CHAPTER ONE 1.1 Background to the Study Mathematics serves as bedrock for other science subjects and at the same time, strengthens and sharpens the intellectual skills of students. Mathematics is a very important subject. It is also described as the pivot of all civilizations and technological development (Amarasinghe & Lambdin 2000). These descriptions point the important position accorded to mathematics as a key factor in the development of any nation. The Nigeria educational system is geared towards rapid technological growth of the nation. And in view of this, the National Policy on Education stipulated that mathematics should be one of the core subjects taught at all levels of secondary and primary schools, since the importance of mathematics cannot be over emphasized in the area of science and technology. This is why mathematics is a compulsory subject for all primary and post primary schools in many countries of the world. The expectation is that, adequate exposure of student to the knowledge of ICT will facilitate their achievement not only in mathematics but also in other areas of human endeavours (Fajola 2001). From birth, a child normally passes through various stages of development to adulthood and is bound to acquire knowledge. This knowledge could either be through formal or non – formal educational system (Kersh, 1995). In both cases, primarily in the formal educational system, an appropriate use of ICT materials could shape the learning habits of students. ICT materials, otherwise known as teaching aids or instructional materials are aimed at facilitating the understanding of the learner. This predicated against the background that the children or students we teach have short attention span and so they learn better if teaching aids are used during the teaching learning process. They could retain good memory if models or real objects that they play with are used. Such retentive memory might be relatively high compared to the verbal speeches made by the instructor (Ebijuwa and ToAnyakoha, 2005). ICT materials are the instruments used by teachers or instructors in a learning environment 1 for teaching which they hope are capable of eliciting in concrete terms the concepts of mathematics or any subject which may seem abstract without the use of the materials. (AlAnsari 2006). Kersh (1995) also agreed that lessons should be more practical and activity oriented as they are better learnt through manipulation of subjects and symbols. The largely expository strategies and method commonly adopted by science teachers is not effective. An effective teaching and learning demands both experimentation and demonstration. This way, we will be assured of good performance not only in mathematics but also in all subjects which uses logic. For students to acquire scientific knowledge and skills through major concept and their effect in technology, the teaching and learning materials which are relevant to the curriculum should be improvised. The most commonly used method of teaching science subject and science related subjects in Nigerian schools is the expository method (explaining or elucidating the topic to be taught), which usually scares students, other than methods such as experimentation, discussion, demonstration, project and discovery methods. The learning of mathematics can be made less abstract to the learner if mathematics teachers adopt more practical approaches to teaching the subject. With this, there will be good performance not only in mathematics but also in science and science related subjects in general. The advent of the computer has opened up possibilities for teachers and learners which is different from the scope of commercial enterprise for which it was earlier targeted. Computer has come to be credited with advantages in education, to the extent that in some cases it has eventually replaced the chalkboard and traditional instruction (Din, 1996). Developing nations like Nigeria that places premium on its educational development, cannot ignore this instructional medium called computer assisted instruction (CAI). Merrell & Tymms 2001; 2 Hussein, 2011 both highlighted the advantages and supported the adoption of computer assisted instruction (CAI) in Nigerian Educational System. Teachers‟ preparation and practices most often do fall short in the area of computer assisted instruction (CAI) for students with dyslexia or dyscalculia making them to be more prone to the learning difficulties than others. Therefore, the need for effective and proper concentration of teachers on the trainees should be more focused on CAI to sponge poor concentration, attention deficits by students and perhaps to achieve the instructional objectives (Luis and Tanoak 2007). Computer assisted instruction (CAI) appears to be a promising intervention for both teachers‟ and students who have attention problems or those who have identified disabilities such as dysgraphia, acaculia, romxgraphia and dyscalculia (Orim & lgwe, 2017). Unfortunately, teachers‟ use of CAI for students appears limited and may not be utilized in ways that are of maximal benefit for at-risk learners (Desiree, Murray & David, 2014). Due to the outcry of the situation, this research work intends to confirm whether there will be a line of change on the performance of these teaming educational beginners if computer assisted instruction is introduced into the teaching and learning of mathematics. Therefore, the focus of this research work is to find out the extent to which Computer Assisted Instructions will affect the performance of students in mathematics in Sokoto metropolis of Sokoto state. 1.2 Statement of the Problem Mathematics seem to be the major problem to many students at virtually all levels (primary, secondary and even tertiary levels of education), most of these problems encountered in mathematics are more or less connected with the abstractions (teaching without demonstrations) been used in most mathematics class, this eventually lead students to build a kind of hatred to the subject and thus leading them to massive failures. There has been a 3 perceived feeling by the researcher that, the ability of the teacher to teach by simply using verbal approach could not enable him/her to achieve the optimum objective of imparting knowledge to students. The reason being that, some teachers though professionally trained but may be or are constrained to express themselves very well for the child to grasp firmly the instructions. Apart from that, students or learners naturally suffer from attack of forgetfulness and so no matter how explicit the teacher might sound, the child may not understand and even grasp what is taught. The learner’s inability to keep meditating over junks of words places him or her in the dilemma of not remembering much of what has been taught, thus causes the performance of the learner to be poor. This is because, a student who is battling with remembering or the one that did not even understand the lesson at all will not have that retentive memory to be able to perform very well. The study was propelled by the very interesting discoveries from literature that instructional strategies among which is Computer Assisted Instructions significantly affects students’ performance. However, a question may be asked whether different instructional approaches will produce the same effects on students in their study of topics like geometry and trigonometry. This is a gap that exists in literature which needs to be filled to enable researchers and mathematics teachers fully appreciate the role of Computer Assisted Instructions in teaching and learning of mathematics. In view of the foregoing the statement of the problem is thus what will be the effectiveness of Computer Assisted Instructions on the Performance of Senior Secondary School Students in Mathematics in Sokoto Metropolis. 1.3 Objectives of the Study The research set to find the effectiveness of Computer Assisted Instructions (CAI) on the performance of Senior Secondary School Students in Mathematics as a general objective; specifically, the researcher aims to achieve the following objectives 4 i. To examine the effectiveness of CAI on the performance of Student in trigonometry over conventional (discussion) method ii. To examine the effectiveness of CAI on the performance of Student in geometry over conventional (discussion) method iii. To compare the effect of CAI on the performance of Male and Female Students in Trigonometry iv. To compare the effect of CAI on the performance of Male and Female Students in Geometry v. To compare the performance of students taught using CAI in Trigonometry and Geometry. 1.4 Research Questions The following questions are raised to guide the study: Research Question 1: What is the difference between the academic performances of Students in trigonometry taught using Computer-Assisted Instruction and those taught using the conventional (discussion) method of teaching? Research Question 2: What is the difference between the academic performances of Students in geometry taught using Computer-Assisted Instruction and those taught using the conventional (discussion) method of teaching? Research Question 3: What is the difference between the performance of Male and Female students taught using CAI in Trigonometry? Research Question 4: What is the difference between the performance of Male and Female students taught using CAI in Geometry? Research Question 5: What is the difference between the academic performances of Students taught using Computer-Assisted Instruction in Trigonometry and Geometry? 5 1.5 Null Hypotheses Following the subject of this research work, five hypotheses are formulated to guide the study. Ho1: There is no significant difference between the academic performances of Students in trigonometry taught using Computer-Assisted Instruction and those taught using the conventional (discussion) method of teaching Ho2: There is no significant difference between the academic performances of Students in geometry taught using Computer-Assisted Instruction and those taught using the conventional (discussion) method of teaching. Ho3: There is no significant difference between the performances of male and female students in trigonometry taught using CAI. Ho4: There is no significant difference between the performances of male and female students in geometry taught using CAI. Ho5: There is no significant difference between the performances of students taught using CAI in geometry and trigonometry. 1.6 Significance of the Study The finding of this research will be beneficial to our teaming students in making them more active as learning is simplified via Computer Assisted Instructions. It is expected that findings from this project work could immensely offer valuable insights to the researchers in education who are likely to use this research work as a reference material to enable them develop the field of teaching learning process of mathematics. To teachers who instruct the students, this work will go a long way in providing credible facts to enable them improve on their routine work. They can achieve this through selfassessment, which equips them to determine when to withdraw or sustain a particular 6 teaching aid. This is because, while some ICT materials may be boring to students, some are interesting to them. It is also significant too that, this inquiry will satisfy the impression of not using instructional materials when the need arises as mathematics teachers will either be discouraged or encouraged to improvise when the materials are lacking due to the findings of this work. Also this research work will go a long way to serve as either a positive or negative step towards enhancing effective teaching and learning of mathematics in the senior secondary schools due to the findings. To government, it will no doubt send a signal on the need for setting an action plan on the realization of ICT compliance mathematics classes where Computer Assisted Instructions are put in place in the state. At the same time take necessary actions to implement a new package for teachers of mathematics who are the brain behind a successful implementation of any policy introduced by the government. Other members of the society may also find it very useful if perused with keen interest as to what input would they place in a view to complimenting government effort in actualizing ICT compliance into the teaching and learning of mathematics. 