) = 0.

Hence Either 2x+3 = O x = -3/2

Or x + 4 = O x = -4

According to Matthew (2000), Factorization method is the easiest way to solve

a quadratic equation and that is the advantage it has over other methods.

Students are more comfortable with using factorization method than with other

methods because of its simple nature.

For example solve x2 + 2x – 8 = 0

:. (x - 2)(x + 4) = 0

:. Either x – 2 = 0 or x + 4 = 0

:. x = 2 or x = -4.

If you do not understand the third line, remember that for (x - 2)(x + 4) to equal

zero, then one of the two brackets must be zero.

Completing the Square

Another method for solving quadratic equation is completing the square.

This method according to Cannon and Smith (2001) follows the following steps.

First Step: Make the coefficient of x2 unit by dividing every term by the

coefficient of x2.

Example 2x2 + 11x + 12 = 0 gives x

2 + 11x + 6 = 0

2 2 2 2

Second Step: Shift the constant to the other side of the equation to have

x2 + 11x = -6

2

xxxii

Third Step: Add half coefficient of x to both sides and square it.

That is 22

2

4

116

4

11

2

11

xx

Fourth Step: Collect like terms, factor out and simplify to have

16

1216

4

112

x

16

25

16

12196

Therefore x +16

25

4

11

x = -11 ± 5

4 4

= -11 ± 5 -6 or -4 -3/2 or -4

4 4

Completing the square method has the advantage of solving any type of

quadratic equation unlike the factorization method that can only solve if the

equation is factorizable. Competing the square can also be used to find the

maximum or minimum point on a graph.

Example: Find the minimum value of the graph y = 3x2 - 6x-3. In this

case, the x2 has a „3‟ in front of it so we start by taking the three out:

y=3(x2-2x-1). This is the same since multiplying it out gives 3x

2- 6x-3 .

Now complete the square for the bit in the bracket:

:. y = 3 (x-1)2 -2

Multiply out the big bracket:

:. y = 3 (x-1)2-6.

xxxiii

We are trying to find the minimum value that this graph can be. (x-1)2

must be zero or positive, since squaring a number always gives a positive

answer. So the minimum value will occur when (x-1)2 = O, which is when x=1.

When x = 1, y = -6. So the minimum point is at (1,-6).

Formulae Method

The general formulae for solving a quadratic equation is

x = a

acbb

2

42 where a, is the coefficient of x

2, b the coefficient of x and c,

the constant. What is required here is to substitute the values of the variables

and simplify.

Example: Solve 2x2 + 11x +12 = 0 by formulae method a=2, b = 11, c = 12.

Substitute in the formulae

3

2

4

6

4

511

4

511

4

2511

4

9612111

22

12241111

2

4 22

x

xx

a

acbb

Or .44

16

4

511

Therefore, x = -2/3, -4.

Graph Method

This method of solving quadratic equation involves forming a table of

value for values of x and y. Then, drawing the graph.

xxxiv

For example:

Solve the equation x2 - x - 2 = 0 with range of x from -4 to + 4

All these methods lead to the solution of any given quadratic equation.

The computer is capable of doing this job. Instead of using hand to do the

computation and graphing, Computer Algebra Application (CAAS) software

can manipulate symbolic expressions or equations, find exact values for

equations and also graph functions and plot relations. Also in using Computer as

a tutor, where the intelligent tutoring application software is applied, it can

equally do the work. Therefore this study seeks to compare the effectiveness of

X -4 -3 -2 -1 0 1 2 3 4

x2 16 9 4 1 0 1 4 9 16

-X 4 3 2 1 0 -1 -2 -3 -4

-2 -2 -2 -2 -2 -2 -2 -2 -2 -2

Y 18 10 4 0 -2 -2 0 4 10

20

15

10

5

5

10

1 2 3 -1 -2 -3 -4

Y axis

Yaxis

X axis X axis

Table of value

xxxv

using computer as tutor and tool in learning these concepts. The advantage that

computer has over manually solving the questions is that, the computer does it

faster and more accurately.

Issues on Retention

Retention is the continuous possession or use of something. It is also the

continuous existence of something, in this case, the retention of ones‟ mental

faculties. Retention of what somebody has learnt so as to be able to retrieve it

when there is need for that is necessary. Inability to remember what one has

learnt is regarded as a loss of memory (Langer, 1997). He further stated that a

loss of memory is a failure to remember the past. The loss of memory or

inability to remember is detrimental and should be avoided.

Chauham (1987) defines retention as a direct correlates of positive transfer

of learning which the primary essence in education is. This indicates that ability

to retain what one has learnt is necessary in education in order to achieve the

positive transfer. Landry (1999) is of the view that human memory is very weak

and so can not retain everything. Based on this, a teacher should be faced with

the problem of improving on students‟ ability to learn, retain and retrieve

information. It is in an attempt to find a solution to this problem that made

many researchers to embark on retention in different fields and with different

methods. It is even more difficult to retain abstract aspects of mathematics such

as algebra than aspects that are easily concretized.

xxxvi

Ogbonna (2007) had retention as a variable in finding the effect of two

constructivist instructed models on students‟ achievement and retention in

number/ numeration. Micheal, (2002) also had retention as a variable in finding

the effect of CAI on students achievement. Iji (2003) and Madu (2004) also

worked on retention. This present study attempted to find out the effect of using

computer as tutor and as tool on retention. These go a long way to show that

forgetting is discountenanced and retention should be encouraged. It is in an

attempt to enhance retention that made psychologists like Hogarth (1980),

Santrock (1988), Wade and Tavris (1996), Bernstein and Clearke-Stwart (1997)

propound these theories of forgetting.

(1) Theory of cue-dependent forgetting which occurs when we lack

necessary cues to locate the items in the memory.

(2) Decay theories which emphasize that representations or memory

traces fade or disappear over time. Without rehearsal, decay occurs in

short term memory and so makes retention limited (Santrock, 1988).

(3) Theories of interference. This is saying that existence of old memories

and new memories either displace or inhibit recall. Interference

according to Bernstein and Clearke-Stwart (1997) causes displacement

or the complete loss of item from the memory.

(4) Motivated forgetting or repression is generally associated with

blocking of memories to avoid embarrassment or protect one‟s ego or

pride (Hogarth, 1980).

xxxvii

These psychologists are of the view that forgetting occur when one is not

able to encode, rehearse or learn information through inattention or interference

in short-term memory before consolidation in long-term memory. With the use

of computer, learners will have the opportunity of rehearsing and interacting

until a concept is registered in the long-term memory.

Landry (1999) noted that forgetting is less favourable and remembering

much more appreciated. He is of the view that human memory is limited and

should be supported with computer technology. Huber (2009) also is of the view

that human components of organizational memories are less than satisfactory in

retaining every day experiences and learning. He suggested that there should be

organizational memory system (OMS) that should put every learning into the

long-term memory where they will be retained. Huber still maintains that

human memory is frail and that one major frailty of human memory is that we

forget. He suggested that to overcome the frailty of human memory, technology

should be employed.

According to Baker (1997), Computer technology enhances retention. He

noted that students retain 30 percent of what they read in textbooks, 40 percent

of teachers‟ lectures and 80-90 percent of computer learning. Also the Digital

Equipment Cooperation in a research paper as cited by Baker has contended that

people remember 25% of what they hear, 45% of what they hear and see and

70% of what they hear, see and do. This statement shows many similarities to

the old Chinese saying: If I hear I know, If I see I remember, If I do I

xxxviii

understand. What computer does is the integration of hearing/seeing/doing for a

better retention and a deeper understanding. Since computer technology has

been identified as effective in enhancing retention the researcher deemed it

necessary to see the mode that is more effective on retention.

Computer and Learning of Mathematics

The use of computer is gradually being introduced into every field in the

society. Computers and related technology are seen as the wave of the future

(Odogwu, 1999). The society has seen many different technologies develop in

its history. These developments have led to many different uses of the computer

in the classroom. Such uses include, but are not limited to drill and practice to

develop skills needed in mathematics, computer-assisted tutorials that provide

students with different methods of answering questions and provide immediate

answers, exploratory software programs to allow students opportunities to

engage in mathematical investigations and programming skills that develop

logical reasoning in students (Wikipedia, 2007). A computer can serve as free

standing or networked workstation that provides tutoring to a student and can be

structured to his or her responses. From the uses, software programmers have

developed different types of software amendable to various uses. According to

Micheal, (2002), such programs include Logo, Math Blaster, Geometer‟s

sketchpad and on line systems like Novanet.

xxxix

Taylor is of the opinion that tutor applications can further be classified

into five categories; drill-and-practice applications, tutorial applications,

simulations, problem-solving applications and games. In drill-and-practice

applications, the computer is used to help the student memorize the appropriate

response to some stimulus. The most common applications include drills on

mathematics facts. Applying it to Algebra, the computer might display the

problem 5x+3x =? And the student would be asked to enter the correct response.

The computer would evaluate the response and give the student appropriate

feedback. If the student entered the incorrect response, the computer would

display the correct answers on the screen and then present the next problem.

In tutorial applications, the primary purpose is to teach new information

(Taylor, 1980). Tutorial applications are similar to a programmed textbook

where information is presented and the student is asked to respond to a question

about the information. For example in Algebra, information could be presented

as: The general form of a quadratic equation is ax2 + bx + c = 0 where a,is the

coefficient of x2, b the coefficient of x and c the constant. A question is asked:

Is 2x + 3x + 4 = 0 a quadratic equation?

The computer after the student‟s response provides feedback concerning

the accuracy of the student‟s response. The cycle is repeated where more

information, questions and feedback are provided. In doing so, the computer is

able to tailor the material to the needs of individual students. If a particular

student is having difficulty, the computer can present remedial materials.

xl

Students who are doing well may skip over elaborations, extra examples or

practice items.

Apart from tutorial application, simulation is also among the five categories

of using computer as tutor in teaching mathematics according to Taylor (1980).

Simulations are representations or models of real systems or phenomena. They

allow students to experience certain phenomena. For example in Algebra,

weighing balance or blocks could be used to represent variable and students will

be expected to solve problems on them.

For example:

Fig 1 Weighing Balance

Problem-solving applications provide settings in which students can learn

and improve on their problem-solving skills. Finally, the games applications are

also used to bring interest and motivation to the learning situation. This will

involve a programme in form of a competitive play between a student and one

or more opponents. All these applications according to Taylor are to explore the

powers associated with using computer as tutor.

Sowmya (2005) in his own view states that computer could be used as

tutor in teaching algebra. He designed an Intelligent Tutoring System (ITS)

which was able to give information, monitor student‟s responses and also tailor

5x 14x + =

/////////////////////////////////////////////////////////////////////

/

xli

the questions presented to match the skill level of the students. His instructional

approach was “learning-by-doing” approach, where students are taught in the

context of solving problems in Algebra. This approach was also recommended

by Schank (1995), who opined that using computer as a tutor scaffolds the

problem-solving task by providing several sub-tasks that break down the main

problem into smaller problems that contribute to the overall solution. For

example, in solving word problems leading to quadratic equation- such as: The

sum of two numbers is 8, their product is 15, find the numbers. In solving this

question, it could be broken down into sub problems like; interpreting the words

of sum and product, defining the variables, putting them in equation form and

solving. But if a student is unable to arrive at the correct answer, he/she can go

back to help page where the computer will give information that will lead to the

solution of the problem. The goal of this design is to encourage students to think

deep about a problem, so as to come up with a solution.

In using computer as a tutor, Landaurer (1995) is of the view that

computer replaces human being in performance of tasks. In this case, computer

could produce diagrams and features that help students learn mathematics and

teach them as well. In this mode, the computer presents the information, guides

the learners to practice and assesses the learner. Students / learners will follow

the programmed instructions and assessment will come both at the beginning

and at the end of a module. Each topic was written as a module. If a student

answered questions correctly at the beginning of a module, he skipped over it. If

xlii

not, the program continues through the module until he gets them correct. In this

approach, the usual pen and paper test or conventional assessment will not be

used rather an active assessment of “drag” and “drop” will be used. With this

approach the student highlights or clicks the mouse on an answer choice and

drops it into a predetermined area. Once the answer is placed in the correct or

incorrect location, the appropriate feedback is provided.

According to Ifeakor (2005), in using computer as a tutor, a Computer

Assisted Instruction (CAI) will be involved. CAI is an automated instructional

technique in which a computer is used to present an instructional programme to

the learner through an interactive process on the computer. This approach is

learner centred and activity oriented. CAI makes possible programmed

instruction which presents students with content, requires the student to respond

actively and immediately gives the student information about the correctness of

the response. In this study, the researcher applied the tutorial application of

using computer as a tutor whereby intelligent tutoring application software was

used. The software presents its content where the students click on quadratic

equation and the lesson begins. The tutoring application presents learning

materials in a more flexible and interactive way, using variable questioning

approaches. For example if you slot in the software in the computer, it

welcomes you to tutorial. Click on quadratic equation and follow the lesson step

by step.

xliii

Means (1994), also noted that computer could be used as an exploratory

tool inform of CD-ROM encyclopedia, simulation, network search tools and

computer-based laboratory. In solving mathematical problems especially

Algebra, computer will be used as tool for learning problem solving methods.

According to Chris (2001) the computer is a sophisticated tool, performing tasks

that should augment human performance. Landauer (1995), in his second phase

of computer application views computer as a tool that assists human. He opined

that in this case, there is no proxy; the computer is subject to the user. The

computer only augments and augmentations according to landauer is the use of

computer to help in doing things faster. These tasks involve manipulation,

communication and transmission of information.

Levy (1997) in his own view of using computer as tool, maintains that a

tool is designed to assist learning and requires more teacher input both in the

planning and usage. This indicates that in using computer as tool, the computer

helps in the process of learning thereby enhancing learning. In using computer

as a tool, students were exposed to a quadratic equation solving program.

For example Enter values for ax2 + bx+c = 0.

a. b. c.

Complex number solution x1 = x2 = .

Solve Start over

xliv

The student with the help of the mouse, puts values for a, b and c and clicks on

solve. The computer gives the values for x1 and x2.

The third mode of computer usage according to Taylor is as “tutee”. The

computer in this case becomes the tutee, or student and the users become the

teachers. The user has to teach the computer to do some task. To do this, the

user has to learn how to communicate with the computer in a language that the

computer understands. This means that the learner must learn how to write

computer programs. The different opportunities that technology provides for

improving classroom instruction have been clearly seen in mathematics

education. Educators believe that technology can help students learn

mathematics and also take care of individual differences that students bring to

the classroom (National Council of Teachers of Mathematics, 2006). Different

forms of technology have evolved year after year. One example is the

calculator. The calculator can change from a tool that does basic mathematics to

a tool that can graph functions. So also is the computer. An example is the

creation of a computer program called Logo. According to Armstrong and

Casement, (2000), Logo was designed to stimulate the cognitive abilities of the

young mind. Students would control a turtle to move according to the

commands issued by the programmer. The purpose was to make the

programmer create visual diagrams according to geometric properties.

There are many softwares that provide tutorial exercise for students‟

learning. Many of the programs were designed to assist students in

xlv

understanding materials and for problem solving. For example the computer

algebra systems (CAS) software, that can manipulate symbolic expressions or

equations (Micheal, 2002). Drill and practice software are generally used to

reinforce skills. Most drill and practice software take a game approach to their

instruction. Other software includes the NOVANET. The applications contained

within NOVANET provide a great opportunity for students to attain a better

understanding of instructed materials. Micheal is of the view that NOVANET is

a computer based, on line learning system whose instructional package provides

an excellent opportunity for students to gain a better understanding in

mathematics especially in Algebra. The NOVANET contains a thorough set of

tutorials that help students understand Algebra. These tutorials include lessons

on equation solving, graphing linear equation and factoring polynomials.

Another software that could be used as a tool in learning algebra is the, I

CAN learn (R) Algebra developed by John R. Lee. I CAN learn (R) is a

computerized algebra program designed primarily to help students achieve

higher in mathematics especially algebra for improving on their thinking and

problem solving skills (John, 1996). He further stated that the, I CAN learn (R)

program contains computer – generated voice instructions and intuitive menus

guide that guides the user. It encourages co-operative learning, group projects,

peer tutoring and good reasoning. Various soft wares are in existence but this

study made use of the Intelligent Tutoring Application software as tutor and

xlvi

Computer Algebra Application software as tool, so as to compare their

effectiveness.

