EFFECT OF USING COMPUTERS AS TUTOR AND TOOL ON STUDENTS ACHIEVEMENT AND RETENTION IN QUADRATIC EQUATIONS IN ENUGU STATE NIGERIA
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CHAPTER ONE
INTRODUCTION
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 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 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 innovations in the society. Hence a better teaching of the concept was suggested.
Harborpeter (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 inservice training and retraining 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 selfchecking and that the visual pictures enhance visualization and sensory perception. The computer has the property of being patient and does not care 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 (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:
 Embedded questions where students must take an active role by answering embedded questions.
 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.
 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.
 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 also to explore the possibilities of computerbased 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 problemSolving 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 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 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 HarborPeters (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 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.
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 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:
 How would the use of computer enhance students’ achievement and retention in quadratic equation?
 How would the use of computer as tutor and tool affect male and female students’ achievement and retention in quadratic equation?
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:
 Compare the effectiveness of using computer and not using computer in learning quadratic equation.
 Compare the effectiveness of using computer as tutor and as tool in learning quadratic equation.
 Find out the mode that enabled student to retain more of what they have learnt
 Ascertain whether the modes have any effect on male and female students’ achievement and retention.
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 inservice 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 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.
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 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.
 What are the mean achievement scores of students who were taught with computer and those who were taught without computer?
 What are the mean achievement scores of students who were taught with computer as tutor and those who were taught with computer as tool?
 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?
 What are the mean retention scores of students who were taught with computer and those who were taught without computer?
 What are the mean retention scores of students who were taught with computer as tutor and those who were taught with computer as tool?
 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?
HO_{1}: There is no significant difference between the mean achievement scores of students who were taught with computer and those who were taught without computer.
H0_{2}: 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.
H0_{3}: There is no significant difference between 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.
H0_{4}: There is no significant difference between the mean retention scores of students who were taught with computer and those who were taught without computer.
H0_{5}: There is no 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.
H0_{6}: There is no significant difference between 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.
H0_{7}: 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.
H0_{8}: There is no significant interaction effect between the modes and gender on retention.
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