1.7 Scope and Delimitation of the Study The research work will consist of all the Senior Secondary Schools in Sokoto State, but due to limited resources and time amidst the nature of the research, the study will limit itself to Senior Secondary School (II) students of schools with ICT facilities in Sokoto Metropolis and the schools are FGC Sokoto (78), UDUMSS (76), FSC Sokoto (76), NCS (76) and GGC Sokoto (76). Also this study was restricted to using a projector to teach the students some selected Algebra topics (Trigonometry and Geometry) that established the basis for the research. 7 1.8 Operational Definitions of Terms The following terms found in this write up are explained or defined in order to facilitate a better understanding of the study. And this is to say that the meaning of each term shall be based on the context of this study. Computer Assisted Instructions (CAI): the use of computers in helping students and teachers understand classroom material contextually and conceptually. Performances: Examining students’ progress base on exposure to some parameters like computer. ICT: This simply means Information and Communication Technology. Abstraction: Teaching theoretical facts without demonstrating it to students Teaching: This refers to the transmission of teachers acquired knowledge or skills to the students or learners. Learning: This is the learner’s ability to effect a change in behaviour as a result of external encounter with new introduced method of teaching (learning). 8 CHAPTER TWO REVIEW OF RELATED LITERATURE This study focused on the effectiveness of Computer Assisted Instructions (CAI) on the performance of Senior Secondary School Students in Mathematics. The review of related literatures was done under the following sub-headings: 2.1 Introduction 2.1.1 Information and Communication Technology 2.1.2 Computer Assisted Instructions 2.2 Computer Assisted Instructions and Role of ICT in Teaching and Learning 2.2.3 Internet 2.2.4. Teaching and Learning 2.3. Why Integrating ICT into the Teaching and Learning 2.3.1 ICT as an aid to Teaching and Learning 2.3.2. ICT as tool for Educational Management 2.3.3. ICT as instrument for Economic Development 2.3.4. ICT as tool for higher technological development 2.3.5. ICT as a course of study 2.4 Theoretical framework 2.4.1 Jean Piaget 2.4.2 Zoltan P. Dienes 2.4.3 Jerome Bruner 2.5 Review of Empirical Studies 2.6 Summary and uniqueness of the study 9 2.1 Introduction Mathematics is a compulsory subject in all secondary schools. Due to its importance the government through the National Communication Commission should be committed in ensuring the provision of high quality Mathematics education in our secondary schools not only in Sokoto State but in the nation as a whole. Though effectively introducing technology into schools is also largely dependent upon the availability and accessibility of ICT resources (e.g. hardware, software and communications infrastructure). Technology is essential in teaching and learning mathematics; it influences the Mathematics that is taught and enhances students’ learning. There are several benefits of using ICT in teaching and learning Mathematics. ICT has the potential to transform the nature of education; improving teacher’s design work, enhancing the roles of students and teachers in the learning process and helping to create a collaborative learning environment. However, there are challenges and opportunities (Khan, Hossain, Hasan & Clement, 2012) which hinder greatly the integration of ICT in teaching and learning Mathematics in secondary schools. The growth of information and communication technologies (ICT) has dramatically reshaped teaching and learning processes. Mathematics teachers are faced with inhibiting challenges or barriers to computer use (Hudson & Porter, 2010). For this reason, there have been several studies which have specifically focused on ICT integration in secondary Mathematics teaching. Drent and Meelissen (2008); Tsai and Chai (2012); and Wachira and Keengwe (2011) describe two types of barriers, currently hampering the integrated use of ICT by teachers: - external (first order) barriers and internal (second order) barriers. Researchers argued that with the introduction of technology, it is possible to de-emphasize algorithmic skills; the resulting void may be filled by an increased emphasis on the development of mathematical concepts. Technology saves time and gives students access to powerful new ways to explore concepts at a depth that has not been possible in the past. The 10 power of computers leads to fundamental changes in mathematics instruction. For example, the ability to build and run complex mathematical models, and easy exploration of "what if" questions through parametric variation has opened up new avenues for mathematics (Dreyfus, 1991). Furthermore, as Munirah (1996) observes, the teaching of calculus has seen a dramatic change now that activities such as exploring data or graphical data analysis have been revolutionized by the computer technology. It is also reported that weaker students often are better able to succeed with the help of technology, and thereby come to recognize that mathematics is not just for their able classmates (Wimbush, 1992). Although there has been much written about the potential of technology to change how mathematics is taught, there does not seem to be much written about how the use of technology changed students’ perception about mathematical problem solving. In everyday ramifications of human life there is one and constant attitude one is attributed to, such a thing is none other than dynamicity; every living creature is dynamic in the way they do things, understand those things and been able to manipulate those things. In those days however the developments we witnessed are too timid and negligible that one cannot precisely say this is the level of development we’ve identified as a result of this effort been made. Nowadays the situation is entirely different as series of efforts have been made to change the way things are done in previous days. One area of concern that is believe to be the universal element of change in the global face is the area of information and communication technology (ICT), all and sundry has now change or are trying to change the direction of their routines to ICT, it has now become the order of the day, it is considered worldwide to be the solution to many cumbersome problems that has been blocking the advancement of many aspects of human endeavour. Information has now become the most strategic resources that has transformed the world economy, changed many facets of life, education being inclusive. We cannot afford to live 11 without communicating to one another such is even the modus operandi in the teaching and learning environment where the teacher communicates to the students while the students respond back in terms of answering or asking questions about their areas of difficulty. Technology been the mastermind of both information and communication plays an intermediate role in a way that any device used in either passing information or communication as the case may be is a product of technology. ICT evidently promotes how a class setting becomes interesting, conducive and attractive in the side of the students. Integrating ICT into our mathematics classroom will no doubt enhances the way and manner students capture readymade information and also are able to keenly retrieve them. 2.1.1 Information and Communication Technology The phrase Information and Communication Technology has been used by academic researchers since the 1980s. Information and communications technology (ICT) is an extended term for information technology (IT) which stresses the role of unified communications and the integration of telecommunications (telephone lines and wireless signals), computers as well as necessary enterprise software, middleware, storage, and audiovisual systems, which enable users to access, store, transmit, and manipulate information. The term ICT is also used to refer to the convergence of audio-visual and telephone networks with computer networks through a single cabling or link system. However, ICT has no universal definition, as "the concepts, methods and applications involved in ICT are constantly evolving on an almost daily basis. The broadness of ICT covers any product that will store, retrieve, manipulate, transmit or receive information electronically in a digital form, e.g. personal computers, digital television, email, robots. For clarity, ICT hierarchy where all levels of the hierarchy contain some degree of commonality in that they are related to technologies that facilitate the transfer of information and various types of electronically mediated communications. Skills, frameworks for the information age 12 is one of many models for describing and managing competencies for ICT professionals for the 21st century. ICT refers to the convergence of Information Technology (IT) and Communication Technology (CT) that ICT is the acquisition, processing, storing and disseminating of vocal, pictorial, textual and numerical information by Microelectronic based combination of computers and telecommunication. ICT is concerned with use of technology in handling, acquiring, processing, storing and disseminating information (Muhammad, 2007). Ebijuwa and ToAnyakoha (2005) define ICT as “tools and as well as means used for collection, capture, process, storage, transmission and dissemination of information”. The computers are used to process and store data, while telecommunications technology provides information communication tools, which make it possible for users to access databases and link them to other computer networks at different locations. “IT and ICT are used somewhat interchangeably. 