Computer usage in teaching mathematics is a welcome development and

this study does not doubt the effectiveness of using computer in teaching

mathematics, rather it seeks to compare two modes of using computer in

teaching / learning of Algebra for effective teaching and learning.

Gender and Mathematics Achievement

The issue of gender disparity has been a thing of great concern. Some

researchers have traced it to the origin of man (Kurumeh, 2004, Ezeliora, 2004).

They are of the opinion that as a boy grows men‟s toys like guns will be

provided to him while women toys like toy babies will be provided to the girls.

Ezeliora stated that even in primary schools, girls are made to produce

handworks like handkerchief, table cloths while boys are made to produce

carved objects and baskets. He noted that when pupils were asked to draw a

scientist in the laboratory, that most of them normally draw a male scientist.

This goes a long way to show that right from that stage of life; pupils feel that a

scientist should be a man not a woman. Girls are prepared to be future mothers

and so they do not think beyond getting married and becoming mothers.

Tracing back to the colonial era in Nigeria, most schools were

predominantly boys with the aim of training or producing literate men to serve

the white men (Lassa, 1995). Franden (2003), in his research on gender

xlvii

differences, found out that there are some gender differences in mathematical

processing and that boys achieved better than girls. He stated that in elementary

schools, boys and girls show the same level of interest and achievement in

mathematics and sciences as they do in literature and history. By the time the

students go to the middle school, females‟ confidence level in mathematics

/science becomes low and consequently their interest and achievement levels.

He attributed this difference to attitudinal, psychological and socio-cultural

factors on girls. He noted that some teachers do not use lady-fair language while

teaching mathematics rather they use languages that discourage girls and give

them the impression that their education should not go beyond the kitchen.

Olagunju (2001) in his own study on 240 students(120boys,120girls) in Ondo

west local government area of Ondo state showed that, there is no significant

difference between male and female students‟ achievement in mathematics. He

equally showed that there is no significant difference between the performance

of younger and older boys and girls in mathematics. He is of the opinion that if

well guided, the girls may even over power the males since they are more

organized. The Nigerian National policy on Education (FRN, 2004) has

reconciled this idea that girls are prepared for marriage while boys are prepared

to be scientists and educators by introducing equal education for all both at

primary, secondary and tertiary levels. Girls are now becoming scientists,

mathematicians and educators.

xlviii

A lot of researches have been carried out in and outside Nigeria, to find

out the effect of gender on mathematics achievement. Some of these researches

showed that males performed better than females (Alio and Harbor-Peters 2000,

Ezugo and Agwagah, 2000). Others recorded that females perform better in

mathematics (Ezeh, 2005 and Ogbonna 2007), while some others recorded no

difference between the two groups (Etukodo, 2002). According to Makhubu

(1996), some of these differences were attributed to psychological, socio-

cultural factors and lack of activities that are student centred and activity

oriented like the use of the computer.

Computer according to Odogwu (2001) dehumanizes. It does not care

whether you are a male or a female and so recorded no significant difference

between male and female students‟ achievement. Micheal (2002) recorded

difference in favour of females as he noted that females were more careful and

patient in handling computer. None of these studies indicated the mode and so

calls for this study that wants to compare the effectiveness of two modes of

computer usage on gender.

Theoretical Framework

Skinner’s Theory of Linear Programming

This study has the theoretical backing of Skinner; a behavouralist, and well

known psychologist who extended the work of Edward. L. Thorndike. Skinner

xlix

was instrumental in popularizing a behavouristic approach to teaching and

learning through his research on the effects of reinforcement.

Skinner as cited by Cleburne, Johnson and Jerry (1992) had interest in teaching

machines and he noted that the teaching machine permits the user to work on

his own and also at his pace. B. F Skinner promulgated the idea of teaching

machine in 1953, after a visit to his daughter‟s fourth grade class where during

arithmetic assignment made two observations:

(a) All students had to proceed at the same pace in the teaching situation

(b) Students had to wait 24hours to learn the accuracy of their responses to

the problems. A few days later, he built a primitive machine to teach arithmetic

(Cleborne et al, 1992). Skinner stated the two improvements to the learning

process brought about by the teaching machine as follows: immediate

reinforcement and individualization. He noted that individualization allows the

learner to work on his/ her own and also at his/her own pace. Skinner‟s interest

was on linear teaching program which requires presentation in small bits,

logical sequence and immediate response from the learner. According to Ozofor

(2001), linear programming is based on the principles of operant conditioning,

one of which states that if the occurrence of an operant is followed by the

presentation of a reinforcing stimulus, the strength is increased. At a point,

skinner‟s Linear programmed learning and teaching machines were challenged

by other theories.

l

Crowder’s Theory of Branching Programming

Another theory that is in support of computer based learning is the

Crowder‟s theory of branching programming. Crowder was a behaviorist who

extended the work of Skinner. As Skinner believed in linear programmed

learning; Crowder believed in branching program. He is of the view that the

branching will enable the learner to retrace his steps back through that position

of the program which his errors indicate that he did not adequately learn.

Crowder‟s preference of the branching program was because he believed that

the program will take care of different exigencies of each individual. Crowder

brought in the idea of personalization. His idea of personalization was that the

sequence of progressing is not linear but is determined by the learner‟s state of

assimilation of the material presented, so that it could be different for each

individual. The computer allows this as it allows the user to move at his own

pace and also review until a concept is understood.

For obvious problems of the early teaching machines, such as its

cumbersomeness, expensiveness and difficulty of repair/maintenance when

broken down, these ideas were not in use until the „70s that brought in Time-

shared Interactive Computer Controlled Information Television (TICCIT) in

1971 and programmed Logic for Automatic Teaching Operation (PLATO IV) in

1976 (Landaurer,1995). These two programs stressed the „personalization‟

aspects of instruction where individual differences are taken care of.

li

The “80s equally witnessed another form of instruction called Integration.

According to Baker (1997), Integration of instruction means bringing in other

media in a single device managed by the central memory of a computer. He

further stated that an integrated multimedia system is one in which several

different presentational channels are used either simultaneously or in sequence

in order to implement a particular instructional strategy. Baker highlighted two

forms of integration as: Integration of media and integration of mode. He

defined mode of instruction as the function a program can perform in assisting

the learner. They include:

Presentation: Introducing learning materials in a defined pattern

Drill and practice: Exercising the learner in mastering the skills

needed.

Tutorial and Dialogue: Presenting learning materials in a more flexible

and interactive way, using variable questioning approaches;

Inquiry and Browsing: Providing the learner with a base of stored

information through which he can freely navigate

Simulation and Games: Allowing for experimenting different courses

of action and learning from the consequences.

Problem solving: Offering a framework of rules and data to assist in

the process of learning while discovering

lii

Testing and Monitoring: Keeping a record of the learner‟s

achievements and, on that basis, suggesting personalized learning.

Piagets Cognitive Theory of Constructivism

Apart from skinner and the working machine the study has the theoretical

backing of Jean piaget, a well known Swiss scholar who propounded

constructivism. Piaget was concerned primarily with cognitive development and

the formation of knowledge. His research led him to conclude that the growth of

knowledge is the result of individual constructions made by the learner (Martin,

1993). According to Martin, constructivism is all about knowledge and learning

and that learning is a self-regulated process of resolving inner cognitive

conflicts that often become apparent through concrete experience, collaborative

discourse and reflection.

A constructivist framework challenges teachers to create environments in

which they and their students are encouraged to think and explore. In the use of

computer in teaching and learning, students are allowed to handle the software

individually and construct their own understanding and meaning. Students are

viewed as thinkers while teachers behave in an interactive manner, guiding and

mediating the environment for students.

According to Papert (1980), Logo programming is noted from the

artificial intelligence and supported by piaget‟s cognitive development theory.

Piaget‟s position as a structuralist in the philology of intellectual inquiring is of

liii

the notion that thinking is a process that occurs not through isolated association

or innate unfolding of genetic disposition, but through relating experience,

connecting things together, inferring consequences, reversing logical position

and organizing stimuli to have a meaningful relationships (Aichele and Peys;

1971). Piaget through observations and numerous experiments established the

following facts:

1. That the thinking of children is different from that of adults.

2. That cognition develops as a set of pattern at a somehow standard rate for

all people.

3. That each person must go through each stage of cognition and no stage

can be omitted.

4. That the basics of all learning are the child‟s own activity as he interacts

with his physical and social environment.

5. That the child‟s mental activity is organized into structures called

schemas or patterns of behaviour.

6. That mental activity is a process of adaptation to environment.

7. That adaptation consists of two opposed but inseparable processes called

assimilation and accommodation.

Assimilation is the process whereby the child fits every new experience

into his pre-existing mental structures. Accommodation is the process of

perpetual modification on mental structures to meet the requirements of each

particular experience.

liv

8. That through the functioning of these structures, a child interprets his new

experience in the light of his old experiences.

9. That mental growth is a social process. The child does not interact with

his physical environment as an individual. He interacts with it as part of a

social group.

10. That accommodation to the environment leads to a continuous

modification of the child‟s behaviour pattern quantitatively and

qualitatively (Aichele and Rays, 1971; 212).

In the use of computer in teaching and learning the piagetian terms of

accommodation and assimilation take place. As the child interacts with the

computer in the process of learning, the initial knowledge “non grasping”

structure is refashioned into a new “grasping” one and that is the process of

accommodation. The child‟s newly created structure allows assimilation of

experience to occur within his mind.

Implication of Piaget’s theory to teaching and learning:

1. Since the child‟s mental growth advances through qualitatively distinct

stages, these stages should be considered while planning the curriculum.

That is teaching a child what he should know at a particular age.

2. Before introducing a new concept to the child, test him to be sure that he

has mastered all the prerequisites for mastering this concept. If he is not

ready for the concept, provide him with experiences that will help him

became ready.

lv

3. The pre-adolescent child makes typical errors of thinking that are

characteristics of his stage of mental growth. Teachers should try to

understand these errors.

4. Teachers can help the child to overcome errors by providing him with

experiences that expose them as errors and point the way to the correction

of the errors.

5. Mental growth is encouraged by the experience of seeing things from

many different points of view.

6. Physical action is one of the bases of learning.

To learn effectively, the child must be a participant in events and not

merely a spectator. To develop his concepts of number and space, it is not

enough that he looks at things. He must also touch things, move them, turn

them; put them together and take them apart.

In using computer in learning mathematics, the child has the opportunity

of touching things, moving them, turning them, putting them together and

taking them apart.

These theories of Skinner, Crowder and Piaget are fully in support of

computer learning as the idea originated from them. So the researcher deemed it

necessary to review these theories as they have great implication to learning in

terms of using machine, programming, individualization, personalization and

integration of instructions.

lvi

Review of Related Empirical Studies

Studies on Male and Female Students’ Achievements and Retention in

Mathematics

Several studies have been carried out to determine the achievement and

retention of male and female students in mathematics / other sciences using

various teaching strategies. One of such studies is Obodo (1990) who conducted

an experimental research on the effect of Target task, delayed formalization and

expository methods of teaching on achievement, retention and interest of Junior

secondary school (JS11) students in Algebra. The design was quasi-

experimental. Purposive and simple random sampling techniques were used in

drawing the subject of the study. The study was conducted in Anambra State

with a sample of 447 JSS11 students.

(1) On the average, the target task, delayed formalization and expository

methods were equally effective.

(2) For the Urban students, the target task and expository methods were more

effective in their algebraic retention.

Also Ozofor (1993), carried out a study on the effect of Target task on

students‟ achievement in probability. A total of two hundred and forty (240)

SS111 students were involved. The study was carried out in Udi Local

Government Area of Enugu State. The design was quasi-experimental. His

findings among other things indicated that, target task approach was more

effective than the talk-chalk approach in teaching conditional probability. There

lvii

was no significant difference between the mean performance of male and

female students exposed to the target task.

Ezeugo and Agwuagah (2000) studied the effect of concept mapping on

students‟ achievement in Algebra. The purpose was to determine the differential

effect of concept mapping on the achievement of male and female students‟

achievement in Algebra. A sample of 387 SSII students formed the subject.

Data were collected using the Algebra Achievement Test (AAT). Concept maps

on quadratic equations and inequalities were drawn and used for the treatment

group while conventional approach was used for the control group. Their

findings indicated that students exposed to concept mapping technique achieved

significantly higher than students who were not exposed to the technique. More

so that male students performed better than females on the concept mapping

technique.

Again Madu (2004), carried out a study on the effect of constructivist –

Based instructional model in students‟ conceptual change and retention in

physics. The study adopted the non-equivalent control group design using 204

SSII physics students in Nsukka Urban of Enugu State for 2001 / 2002 session.

Two secondary schools (one male/one female) were used. The main purpose of

his study was to determine empirically the effect of constructivist based

instructional model PEDDA relative to students‟ conceptual change and

retention in current electricity. His findings indicated that PEDDA model

facilitated concept change and retention of physics concepts.

lviii

Ezeh (2005), carried out a study on the effect of delayed formalization

approach on senior secondary school students‟ achievement in sequences and

series. This study was carried out in Obollo Education Zone of Enugu State. The

design was quasi-experimental. A sample of 240 senior secondary two (SS11)

students of which 130 were males and 110 were females was used for study.

The findings among other things indicated that:

(i) Delayed Formalization Approach, is effective in teaching and learning

of mathematics and hence enhanced their achievement. Also that,

female students achieved more than their male counterparts with the

delayed formalization approach.

Furthermore, Ogbonna (2007), also carried out a study on the effect of two

constructivist instructional models on students‟ achievement and retention in

Number and Numeration. The study was carried out in Abia State. It was a

quasi-experimental design with a sample of 290 JSIII students. His findings

revealed that students who were taught with the two constructivist instructional

models (IEPT and TLC) achieved and retained higher than those taught with the

conventional method. Also that, female students performed better than male

students.

All these studies reviewed used various techniques to find out the

achievement of male and female students in mathematics / other sciences, but

none of the studies tried to compare the effectiveness of using computer as tutor

lix

and tool in teaching mathematics, and so calls for the need for this present

study.

Studies on the Effect of Modes of Computer on Achievement and Retention

Advances in computer technology have motivated teachers to reassess the

computer and consider it an integral part of daily learning (Matthew, 2000).

Researchers have equally carried out studies on the use of computer in teaching

mathematics. Such researchers include: John (1996), Ozofor (2001), Etukodo

(2002), Micheal (2002), Iji (2003), and Ifeakor (2005).

John (1996), carried out a six – week research on the effect of I CAN

learn software as a tool on students‟ achievement and retention in Algebra. He

adapted a quasi-experimental research design (treatment Vs. Control group

design) with 124 ninth-grade beginning Algebra I students assigned to five

treatment classes using a combination of computer and teacher instruction and

68 students assigned to teacher instruction only as control group. Results of his

findings indicated that I CAN learn (R) Students performed better than control

students by a statistically significant margin on both the pre test and post test. In

addition, he observed that, students‟ retention of materials appeared to be

greater with I CAN learn (R) computer assisted instruction.

Also, Ozofor (2001), carried out a study on the effect of two modes of

computer Aided instruction on students‟ achievement and interest in statistics

and probability. His study was carried out in Enugu education zone of Enugu

lx

State. A sample of ten intact classes, made up of between 20 to 40 students was

used for the study. The design was quasi-experimental. His finding among other

things indicated that: Students performed better with the Computer Assisted

Instruction than with the conventional method and also that students performed

better and became more interested in tacking mathematics problems when drill

and practice method was used than when the tutorial method was used. More so,

that practicing at the computer terminals stimulated more and helped students

retain more of what they have learnt; that female students performed better than

their male counterparts when drill and practice method was used. This study is

different from the present study in that, the present study will compare computer

as tutor and as tool using intelligent tutoring application and computer Algebra

application software respectively.

Again Etukodo (2002) in his own research on the effect of computer

Assisted Instruction on gender and performance of Junior Secondary School

Students in mathematics, reported that there was no significant difference

between male and female students achievement in mathematics. He carried out

his research in Ogba / Egbema / Ndoni Local Government Area of River State.

A sample of 40 students was used for each group, 20 were males while 20 were

females. The design was quasi-experimental.

Micheal (2002) carried out a study on Computer-Assisted Instruction

versus Traditional Classroom Instruction: Examining students‟ Factoring

Ability in High School Algebra one. The purpose of his study was to examine

lxi

the effectiveness of computer – assisted instruction compared to the traditional

instruction of a classroom teacher in mathematics. The study also examined the

perceptions of students‟ experiences using computer assisted instruction and its

ability to meet their educational needs. He used the computer as a tool. The

study was carried out in North Carolina. Four research questions guided the

study. A sample of 50 students was used; 25 in the experimental group that used

on-line learning system, called NOVANET to learn factoring in Algebra while

the other 25 students received traditional classroom instruction on factoring.

The design of the study was quasi-experimental. His findings indicated that;

there was no significant difference between the two forms of instruction.

Students also did not show any significant difference in retaining the

information taught. Some students did recognize the power of the computer and

suggested that both forms of instruction be integrated.

Another study by Iji (2003), on the effect of Logo and Basic Programmes

on Achievement and retention in Geometry was reviewed. The study was

carried out in Ahoda Education zone of River State. The main purpose was to

determine the efficacy of the use of Logo and Basic Programme methods in

teaching junior secondary geometry in Nigeria. The design was quasi-

experimental. A sample of two hundred and eight five (285) JS1 students drawn

from 3out of 6 co-educational schools that have computers in Ahoda zone was

used. 184 students were in experimental group while 101 students were in

control group. His findings indicated that students taught with Logo and Basic

lxii

programmes achieved higher than those taught with the conventional method;

Students retained more with logo and Basic programmes than with the

conventional method; That the difference between the mean gain retention

scores of the high and low achievers was significant; That high achievers

achieved higher and retained higher; Finally that, though there was interaction

effect between method and students‟ ability levels on achievement and

retention, but the interaction was statistically not significant.

Further more, Ifeakor (2005) carried out a study on the effect of

commercially produced CAI package on students‟ achievement and interest in

secondary school chemistry. His design was quasi-experimental. A sample of

140 SSI chemistry students in Onitsha North of Anambra State was used. His

findings indicated a significant effect on students overall cognitive achievement

and interest in chemistry and also gender was not significant.

All these studies reviewed tried to find out the effect of computer and

CAI on students‟ achievement and retention but none of them took time to

compare the effect of computer as tutor and as tool on students‟ achievement

and retention and so the need for this present study.

lxiii

Summary of the Literature Review

Poor achievement of students in mathematics was attributed to poor

method of teaching, lack of interest among students, poor text books, lack of

computers, unavailability of instructional materials and teachers‟

undedicatedness, and lack of knowledge. The review revealed that students have

performed so low in mathematics over the years, that it becomes a thing of great

concern to educators, researchers and mathematicians. It is in an attempt to find

a solution to poor achievement of students in mathematics that inspired

researchers to search for methods of teaching that will improve students‟

achievement in mathematics. This led to the introduction of computers in

teaching mathematics especially now that computer is in vogue in the country to

meet up with the technological challenges in Nigeria today. The review revealed

that Algebra is noted as a generalization of Arithmetic and an important aspect

of school mathematics as it serves as a gate way to other areas of mathematics.

Quadratic Equation is one form of Algebra. The various methods of solving

quadratic equations which students should be exposed to were reviewed. They

are: factorization method, completing the square method, graph method and

formulae method.

The review also revealed that students‟ inability to retain what they have

learnt was also one of the reasons for poor achievement in mathematics. It is

therefore pertinent to look for avenues; materials that will enable students

remember what they have learnt. One of such avenues is the computer which

lxiv

will enable students to visualize and learn a concept repeatedly until it is

mastered. Thereby supporting the Chinese adage that “what I hear, I know, what

I see, I remember and what I do, I understand. Retention was reviewed as the

continuous possession or use of something and it is very important for the

sustenance of achievement. The review revealed some psychologists‟ idea about

forgetting; that forgetting occurs when one is not able to encode, rehearse or

learn information through in attention or interference in short –term memory

before consolidation in the long term memory.

In the course of the review, the researcher observed that technology is

advancely coming into the mathematics classroom. Teachers and students are

fast embracing the use of computers in teaching/learning of mathematics. This

is why the review revealed students‟ comments on the use of computers as

being patient, does not care how often a mistake is made, gives immediate

feedback, easy to use among other things. The reviews equally revealed that

various computer software have different uses. The review equally brought to

the focus that gender disparity has stayed long in the system and up till now,

there is still no clear distinction as to which sex performs better than the other in

mathematics achievement. Having reviewed other peoples‟ work on the use of

computer, achievement of students in mathematics, retention and gender, this

work seeks to compare the use of computer as tutor and tool in algebraic

achievement and retention of male and female students.

lxv

Finally the review unveiled theories that are associated with the work.

Theory of skinner‟s working machine who believed in linear programmed

learning, and theory of Crowder‟s branching program who believed in

branching program, and Piagets‟ cognitive theory of constructivism. All these

theories were reviewed as they relate to the use of computer in teaching

mathematics.

It is pertinent to appreciate that the opinions and research findings got

from the works, which have been reviewed, contributed in giving this study a

sharp focus.

lxvi

CHAPTER THREE

RESEARCH METHODS

This chapter is discussed under the following sub headings: Research

Design, Areas of Study, Population of the Study, Sample and Sampling

Technique, Instrument for Data Collection, Validity and Reliability of

Instruments, Experimental procedure and Method of Data Analysis.

Research Design

The design of this study is quasi-experimental research design. The quasi

experimental design is chosen because it controls the internal validity threats of

the initial group equivalence and researcher‟s selection bias, since there was no

randomization of the subjects into groups. Intact classes, which were already

organized, were used. This did not disrupt the school setting in terms of

classroom schedules, and so accommodated the study.

Table 1: An illustration of non-randomized pretest – posttest design

S Grouping Pretest Research Condition Post-test

- Group1 01 Treatment or (X1) 02

- Group2 01 Treatment or (X2) 02

- Group3 01 Control or (X3) 02

X1 denotes treatment X1

X2 denotes treatment X2

X3 denotes control X3

01 denotes pre-testing

02 denotes post-testing (Ali, 1996:67)

56

lxvii

Area of the Study

The study was carried out in Nsukka Education Zone of Enugu state. The

zone is made up of three Local Government Areas: Nsukka, Igbo-Etiti and

Uzouwani. Nsukka Local Government Area was purposively chosen because

eight secondary schools out of 29 secondary schools have computer facilities

and electricity. The schools are St. Theresa‟s College Nsukka, Queen of the

Holy Rosary Nsukka, Boys Secondary School Nru, Girls‟ Secondary School

Ibeagwa-Aka, Boys High School Umuabor, Girls Secondary School Opi, St.

Cyprian Girls Secondary School and Nsukka High School.

Population of the Study

The population for the study is all the Senior Secondary Two (SS II)

students in Nsukka Education Zone. According to available records at Nsukka

zonal office of post primary school management board, the total number of SSII

students in the eight schools that have computer facilities were 1,109 students.

Sample and Sampling Technique

The sample for this study comprises of two hundred and seventy one

(271) SS II students drawn from six schools. Out of the eight schools in Nsukka

zone that have computer facilities, boys‟ schools were grouped and from the

group, three schools were randomly selected. Then girls‟ schools were equally

grouped and from the group, three schools were randomly selected, making a

total of six schools. Three, were boys‟ schools while three, were girls‟ schools.

lxviii

There were a total of 132 males and 139 females. The researcher randomly

selected one class from each school making a total of 6 intact classes. Only SS

II students were selected. The three boys‟ schools and three girls‟ schools were

assigned to experimental group 1, II and the control group using simple random

sampling technique.

Instrument for Data Collection

Instrument used for data collection was the Quadratic Equation

Achievement Test (QEAT). This instrument was developed by the researcher

following the table of specification on Appendix A. There were 30 multiple

choice items covering the four methods of solving quadratic equation. Out of

the 30 questions, 18 were of higher order while 12 were of lower order. One test

was used for pretest, posttest and retention test. For retention test, adjustment

was made in the numbering and the options were equally interchanged. This

was to reduce the effect of posttest on the retention test.

Validity of Instrument

Test blue print and test items were subjected to content and face validity.

Validators were to look out for the clarity and suitability of test items. They

were to restructure any item that was not correctly formulated and equally to

remove any ambiguous or double barreled statement. Validators‟ advice enabled

the researcher to include other items that were not earlier included.

lxix

The instrument was equally subjected to content validation where the

validators checked if the items covered the content/unit to be taught, the

objectives of the lesson to be covered, and whether the items are suitable for the

level of the students to be taught. Experts certified that the instrument is valid

for the purpose of the present study. The Instrument (QEAT) has item difficulty

of 0.42 to 0.76 and discriminating indices of between 0.32 and 0.80. There were

equally distracter indices of between + 0.05 to +0.08. Stability coefficient of

0.74 was established for QEAT through test-retest method. The computations

are shown on Appendix K and L respectively.

Reliability of Instrument

There was a trial testing of the Quadratic Equation Achievement test to

estimate the internal consistency and stability of the instrument. The researcher

administered the instrument to SS II students in a school in Obollo Education

Zone which is outside the Education Zone selected for the study. The internal

consistency was computed using Kuder Richardson formula (K – R 20) and

recorded a coefficient of 0.80. The computation is shown on Appendix I.

Experimental Procedure

One class in each school was assigned to experimental group I, II or

control, making a total of two classes for each of the groups.

lxx

Table 2: Classes used for the Study

Schools Exp I Exp II Control

Boys 1 1 1

Girls 1 1 1

Total 2 2 2

For each group, the teacher gave an overview of Quadratic Equation and

what the students are expected to learn. Those in Experimental group 1 were

taken to Mathematics laboratory or computer room where they were given

Intelligent Tutoring Application (ITAS) software on Quadratic Equation. The

software gave tutorial to students like a human tutor. It adopts a “learning-by-

doing” approach where the students follow the step by step instructions, answer

questions and are assessed by the computer. Those in experimental group 2

were also taken to mathematics laboratory or computer room where the teacher

after teaching them demonstrated with the Computer Algebra Application

(CAAS) software to show how computer can solve quadratic equations and

draw graphs. Students in control group were taught quadratic equation without

computer but with the conventional method. In this case, those in experimental

group 1 used computer as tutor while those in the experimental group 2 used

computer as tool and those in group III did not use computer.

Two graduate teachers of mathematics education that are computer

literate were used for the study as research assistants. There were two days

lxxi

training for the research assistants where they were coordinated on how to

handle the two groups. They were exposed to the:

(i) purpose of the research

(ii) concepts to be taught

(iii) procedure for administering the instrument so as to ensure homogeneity

of instructional situation across the groups.

(iv) Teacher for experimental group I was trained to use intelligent tutoring

application software (ITAS) while Teacher for experimental group II was

trained to use Computer Algebra Application Software (CAAS). Then

teacher for the control group did not use computer at all, but used the

conventional method of teaching quadratic equation.

Five research assistants were trained after which three best ones were

selected and used for the study. The researcher visited the six secondary

schools, and with the help of research assistants administered the pre test,

posttest and retention test. The time allocated for pretest, posttest and retention

test was 11/2 hours each. The tests were scored following the marking schemes

on Appendix D and F.

Lesson Note

Three lesson notes were prepared and used for the study by the

researcher. The first one, second, third lesson note were for the experimental

group 1, 2, and control group respectively. The lesson note for the experimental

group 1 contained the tutorial in the Intelligent Tutoring application software

(ITAS) while the lesson note for the experimental group 2 contained the

demonstrations using Computer Algebra application software (CAAS) and the

lxxii

lesson note for the control group followed the conventional method. The lesson

notes are on Appendix B. The notes were face and content validated by three

experts in measurement and evaluation/mathematics education. Their comments

are on Appendix H.

Reduction of Experimental Bias

The actual teaching of the experimental groups was not done by the

researcher but by the research assistants. This was to remove teacher variability.

Control of the Effect of Pre-test on Post –test

The period between the pre-test and post-test was six weeks. This period

was long enough to disallow the pre-test from affecting the post-test. The period

between the post test and retention test was two weeks and the questions for the

retention test were restructured, and interchanged to prevent the effect of post

test on retention test.

Control of Hawthorne Effect

Hawthorne effect occurs when students are aware that they are being used

for experiment. To control this, the research assistants were introduced as new

teachers for the classes. This reduced the suspicion that the teachers were using

them for an experiment.

lxxiii

Method of Data Analysis

Research questions were answered using means and standard deviation.

Research hypotheses were tested using Analysis of covariance (ANCOVA) at

P < .05. The pre-test scores were used as covariate to the post-test scores.

Analysis of covariance (ANCOVA) served as a controller for the initial

differences across groups as well as increased the precision due to the

extraneous variables thus reducing the error variance (Ferguson, 1981).

ANCOVA is a procedure for testing the statistical significance of the difference

in means of two selected groups on their pretest and posttest results.

lxxiv

CHAPTER FOUR

RESULTS

This chapter presents the following: Statistical analysis of data collected,

sequential presentation of results as well as relevant interpretations based on the

research questions and the tested hypotheses.

Research Question I

What are the mean achievement scores of students who were taught with


Table 3: Mean Achievement Scores and Standard Deviation of Students

who were taught with computer and without computer

Group Pretest posttest Mean gain

Tutor Group N 90 90

Mean 18.4222 37.8000 19.3778

Std. Deviation 6.32629 9.44672

Control N 87 87

Mean 18.8391 27.1034 8.2643


Tool Group N 94 94

Mean 18.2340 50.6170 32.383


Total N 271 271

Mean 18.4908 38.8118


Table 3 shows the mean achievement score of students who were taught

with computer as tutor and tool and those who were taught without computer.

Students who were taught with computer as tutor had a mean of 37.8 in the

posttest and standard deviation of 9.4467. Students who were taught with

64

lxxv

computer as tool had a mean of 50.6170 and standard deviation of 1.097 while

students who were taught without computer had a mean of 27.1034 and standard

deviation of 8.7178. The mean achievement scores of students taught with

computer both as tutor and tool were higher than the mean achievement score of

students taught without computer. For the pre-test, the mean achievement scores

of students taught with computer as tutor, tool and control were respectively

18.42, 18.23 and 18.84. This indicates that the students were at the same level

before the experiment.

Research Question 2

What are the mean achievement scores of students who were taught with


Table 4: Mean Achievement scores and standard Deviation of students

taught with computer as tutor and as tool

Modes/Groups Pretest posttest Mean gain

Tutor Group N 90 90

Mean 18.4222 37.800


Tool Group N 94 94

Mean 18.2340 50.6170 12.8170


Table 4 reveals that the mean achievement score of students taught with

computer as tutor was 37.8 in the posttest with standard deviation of 9.45 while

the mean achievement score of students taught with computer as tool was 50.62

with standard deviation of 1.0972. This indicates that students who were taught

lxxvi

with computer as tool achieved higher than students taught with computer as

tutor.