2.1.2 Computer Assisted Instruction The computer is a technological innovation under the control of stored programme that can perform some of the intellectual roles of man even beyond human capability. It is a powerdriven machine equipped with keyboards, electronic circuits, storage compartments, and recording devices for the high speed performance of mathematical operations. Reith (1993) defines computer as an electronic device which stores information on disc or magnetic tape; analyses it and produces information as required from the data on the tape. Sharing the same view with Reith (1993), Kingsley (1995) sees computer as a device that accepts data in one form and processes it to produce data in another form. Adekemi (2001) defines computer as a combination of related devices capable of solving problems by accepting data, performing described operations on the data, and supplying the results of these operations. Hence, computer could be said to be a man-made machine made up of electronic components that operates information at a very high speed to produce results that are meaningful to the user. It 13 is basically a processor of information. Computer is a machine designed to make life easier due to its speed, accuracy, ability to store large quantity of information and to carry out long and complex operation without human intervention. Computers, irrespective of type and size have five basic parts namely, Input Unit, Memory Units, Control Units (CU), Arithmetic and Logic Units (ALU) and Output Units. Both ALU and CU are joined into one piece of hardware known as the Central Processing Unit (CPU) which is the brain of the computer (CMP for SSCE, 2014 edition, P. 3). Since ancient times, simple manual devices like the abacus aided people in doing calculations. Early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analogue calculations in the early 20th century. The first digital electronic calculating machines were developed during World War II. The speed, power, and versatility of computers increased continuously and dramatically since then, to the point that artificial intelligence may become possible in the future. Conventionally, a modern computer consists of at least one processing element, typically a central processing unit (CPU), and some form of memory. The processing element carries out arithmetic and logical operations, a sequencing and control unit can change the order of operations in response to stored information. Peripheral devices include input devices (keyboards, mouse, etc.), output devices (monitors, printers, etc.), and input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and they enable the result of operations to be saved and retrieved. Computer encompasses almost all facets of human endeavours. So much has been written on it and its relatedness to all areas of human disciplines, which include computer/information technology, engineering, agriculture etc. According to McCormick (1993), computers can be used to diversify, develop and improve the pedagogical relation of teaching and learning. Also, technological development can only 14 be enhanced through proper acquisition of scientific knowledge: which can only be realized through relevant training in Science, Mathematics and Computer Education. The advent of the computer has opened up possibilities for teachers and learners which is different from the scope of commercial enterprise for which it was earlier targeted. Computer has come to be credited with advantages in education, to the extent that in some cases it has eventually replaced the chalkboard and traditional instruction (Din, 1996). Developing nations like Nigeria that places premium on its educational development, cannot ignore this instructional medium called computer assisted instruction (CAI). Merrell & Tymms 2001; Hussen, 2011 both highlighted the advantages and supported the adoption of computer assisted instruction (CAI) in Nigerian Educational System. Teachers‟ preparation and practices most often do fall short in the area of computer assisted instruction (CAI) for students with dyslexia or dyscalculia making them to be more prone to the learning difficulties than others. Therefore, the need for effective and proper concentration of teachers on the trainees should be more focused on CAI to sponge poor concentration, attention deficits by students and perhaps to achieve the instructional objectives (Lui and Tannock 2007). 2.1.3 Internet The Internet has revolutionized the computer and communications world like nothing before. The invention of the telegraph, telephone, radio, and computer set the stage for this unprecedented integration of capabilities (Walmiki &Ramakrishnegowda 2009). The Internet is at once a world-wide broadcasting capability, a mechanism for information dissemination, and a medium for collaboration and interaction between individuals and their computers without regard for geographic location. The Internet represents one of the most successful examples of the benefits of sustained investment and commitment to research and development of information infrastructure. Beginning with the early research in packet 15 switching, the government, industry and academia have been partners in evolving and deploying this exciting new technology. The Internet today is a widespread information infrastructure, the initial prototype of what is often called the National (or Global or Galactic) Information Infrastructure. Its history is complex and involves many aspects - technological, organizational, and community. And its influence reaches not only to the technical fields of computer communications but throughout society as we move toward increasing use of online tools to accomplish electronic commerce, information acquisition, and community operations. The Internet has changed much in the two decades since it came into existence. It was conceived in the era of time-sharing, but has survived into the era of personal computers, client-server and peer-to-peer computing, and the network computer. It was designed before LANs existed, but has accommodated that new network technology, as well as the more recent ATM and frame switched services. It was envisioned as supporting a range of functions from file sharing and remote login to resource sharing and collaboration, and has spawned electronic mail and more recently the World Wide Web. But most important, it started as the creation of a small band of dedicated researchers, and has grown to be a commercial success with billions of dollars of annual investment. One should not conclude that the Internet has now finished changing. The Internet, although a network in name and geography, is a creature of the computer, not the traditional network of the telephone or television industry. It will, indeed it must, continue to change and evolve at the speed of the computer industry if it is to remain relevant. It is now changing to provide new services such as real time transport, in order to support, for example, audio and video streams. In the arena of teaching and learning internet plays a vital role in the way researches, assignments and other educational activities are carried out. 2.1.4 Teaching and Learning 16 A teacher is anyone who affects the environments so that others learn. Teaching at its most literal level educating, imparting knowledge is the most fundamental part of a teacher’s job. It is more obvious than (though just as important as) inspiring, motivating and forming relationships. However, just like many other elements of the job, the act of teaching is personal. No two teachers are the same. The way you teach is unique to you and by teaching, you bring yourself to the classroom: your personality, your experiences and your ambitions. Your pedagogy your teaching style is shaped by these characteristics, influenced by your own education, and becomes the guide you use to teach your students. However, learning is a cooperative effort, requiring engagement on the parts of both students and teachers. Each student also has their own learning style: They learn at their own pace and in their own ways. While it is important to establish your teaching style, you should also be flexible enough to take the learning styles of your students into account. You can be guided by a general pedagogy while also being considerate of your students varying needs. Great teachers find balance between a curriculum-centred and a student-centred approach. Learning is skill acquisition and increased fluency. Teachers’ computer competence is a major predictor of integrating ICT in teaching. Evidence suggests that majority of teachers who reported negative or neutral attitude towards the integration of ICT into teaching and learning processes lacked knowledge and skills that would allow them to make an “informed decision” (Bordbar, 2010). 2.2 Computer Assisted Instructions and Role of ICT in Teaching and Learning According to Daniels (2002) ICTs have become within a very short time, one of the basic building blocks of modern society. Many countries now regard understanding ICT and mastering the basic skills and concepts of ICT as part of the core of education, alongside reading, writing and numeracy. However, there appears to be a misconception that ICTs 17 generally refers to ‘computers and computing related activities’. This is fortunately not the case, although computers and their application play a significant role in modern information management, other technologies and/or systems also comprise of the phenomenon that is commonly regarded as ICTs. Pelgrum and Law (2003) state that near the end of the 1980s, the term ‘computers’ was replaced by ‘IT’ (information technology) signifying a shift of focus from computing technology to the capacity to store and retrieve information. This was followed by the introduction of the term ‘ICT’ (Information and Communication Technology) around 1992, when e-mail started to become available to the general public. According to a United Nations report (1999) ICTs cover Internet service provision, telecommunications equipment and services, information technology equipment and services, media and broadcasting, libraries and documentation centres, commercial information providers, network-based information services, computing skills in everyday life. Hepp, Hinostroza, Laval and Rehbein (2004) claim in their paper “Technology in Schools: Education, ICT and the Knowledge Society” that ICTs have been utilized in education ever since their inception, but they have not always been massively present. Although at that time computers have not been fully integrated in the learning of traditional subject matter, the commonly accepted rhetoric that education systems would need to prepare citizens for lifelong learning in an information society boosted interest in ICTs (Pelgrum, W.J., Law, N., 2003). The 1990s was the decade of computer communications and information access, particularly with the popularity and accessibility of internet-based services such as electronic mail and the World Wide Web (WWW). At the same time the CD-ROM became the standard for distributing packaged software (replacing the floppy disk). As a result, educators became more focused on the use of the technology to improve student learning as a rationale for investment. Any discussion about the use of computer systems in schools is built upon an 18 understanding of the link between schools, learning and computer technology. When the potential use of computers in schools was first mooted, the predominant conception was that students would be ‘taught’ by computers (Mevarech & Light, 1992). In a sense it was considered that the computer would ‘take over’ the teacher’s job in much the same way as a robot computer may take over a welder’s job. Collis (1989) refers to this as “a rather grim image” where “a small child sits alone with a computer”. However, the use of information and communication technologies in the educative process has been divided into two broad categories: ICTs for Education and ICTs in Education. ICTs for education refers to the development of information and communications technology specifically for teaching/learning purposes, while the ICTs in education involves the adoption of general components of information and communication technologies in the teaching learning process. 