Research Question 3

What are the mean achievement scores of male and female students who

were taught with computer and those who were taught without computer?

lxxvii

Table 5: Mean Achievement Scores and standard Deviation of male and

female students who were taught with computer and without

computer

Group Sex Pretest posttest

Tutor Group Male N 40 40

Mean 16.9000 40.0500

Std. Deviation 6.56643 1.03005E1

Female N 50 50

Mean 19.6400 36.0000


Total N 90 90

Mean 18.4222 37.8000


Control Male N 42 42

Mean 18.4048 27.8333


Female N 45 45

Mean 19.2444 26.4222


Total N 87 87

Mean 18.8391 27.1034


Tool Group Male N 50 50

Mean 17.8400 51.3400


Female N 44 44

Mean 18.6818 49.7955


Total N 94 94

Mean 18.2340 50.6170


Table 5 shows the mean achievement scores and standard deviation of

male and female students who were taught with computer both as tutor and as

tool and also those that were taught without computer. For tutor group, male

lxxviii

students had a mean of 40.05 with standard deviation of 1.030 while female

students had a mean of 36.0 with standard deviation of 8.38 in the posttest. For

tool group, male students had a mean of 51.34 with standard deviation of 9.79

while female students had a mean of 49.80 with standard deviation of 1.22. For

students in the control group, male students had a mean of 27.83 with standard

deviation of 9.01 while female students had a mean of 26.42 with standard

deviation of 8.48. This indicated that male students taught with computer both

as tutor and tool achieved higher than male students taught without computer. In

the same vein, female students who were taught with computer both as tutor and

as tool achieved higher than female students taught without computer. Also

male students who were taught with computer both as tutor and as tool achieved

higher than female students who were taught with computer as tutor and as tool.

lxxix

Research Question 4

What are the mean retention scores of students who were taught with


Table 6: Mean retention scores of students taught with computer and

without computer

Group posttest retention Mean gain

Tutor Group N 90 90

Mean 37.8000 40.6111 3.81111


Control N 87 87

Mean 27.1034 28.0575 0.9541


Tool Group N 94 94

Mean 50.6170 51.7021 1.0851


Total N 271 271

Mean 38.8118 40.4280


Table 6 indicated that the mean retention score of students taught with

computer both as tutor and tool were 40.6111 and 51.7021 respectively with

standard deviations of 8.67 and 1.06. Students that were taught without

computer had a mean of 28.06 with standard deviation of 9.35. This indicated

that students taught with computer both as tutor and tool retained higher than

those taught without computer.

lxxx

Research Question 5

What are the mean retention scores of students who were taught with


Table 7: Mean retention score of students taught with computer as tutor

and tool

Mode/Group posttest retention Mean gain

Tutor Group N 90 90

Mean 37.8000 40.6111 3.81111


Tool Group N 94 94

Mean 50.6170 51.7021 11.0910

Std. Deviation 1.0616

Table 7 indicates that students that were taught with computer as tutor

had a mean retention score of 40.61with standard deviation of 1.06 while

students that were taught with computer as tool had a mean retention score of

51.70 with standard deviation of 1.097. This indicated that students who were

taught with computer as tool retained higher than students taught with computer

as tutor.

lxxxi

Research Question 6

What are the mean retention scores of male and female students who

were taught with computer as tutor and those who were taught with computer as

tool?

Table 8: Mean retention scores and standard deviation of male and female

students who were taught with computer as tutor and as tool

Group Sex posttest retention

Tutor Group Male N 40 40

Mean 40.0500 40.1500


Female N 50 50

Mean 36.0000 40.9800


Total N 90 90

Mean 37.8000 40.6111


Tool Group Male N 50 50

Mean 51.3400 51.0800


Female N 44 44

Mean 49.7955 52.4091


Total N 94 94

Mean 50.6170 51.7021


Table 8 revealed that male students who were taught with computer as

tutor had a mean retention score of 40.15 and standard deviation of 1.05 while

female students who were taught with computer as tutor had a mean retention

score of 40.98 and standard deviation of 7.02. Male students who were taught

with computer as tool had a mean retention score of 51.08 with standard

lxxxii

deviation of 9.40 while female students who were taught with computer as tool

had a mean retention score of 52.41 with standard deviation of 1.19. This result

indicated that female students who were taught with computer both as tutor and

as tool retained more than their male counterpart who were taught with

computer as tutor and tool.

Research Hypothesis

H01: there is no significant difference between the mean achievement scores of

students who were taught with computer and those who were taught without

computer.

Table 9: ANCOVA Table of Students’ scores in the Quadratic Equation

Achievement Test (QEAT)

Source

Type III Sum

of Squares df

Mean

Square F Sig. Result

Corrected Model 26021.050a 6 4336.842 46.218 .000 S

Intercept 36894.217 1 36894.217 393.183 .000 S

Pretest 438.738 1 438.738 4.676 .031 S

Group 25051.040 2 12525.520 133.485 .000 S

Sex 456.915 1 456.915 4.869 .028 S

Group * Sex 128.280 2 64.140 .684 .506 NS

Error 24772.352 264 93.835

Total 459016.000 271

Corrected Total 50793.402 270

S = significant at 0.05 probability level

NS = Not significant at 0.05 probability level.

Table 9 indicated that the use of computer in teaching quadratic equation

is a significant factor in the mean achievement scores of students who were

taught with computer and without computer. This is because with the 95%

lxxxiii

confidence interval of difference, the value of F, its degree of freedom and its P-

value significant, the value of F is46.218, and the result of the test is significant

beyond the .05 level of significant as .000 is less than 0.05. Therefore the null

hypothesis of no significant difference is hereby rejected. This means that there

is a significant difference in the mean achievement scores of students taught

with computer and those taught without computer.

Hypothesis 2

H02: There is no significant difference between the mean achievement scores of

students who were taught with computer as tutor and those who were taught

with computer as tool.

Table 10: ANCOVA table of students who were taught with computer as

tutor and as tool on achievement

Source

Type III Sum

of Squares df Mean Square F Sig. Result


Intercept 37469.739 1 37469.739 358.729 .000 S

Pretest 21.500 1 21.500 .206 .651 NS

Group 7173.694 1 7173.694 68.680 .000 S

Sex 374.368 1 374.368 3.584 .060 NS

Group * Sex 77.062 1 77.062 .738 .392 NS

Error 18696.780 179 104.451

Total 388570.000 184




Table 10 indicated that the mode of computer usage is a significant factor

in the mean achievement scores of students in the Quadratic Equation

Achievement Test. This is because with the 95% confidence interval of

lxxxiv

difference, the value of f, its degree of freedom and its P-value significant, the

value of F is 19.136 and the result of the f-test is significant beyond the 0.05

level of significant as .000 is less than 0.05. This hypothesis 2 of no significant

difference in the mean achievement scores is therefore rejected. This means that

there is a significant difference in the mean achievement scores of students

taught with computer as tutor and those who were taught with computer as tool.

The experimental group II (tool) achieved significantly higher than the

experimental group I (tutor) in the Quadratic Equation Achievement Test.

Hence the use of computer as tool influenced achievement more than the use of

computer as tutor.

Hypothesis 3


of male and female students‟ who were taught with computer as tutor and those

who were taught with computer as tool.

Table 10 indicated that sex is not a significant factor in the mean

achievement scores of students who were taught with computer as tutor and as

tool. This is because with the 95% confidence interval of difference, the value

of F, its degree of freedom and its P-value significant, the value of F is. 738, and

the result of F test is not significant beyond the 0.05 level as .392 is greater than

.05. This hypothesis 3 of no significant difference in the mean achievement

scores is therefore not rejected. This means that there is no significant difference

lxxxv

in the mean achievements scores of male and female students taught with

computer as tutor and as tool.

Hypothesis 4


students who were taught with computer and those who were taught without

computer.

Table 11: ANCOVA Table of Students’ Scores on Retention

Source Type III Sum of Squares df

Mean Square F Sig. Results


Intercept 1700.515 1 1700.515 47.038 .000 S

posttest 15030.561 1 15030.561 415.761 .000 S

Group 827.403 2 413.701 11.443 .000 S

Sex 636.048 1 636.048 17.594 .000 S

Group * Sex 25.855 2 12.927 .358 .700 NS

Error 9544.114 264 36.152

Total 492890.000 271




Table 11, indicated that, there is a significant difference between the

mean retention scores of students who were taught with computer and those

who were taught without computer. This is because with the 95% confidence

interval of difference, the value of F, its degree of freedom and its p-value

significant, the value of F is 186.326, and the result of F test is significant

beyond .05 level as .000 is less than .05. Hypothesis 4 of no significant

difference in the mean retention scores is therefore rejected. Which means that,

lxxxvi

there is a significant difference in the mean retention scores of students who

were taught with computer and those who were taught without computer?

Therefore students who were taught with computer retained significantly higher

than students who were taught without computer.

Hypothesis 5


students who were taught with computer as tutor and those who were taught

with computer as tool.

Table 12: ANCOVA Table of Students who were taught with Computer as

Tutor and as Tool on Retention

Source

Type III Sum

of Squares df

Mean

Square F Sig. Results


Intercept 1806.133 1 1806.133 44.145 .000 S

posttest 9792.840 1 9792.840 239.353 .000 S

Group 146.386 1 146.386 3.578 .060 S

Sex 430.765 1 430.765 10.529 .001 S

Group * Sex 19.580 1 19.580 .479 .490 NS

Error 7323.556 179 40.914

Total 416879.000 184


S= Significant at 0.05 probability level

NS = Not Significant at 0.05 probability level

Table 12 shows that there is a significant difference between the mean

retention scores of students who were taught with computer as tutor and those

who were taught with computer as tool. This is because with the 95%

confidence interval of difference, the value of F, its degree of freedom and its P-

value significant, the value of F is 94.744, and the result of F test is significant

lxxxvii

beyond the 0.05 level as .000 is less than .05. Therefore hypothesis 5 of no

significant difference is rejected. The result indicated that students who were

taught with computer as tool retained significantly higher than students who

were taught with computer as tutor.

Hypothesis 6


male and female students who were taught with computer as tutor and those

who were taught with computer as tool. Hypothesis 6 is tested with table 12.

In table 12, it was indicated that sex is not significant among the groups

(tutor and tool). The table 12 shows the value of F to be .479 and that the result

of F test is not significant beyond the 0.05 level of significant as .490 is greater

than 0.05. Therefore hypothesis 6 of no significant difference is not rejected.

This indicates that there is no significant difference between the mean retention

scores of male and female student taught with computer as tutor and as tool in

the Quadratic Equation Retention Test.

Hypothesis 7

H07: There is no significant interaction effect between modes and gender on

students‟ achievement

lxxxviii

Table 13: ANCOVA Table showing Interaction Effect between Modes and

Gender in the Quadratic Equation Achievement Test (QEAT)

Source

Type III Sum

of Squares df

Mean

Square F Sig. Result


Intercept 36894.217 1 36894.217

39`3.18

3 .000 S

Pretest 438.738 1 438.738 4.676 .031 S

Group 25051.040 2 12525.520 133.485 .000 S

Sex 456.915 1 456.915 4.869 .028 S

Group * Sex 128.280 2 64.140 .684 .506 NS

Error 24772.352 264 93.835

Total 459016.000 271


S= Significant at 0.05 probability level

NS = Not Significant at 0.05 probability level

Table 13 shows the interaction effect between modes (groups) and gender

on students‟ achievement. In table 13, it was indicated that the interaction

between modes and gender is not significant. This is because the value of F is

.684. With the 95% confidence interval of difference, the value of F, its degree

of freedom and its P-value of .506, the result of F test is not significant beyond

0.05 level as .506 is greater than .05. Therefore, the null hypothesis of no

significant interaction effect is not rejected. This implies that there is no

significant interaction effect between modes and gender on students‟

achievement.

Hypothesis 8

H08: There is no significant interaction effect between modes and gender on

retention

lxxxix

Table 11 above shows the interaction effect between modes (groups) and

gender on students‟ retention. In the table, it was indicated that the interaction

between modes and gender is not significant. This is because with the 95%

confidence interval of difference, the value of F, its degree of freedom and its P

value significant, the value of F is .358, and the result of F test is not significant

beyond the 0.05 level as .700 is greater than 0.05. Hypothesis 8 of no significant

interaction effect is therefore not rejected. This implies that there is no

interaction effect between modes and gender on retention.

Summary of Findings

Based on the results of the analysis of data presented in this chapter, the

following major findings came up.

(a) The mean achievement scores of students taught with computer (37.8 for

tutor and 50.62 for tool) were statistically higher than the mean

achievement score of students taught without computer (27.10).

(b) The mean achievement scores of students who were taught with computer

as tool (50.62) was statistically higher than the mean achievement score of

students taught with computer as tutor (37.8).

(c) Male students taught with computer both as tutor (40.05) and tool (51.34)

had statistically higher mean than male students taught without computer

(27.83).

xc

(d) Female students taught with computer (both as tutor 36.0) and tool (49.50)

had statistically higher means than female students taught without

computer (26.42).

(e) Male students who were taught with computer both as tutor and tool had

higher means (40.05, 51.34) than female students taught with computer

both as tutor and tool (36.0, 49.50) on achievement. Though the difference

was not statistically significant.

(f) Students that were taught with computer both as tutor and tool had higher

mean retention scores (40.61, 71.70) respectively than students who were

taught without computer (28.06).

(g) Students that were taught with computer as tool retained higher (51.70)

than students that were taught with computer as tutor (40.05).

(h) Female students that were taught with computer both as tutor and tool

(40.98, 52.41) retained higher than male students that were taught with

computer both as tutor and tool (40.15, 51.08). Though the difference was

not statistically significant.

(i) The interaction effect of modes and gender on students‟ achievement was

not statistically significant.

(j) The interaction effect of modes and gender on students‟ retention was not

statistically significant.

xci

CHAPTER FIVE

DISCUSSION, CONCLUSION, IMPLICATION AND

RECOMMENDATIONS

In this chapter, the results of the analysis of data were discussed. The

discussions were made under the following sub-headings:

Effect of computer on students‟ achievement in Quadratic Equation

Effect of computer on students‟ retention in Quadratic Equation

Interaction effects of Methods and Gender

Conclusions based on the results were also drawn. Educational Implication of

the study, Limitation of the study, Recommendations and Suggestion for further

studies were highlighted.

Finally, the summary of the entire study was presented.

Effect of Computer on Students’ Achievement in Quadratic Equation

The results in table 4 show that students in experimental group II (tool)

had a higher mean achievement score in Quadratic Equation than students in

experimental group I (tutor). This is further confirmed by the result in table 10

which indicated that mode of computer usage is a significant factor in the mean

achievement scores of students in Quadratic Equation. This means that students

who were taught with computer as a tool achieved higher than those who were

taught with computer as tutor. The reason for the better achievement by the

experimental group II was because, no matter the garget or instrument that one

discusses with, it cannot be compared with human being whom you can ask

81

xcii

questions, watch his countenance and feel his presence. This is in agreement

with Taylor (1980), who stated that the computer cannot replace the teacher.

Actually, the teacher‟s place cannot be replaced rather teachers should use the

various technologies, innovations and strategies to augment their teachings and

as teaching aids. Thus this result adopts the use of computer as tool for

meaningful learning/teaching of mathematics. This result is in support of

Michael (2002) who indicated that it is good to use computer in teaching as it

will take care of poor method of teaching and poor textbooks prevalent in

schools.

Again it can be observed from table 4 that the mean achievement scores

for both the experimental groups 1, 11 and control are generally low. This

shows a general poor performance of students in mathematics which goes to

support the WAEC Chief Examiners Report of 2006 and 2007 that students

perform poorly in mathematics and suggested that teachers should intensify

effort in bringing out strategies that will improve students‟ performance for a

meaningful teaching and learning of mathematics.

Effect of Computer on Students’ Retention in Quadratic Equation

Results from table 6 showed that students in experimental group II

obtained a higher mean retention score compared with students in experimental

group 1 and control group. This indicated that students that were taught with

computer as tool retained more than students that were taught with computer as

xciii

tutor and students in control group. This result agrees with Micheal (2002) who

reported that students that were taught with computer retained more than

students that were taught with the conventional method. In his own study he

compared the use of computer as tool and the conventional method. More so, Iji

(2003), in his own study observed that students who used Logo and Basic

programmes retained more than students who used conventional method. In

both programmes, computer was used as a tool. These studies agreed with this

present work on comparing computer with the conventional method. But this

study goes further to compare computer as tutor and as tool and also the

conventional method.

Table 6 indicated that there was a significant difference between the mean

retention scores of students that were taught with computer and those that were

taught without computer. Also students that were taught with computer as tool

retained more than students that were taught with computer as tutor.

Interaction Effects of Method and Gender

The results from table 5 indicated that male students performed higher

than their female counterpart in using computer as tutor and as tool. More so

male students that were taught with computer performed higher than male

students that were taught without computer. Like wise female students that were

taught with computer performed higher than female students that were taught

without computer. However, testing for significance, the results in table10

xciv

indicated that the difference in the mean achievement of male and female

students was not statistically significant. This result goes to support Odogwu

(2001), who indicated that the computer dehumanizes and does not care whether

you are a male or a female. The use of computer in teaching mathematics is

therefore a good strategy of bridging the gap that ever existed between male and

female students‟ achievement in mathematics as reported by Alio, and Harbor-

Peter (2000), Ezugo and Agwagah (2000), Ezeh (2005) and Ogbonna (2007).