2.2.1 ICT enhancing the quality and accessibility of education ICT increases the flexibility of delivery of education so that learners can access knowledge anytime and from anywhere. It can influence the way students are taught and how they learn as now the processes are learner driven and not by teachers. This in turn would better prepare the learners for lifelong learning as well as to improve the quality of learning. In concert with geographical flexibility, technology-facilitated educational programs also remove many of the temporal constraints that face learners with special needs (Moore & Kearsley, 1996). Students are starting to appreciate the capability to undertake education anywhere, anytime and anyplace. One of the most vital contributions of ICT in the field of education is- Easy Access to Learning. With the help of ICT, students can now browse through e-books, sample examination papers, previous year papers etc. and can also have an easy access to resource persons, mentors, experts, researchers, professionals, and peers-all over the world. This flexibility has heightened the availability of just-in-time learning and provided learning 19 opportunities for many more learners who previously were constrained by other commitments (Young, 2002). Wider availability of best practices and best course material in education, which can be shared by means of ICT, can foster better teaching. ICT also allows the academic institutions to reach disadvantaged groups and new international educational markets. As well as learning at any time, teachers are also finding the capabilities of teaching at any time to be opportunistic and able to be used to advantage. Mobile technologies and seamless communications technologies support 24x7 teaching and learning. Choosing how much time will be used within the 24x7 envelope and what periods of time are challenges that will face the educators of the future (Young, 2002). Thus, ICT enabled education will ultimately lead to the democratization of education. Especially in developing countries like India, effective use of ICT for the purpose of education has the potential to bridge the digital divide. India has a billion-plus population and a high proportion of the young and hence it has a large formal education system. The demand for education in developing countries like India has skyrocketed as education is still regarded as an important bridge of social, economic and political mobility (Amutabi and Oketch, 2003). There exists infrastructure, socio- economic, linguistic and physical barriers in India for people who wish to access education (Bhattacharya and Sharma, 2007). This includes infrastructure, teacher and the processes quality. There exist drawbacks in general education in India as well as all over the world like lack of learning materials, teachers, remoteness of education facilities, high dropout rate etc. (UNESCO,2002). Innovative use of Information and Communication Technology can potentially solve this problem. Internet usage in home and work place has grown exponentially (McGorry, 2002). ICT has the potential to remove the barriers that are causing the problems of low rate of education in any country. It can be used as a tool to overcome the 20 issues of cost, less number of teachers, and poor quality of education as well as to overcome time and distance barriers (McGorry, 2002). People have to access knowledge via ICT to keep pace with the latest developments (Plomp, Pelgrum & Law, 2007). ICT can be used to remove communication barriers such as that of space and time (Lim and Chai, 2004). ICTs also allow for the creation of digital resources like digital libraries where the students, teachers and professionals can access research material and course material from any place at any time (Bhattacharya and Sharma, 2007; Cholin, 2005). Such facilities allow the networking of academics and researchers and hence sharing of scholarly material. This avoids duplication of work (Cholin, 2005). ICT eliminating time barriers in education for learners as well as teacher. It eliminates geographical barriers as learners can log on from any place (Sanyal, 2001; Mooij, 2007; Cross and Adam, 2007; UNESCO, 2002; Bhattacharya and Sharma, 2007). ICT provides new educational approaches (Sanyal, 2001). It can provide speedy dissemination of education to target disadvantaged groups (UNESCO, 2002; Chandra and Patkar, 2007). ICT enhances the international dimension of educational services (UNESCO, 2002). It can also be used for non-formal education like health campaigns and literacy campaigns (UNESCO, 2002). Use of ICT in education develops higher order skills such as collaborating across time and place and solving complex real world problems (Bottino, 2003; Bhattacharya and Sharma, 2007; Mason, 2000; Lim and Hang, 2003). It improves the perception and understanding of the world of the student. Thus, ICT can be used to prepare the workforce for the information society and the new global economy (Kozma, 2005). Plomp et al (2007) state that the experience of many teachers, who are early innovators, is that the use of ICT is motivating for the students as well as for the teachers themselves. Bottino (2003) and Sharma (2003) mention that the use of ICT can improve performance, teaching, administration, and develop relevant skills in the disadvantaged communities. It also improves the quality of education by 21 facilitating learning by doing, real time conversation, delayed time conversation, directed instruction, self-learning, problem solving, information seeking and analysis, and critical thinking, as well as the ability to communicate, collaborate and learn (Yuen et al, 2003). A great deal of research has proven the benefits to the quality of education (Al-Ansari 2006). Hepp, Hinostroza, Laval and Rehbein (2004) state that the literature contains many unsubstantiated claims about the revolutionary potential of ICTs to improve the quality of education. They also note that some claims are now deferred to a near future when hardware will be presumably more affordable and software will become, at last, an effective learning tool. 2.2.2 ICT enhancing learning Environment ICT presents an entirely new learning environment for students, thus requiring a different skill set to be successful. Critical thinking, research, and evaluation skills are growing in importance as students have increasing volumes of information from a variety of sources to sort through (New Media Consortium, 2007). ICT is changing processes of teaching and learning by adding elements of vitality to learning environments including virtual environments for the purpose. ICT is a potentially powerful tool for offering educational opportunities. It is difficult and maybe even impossible to imagine future learning environments that are not supported, in one way or another, by Information and Communication Technologies (ICT). When looking at the current widespread diffusion and use of ICT in modern societies, especially by the young the so-called digital generation then it should be clear that ICT will affect the complete learning process today and in the future. Authenticity is an important issue which should be addressed in the design and development of learning environments (Collins, 1996). Learning environments need to reflect the potential uses of knowledge that pupils are expected to master, in order to prevent the acquired knowledge from becoming 22 inert (Bransford, Sherwood, Hasselbring, Kinzer, & Williams, 1990; Duffy & Knuth, 1990). In addition, teachers should stimulate pupils to engage in active knowledge construction. This calls for open-ended learning environments instead of learning environments which focus on a mere transmission of facts (Collins, 1996; Hannafin, Hall, Land, & Hill, 1994; Jonassen, Peck, & Wilson, 1999). ICT may contribute to creating powerful learning environments in numerous ways. ICT provides opportunities to access an abundance of information using multiple information resources and viewing information from multiple perspectives, thus fostering the authenticity of learning environments. ICT may also make complex processes easier to understand through simulations that, again, contribute to authentic learning environments. Thus, ICT may function as a facilitator of active learning and higher-order thinking (Alexander, 1999; Jonassen, 1999). The use of ICT may foster co-operative learning and reflection about the content (Susman, 1998). Furthermore, ICT may serve as a tool to curriculum differentiation, providing opportunities for adapting the learning content and tasks to the needs and capabilities of each individual pupil and by providing tailored feedback (Mooij, 1999; Smeets & Mooij, 2001). As Stoddart and Niederhauser (1993) point out, ICT may fit into a spectrum of instructional approaches, varying from traditional to innovative. Another aspect which may of course influence the use of ICT is access to technology (Kennewell, Parkinson, & Tanner, 2000). This refers not only to the number of computers, but also to the placement of the equipment, e.g. in the classroom or in a computer room. Kennewell et al. (2000) feel it is essential that computers be placed in the classroom, in order to maximize the opportunities for curriculum activity. ICT environment improves the experience of the students and teachers and to use intensively the learning time for better results. The ICT environment has been developed by using different software and also the extended experience in developing 23 web based and multimedia materials. ICTs have an important role to play in changing and modernizing educational systems and ways of learning. 2.2.3 ICT enhancing learning motivation ICTs can enhance the quality of education in several ways, by increasing learner motivation and engagement, by facilitating the acquisition of basic skills, and by enhancing teacher training. ICTs are also transformational tools which, when used appropriately, can promote the shift to a learner centred environment. ICTs, especially computers and Internet technologies, enable new ways of teaching and learning rather than simply allow teachers and students to do what they have done before in a better way. ICT has an impact not only on what students should learn, but it also plays a major role on how the students should learn. Along with a shift of curricula from “content-centred” to “competence-based”, the mode of curricula delivery has now shifted from “teacher centred” forms of delivery to “studentcentred” forms of delivery. ICT provides- Motivation to Learn. ICTs such as videos, television and multimedia computer software that combine text, sound, and colourful moving images can be used to provide challenging and authentic content that will engage the student in the learning process. Interactive radio likewise makes use of sound effects, songs, dramatizations, comic skits, and other performance conventions to compel the students to listen and become more involved in the lessons being delivered. Some of the parents of the respondents opined that their children were feeling more motivated than before in such type of teaching in the classroom rather than the stereotype 45 minutes’ lecture. They were of the view that this type of learning process is much more effective than the monotonous monologue classroom situation where the teacher just lectures from a raised platform and the students just listen to the teacher. 24 ICT changes the characteristics of problems and learning tasks, and hence play an important task as mediator of cognitive development, enhancing the acquisition of generic cognitive competencies as essential for life in our knowledge society. Students using ICTs for learning purposes become immersed in the process of learning and as more and more students use computers as information sources and cognitive tools (Reeves and Jonassen, 1996), the influence of the technology on supporting how students learn will continue to increase. Learning approaches using contemporary ICTs provide many opportunities for constructivist learning through their provision and support for resource-based, student centred settings and by enabling learning to be related to context and to practice (Berge, 1998; Barron, 1998). The teachers could make their lecture more attractive and lively by using multi-media and on the other hand the students were able to capture the lessons taught to them easily. As they found the class very interesting, the teachings also retained in their mind for a longer span which supported them during the time of examination. More so than any other type of ICT, networked computers with Internet connectivity can increase learner motivation as it combines the media richness and interactivity of other ICTs with the opportunity to connect with real people and to participate in real world events. ICT-enhanced learning is studentdirected and diagnostic. Unlike static, text- or print-based educational technologies, ICTenhanced learning recognizes that there are many different learning pathways and many different articulations of knowledge. ICTs allow learners to explore and discover rather than merely listen and remember. The World Wide Web (WWW) also provides a virtual international gallery for students’ work (Loveless, 2003). ICT can engage and inspire students, and this has been cited as a factor influencing ready adaptors of ICT (Long, 2001). 