Results from table 13 revealed that there is no significant interaction

effect between modes and gender on students‟ achievement. This result is in

concordance with Olagunju (2001) and Etukodo (2002) whose results indicated

that there was no significant difference between male and female students‟

achievement in mathematics. Equally, this result agrees with Franden (2003)

who revealed that male students perform better then female students in

mathematics though the difference is not statistically significant. Franden

attributed the difference to attitudinal, psychological and socio-cultural factors

on girls. However, this result disagrees with Ogbonna (2007) whose result

indicated that females perform better than males in mathematics.

The results in table 8 revealed that female students had a higher mean on

retention when computer was used both as tutor and as tool, but when tested,

table 12 revealed that there was no significant difference between male and

female students achievement on retention. For the interaction effect of method

and gender on retention, results in table 13 revealed that there is no significant

xcv

interaction effect between modes and gender on retention. This result agrees

with Ogbonna (2007) whose result indicated that female students retained more

than their male counterpart in Number and Numeration and also disagrees with

her as Ogbonna established a significant interaction effect between method and

gender on students‟ retention as this study recorded no interaction effect.

However, this result agrees with Micheal (2002) whose result indicated that

there is no significant difference in the mean retention scores of male and

female students in mathematics and also no interaction effect between method

and gender on students‟ achievement and retention.

xcvi

Conclusion

The following conclusions are made based on the findings of this study.

The results of this study provided the empirical evidence that the use of

computer as a tool enhanced students‟ achievement and retention in Quadratic

Equation more than the use of computer as a tutor. Thus the effectiveness of

computer in teaching mathematics depends on the mode of usage. Moreso, that

the use of computer in teaching quadratic equation is better than teaching

quadratic equation without computer.

Secondly male and female students who were taught with computer performed

higher than their counterparts that were taught without computer.

Male students performed higher than female students in the quadratic equation

achievement test, but female students retained more than their male counterpart,

though none of them were statistically significant.

Also, there was no significant difference between the mean achievement

and retention scores of male and female students that were taught with computer

as tutor and tool in Quadratic Equation. Thus the computer did not recognize

whether a male or a female student was using it. This implies that gender has no

significant effect on achievement and retention of students in the Quadratic

Equation Achievement and Retention Tests. In general, the use of computer as a

tool has proved to be viable in enhancing the meaningful teaching and learning

of Quadratic Equation.

xcvii

Implication of the Study

The results of this study have some obvious implications to the teacher in

the sense that the teacher will now know that using computer to augment his

teaching is better than using computer as a teacher. Teachers should therefore

apply this knowledge from the findings of this work in their teachings especially

now that computers are relatively available in schools. Teachers should equally

try to be computer literate, so that they will be able to make use of the computer

in teaching.

Since the efficacy of the use of computer as a tool has been indicated in

this study, States and Federal Ministries of Education should organize seminars

and workshops where teachers, textbook authors and curriculum planners will

be taught the various ways of using computer for effective teaching and learning

of quadratic equation. There should be training of students to enable them to be

computer literate so as to fit in, in this society of technological advancement.

The results of this study also calls for a critical review of the secondary

school mathematics curriculum with the aim of including computer learning and

increasing the time for class lessons so as to accommodate the use of computers

in learning. It could also provide an alternative instructional method that could

be employed by teachers to enhance gender equity in mathematics achievement

and retention. Furthermore, other researchers will use these findings for further

studies by using it as a reference point.

xcviii

Limitations of the Study

The conclusions and generalization of the results of this study have the

following limitations.

1. There might have been little pretest- posttest interference even though

that the interval between the pretest and posttest was six weeks.

2. The work was limited to quadratic equation alone, and did not spread

to other areas of mathematics.

3. Non availability of computers in school posed a lot of problems in the

sense that the researcher had to hire Cyber Café to enable students has

access to computers.

4. Most computers found in some schools are not in use, but were fully

packed for the fact that they do not have a capable hand to handle

them. This delayed this work as the researcher spent more time

teaching the students the basic fundamentals of using computers.

5. Another limitation was the Hawthorne effects. Hawthorne effects can

be reduced when the normal lesson periods and usual classrooms are

used for the conduct of the study, which the researcher did. But the

seriousness of the lessons, framing of the test items on quadratic

equation only and the strictness in administering the tests were enough

to inform the students that the lessons were not ordinary class lessons.

xcix

Recommendations

The following recommendations were mode based on the findings of this

study

1. Since the use of computer as a tool enhances achievement and

retention in mathematics, the mathematics teacher should use it as one

of the strategies to be employed in classroom.

2. Workshops / Seminars should be organized by the Government for

mathematics teachers to enable teachers learn how to use computer in

teaching mathematics especially quadratic equation.

3. Computers should be made available in schools, by the Government

so that every student will have access to computers and make use of

them in learning.

4. Parents should equally be encouraged to buy computers for students to

use at home after normal classes. This will help students to practice

what they have learnt in school and equally discourage them from

engaging in unnecessary ventures after school.

5. Programmers and software producers should be encouraged to use

mathematics curriculum in the production of software and equally

arrange them according to classes.

c

Suggestion for further Studies

Similar investigations should be carried out to determine the effect of the

use of computer in other areas of mathematics and sciences and equally

compare other modes of computer usage especially the use of computer as a

tutee. Other software like Novanet, Maths Blaster and Blackjack could equally

be used. Secondly, similar studies can be replicated in other Education zones,

States of the Federation with larger samples. Finally, the researcher equally

suggests that students and teachers in the rural areas should be remembered, so

that they will be part of this innovative practice.

Summary of the Study

This study compared the effectiveness of computer as tutor and as tool in

teaching and learning of Quadratic Equation. This study was carried out in

Nsukka Education Zone of Enugu State. A sample of two hundred and seventy

one (271) students made up of one hundred and thirty two (132) males and one

hundred and thirty nine (139) females were randomly selected from the 1,109

SS II students in the eight schools that have computers in the zone. Two intact

classes were selected from each of the three schools drawn and used as

Experimental group I (computer as tutor) or as Experimental group II (computer

as tool) or as control group. On the whole, six intact classes were used for the

three groups making a total of two classes for each group.

The design of this study was quasi-experimental. Six research questions

and eight hypotheses guided this study. Two soft wares were used; Computer

ci

Algebra Application Software (CAAS) for students in Experimental group II

and Intelligent Tutoring Application Software (ITAS) for students in

Experimental group1, then those in control group did not use any software.

Instrument used for data collection was the Quadratic Equation

Achievement Test (QEAT) developed by the researcher using a table of

specification and made up of 30 multiple choice items. Quadratic Equation

Retention Test was also developed by the researcher from the Quadratic

Equation Achievement Test. The only difference was that the questions were

restructured and interchanged to avoid the effect of the posttest on retention test.

There were three lesson notes, one for the experimental group I, one for the

experimental group II and the other one for the control group. They were

validated by experts in mathematics education and measurement and evaluation.

There was a trial testing to estimate the internal consistency and stability of the

instrument. There was a pretest, posttest and retention test.

Eight research questions guided this study and were answered using mean

and standard deviation while the six hypotheses were tested using Analysis of

covariance (ANCOVA). Data generated from the tests administered to the

students were to compare the effectiveness of computer as tutor with computer

as tool, and also compare the effectiveness of using computer and not using

computer in teaching quadratic equation.

Results showed that students who were taught with computer as tool

achieved and retained higher than students who were taught with computer as

cii

tutor in both the posttest and retention test. It equally revealed that students that

were taught with computer achieved higher than students that were taught

without computer. The result also showed that male students achieved higher

than the female students, though the difference was not statistically significant.

The results had some implications to teachers, educators, students,

parents, computer programmers, software developers, States and Federal

Ministries of Education and other researchers. One of which was to organize

seminars and workshops to educate teachers on using computer in teaching

quadratic for effective teaching and learning.

This study recommended among other things that since computer as tool

is found to be a facilitative instructional strategy for improving achievement and

retention in quadratic equation, teachers should adopt it in teaching.

ciii

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cx

APPENDIX A

Table of Specification or Test blue Print

N/S Content dimension Ability process dimension

Lower cognitive

process

Higher Thinking

Process

Total

% 40 60 100

1. Quadratic Equation by

Factorization method

20 2 (1,2) 4 (3,4,5,6) 6


Completing the square

30 4 (7,8,9,13) 5 (10,11,12,14,15) 9


Formulae

20 2 (16,17) 4 (18,19,20,21) 6

4. Quadratic Equation by Graph

method.

30 4 (22,23,24,30) 5 (25, 26,27,28,29) 9

Total 100 12 18 30

Percentages were allocated to the contents based on the National

Mathematics Curriculum. Volume of content, time spent in teaching them and

the difficulty levels of the contents, were considered

cxi

APPENDIX B

LESSON NOTES

Lesson note for experimental group I (computer as tutor)

Subject: Mathematics

Topic: Quadratic equation by factorization method

Class: SSII

Duration: 40mins (3periods)

Instructional Aid: Chalk, Textbook, Chalkboard, Computer and intelligent

tutoring Application (ITAS) software

Instructional objectives: By the end of the lesson, students should be able to

(i) Solve quadratic equation by factorization method

(ii) Form equations when roots are given.

Content

development

Teacher’s Activities Students’

Activities

Strategies

Entry behaviour 1) The teacher allows students some

seconds to settle down while she wipes

the board.

2) The teacher assumes that students have

known how to solve linear equation

3) The teacher tests the assumed

knowledge by giving the students a

linear equation to solve. 2x + 4 = - 6,

find x.

4) The teacher introduces the day‟s lesson

by writing Quadratic equation by

factorization method on the

chalkboard.

5) The teacher explains by telling

students that the general form of any

quadratic equation is ax2 + bx + c = 0

where a is the coefficient of x2, b the

coefficient of x and c the constant for a

≠0.

6) The teacher takes the students to maths

laboratory or computer room where

she pairs students, one computer to

five students, depending on the

availability of computers in the school.

The teacher begins with a placement

Students solve the

equation in their

exercise books.

Students will use

the mouse and

keyboard to go

through the

tutorial.

Learning by

doing.

cxii

test before beginning the computer-

based instruction. The placement

provides the information of where to

place the user. The user (student) goes

on at his/her own pace until the lesson

is completed. The tutorial is as

follows: this is the intelligent tutoring

Application Software which you will

use in learning Quadratic Equation.

The general form of quadratic equation

is ax2+bx+c =0 where a is the coeff of

x2,b the coeff of x and c the constant

for a≠0. Methods: (1) factorization (2)

completing the square (3) formular (4)

graph. (1) Factorization method: To

factorize a given expression, you will

first get the factors. For example, the

quadratic equation x2+7x+10 = 0.

Factors of 10 that will equal 7 when

added are 2 and 5. The equation now

gives (x+2)(x+5) = 0 which implies x

=-2 and -5. Eg2. A quadratic equation

whose coefficient of x2 is not unity

could be solved as shown. 6x2-7x+2 =

0. The factors are got by multiplying 6

by 2 to get 12 and finding the factors

of 12. The equation is broken down to

(6x2-3x)-(4x-2) = 0. Therefore x = 2/3

and ½. Further examples: If roots – 2

and -5 are given, equation is formed as

x2-(-2+-5) x + (-2x-5) = 0 x

2 + 7x +

10 = 0. The students use a

combination of the mouse and

keyboard to proceed through the

tutorials. Students used the mouse to

click correct answers or move objects

according to the direction of intelligent

tutoring application software and use

the keyboard to enter responses to

open-ended questions. The tutorial

continues until the end with

assessment being done from time to

time.

Exercise:

cxiii

Solve x2-7x+6 =0 (a) -2,3 (b) 2,3 (c) -2,-3

(d) 2,3. If you get the correct answer, move

to the next stage, if not, repeat the tutorial.

Evaluation: The teacher evaluates by giving

a take home assignment. Solve the quadratic

equations by factorization method

(1) 3x2 – 13x + 10 = 0

(2) x2 – 7x+6 = 0. (3) Form the equation

whose roots are -2 and 3

Use their

computer to

practice

Learning by

doing.

Questioning.

Lesson Note for Teaching the Experimental group-2 Quadratic Equation

by factorization method


Topic: Quadratic Equation by Factorization Method

Class: SS11

Duration: 40 minutes (3 periods)

Instructional Aids: Chalk, Textbook, Chalkboard, Computer and Computer

Algebra Application Software (CAAS).

Instructional Objective: By the end of the lesson, students should be able to

(i) Solve quadratic equation by factorization method

(ii) Form equations when roots are given.

Content

Development

Teachers Activities Students’

Activity

Strategies

Entry

Behaviour

1) The teacher allows students some

seconds to settle down while she wipes

the board.

2) The teacher assumes that students have

known how to solve linear equation

3) The teacher tests the assumed knowledge

by giving students a linear equation to

find the value of x. Find x in the equation

2x + 4 = - 6.

4) The teacher introduces the days lesson by

writing Quadratic equation

5) The teacher explains by telling students

that the general form of any quadratic

equation is ax2 + bx +c = 0 where a is the

coefficient of x2, b the coefficient of x

Ask

questions

and put

down in

their

various

notes.

Note taking and

Questioning

Listening and

questioning

cxiv

and c the constant where a≠0. To solve a

quadratic equation by factorization

method, the factors of the constant must

be found. If the coefficient of x2

is not

unity, then the factors are found by first

multiplying the coefficient of x2 by the

constant Example: Solve the quadratic x2

+ 7x + 10 = 0 by factorization.

Solution: The constant is 10. Factors of 10 are 2

and 5, -2 and -5, 10 and 1, -10 and 1. But the

one that will equal 7 when added are 2 and 5.

Therefore (x+2)(x+5) = 0. Example 2. Solve the

quadratic 6x2- 3x -4x +2 = 0.

Then group to have (6x2-3x) - (4x-2) = 0

3x( 2x - 1) – 2 (2x - 1) = 0

(3x - 2)(2x - 1) = 0 3x – 2 = 0

χ= 2/3. If 2x – 1 = 0 x = 1/2. Therefore

the roots of the quadratic are

1/2 and 2/3.

The teacher informs students that roots of a

quadratic equation could be given and one is

expected to find the equation. For example:

Given the roots – 2 and -5 form the equation.

The equation gives x2- (sum of roots) x +

product of roots = 0.

:. χ2 – (-2 + -5)x + (-2 x -5) = 0 x

2 – 7x + 10

= 0

= x2 + 7x + 10 = 0

Questioning

The teacher at this stage takes the students to

maths laboratory or computer room where she

uses CAAS software to demonstrate how the

computer can do the manipulations of sum and

product in solving quadratic equation. She goes

further to demonstrate its computational power

and also to show that CAAS can manipulate

symbolic expressions or equations and find their

values. The software is as follows: Finding the

factors of numbers. If you have an equation of

the form, ax2+bx+c = 0, it could be factorized

for you. Just enter the product of a and c and

click on factorize for example the equation 2x2-

8x+6 =0.

Demonstration

cxv

Lesson Note for Teaching the Control group Quadratic Equation by

Factorization


Topic: Quadratic equation by factorization method

Class: SS11

Duration: 40minutes (3 periods)

Instructional Aids: Chalk, Textbook, Chalkboard,

Instructional Objectives: By the end of the lesson, student should be able to

(i) Solve quadratic equation by factorization method.

(ii) Form equations when roots are given

Enter the value of “a” X “c”

Click on factorize

Then all the possible factors are displayed with

the sum. Then click on Ok.

Evaluation: The teacher evaluates by giving a

take home assignment from the students‟ text.

(1) 3x2 – 13x + 10 = 0. (2) x

2 – 7x + 6 = 0. (3)

Form the equation whose roots are -2 and 3.

Note taking and

Questioning

Factorize

Ok

cxvi

Entry

Behaviour

(1) The teacher allows students some

seconds to settle down while she

wipes the board.

(2) The teacher assumes that students

have known how to solve Linear

equation

(3) The teacher tests the assumed

knowledge by giving the students

a linear equation to solve (1)

Solve the equation 2x + 4 = -6.