2.2.4 ICT enhancing the scholastic performance Based on the extensive usage of ICTs in education the need appeared to unravel the myth that surrounds the use of information and communication technology (ICT) as an aid to teaching 25 and learning, and the impact it has on students’ academic performance. ICTs are said to help expand access to education, strengthen the relevance of education to the increasingly digital workplace, and raise educational quality. However, the experience of introducing different ICTs in the classroom and other educational settings all over the world over the past several decades suggests that the full realization of the potential educational benefits of ICT. The direct link between ICT use and students’ academic performance has been the focus of extensive literature during the last two decades. ICT helps students to their learning by improving the communication between them and the instructors (Valasidou and Bousiou, 2005). The analysis of the effects of the methodological and technological innovations on the students’ attitude towards the learning process and on students’ performance seems to be evolving towards a consensus, according to which an appropriate use of digital technologies in education can have significant positive effects both on students’ attitude and their achievement. Research has shown that the appropriate use of ICTs can catalyse the paradigmatic shift in both content and pedagogy that is at the heart of education reform in the 21st century. Kulik (2003) meta-analysis study revealed that, on average, students who used ICT-based instruction scored higher than students without computers. The students also learned more in less time and liked their classes more when ICT-based instruction was included. Fuchs and Woessman (2004) used international data from the Programme for International Student Assessment (PISA), they showed that while the bivariate correlation between the availability of ICT and students’ performance is strongly and significantly positive, the correlation becomes small and insignificant when other student environment characteristics are taken into consideration. Attwell and Battle (1999) examined the relationship between having a home computer and school performance, their findings suggest that students who have access to a computer at home for educational purposes, have 26 improved scores in reading and math. Becker (2000) found that ICT increases student engagement, which leads to an increased amount of time students spend working outside class. Coates & Humphreys (2004) showed that students in on-campus courses usually score better than their online counterparts, but this difference is not significant here. ICTs especially computers and Internet technologies enable new ways of teaching and learning rather than simply allow teachers and students to do what they have done before in a better way. ICT helps in providing a catalyst for rethinking teaching practice (Flecknoe,2002), developing the kind of graduates and citizens required in an information society improving educational outcomes and enhancing and improving the quality of teaching and learning (Wagner, 2001). ICT can help deepen students’ content knowledge, engage them in constructing their own knowledge, and support the development of complex thinking skills (Kozma, 2005; Kulik, 2003; Webb & Cox, 2004). Studies have identified a variety of constructivist learning strategies (e.g., students work in collaborative groups or students create products that represent what they are learning) that can change the way students interact with the content (Windschitl, 2002). ICTs have the potential for increasing access to and improving the relevance and quality of education. The use of ICT in educational settings, by itself acts as a catalyst for change in this domain. Students using ICTs for learning purposes become immersed in the process of learning and as more and more students use computers as information sources and cognitive tools (Reeves and Jonassen, 1996), the influence of the technology on supporting how students learn will continue to increase. 2.3 Why integrating ICT into the teaching and learning The question of why information and communication technology be integrated into the teaching and learning in Nigeria may appear too simplistic and unnecessary. However, the political conditions in Nigeria for the past thirty years leave no room for continuity. Over the 27 years, political power in Nigeria has been used to entrench mediocrity, corruption in high places, misplace priority, and consumer culture. The direct effect of these is a battered economy and an educational system that is decaying by the day. In 1988, in an attempt to keep pace with development in computer education, Nigeria enacted a Policy on Computer Education. According to Okebukola (2007). The plan was to establish pilot schools and thereafter diffuse the innovation, first to all secondary schools and then to the Primary schools. Unfortunately, beyond the distribution and installation of computers in the Federal Government Colleges, the project did not really take off the ground (P.16). Okebukola (2007) concluded that computer is not part of classroom technology in over 90% of public schools in Nigeria. Thus the chalkboard, marker board and textbooks continue to dominate classroom activities in most secondary schools in Nigeria. If a country such as Uganda which has less than one-fifth of Nigeria’s resources, is now using information and communication technology to help secondary school’s students to become better information users, why is Nigeria lagging behind? The answer is simply mismanagement of the huge resources of the country and inability of political leaders to prioritize Nigeria’s developmental needs. There is no doubt that in the current harsh economic competition, the private sector in Nigeria has embraced ICT to stay afloat. The banking sector, insurance, manufacturing industries and multinational companies in the oil sector have embraced multimedia technology to bring innovative solutions to their current challenges. If Nigeria wants to be a major player in the global market place of ideas and prepare her citizens for the new environment of today and the future, the country should embrace ICT for the following reasons: ICT as aids to teaching and learning; ICT as a tool for management; ICT as instrument for economic development; ICT as instrument of high technological development, and ICT as a course of study. 28 2.3.1 ICT as aids to teaching and learning The importance of ICT is quite evidence from the educational perspective. Though the chalkboard, textbooks, radio/television and film have been used for educational purpose over the years, none has quite impacted on the educational process like the computer. While television and film impact only on the audio-visual faculties of users, the computer is capable of activating the senses of sight, hearing and touch of the users. ICT has the capacity to provide higher interactive potential for users to develop their individual, intellectual and creative ability. The main purpose of ICT “consists just in the development of human mental resources, which allow people to both successfully apply the existing knowledge and produce new knowledge” (Shavinina, 2001). The collective and rigid nature of learning and the passive nature of the learning associated with the use of radio, television and film do not contribute any innovative changes to traditional methods in education system. Information and communication technologies are being used in the developed world for instructional functions. Today, computers perform a host of functions in teaching and learning as many nations are adding computer literacy, reading and writing literacy as skills students will need for succeeding in a technologically developed world (Thomas, 1987). At the instructional level, computers are used by pupils to learn reading, mathematics, social studies, art, music, simulation and health practices. In educational multimedia application Shavinina (1997) asserted that today’s learning contents are domain-specific products and that they dominate the world market. According to Shavinina (1997), domain-specific educational multimedia is directed to knowledge acquisition skills development in the language arts, history, physics, literature, biology and so on. There is no doubt that ICT provides productive teaching and learning in order to increase people’s creative and intellectual resources especially in today’s information society. 29 Through the simultaneous use of audio, text, multicolour images, graphics, motion, ICT gives ample and exceptional opportunities to the students to develop capacities for high quality learning and to increase their ability to innovate. Nigeria cannot afford to lag behind in using multimedia to raise the intellectual and creative resources of her citizens. This is particularly important for children whose adulthood will blossom in a cyber-environment entirely different from that of the present (Shavinina, 1997). Nigerian children need to be taught by radically new educational programme and variety of educational contents with multimedia playing key role. 2.3.2 ICT as tool for Educational Management It is not uncommon to find that many establishments in Nigeria, including educational institutions still keep records in files and tucked them away in filling cabinets where they accumulate dust. Many of these files are often eaten up by rodents and cockroaches thus rendering them irretrievable. A great deal of routine administrative work in government establishment is still done manually with the state and the Federal government showing little or no interest in embracing ICT. The official administrative drudgery in government offices and education institutions can be better managed through ICT. Educational administrative functions include a wide variety of activities such as educational governance, supervision, support services, infrastructure, finance, budgeting, accounting, personnel selection and training system monitoring and evaluation, facilities procurement and management, equipment maintenance, research, and so on (Thomas, 1987). In most Nigeria schools, officials still go through the laborious exercise of manually registering students, maintaining records of pupil, performance, keeping inventory list of supplies, doing cost accounting, paying bills, printing reports and drawing architectural designs. The huge man-hour spend on these exercises can be drastically reduced with ICT to enhance overall management procedure. Thomas (1987) said that “Computers bring great 30 speed and accuracy to each of these tasks, along with the convenience of storing large quantities of information on ‘small disks or tapes. The prevailing condition in school management in Nigeria is disheartening and discouraging. The country seems to be living in prehistoric times in the educational management while even developing countries in Africa such as South Africa, Kenya, Uganda and Tanzania are far ahead of Nigeria in ICT applications. Despite its huge material resources and population endowment, Nigeria cannot be counted among progressive nations using ICT in educational management, as technology has become a critical tool for achieving success in education. 2.3.3 ICT as instrument of economic development The present government in Nigeria is pursuing the deregulation of the economy with a passion that has never been seen in the country. It is striving for a private sector driven economy hence it is selling its shares in many companies so that they can fully be managed by the private sector. Most of these companies in which government hold majority shares have been mismanaged over the years that they have become a huge burden and a financial drain-pipe to government, hence deregulation in the country today. The importance of ICT in Nigeria strongly manifests itself from an economic standpoint. Today, as a result of globalization, industrial competition is increasingly harsh and companies must not only come up with innovative products and services to the global market but most do so with unprecedented speed. For the companies to survive, they need intellectual and creative employees who’s “novel ideas are to a certain extend a guarantee of companies’ existence” (Shavinina 2001). Contemporary society strongly needs highly able minds that could productively solve many economic problems of today. Such highly able minds are nurtured by a country’s educational institutions. Nigeria lags considerably behind others in the development of small and medium scale enterprises, which are the mainstay of modern economy and society. Modern society desperately needs highly able citizens who can 31 bring innovative solutions to its current challenges and at the same time produce new ideas for on-going socio-economic and political advancement (Shavinina, 1997). Nigeria can only be part of such modern society if ICT facilities are deployed to all sectors of the economy. Because, the country is already on the wrong side of the digital divide, it must lay the proper foundation for ICT use in the education sector. 2.3.4 ICT as tool for higher technological development In today’s world, not only are we surrounded by technology, but our primary means of reaching others in far and near places are mediated by technology. According To Elluh (1989), “technology is progressively facing the two previous environments: nature and society”. The environment he talked about is that which enables us to live, sets us in danger and it is immediate to us and mediates all else. He asserted that modern man cannot live without our gadgets. This is what makes human subservient to technology rather that technology being subservient to humanity. There is no doubt that one of today’s realities is an extremely fast development of hightechnology. This has resulted in a huge change of the individual’s life in business and private settings. There is strong need to know and use modern technology in our social life, the economy, the business and education. New and sophisticated breakthroughs in high technology encourage companies to introduce technological innovations rapidly into their business practices. The United States Space Programme has benefited immensely from rapid development in high-tech and today’s information and communication technology. In many parts of the developed world, cellular, satellite, and wireless technologies combined with innovative business practices are beginning to make up for the shortcomings of the traditional wire line technologies. Nigeria was introduced to cellular technologies a little over two years ago and this has revolutionized the communication industry in the country, though majorities of Nigerians are yet to benefit from the services due to high cost. 32 If Nigeria must be part of developed world in the near future, it must embrace technology and discard some of the old habits and perspectives and retool completely. There is need for the country to re-strategize and expand its vision so as to cope with the challenges of a technological society. 2.3.5 ICT as a course of study The most challenging aspect of the post-industrial era is how to meet the demand of the information society that modern man is trying to build. The role of education in developing modern society cannot be overemphasized. In fact, society and education are highly interdependent. As society changes, the educational system has to change accordingly (Westera and Sloep, 2001). Today employers of labour are in search of graduates with requisite knowledge, skill and training that would help to solve problems that do not yet exist today. In recent years thousands of university graduates found it difficult to secure good paying jobs. This has been due to the fact that there are no jobs out there as many government establishments and private companies are even retrenching workers as a result of hard times being experienced by the economy. Though the Nigerian government has opened its doors to foreign investors and many of them are coming in, Nigerian graduates are not properly trained for the new positions that are opening up in the new companies being established. There is a high demand for highly skilled and technologically trained workers. Unfortunately, most Nigerian graduates acquired overdose of theoretical knowledge, which does not match well with the demands of workplace practice. Modern companies need employees that are proactive, enterprising, responsible and self-reliant professional. According to Walton (1995), modern employees represent the business’ human capital. Nigeria needs to replace the traditional pedagogical practices that still underpin its educational system. In a report of the World Bank sponsored research study on the state of 33 the Nigerian graduate, Dabalen and Oni (2000) asserted that Nigerian University graduates of the past decade are poorly trained and unproductive on the job. The report indicted Nigerian University graduates as deficient in mastery of the English language and requisite technical skills. Such development calls for a rethinking of the objectives education should pursue. In order to revolutionize Nigeria educational system, the country needs ICT not only as tools for communication but also as a field of study. Modern companies, especially those operated by the new foreign investors need skilled workers with basic knowledge in algorithm, flow chart design, complex programming, and web design. Nigeria also needs computer technicians and engineers. These new fields of study could be introduced as areas of study in Nigeria universities and polytechnics. Though, few Nigeria universities are already having computer study as part of their academic programs, most of them are still theoretical in nature to impact meaningfully on the society. Nigeria needs to establish a virtual learning company along the model developed and implemented at the Open University of the Netherlands. The Netherlands virtual Company was established to answer to future challenges of modern society. According to Westera & Sloep, (2001), the Netherlands Virtual Company; “Is a distributed, virtual learning environment that embodies the functional structures of veracious companies; it offers students a rich and meaningful context that resembles the context of professional working in many respects; it aims to bridge the gap between education and professional working, between theory and practice between knowledge and skills.”(P.116) The virtual Learning Company is regarded as a state of the art cyber education, which strives to bring together the context of education and workplace. Nigeria has just launched its own version of Open University in Abuja after so many years of planning. The Nigeria Open University has a lot to learn from the Netherlands example by offering a concrete and 34 meaningful environment that closely resembles the student’s future workplaces. The Nigeria University Commission recently established a virtual learning website but its impact is yet to be seen and it is too early to be assessed. 2.4 Theoretical Framework The major theoretical rationale for the use of manipulative materials in a laboratory-type setting has been attributed to the works of Piaget, Bruner, and Dienes. Each represents the cognitive viewpoint of learning, a position that differs substantially from the connectionist theories that were predominant in educational psychology during the first part of the twentieth century. Modern cognitive psychology places great emphasis on the process dimension of the learning process and is at least as concerned with "how" children learn as with "what", it is they learn. The objective of true understanding is given highest priority in the teaching/learning process, and it is generally felt that such understanding can only follow the individuals' personalized perception, synthesis, and assimilation of relationships as these are encountered in real situations. Emphasis is placed, therefore, on the interrelationships between parts as well as the relationship between parts and whole. Each of these men subscribes to a basic tenet of Gestalt psychology, namely that the whole is greater than the sum of its parts. Each suggests that the learning of large conceptual structures is more important than the mastery of large collections of isolated bits of information. Learning is thought to be intrinsic and, therefore, intensely personal in nature. It is the meaning that each individual attaches to an experience which is important. It is generally felt that the degree of meaning is maximized when individuals are allowed and encouraged to interact personally with various aspects of their environment. This, of course, includes other people. It is the physical action on the part of the child that contributes to her or his understanding of the ideas encountered. 35 Proper use of manipulative materials could be used to promote the broad goals alluded to above. The researcher discusses each of these men more fully since each has made distinct contributions to a coherent rationale for the use of manipulative materials in the learning of mathematical concepts and thus integrating ICT into the teaching and learning of mathematics. 