(4) The teacher introduces the lesson

by writing Quadratic equation by

factorization method on the

chalkboard. She goes further to

explain how to solve.

(5) The teacher writes/solves

example on the chalkboard. Example 1: Solve the equation x

2 + 7x

+ 10 = 0

Factors of 10 that will equal 7 when

added are 2 and 5.

The equation equals (x+2)(x+5) = 0.

x+2 = 0 or x + 5 = 0

If x + 2 = 0, If x + 5 = 0

x = -2 x = -5.

Eg. 2 A quadratic equation whose

coefficient of x2 is not unity is solved as:

6x2 – 7x+2 =0

The factors are got by multiplying 6 by

2 to get 12 and finding the factors of 12.

The equation is broken down to (6x2-

3x)-(4x-2) =0

3x(2x-1) -2(2x-1)

(3x-2)(2x-1) = 0

If 3x – 2 = 0 x = 2/3

If 2x – 1 = 0 x = ½.

Further examples: The teacher gives

roots and teaches how the equation

could be formed.

If the roots of an equation are -2 and -5,

the equation is formed by x2 – (sum of

roots)x + (product of roots) = 0

Copy note, ask

questions and pay

attention

Copy notes and

pay attention

Questioning

cxvii

Lesson Note for Teaching the Experimental Group1, Quadratic Equation

by Completing the Square Method


Topic: Quadratic equation by completing the square

Class: SS11

Duration: 40 mins (3periods)

Instructional Aid: Chalk, Textbook, Chalkboard, Computer and Intelligent

tutoring application software.

Instructional: By the end of the lesson, students should be able to solve

quadratic equation by completing the square.

Content

Development

Teacher’s Activities Students

Activity

Strategies

Entry

behaviour



wipes the board.

2) The teacher assumes that students

have known how to solve quadratic

equation by factorization method.



quadratic equation to solve by

Students will

use the mouse

and key board

in going

through the

lesson.

Learning by

doing

Factorization

method

x2 – (-2+-5) x + (-2x-5) = 0

x2 + 7x + 10 = 0.

Exercise: solve x2 – 7x + 6 = 0

(a) -2, 3 (b) 2,3 (c) -2,-3 (d) 2,3.

Evaluation: The teacher gives a take

home assignment from the students‟ text

book. Factorize (1) 3x2-13x+10 = 0

(2) x2 – 7x+6 = 0

(3) Form the equation whose roots are -2

and 3.

Copy on their

assignment book.

Questioning

cxviii

factorization (1) Solve the equation

x2 – 2x -3 = 0.

4) The teacher introduces the lesson by

writing Quadratic equation by

completing the square on the

chalkboard. She goes further to tell

students that an intelligent tutor will

be given to them that will teach

them the concept.

5) The teacher takes the students to

maths laboratory or computer room

where she pairs students, one

computer to five students (1:5)

depending on the availability of

computers.

6) The teacher helped the students to

enter the system and they move on

at their group pace until the lesson is

completed. They followed the

lesson step by step and used the

mouse and keyboard for clicking

correct answers and to enter

responses to open-ended questions

respectively. Next stage:

quadratic by completing the square

Rule 1. Make coeff of x2 unity

2. Add ½ coeff of x to both sides and

square eg. The quadratic x2+7x+10 = 0.

The coefficient is unity. Move to second

stage Add ½ coefficient of x and square.

Coefficient of x is 7. Half of 7 is 7/2. Add

to both sides to get x2+7x+(7/2)

2 = -

10+(7/2)2. Therefore (x+7/2)

2 = -10+49/4=

-40+49 = 9

4 4

(x+ 7/2)2 = 9/4 x + 7/2 = ±√9/4.

Therefore x = -7/2 ± 3/2 = -4/2 or -10/2

x = -2 or -5. E.g2 If coefficient of X2 is

not unity like 6x2 – 7x+2 =0. Following

the rules equals:

6x2 – 7x = -2 x

2 – 7x = -2

6 6 6 6 6

coefficient of x is -7/6 and half of it gives

cxix

– 7/12 Therefore Adding the square to

both sides equals

x2 – 7/6x + (-7/12)

2 = - 2/6 + (-7/12)

2.

Therefore Adding the square to both sides

gives x2 -

7x + (-7)

2 = - 2 + (-7)

2

6 12 6 12

(x - 7)2 = -2 + 49

12 6 144

Therefore x = 2/3 or 1/3

In so doing, the tutorial will continue until

the lesson ends with assessment from time

to time.

Exercise:

Solve x2-7x+6 =0 (a) -2,3 (b) 2,3 (c) -2,-3

(d) 2,3. If you get the correct answer,

move to the next stage, if not, repeat the

tutorial.

Students follow

the lesson step

by step

Learning by

doing

Quadratic

Equation by

completing

the square.

Evaluation: The teacher evaluates by

giving a take home assignment. Solve the

quadratic equation by completing the

square and compare the answers with that

of factorization method. (1) 3x2 – 13x + 10

=0

(2) x2 – 7x + 6 = 0.

Copy inside

their exercise

books to be

submitted later.

Questioning

Lesson Note for Teaching the Experimental group 2- Quadratic Equation

by completing the square


Topic: Quadratic equation by completing the square

Class: SS11



Algebra Application (CAAS) Software.

Content

Development

Teacher’s Activity Student Activity Strategies

Entry

Behaviour

(1) The teacher allows students some


cxx

wipes the board.


have known how to solve

quadratic equation by

factorization method.

(3) The teacher tests the assumed

knowledge by giving a quadratic

equation for students to solve

using factorization method. Solve

the equation x2- 2x – 3 = 0


by telling students that in solving

quadratic equation by completing

the square, they should follow the

rule and arrive at the correct

answer just as in factorization:

For example to solve the

quadratic x2- 2x – 3 = 0 by

completing the square

Rule

(1) First make the coefficient of x2

unity. In this case, the coefficient is

unity. (2) Add ½ coefficient of x and

square it. This gives (1/2 of -2)2

(-1)2

= 1. Then add to both sides to

have x2 – 2x + 1=3+1 x

2 – 2x + 1

2 =

3 +1. (x - 1)2 = 4

:. x = 1± 2 x = 1+2 or x = 1 – 2.

x = 3 or x = -1. This gives the same

answer as got in using factorization

method.

Students solve the

problem

Students listen and

ask questions

Questioning

Questioning

Quadratic

Equation by

completing

the square

But if the coefficient is not unity. For

example using the example on

factorization method; 6x2 – 7x+2 = 0.

Rule (1) Make coefficient of x2 unity by

dividing every number by 6 to have 6x2/6

-7x/6 = - 2/6. x2 – 7x/6 = - 1/3.

(2) Add ½ coefficient of x to both sides

to have (1/2 of -7/6)2 = (-7/12)

2.

(x – 7/12)2 = -1/3 + 49/144 = -48+49

144

= 1/144

(x-7/12)2 = 1/144. Therefore

Pay attention and

ask questions

Questioning

cxxi

Lesson Note for Teaching the Control Group Quadratic Equation by

Completing the Square


Topic: Quadratic Equation by completing the square

Class: SS11


Instructional Aids: Chalkboard and textbook

x – 7/12 = ±√1/144. x – 7/12 ± 1/12.

7/12 + 1/12 or 7/12 – 1/12

7+1 or 7-1 = 8/12 or 6/12 = 2/3 or 1/3

12 12

Computer as

tool.

which was the answer got in using

factorization method. The teacher at this

stage takes the students to maths

laboratory or computer room where she

uses, CAAS to demonstrate the

computational powers of computer.

Enter values for ax2 + bx + c = 0

a = b = , c =

Complex number solution x1 = ,

x2 = .

The student with the help of the mouse

enters values on the boxes for a, b and c

and then click on solve. Then computer

completes and gives the answer.

Students watch

and pay attention

with enthusiasm.

Demonstration

and learning

by doing.


giving a take home assignment: Solve

the following quadratic equation by

method of completing the square.

(1) 3x2- 13x +10 = 0

(2) x2 – 7x +6 = 0

Students write

down the

assignment in

their exercise

books.

Solve Start over

cxxii

Content

Development

Teacher’s Activity Student Activity Strategies

Entry

Behaviour

(1) (1) The teacher allows students

some seconds to settle down

while she wipes the board.


have known how to solve

quadratic equation by

factorization method.

(3) The teachers test the assumed

knowledge by giving a quadratic

equation for students to solve

using factorization method. Solve

the equation x2- 2x – 3 = 0


by telling students that in solving

quadratic equation by completing

the square, they should follow the

rule and arrive at the correct

answer just as in factorization:

For example to solve the

quadratic x2- 2x – 3 = 0 by

completing the square

Rule

(1) First make the coefficient of x2

unity. In this case, the coefficient is

unity. (2) Add ½ coefficient of x and

square it. This gives (1/2 of -2)2

(-1)2

= 1. Then add to both sides to

have x2 – 2x + 1=3+1 x

2 – 2x + 1

2 =

3 +1. (x - 1)2 = 4

:. x = 1± 2 x = 1+2 or x = 1 – 2.

x = 3 or x = -1. This gives the same

answer as got in using factorization

method.

The teacher gives further examples

2x2- 8x + 6 = 0

2x2 – 8x = -6

2 2 2

x2 – 4x = -3

Copy note and pay

attention

Questioning

cxxiii

x2 – 4x + (2)

2 = -3+2

2

(x-2)2 = -3 + 4

(x-2)2 = 1

x – 2 = ±√1

x = 2 ±√1

x = 2+1 or 2-1

3 or 1.

Quadratic

Equation by

completing

the square

But if the coefficient is not unity. For

example using the example on

factorization method; 6x2 – 7x+2 = 0.

Rule (1) Make coefficient of x2 unity by

dividing every number by 6 to have 6x2/6

-7x/6 = - 2/6. x2 – 7x/6 = - 1/3.

(2) Add ½ coefficient of x to both sides

to have (1/2 of -7/6)2 = (-7/12)

2.

(x – 7/12)2 = -1/3 + 49/144 = -48+49

144

= 1/144

(x-7/12)2 = 1/144. Therefore

x – 7/12 = ±√1/144. x – 7/12 ± 1/12.

7/12 + 1/12 or 7/12 – 1/12

7+1 or 7-1 = 8/12 or 6/12 = 2/3 or 1/3

12 12

Pay attention and

ask questions

Questioning


giving a take home assignment: Solve

the following quadratic equation by

method of completing the square.

(1) 3x2- 13x +10 = 0

(2) x2 – 7x +6 = 0

Students write

down the

assignment in

their exercise

books.

cxxiv

Lesson Note for teaching the Experimental group 1- Quadratic Equation

by general formulae


Topic: Quadratic equation by general formulae

Duration: 40mins (3periods)

Instructional Aid: Chalk, Textbook, Chalkboard, Computer and

Intelligent tutoring application software (ITAS).

Instructional objective: By the end of the lesson, students should be able to

solve quadratic equation by the general formulae.

Content

Development

Teachers Activity Students’

Activity

Strategies

Entry

Behaviour

1) The teacher takes students to the maths

laboratory or computer laboratory where

they used the intelligent tutor. The teacher

paired students according to the

availability of computers. She helped them

enter the system and with the mouse and

keyboard they entered, scrolled through

the tutorials at their own pace until the

lesson is completed. They followed the

lesson step by step, use the mouse to click

correct answers and also used the

keyboard to enter responses to open-ended

questions. The tutorial continued until the

lesson ends with assessment from time to

time.

for example the tutorial is as follows: The

general formular is stated as x = -b ±√b2-4ac

2a


coefficient of x and c the constant for a ≠0.

Then a quadratic equation to be solved is

given and values of a, b and c are identified

and substituted to give the correct answer.

Enter values for a, b and c below and press

get results

The students

list the

values of a, b

and c on

their exercise

books.

The students

use the

mouse and

keyboard to

scroll

through the

tutorial and

answer

questions.

Questioning

Learning by

doing.

cxxv

a b c

x2 x

x1 , x2 , Discriminant

Evaluation: The teacher evaluates by giving

them the same assignment given to the

control group. Solve the quadratic equation

using the general formulae

(1) 3x2 – 13x + 10 = 0

(2) x2 – 7x +6 = 0

Students

copy down

the

assignment

in their

exercise

books.


by the use of General Formulae



Class: SS11



Algebra Application Software (CAAS)

Content

Developme

nt

Teachers activity Student

Activity

Strategies

Entry

behaviour



wipes the board.



equation by factorization method

and can identify the values of a, b

and c.


Students list

the values of

Questioning

Get result Clear Result

Ok

cxxvi


quadratic equation to list the values

of a, b and c. List the values of a, b

and c in the equation 6x2 + 7x – 12 =

0 .

a, b and c .

Quadratic

Equation by

general

formulae

4) The teacher introduces the use of

formulae by telling students that the

formulae for solving a quadratic

equation is stated as

a

acbbx

2

42


coefficient of x and c the constant for a≠0.

She goes further to explain that in any

given quadratic equation, you can use the

method. For example solve the quadratic

equation

6x2 - 7x + 2 = 0 using the general

formulae. Solution:

a = 6, b = -7 and c = 2

62

26477 2

x

xxx

12

48497

12

48497

= 7± 1

12.

:. x = 7+1 or 7-1 2/3 and 1/2.

12. 12

The teacher refers students to the answers

got in factorization and completing the

square method and tells them that they are

the same with that of the general formulae,

which indicates that no matter the method

you use, you must arrive at the same

answer. The teacher at this stage takes the

students to maths laboratory or computer

room where she uses CAAS software to

demonstrate, as follows: The formular x =

Students pay

attention and

ask questions.

They also put

the solution

down in their

note books.

Students are

given other

examples to

solve.

Questioning

Demonstrate

cxxvii

Lesson Note for Teaching the Control Group Quadratic Equation by

General formulae



Class: SS11



-b±√b2-4ac .

2a

In the quadratic equation 6x2-7x+2 = 0 a =

6, b = -7 and c = 2. The moment these

values are given to the computer and

placed at the predetermined boxes, the

values of x are given. This indicates that

the computer did the computation and only

supplies the students with the answers.

Demonstrati

on of how

computer

does the

calculation

This was to show the computational power

of the computer. The numbers for the

variables a; b and c are keyed in, while the

computer substitutes the values and comes

out with the correct answers.

Student watch

with

enthusiasm and

also are

allowed to

handle the

mouse and

keyboard to

practice the

teacher‟s

demonstration.

Learning by

doing and

questioning

EVALUATION The teacher evaluates by giving a take

home assignment where students are to

solve two equations they have been solving

with formulae method. Solve the quadratic

equations given with the general formulae

method. (1) 3x2 – 13 + 10

(2) x2- 7x + 6 = 0.

cxxviii

Instructional Objectives: By the end of the lesson, students should be able to

solve quadratic equation by formular method

Content

Developme

nt

Teachers activity Student

Activity

Strategies

Entry

behaviour



wipes the board.



equation by factorization method

and can identify the values of a, b

and c.



quadratic equation to list the values

of a, b and c. List the values of a, b

and c in the equation 6x2 + 7x – 12 =

0 .

Students list

the values of

a, b and c .

Questioning

Quadratic

Equation by

general

formulae

4) The teacher introduces the use of

formulae by telling students that the

formulae for solving a quadratic

equation is stated as

x = -b ±√b2 – 4ac

2a where a is the coefficient

of x2, b the coefficient of x and c the

constant for a≠0. She goes further to

explain that in any given quadratic

equation, you can use the method. For

example solve the quadratic equation

6x2 - 7x + 2 = 0 using the general

formulae. Solution:

a = 6, b = -7 and c = 2

62

26477 2

x

xxx

12

48497

12

48497

= 7± 1

Students pay

attention and

ask questions.

They also put

the solution

down in their

note books.

Students are

given other

example to

solve.

Questioning

cxxix


by graph Method


Topic : Quadratic equation by graph method

Class: SS11

12.

:. x = 7+1 or 7-1 2/3 and 1/2.

12. 12

The teacher refers students to the answers

got in factorization and completing the

square method and tells them that they are

the same with that of the general formulae,

which indicates that no matter the method

you use, you must arrive at the same

answer.