2.4.1 Jean Piaget Piaget's contribution to the psychology of intelligence has been compared to Freud's contributions to the psychology of human personality. Piaget has provided numerous insights into the development of human intelligence, ranging from the random responses of the young infant to the highly complex mental operations inherent in adult abstract reasoning. He has established the framework within which a vast amount of research has been conducted, particularly within the past two decades. In his book The Psychology of Intelligence (1971), Piaget formally develops the stages of intellectual development and the way they are related to the development of cognitive structures. His theory of intellectual development views intelligence as an evolving phenomenon occurring in identifiable stages having a constant order. The age at which children attain and progress through these stages is variable and depends on factors such as physiological maturation, the degree of meaningful social or educational transmission, and the nature and degree of relevant intellectual and psychological experiences. Piaget regards intelligence as effective adaptation to one's environment. The evolution of intelligence involves the continuous organization and reorganization of one's perceptions of, and reactions to, the world around him. This involves the complementary processes of assimilation (fitting new situations into existing psychological frameworks) and accommodation (modification of behaviour by developing or evolving new cognitive structures). The effective use of the assimilation-accommodation cycle continually restores equilibrium to an individual's 36 cognitive framework. Thus the development of intelligence is viewed by Piaget as a dynamic, non-static evolution of newer and more complex mental structures. Piaget's now-famous four stages of intellectual development (sensorimotor, preoperational, concrete operations, and formal operations) are useful to educators because they emphasize the fact that children's modes of thought, language, and action differ both in quantity and quality from that of the adult. Piaget has argued persuasively that children are not little adults and therefore cannot be treated as such. "Perhaps the most important single proposition that the educator can derive from Piaget's work, and its use in the classroom, is that children, especially young ones, learn best from concrete activities" (Ginsberg & Opper 1969). This proposition, if followed to its logical conclusion, would substantially alter the role of the teacher from expositor to one of facilitator, that is, one who promotes and guides children's manipulation of and interaction with various aspects of their environment. While it is true that when children reach adolescence their need for concrete experiences is somewhat reduced because of the evolution of new and more sophisticated intellectual schemas, it is not true that this dependence is eliminated. The kinds of thought processes so characteristic of the stage of concrete operations are in fact utilized at all developmental levels beyond the ages of seven or eight. Piaget's crucial point, which is sometimes forgotten or overlooked, is that until about the age of eleven or twelve, concrete operations represent the highest level at which the child can effectively and consistently operate. Piaget has emphasized the important role that social interaction plays in both the rate and quality with which intelligence develops. The opportunity to exchange, discuss, and evaluate one's own ideas and the ideas of others encourages decent ration (the diminution of egocentricity), thereby leading to a more critical and realistic view of self and others. 37 I t would be impossible to incorporate the essence of these ideas into a mathematics program that relies primarily (or exclusively) on the printed page for its direction and "activities." To be sure, Piaget speaks to much more than the learning of mathematics per say. Intellectual development is inextricably intertwined with the social/psychological development of children, but it should be noted that mathematics and science, with their wide diversity of ideas and concepts and their capacity for being represented by concrete isomorphic structures, are especially well suited to the promotion of these ends. It is generally felt that the basic components of a theoretical justification for the provision of active learning experiences in the mathematics classroom are embedded in Piaget's theory of cognitive development. Dienes and Bruner, while generally espousing the views of Piaget, have made contributions to the cognitive view of mathematics learning that are distinctly their own. The work of these two men lends additional support to this point of view. 2.4.2 Zoltan P. Dienes Unlike Piaget, Dienes has concerned himself exclusively with mathematics learning; yet like Piaget, his major message is concerned with providing a justification for active student involvement in the learning process. Such involvement routinely involves the use of a vast amount of concrete material. Rejecting the position that mathematics is to be learned primarily for utilitarian or materialistic reasons, Dienes (1969) sees mathematics as an art form to be studied for the intrinsic value of the subject itself. He believes that learning mathematics should ultimately be integrated into one's personality and thereby become a means of genuine personal fulfilment. Dienes has expressed concern with many aspects of the status quo, including the restricted nature of mathematical content considered, the narrow focus of program objectives, the overuse of large-group instruction, the debilitating nature of the punishment- reward system (grading), and the limited dimension of tile instructional 38 methodology used in most classrooms. Dienes's theory of mathematics learning has four basic components or principles. Each will be discussed briefly and its implications noted. 1 The Dynamic Principle: This principle suggests that true understanding of a new concept is an evolutionary process involving the learner in three temporally ordered stages. The first stage is the preliminary or play stage, and it involves the learner with the concept in a relatively unstructured but not random manner. For example, when children are exposed to a new type of manipulative material, they characteristically 'play' with their newfound 'toy.' Dienes suggests that such informal activity is a natural and important part of the learning process and should therefore be provided for by the classroom teacher. Following the informal exposure afforded by the play stage, more structured activities are appropriate, and this is the second stage. It is here that the child is given experiences that are structurally similar to the concepts to be learned. The third stage is characterized by the emergence of the mathematical concept with ample provision for reapplication to the real world. The dynamic principle establishes a general framework within which learning of mathematics can occur. The remaining components should be considered as existing within this framework. 2 The Perceptual Variability Principle: This principle suggests that conceptual learning is maximized when children are exposed to a concept through a variety of physical contexts or embodiments. The experiences provided should differ in outward appearance while retaining the same basic conceptual structure. The provision of multiple experiences (not the same experience many times), using a variety of materials, is designed to promote abstraction of the mathematical concept. When a child is given opportunities to see a concept in different ways and under different conditions, he or she is more likely to perceive that concept 39 irrespective of its concrete embodiment. For example, the regrouping procedures used in the process of adding two numbers are independent of the type of materials used. We could therefore use tongue depressors, chips, and abacus or multi base arithmetic blocks to illustrate this process. When exposed to a number of seemingly different tasks that are identical in structure, children will tend to abstract the similar elements from their experiences. It is not the performance of anyone of the individual tasks that is the mathematical abstraction but the ultimate realization of their similarity. 3 The Mathematical Variability Principle: This principle suggests that the generalization of a mathematical concept is enhanced when the concept is perceived under conditions wherein variables irrelevant to that concept are systematically varied while keeping the relevant variables constant. For example, if one is interested in promoting an understanding of the parallelogram, this principle suggests that it is desirable to vary as many of the irrelevant attributes as possible. In this example, the size of angles, the length of sides, the position on the paper should be varied while keeping the relevant attribute-opposite sides parallel-intact. Dienes suggests that the two variability principles be used in concert with one another since they are designed to promote the complementary processes of abstraction and generalization, both of which are crucial aspects of conceptual development 4 The Constructivity Principle: Dienes identifies two kinds of thinkers: the constructive thinker and the analytic thinker. He roughly equates the constructive thinker with Piaget's concrete operational stage and the analytical thinker with Piaget's formal operational stage of cognitive development. This principle states simply that "construction should always precede analysis." It is analogous to the assertion that children should be allowed to develop their concepts in a global intuitive manner emanating from their own experiences. According to Dienes, these experiences carefully selected by the teacher form the cornerstone upon which all mathematics learning is based. At some future time, attention will be directed toward the 40 analysis of what has been constructed; however, Dienes points out that it is not possible to analyze what is not yet there in some concrete form. 2.4.3 Jerome Bruner Greatly influenced by the work of Piaget and having worked for some time with Dienes at Harvard, Bruner shares many of their views. Interested in the general nature of cognition (conceptual development), he has provided additional evidence suggesting the need for firsthand student interaction with the environment. His widely quoted (and hotly debated) view that "any subject can be taught effectively in some intellectually honest form to any child at any stage of development" (Bruner 1966) has encouraged curriculum developers in some disciplines (especially social studies) to explore new avenues of both content and method. In recent years Bruner has become widely known in the field of curriculum development through his controversial elementary social studies program, Man: A Course of Study (1969). Bruner's instructional model is based on four key concepts: structure, readiness, intuition, and motivation. These constructs are developed in detail in his classic book, The Process of Education (1960). Bruner suggests that teaching students the structure of a discipline as they study particular content leads to greater active involvement on their part as they discover basic principles for themselves. This, of course, is very different from the learning model that suggests students be receivers rather than developers of information. Bruner states that learning the structure of knowledge facilitates comprehension, memory, and transfer of learning. The idea of structure in learning leads naturally to the process approach where the very process of learning (or how one learns) becomes as important as the content of learning (or what one learns). This position, misunderstood by many, has been the focus of considerable controversy. The important thing to remember is that Bruner never says that content is unimportant. 41 Bruner (1966) suggests three modes of representational thought. That is, an individual can think about a particular idea or concept at three different levels. "Enactive" learning involves hands-on or direct experience. The strength of enactive learning is its sense of immediacy. The mode of learning Bruner terms "iconic" is one based on the use of the visual medium: films, pictures, and the like. "Symbolic" learning is that stage where one uses abstract symbols to represent reality. Bruner feels that a key to readiness for learning is intellectual development, or how a child views the world. Here he refers to the work of Piaget, stating that "what is most important for teaching basic concepts is that the child be helped to pass progressively from concrete thinking to the utilization of more conceptually adequate modes of thought". Bruner suggests that readiness depends more upon an effective mix of these three learning modes than upon waiting until some imagined time when children are capable of learning certain ideas. Throughout his writing is the notion that the key to readiness is a rich and meaningful learning environment coupled with an exciting teacher who involves children in learning as a process that creates its own excitement. Bruner clings to the idea of intrinsic motivation learning as its own reward. It is a refreshing thought. In short, a general overhaul of existing pedagogical practices, teacher-pupil interaction patterns, mathematical content, and mode of presentation, as well as general aspects of classroom climate would be called for if the views of Piaget, Dienes, and Bruner were to be taken seriously. Each in its own way would promote a revolution in school curricula, one whose major focus would be method as well as content. By and large the process of learning and teaching will be more interactive when it is made in such a way that the teacher demonstrate and explains whereas the students attends, view and retrieve the mathematical concepts, theories and principles capable of reshaping their memory. 