The teacher gives further examples

2x2- 8x + 6 = 0

a = 2, b = -8, c = 6

22

62488

2

4 22

x

xx

a

acbbx

4

48648

4

48

4

48

4

48

4

168

or

.134

4

4

12oror

Students pay

attention and

write down in

their note

books.

Questioning


giving a take home assignment: Solve the

following quadratic equation by formular

method.

(1) 3x2- 13x +10 = 0

(2) x2 – 7x +6 = 0

Students write

down the

assignment in

their exercise

books.

cxxx


Instructional Aids: Chalk, Textbook, Chalkboard, Computer intelligent

tutoring Application Software (ITAS).


solve quadratic equations by graph method.

Content

Development

Teachers Activity Students

Activity

Strategies

Entry

Behaviour

Testing

Assumed

knowledge

Quadratic

Equation by

graph method.



wipes the board.


have known how to draw linear

graphs.


knowledge by asking students to list

what is required in drawing a linear

graph. For example

(1) Graph sheet (2) x and y axes (3) Table

of value

4) The teacher introduces graph method by

telling students that in drawing a quadratic

graph, they will also need a graph sheet,

identify the x and y axes and also prepare

a table of value that will enable them plot

values on the graph.

5) The teacher takes them to maths

laboratory or computer lab where they

used the tutorial for their lesson. The

teacher paired the students according to

the availability of computers. She helped

them entered the system with the mouse

and keyboard. The tutorial gives the

teaching as follows: In general, the graph

of a quadratic equation y = ax2+bx+c is a

parabola. If a >0, then the parabola has a

minimum point and opens upwards (U

shaped) e.g x2+2x-3 =0. If a<0, then the

parabola has a maximum point it opens

downwards (n-shaped) e.g -2x2+5x+3 =0.

In order to sketch the graph of the

The students

list the

requirement for

drawing a

linear graph.

Student use the

mouse and

keyboard to

scroll through

the lesson and

answer

question

Questioning

Learning by

doing

cxxxi

quadratic equation you follow these steps:-

(a) Check if a >0 or a <0. to decide

whether it is u-shaped or n shaped.

(b) The vertex: The co-ordinate of the

minimum point or maximum point is

given by x = -b

2a.

(c) The coordinates of the y – intercept

(Substitute x = 0).

(d) The coordinates of the x intercepts

(Substitute y = 0).

(e) Sketch the parabola.

The computer then forms the table of

value and draws the graph. Student

watched the computer draw the graph.

There will be assessment at intervals and

students used the mouse to click correct

answers and the keyboard to entered

responses to open-ended questions. The

tutorial continued until the lesson is ended


giving them the same assignment given to

those in experimental group 2. Solve the

quadratic equation by graph method

(1) 3x2 -13x +10 = 0

(2) x2 -7x + 6 = 0

Students copy

the assignment.

Lesson Note for Teaching the Experimental Group 2- Quadratic Equation

by graph Method


Topic: Quadratic equation by graph method

Class: SS11


Instructional Aids: Chalk, Textbook, Chalkboard, Computer and

Computers Algebra Application (CAAS) Software.



Content

Development


Activity

Strategies

cxxxii

Entry

Behaviour

Testing

Assumed

knowledge

Quadratic

Equation by

graph method.

The teacher allows students some seconds to

settle down while she wipes the board.

The teacher assumes that students have

known how to draw linear graphs.

The teacher tests the assumed knowledge by

asking students to list what is required in

drawing a linear graph. For example

(1) Graph sheet (2) x and y axes (3) Table of

Value.

The teacher introduces graph method by



identify the x and y axes and also prepare a

table of value that will enable them plot

values on the graph. The teacher gives

example. Solve the quadratic equation 6x2 –

7x+2 = 0. by graphing with the interval -3≤ x

≤ 3.

Solution: First prepare a table of value as

shown:

x -3 -2 -1 0 1 2 3

6x3 54 24 6 0 6 24 54

-7x 21 14 7 0 -7 -14 -21

+2 2 2 2 2 2 2 2

y 77 40 15 2 1 12 35

Secondly, if a scale is not given, choose a

scale that will suit the table, then draw the

graph as shown:

Students pay

attention and

ask questions

Questioning

-3 -2 -1 0 1 2 3 4

80

60

40

20

-20

*

*

*

* *

*

*

Y

Y

X X

cxxxiii

The teacher at this stage takes students to

mathematics laboratory or computer room

where she will use CAAS software to

demonstrate how a computer does the

graphing. Instead of drawing by hand,

students will watch the computer draw the

relations and find their values, the moment

the values are given.

Students

watch with

enthusiasm

Demonstrati

on and

Learning by

doing.

Evaluation: The teacher gives students two

equations to use graph method in finding their

roots (1) 3x2-13x+10 (2) x

2-7x+6 =0 with

interval -2≤ x ≤2 and scale of 2cm to 1 unit

on x axis and 2cm to 10 units on y axis,

Puts down

the

assignment in

their notes.

Questioning

Lesson Note for Teaching the Control Group Quadratic Equation by graph

Method


Topic: Quadratic equation by graph method

Class: SS11





Content

Development


Activity

Strategies

Entry

Behaviour

Testing

Assumed

knowledge

(1) The teacher allows students some seconds

to settle down while she wipes the board.

(2) The teacher assumes that students have

known how to draw linear graphs.

(3) The teacher tests the assumed knowledge

by asking students to list what is required

in drawing a linear graph. For example

(1) Graph sheet (2) x and y axes (3) Table of

Value.

The teacher introduces graph method by



identify the x and y axes and also prepare a

table of value that will enable them plot

cxxxiv

Quadratic

Equation by

graph method.

values on the graph. The teacher gives

example. Solve the quadratic equation 6x2 –

7x+2 = 0. by graphing with the interval -3≤ x

≤ 3.

Solution: First prepare a table of value as

shown:

x -3 -2 -1 0 1 2 3

6x3 54 24 6 0 6 24 54

-7x 21 14 7 0 -7 -14 -21

+2 2 2 2 2 2 2 2

y 77 40 15 2 1 12 35

Secondly, if a scale is not given, choose a

scale that will suit the table, then draw the

graph a shown in the graph sheet attached.

Students pay

attention and

ask questions

Questioning

The teacher gives further examples:

To solve the equation

6x2 + 7x – 12 = 0

First form the table of value.

x -2 -1 0 1 2

6x2 24 6 0 6 24

7x -14 -7 0 7 14

-12 -12 -12 -12 -12 -12

y -2 -13 -12 1 16

2) Choose scale if you were not given scale.

(3) Draw the graph.

The teacher shows on the chalkboard how to

draw

Students pay

attention and

ask questions

Students

draw graphs

on their

graph

sheets.

-3 -2 -1 0 1 2 3 4

80

60

40

20

-20

*

*

*

* *

*

*

Y

Y

X X

cxxxv

Evaluation: The teacher gives students two

equations to use graph method in finding their

roots (1) 3x2-13x+10 (2) x

2-7x+6 =0 with

interval -2≤ x ≤2 and scale of 2cm to 1 unit

on x axis and 2cm to 10 units on y axis,

Students

write down

the

assignment in

their notes.

Questioning

cxxxvi

APPENDIX C

TEACHER MADE ACHIEVEMENT TEST FOR PRETEST AND POSTTEST

TIME: 11/2hrs

1. Factorize the following expression 2x2 + x – 15 = 0.

(a) (2x+5)(x-3)

(b) (2x-5)(x +3)

(c) (2x - 5)(x - 3)

(d) (2x-3)(x + 5)

(e) (2x+5)(x+3)

2. Factorize the equation 6x2-x-1=0.

(a) (x-1)(6x-1)

(b) (2x-1)(x -1)

(c) (2x -1)(3x-1)

(d) (2x-1)(3x+1)

(e) (2x+1)(3x-1)

3. Solve the equation 3a + 10 = a2

(a) a = 5 or 2

(b) a = -5 or 2

(c) a = 10 or 0

(d) a = 5 or -2

(d) a = -5 or -2

4. Find the equation whose roots are -1/3 and 2

cxxxvii

(a) 3x2 + 5x – 2 = 0

(b) 3x2 – 5x – 2 = 0

(c) 3x2 + 5x + 2 = 0

(d) 3x2 – 5x + 2 = 0

(e) 3x2 – 2x + 5 = 0

5. The equation whose roots are -2 and 3 is

(a) 2x2 + 3x+1 = 0

(b) x2

- 3x + 1 = 0

(c) x2 + x – 6 = 0

(d) x2 – x + 6 = 0

(e) x2 – x – 6 = 0

6. Find the solution of the quadratic equation by factorization method. 6x2-

7x-5=0

(a) x = 1/3 or – 2

1/2

(b) x = 1/3 or 2

1/2

(c) x = 12/3 or – 1/2

(d) x = 12/3 or 1/2

(e) x = 5/6 or -1

7. Which of these is true about completing the square

(a) The coefficient of x2 must be unity

(b) The constant must be on the left land side

(c) The two sides must be equal

cxxxviii

(d) The two roots must be the same

(e) None of the above.

8. By completing the square, the solution of the quadratic 5x2 = 7x +3 is

(a) -1.7 or -0.3

(b) 4.2 or -3.7

(c) 1.7 or -0.3

(d) -4.2 or 3.7

(e) 0.3 or 1.7

9. What must be added to x2 +6x to make it a perfect square

(a) 8

(b) 16

(c) 32

(d) 64

(e) 12

10. By competing the square, the solution of the equation 2m2 = 19m – 35 is

(a) m = 1.48 or 1.08

(b) m = 1.49 or -1.08

(c) m = -1.48 or 1.07

(d) m = -1.48 or 1.08

(e) m = 1.49 or -1.07

11. Find a solution to the equation 2x2 – 4x – 3 = 0

cxxxix

(a) x = 21/2 or -1/2

(b) x = 2 or -1/2

(c) x = -21/2 or 1/2

(d) x = -2 or 21/2

(e) x = -2 or 1/3

12. Given that (2x-1)(x+5) = 2x2 – mx – 5. What is the value of m

(a) 11

(b) 5

(c) -9

(d) -10

(e) -5

13. Which of these is true about perfect square

(a) The square must be perfect

(b) All negative numbers are positive

(c) Half coefficient must be added.

(d) The square must be completed.

(e) The square of half the coefficient of terms whose variable is to power

must be added.

14. Solve by completing the square the equation (y+3)(y-5) = 2y -2.

(a) 3 or -5

(b) 7 or -3

(c) 7 or 3

cxl

(d) -3 or 5

(e) -3 or -5


(a) The constant must be on the left hand side

(b) The square of half the coefficient of x, must be added to both side.

(c) The square of coefficient of x2 must be added to added to both sides.

(d) The roots must be in power

(e) None of the above

16. In the general formula, C can be called

(a) The coefficient of x2

(b) The coefficient of x

(c) The constant of x2

(d) A number in the equation

(e) The coefficient of x0.

17. In the equation 2x2 – 4x – 3 = 0, the sum of roots and product of roots are

respectively.

(a) 4x and 6x2

(b) -4x and -6x2

(c) 4 and -6

(d) 6 and -4

(e) 4 and -3

cxli

18. If the general formulae is used to find a solution to the equation 2k2 = 3k

+ 5, the value of k is

(a) 0.43 or 2.9

(b) -0.44 or 2.9

(c) 0.43 or -2.9

(d) -0.43 or -2.9

(e) -0.43 or 2.9

19. The general formular for solving a quadratic equation is x =

(a) -b+ √b2 – 4bc

2

(b) -b+ √b2 – 4ab

2 a

(c) -b±√b2 – 4ac

2b

(d) -b±√b2 – 4ac

2a

(e) b -√b2 – 4ac

2a

20. Find the value of 6a2 + 11a-10 when a = -1

(a) +10

(b) -6

(c) -17

(d) -15

(e) +6

cxlii

21. The value of m in the equation m2 – 7m + 11 =0 is

(a) m = 7

(b) m = -11

(c) m = 7±√5

2

(d) m = 5 ±√3

2

(e) m = 12.

22. What is the equation of the curve in figure 1.

(a) x2 – x – 6 = 0

(b) x2 – x + 6 = 0

(c) x2 + x – 6 = 0

(d) 2x2 – x – 6 = 0

(e) 2x2 + x + 6 = 0

Use the graph in figure 2 to answer questions 23 and 24.

23. What is the equation of the curve

(a) 4 – x + x2

(b) -3 -2x –x2

(c) 3 + 2x + x2

(d) 3 -2x –x2

(e) 3 +2x –x2

24. The values of x when y is -1 are approximately

(a) -3.0 and 1.0

cxliii

(b) 1.2 and -3.2

(c) 0.8 and -2.7

(d) -1.0 and 3.0

(e) -1.0 and 4.0

25. In figure 3, find the values of x when y = -1.5

(a) -1.4 and 2.5

(b) -1.4 and -2.5

(c) + 1.4 and + 2.5

(d) -1.3 and 2.7

(e) 1.3 and -2.7

26. What is the maximum value of the graph in figure 3

(a) 2.25

(b) 3.20

(c) 2.05

(d) -4.00

(e) 2.00


(a) x2 + 5x – 3 = 0

(b) 2x2 – 5x +7 = 0

(c) 2x2 – 5x + 3 = 0

(d) 3x2 + 7x – 5 = 0

(e) 5x2 – 7x – 12 = 0

cxliv

28. What is the minimum value of the graph in figure 4.

(a) 11.23

(b) -10.02

(c) -11.20

(d) 10.20

(e) 17.00

29. What is the equation of the line PQ in figure 4.

(a) y = x + 1

(b) y = 2x + 1

(c) y = x – 2

(d) y = 2x – 3

(e) y = x -5

(30) Which of these is not important in plotting of a quadratic equation graph

(a) Table of value

(b) Range of values for x

(c) Scale

(d) Points of intercepts

(e) None of the above

cxlv

APPENDIX D

Solution for the TMAT /Marking Scheme

1. B 16. E

2. D 17. B

3. D 18. C

4. B 19. D

5. E 20. D

6. C 21. C

7. A 22. A

8. C 23. D

9. D 24. B

10. A 25. A

11. A 26. A

12. C 27. E

13. E 28. C

14. B 29. D

15. B 30. D

Each correct answer attracts 3 marks

cxlvi

APPENDIX E

Teacher Made Achievement Test for Retention

1. Factorize the equation 6x2-x-1 = 0

(a) (x-1)(6x-1)

(b) (2x-1)(3x-1)

(c) (2x+1)(3x-1)

(d) (2x-1)(x-1)

(e) (2x-1)(3x+1)

2. Factorize the following expression 2x2+x-15 = 0

(a) (2x+5)(x-3)

(b) (2x-5)(x+3)

(c) (2x-5)(x-3)

(d) (2x-3)(x+5)

(e) (2x+5)(x+3)

3. Find the equation whose roots are -1/3 and 2.

(a) 3x2-2x + 5 = 0

(b) 3x2 – 5x +2 = 0

(c) 3x2 + 5x + 2 = 0

(d) 3x2 – 5x -2 = 0

(e) 3x2 + 5x -2 = 0

4. Solve the equation 3a + 10 = a2

(a) a = 5 or – 2

(b) a = -5 or -2

(c) a = 10 or 0

(d) a = -5 or 2

(e) a = 5 or 2

cxlvii

5. The equation whose roots -2 and 3 is

(a) 2x2 + 3x + 1 = 0

(b) x2 – 3x + 1 = 0

(c) x2 = x – 6 = 0

(d) x2 – x + 6 = 0

(e) x2 + x – 6 = 0

6. Find the solution of the equation by factorization method 6x2 – 7x – 5 = 0

(a x= 12/3 or -1/2

(b) x = 1/3 or -21/2

(c) x = 1/3 or 21/2

(d) x = 5/6 or -1

(e) x = 12/3 or ½

7. By completing the square, the solution of the quadratic 5x2 = 7x+3 is

(a) -1.7 or 0.3

(b) -4.2 or 3.7

(c) 4.2 or -3.7

(d) 0.3 or 1.7

(e) 1.7 or – 0.3

(8) What must be added to x2 + 6x to make it a perfect square

(a) 12

(b) 32

(c) 16

(d) 8

(e) 64

cxlviii


(a) The coefficient of x2 must be unity

(b) The two sides must be equal

(c) The constant must be on the left land side

(d) The two roots be the same


10. Given that (2x - 1)(x+5) = 2x2 – mx - 5 . What is the value of m.

(a) -5

(b) -9

(c) 5

(d) 11

(e) -10

11. By completing the square, the solution of the equation 2m2 = 19m – 35 is

(a) m = -1.48 or -1.08

(b) m = -1.48 or 1.07

(c) m = -1.48 or 1.07

(d) m = 1.48 or 1.08

(e) m = 1.49 or -1.07

12. Find a solution to the equation 2x2 – 4x – 3 = 0

(a) x = 2 or -1/2

(b) x = 21/2 or – ½

(c) x = 1/2 or -21/2

(d) x = -2 or 1/3

(e) x = 2 or -1/2

cxlix

13. Solve by completing the square, the equation (y+3)(y-5) = 2y -2.

(a) 3 or -5

(b) 7 or -3

(c) 7 or -3

(d) -3 or 5

(e) -3 or -5.

14. Which of these is true about perfect square

(a) The square must be perfect

(b) All negative numbers are positive

(c) Half coefficient must be added

(d) The square must be completed

(e) The square of half the coefficient of terms whose variable is to power I

must be added.

15. Which of these is true about completing the square.

(a) The roots must be in power

(b) The square of coefficient of x2 must be added to both sides

(c) The square of half the coefficient of x must be added to both sides.

(d) The constant must be on the left hand side


16. The general formular for solving a quadratic equation is

(a) -b±√b2 – 4ac

2a

(b) b -√b2 + 4ac

2a

(c) -b±√b2 -4bc

2

(d) -b±√b2 – 4ab

2a

(e) b±√b2-4ac

2b

cl

17. If the general formulae is used to find a solution to the equation 2k2

=

3k+5, the value of k is

(a) 0.43 or 2.9

(b) -0.44 or 2.9

(c) 0.43 or -2.9

(d) -0.43 or -2.9

(e) -0.43 or 2.9

18. In the equation 2x2 – 4x-3 = 0, the sum of roots and product of roots are

respectively.

(a) 4x and 6x2

(b) -4x and -6x2

(c) 4 and -6

(d) 6 and -4

(e) 4 and -3

19. In the general formulae, C can be called

(a) The coefficient of x2

(b) The coefficient of x

(c) The constant of x2

(d) A number in the equation

(e) The coefficient of x0

20. The value of m in the equation m2 – 7m +11 = 0 is

(a) m = 7

(b) m = -11

(c) m = 7±√5

2

(d) m = 5±√3

2

(e) m = 12

cli

21. Find the value of 6a2 + 11a -10 when a = -1

(a) +10

(b) -6

(c) -17

(d) -15

(e) +6

22. What is equation of the curve in figure 1

(a) x2 + x – 6 = 0

(b) x2 – x + 6 = 0

(c) x2 – x – 6 = 0

(d) 2x2 – x – 6 = 0

(e) 2x2 + x+6 = 0

Use the graph in figure 2 to answer questions 23 -25 .

23. What is the minimum value of the graph

(a) 10.02

(b) -10.05

(c) -11.0

(d) 11.23

(e) 10.20

24. What is the equation of the curve

(a) x2-3x – 5 = 0

(b) 2x2-3x+10=0

(c) 2x2 + 3x-10=0

(d) x2 -3x + 5 = 0

(e) 2x2 – 3x – 10 =0

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25. What is the corresponding value of x when y is minimum

(a) x = 2

(b) x =1

(c) x=-2

(d) x = -1

(e) x = 2.5


(a) 4-x + x2

(b) -3 – 2x – x2

(c) 3 + 2x + x2

(d) 3 – 2x – x2

(e) 3 + 2x – x2

27. From figure 3, what is the value of x when y is -1.

(a) -3.0 and 1.0

(b) 1.2 and -3.2

(c) 0.8 and -2.7

(d) -1.0 and 3.0

(e) -1.0 and 4.0

28. The roots of the equation in figure 3 are

(a) -3 and 1

(b) 3 and 1

(c) -4 and 2

(d) 0 and 1

(e) 4 and -2

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29. What is the equation of the line in figure 2.

(a) y = 2x -3

(b) y = 2x+3

(c) y = x +2

(d) y = x -2

(e) y = 2x +2

30. The maximum value of y and the value of x at which y is maximum in

figure 3 are responsively

(a) -4 and -1

(b) -4 and +1

(c) 4 and -1

(d) -3 and 1

(e) 3 and -1.

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APPENDIX F

Solution for the TMAT / Marking Scheme

1. E 16 A

2. B 17 C

3. D 18 B

4. A 19 E

5. C 20 C

6. A 21 D

7. E 22 C

8. E 23 C

9. A 24 E

10. B 25 B

11. A 26 D

12. B 27 B

13. C 28 A

14. E 29 B

15. C 30 C

Each correct answer attracts 3 marks.

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APPENDIX G

VALIDATORS‟ LETTER

Department of Science Education

University of Nigeria,

Nsukka

14th February, 2008.

Sir/madam,

VALIDATION OF RESEARCH INSTRUMENTS

I am a PG student of this University carrying out a research on

“Comparative Effect of using Computer as Tutor and Tool on Students

Achievement and Retention in Quadratic Equation. I am carrying out the

research under Dr. K.O. Usman.

Kindly read through the purpose of the study, Research questions,

Hypotheses, Test blue print, Teacher made Quadratic Equation achievement,

Test and finally the lesson notes for experimental group 1 and experimental

group 2.

Assess and comment on the appropriateness of expressional standard,

language, arrangement, content of materials and suitability to see if they are in

accordance with the present research.

Your comments will be of great help to this study.

Thanks for your co-operation.

Yours Faithfully

Ezeh, S.I. (Mrs.)

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APPENDIX H

VALIDATORS‟ REPORT

The validators after going through the research questions, Test blue print,

Teacher made Achievements Test, made the following recommendations.

1. That the test blue print instead of having six levels should have two

levels: Higher and lower levels.

2. That instead of having three tests for pretest, post test and retention

test, that one test could be used where the options are interchanged to

avoid the effect of post test on the retention test.

3. That the achievement tests should conform to the test blue print.

4. That the research questions be reformed to move double edged

questions.

5. That the lesson notes be restructured, so as to indicate those things that

differentiated computer as tool from computer as tutor.

6. That the number of Teacher made Achievement test be increased to 30

questions.

7. Finally that the instrument is suitable for the present research.

clvii

APPENDIX I

Scores for Multiple Choice Test Using Kudar Richardson formulae

(K – R 20) to find Internal Consistency

Items No of

Passes

No of

failures

P Q Pq

1 17 23 0.43 0.57 0.25

2 13 27 0.33 0.67 0.22

3 15 25 0.38 0.62 0.24

4 11 29 0.28 0.72 0.20

5 16 24 0.40 0.60 0.24

6 9 31 0.23 0.77 0.18

7 8 32 0.20 0.80 0.16

8 15 25 0.38 0.62 0.24

9 12 28 0.30 0.70 0.21

10 11 29 0.28 0.72 0.20

11 12 28 0.30 0.70 0.21

12 9 31 0.23 0.77 0.18

13 12 28 0.30 0.70 0.21

14 8 32 0.20 0.80 0.16

15 6 34 0.15 0.85 0.13

16 9 31 0.23 0.77 0.18

17 8 32 0.20 0.80 0.16

18 8 32 0.20 0.80 0.16

19 11 29 0.28 0.72 0.20

20 4 36 0.10 0.90 0.09

21 5 35 0.13 0.87 0.11

22 9 31 0.23 0.77 0.18

23 6 34 0.15 0.85 0.13

24 8 32 0.20 0.80 0.16

25 5 35 0.13 0.87 0.11

26 3 37 0.13 0.87 0.11

27 4 36 0.10 0.90 0.09

28 1 39 0.03 0.97 0.03

29 2 38 0.5 0.95 0.05

30 1 39 0.3 0.97 0.03

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P = proportion of the tastes that passed correctly ∑pq = 4.82.

q = proportion of the tastes that failed.

S.d = 4.61 Variance = 21.28

X = 6.45.

K – R20 = k/k- 1 [1-∑pq]

S2t

Where k = no of items St is variance of total score

30/30-1 [1- 4.82]

21.28.

1.03 (1-0.23)

1.03 (0.77)

= 0.796

~ 0.80

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APPENDIX J(1)

EIGHT SCHOOLS USED FOR THE RESEARCH

Schools Population of SSII students

STC Nsukka 194

QRSS Nsukka 153

GSS Ibagwa-aka 89

BSS Nru 77

NHS Nsukka 190

CHS Umabor 158

GSS Opi 106

St Cyprian GSS Nsukka 145

Total 1109

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APPENDIX J(2)

Schools in Nsukka L.G.A. Population of SSII Students

STC Nsukka 194

CSS Ede Oballa 237

QRSS Nsukka 153

CSS Opi-agu 82

CSS Eha-Ndiagu 2

GSS Ibeagwa Ani 86

CSS Isienu 75

Model Sec. Sch. Nsukka 173

CSS Edem 124

BSS Nru 77

CSS Lejja 54

NHS Nsukka 190

Opi High Sch. 169

CSS Ezebunagu 32

CSS Obimo 75

Lejja High Sch. 145

CSS Alor-uno 51

CHS Umabor 158

CSS Obukpa 128

Girls Sec. Sch. OPi 106

CSS Okpuje 50

Urban Girls Sec. Sch. 169

St. Cyprian Girls Sec. Scho. 145

And 6 Other Junior Secondary schools -

Total: 29 Secondary Schools 2,675.

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APPENDIX K

To test for stability, Raw score method of Pearson product moment correlation

coefficient is used

S/N X Y XY X

2 Y

2

1. 40 38 1520 1600 1444

2. 40 48 1920 1600 2304

3. 32 40 1280 1024 1600

4. 34 30 1020 1156 900

5. 50 48 2400 2500 2304

6. 50 46 2300 2500 2116

7. 30 30 900 900 900

8. 20 20 400 400 400

9. 20 20 400 400 400

10. 20 15 300 400 225

11. 14 18 252 196 324

12. 18 20 360 324 400

13. 40 40 1600 1600 1600

14. 50 50 2500 2500 2500

15. 60 62 3720 3600 3844

16. 70 72 5040 4900 5184

17. 72 74 5328 5184 5476

18. 32 30 960 1024 900

19. 06 10 60 36 100

20. 60 50 3000 3600 2500

758 761 35260 35444 35421

clxii

The formular is

2222 YYNXXN

YXXYNr

57912135421205745643544420

7617583526020

X

579121708420574564708880

576838705200

129200134316

128362

74.0

clxiii

APPENDIX L

Options

Item I A B C D E Total

Upper group 1 5 2 1 1 10

Lower group 1 4 1 2 2 10

2 8 3 4 3 20

(a) Item P = N

LU

2

where U = No in the upper 1/3 of the group who

passed the item

L = no of students in the lower 1/3 of the group.

N = total no of students in the upper on the lower 1/3 of the group

P = 45.020

9

102

45

2

XN

LU

(b) Item Discrimination Index, d = 1.010

1

10

45

N

LU

(c) Distracter Indices (D.1).

D. I of C = 2-1 = 1 = 0.1

10 10

D. I of C = 2-1 = 1 = 0.1

10 10

D. 1 of D = 2-1 = 0.1

10

D. 1 of E = 2-1 = 0.1

10

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Item 2 A B C D E Total

Upper group 1 1 1 6 1 10

Lower group 1 1 2 4 2 10

2 2 3 10 3 20

(a) Item difficulty P = U+L = 6+4 = 10 = 0.5

2N 2X10 20

(b) Item discrimination Index, d = U –L = 6-4 = 2 = 1 = 0.2

N 10 10 5

(c) Distracter Indices

D. 1 of A = 1-1 = 0 =

10 10

D. 1 of B = 1-1 = 0

10

D. 1 of C = 2-1 = 1 = 0.1

10 10

D. 1 of E = 2-1 = 0.1

10

Options

Item 3 A B C D E Total

1 1 1 7 2 12

2 2 2 5 3 12

3 3 3 10 5 24

(a) Item difficulty P = U+L = 7+3 = 10 .42

2N 2X12 24

(b) Item Discrimination Index d = U-L = 7-3 = 4 = 0.33

N 12 12 z

(c) D.1 of A = 2-1 = 1 = 0.08

12 12

D.1 of C = 2-1 = 1 = 0.08

12 12

D.1 of E = 3-2 = 1 = 0.08

12 12

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Table of Contents

TABLES PAGES

TITLE PAGE………………………………………………………………………………..i

APPROVAL PAGE………………………………………………………………………...ii

CERTIFICATION ………………………………………………………………………...iii

DEDICATION……………………………………………………………..………………iv

ACKNOWLEDGEMENTS………………………………………………………………...v

TABLE OF CONTENTS…………………………………………………………………..vi

LIST OF TABLES………………………………………………………………………..viii

LIST OF APPENDIX ……………………………………………………………………...ix

ABSTRACT ………………………………………………………………………………….x

CHAPTER ONE: INTRODUCTION ……………………………………………………...1

Background of the Study…………………………………………………………………1

Statement of the Problem ................................................................................................. xx

Purpose of the Study ....................................................................................................... xxi

Significance of the Study ............................................................................................... xxii

Scope of the Study ........................................................................................................xxiii

Research Questions ....................................................................................................... xxiv

Research Hypotheses ..................................................................................................... xxv

CHAPTER TWO:LITERATURE REVIEW ................................................................... xxvi

Conceptual Framework ................................................................................................. xxvi

Conceptual Framework ................................................................................................ xxvii

Poor Achievement of Students in Mathematics ........................................................... xxvii

Concepts in Algebra ....................................................................................................xxviii

Factorization Method ..................................................................................................... xxx

Completing the Square .................................................................................................. xxxi

Formulae Method ........................................................................................................xxxiii

Graph Method .............................................................................................................xxxiii

Issues on Retention ...................................................................................................... xxxv

Computer and Learning of Mathematics ..................................................................xxxviii

Gender and Mathematics Achievement ......................................................................... xlvi

Theoretical Framework ............................................................................................... xlviii

Skinner‟s Theory of Linear Programming .................................................................. xlviii

Crowder‟s Theory of Branching Programming .................................................................. l

Piagets Cognitive Theory of Constructivism ....................................................................lii

Review of Related Empirical Studies .............................................................................. lvi

Studies on Male and Female Students‟ Achievements and Retention in Mathematics ... lvi

Studies on the Effect of Modes of Computer on Achievement and Retention ................ lix

Summary of the Literature Review ............................................................................... lxiii

CHAPTER THREE:RESEARCH METHODS ................................................................ lxvi

Research Design............................................................................................................. lxvi

Area of the Study ..........................................................................................................lxvii

Population of the Study .................................................................................................lxvii

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Sample and Sampling Technique..................................................................................lxvii

Instrument for Data Collection ................................................................................... lxviii

Validity of Instrument ................................................................................................. lxviii

Reliability of Instrument ................................................................................................ lxix

Experimental Procedure ................................................................................................. lxix

Reduction of Experimental Bias ...................................................................................lxxii

Control of the Effect of Pre-test on Post –test ..............................................................lxxii

Control of Hawthorne Effect ........................................................................................lxxii

Method of Data Analysis ............................................................................................ lxxiii

CHAPTER FOUR:RESULTS .......................................................................................... lxxiv

Summary of Findings ................................................................................................. lxxxix

CHAPTER FIVE:DISCUSSION, CONCLUSION, IMPLICATION AND

RECOMMENDATIONS ...................................................................................................... xci

Effect of Computer on Students‟ Achievement in Quadratic Equation .......................... xci

Effect of Computer on Students‟ Retention in Quadratic Equation .............................. xcii

Interaction Effects of Method and Gender.................................................................... xciii

Conclusion .................................................................................................................... xcvi

Implication of the Study............................................................................................... xcvii

Limitations of the Study.............................................................................................. xcviii

Recommendations ......................................................................................................... xcix

Suggestion for further Studies ........................................................................................... c

Summary of the Study ....................................................................................................... c

REFERNCES ........................................................................................................................ ciii

EZEH, Sussan Ijeoma PG/ Ph.D/06/40953

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