2.5 Review of Empirical Studies 42 Lidon (2017) conducted a study to determine the effects of computer-aided instruction on mathematics performance of pupils at the Grade 4 level in Region 5, Guyana, South America. The focus was due to the trend of poor performances in mathematics at the National Grade 4 assessments for the past 5 years in the region. Four intact Grade 4 classes in two primary schools were used in the study. Two classes were used as experimental group and the other two as control group. The Quasi Experimental, Non-equivalent Control Group design was employed for the study. The instrument which was used for data collection was a teachermade test. The reliability coefficient of the instrument was .553, significant at alpha .01. The findings of the study indicated that there was a significant difference between the academic performance of pupils in mathematics who were taught using computer aided instruction and those who were taught using the traditional method of teaching. Second, there was a significant difference between the academic performance of male and female pupils who were taught using computer-aided instruction and those who were taught using the traditional method of teaching. Based on the findings of the study, some recommendations were made and among such were that computer-aided instruction should be integrated into the teaching of mathematics at the Grade 4 level in the area of study. Adeosun, Jimoh & Salami (2014) conducted a study to critically look into the effect of ICT supported mathematics instructions on the academic performance of students with disabilities in Ogun State, the study adopted a sort of non-linear approach to data collection, chi square was used to analysed the data obtained by the use of questionnaires distributed to the teachers of JSS 1 and SS 1 of the two selected schools in Ogun State. The study showed that there is significant difference between the academic performance of students with abilities taught using ICT supported mathematics instructional materials and those taught using whiteboard methods. 43 In a related study, Anyamene, Nwokolo, Anyachebelu & Anemelu (2012) conducted a study to investigate the effect of computer-assisted instruction (CAI) package on the performance of Senior Secondary Students in Mathematics (Algebra) in Awka, Anambra State, Nigeria. The study examined the significance of retention achievement scores of students taught using computer-assisted instruction and conventional method. The sample consisted of forty senior secondary school students drawn from two secondary schools. Stratified random sampling was used to select 40 students (20 males and 20 females). Three research questions and three hypotheses were formulated, and was tested at 0.05 level of significance. The Algebra Achievement Test (AAT) was made of 50 items of multiple-choice objective type, developed and validated for data collection. In the same vein, the Algebra Achievement Test (AAT) was administered to students as Pretest and Post-test. The results were analysed using t-test statistic to test the hypotheses. The result indicated that students taught using (CAI) package performed significantly better than their counterparts taught using the conventional method of instruction. Students taught using CAI performed better than the control group in retention test. Also there was no significant difference in the post-test performance scores of male and female students taught using CAI of package. Based on the finding of their research, it was recommended that ComputerAssistant Program should be encouraged for teaching and learning of mathematics. Amarasinghe & Lambdin (2000) described three different varieties of technology usage: using technology as a data analysis tool, II-using technology as a problem-solving/ mathematical modelling tool, and III-using technology to integrate mathematics with a context. Meanwhile researchers (Balacheff & Kaput, 1996; Kilpatrick & Davis, 1993) have discussed the impact of technological forces on learning and teaching mathematics. 44 Matthew, Joro and Manasseh (2015) conducted a study to investigate the role of ICT in educational system in Nigeria. The study observed that Nigeria still experience a lag in its ICT implementation, and this continue to widen the digital and knowledge divides and the access to ICT facilities is a major challenge facing most African countries. The study concludes that despite the roles ICT can play in education, schools in Nigeria have yet to extensively adopt them for teaching and learning. Efforts geared towards integration of ICT into the school system have not had much impact. Problems such as poor policy, project implementation strategies and poor information infrastructure militate against these efforts. The study recommended that efforts should be made by government to post and provide teachers skilled in ICT to each school to impart ICT skills to the student and also should stabilize electricity supply in Nigeria. Abubakar, Daniel & Adetimirin, Airen (2015) also conducted a study to investigate how computer literacy predisposes postgraduate students to use e-resources. The survey research design and multi-stage sampling technique were used to select 2726 postgraduate students from 16 Nigerian universities. A questionnaire and computer test was used to collect data and data was analysed using percentages and Pearson’s product moment correlation. The postgraduates’ computer literacy level was average (56.3%). They used only few of the eresources in their libraries and the frequency of usage was low (weighted average X = 2.45). The study showed that computer literacy had positive relationship with postgraduates’ usage of e-resources that was positive, very strong and significant (r= .740; d f=2284; p< .05). This shows that the more the postgraduates are exposed to computer literacy skills, the better the use of e-resources for their researches. It also showed that computer literacy is necessary to influence use of e-resources by the postgraduates’ and therefore recommended that computer literacy programme should be introduced for new entrant postgraduates. 45 Chukwudi & Godspower (2007), investigated the role of ICT on University of Benin undergraduate students’ academic performance. The study uses questionnaires which were distributed among 100 students both full time and part- time students. The survey includes male and female undergraduate students from diverse age bracket and faculties in the University of Benin. A total of 93 questionnaires were returned and data were analysed using the statistical packages for social sciences (SPSS) 16.0 software. The percentages of the responses were also calculated. The study revealed that there was 100% technological usage, with the new generation of mobile phones called smart phone, the respondents are capable of sending emails, files and multimedia at an amazing speed, through the mobile phones, laptop, IPads and desktop. The study also found that 83.9% of the students of the university visit social network sites on a regular basis. Other sites such as chat engine, entertainment site and adult sites were also visited. It was also revealed by the study that 60.9% of the students in addition to the social network surfing also surf academic related sites. The study also revealed that 6% of the students could make a first degree, 31% second class upper, 43% second class lower and 20% third class degree. The study affirmed that ICT have negative impact on students’ academic performance. It seems to have a profound impact on the process of learning in higher education by offering new possibilities for students and researchers. However, with the recent proliferation of ICT tools and services, students are finding it difficult to curtail its negative appeal. 2.6 Summary and Uniqueness of the Study Researches have been conducted in many countries across the globe as regards effectiveness of Computer Assisted Instructions on the performance of students in mathematics and other 46 related subjects amidst other researchers who conducted surveys to investigate the impact of Computer Assisted Instructions on the teaching and learning of mathematics and thus arouse the interest of the researcher on what will happen if the research is extended to Sokoto State, will the findings be the same or something different will emerge, what will make this research unique from the earlier one(s) conducted. This will tell the uniqueness of the study. 47 CHAPTER THREE RESEARCH METHODOLOGY 3.1 Introduction The chapter will present the research design, population of the study, sample and sampling techniques, instrumentation, validity of the instrument and analysis or method of analysis of this research study. 3.2 Research Design This study follows a quasi-experimental research design, as it entails CAI and its effectiveness on the performance of students in Mathematics. The study will have two groups (Control and Experimental Group). Experimental group will be the subjects of this study. They are students who will be taught using CAI while the control group will be students taught using the conventional method of teaching mathematics. Both two groups will have classes twice weekly throughout the period of this study. In order to establish the effectiveness of the Computer Assisted Instructions, the researcher will eventually administer similar questions to the two groups. The performance of these two groups will be used to establish the difference between the two teaching strategies i.e. Computer Assisted Instruction and Conventional Methods of Teaching 3.3 Population of the Study The population of the study consists of all senior secondary school students in Sokoto State the total population of students is 71108 out of this 47770 are male while 23338 are females. The following table shows the number of public and private schools and their corresponding number of students in Sokoto state. 48 Table 3.1: Public and Private Schools and the Number of Students in Sokoto State S/No School Type No. of Schools Male Female Students Students Total 1 Public 83 41839 20104 61943 2 Private 30 5931 3234 9165 47770 23338 71108 Grand Total Source: Ministry of Basic and Secondary Education Sokoto State, (2020) 3.4 Sample and Sampling Technique A sample of 664 students drawn out of 71108 students in Sokoto State will be used for the research, this number represent the intact class in each of the schools identified for the research. The list of the schools and the number of SS II students are shown below: Table 3.2: Sample for the Study S/No Name of school School Type Sample of Students 1. S D U S S Sokoto Boys Only 111 2. Nagarta Science College Sokoto Boys Only 124 3. Government Girls college Sokoto Girls only 103 4. Habsatu Ahmadu Girls Arabic S S Girls Only 129 5. Sheikh Abubakar Gummi Memorial Boys Only 95 6 Women Center for Continuous Education Girls Only 102 Total 664 Source: Examination offices of the Schools (from 12th to 30th September 2020) 3.5 Instrumentation For the purpose of this study, data collection and analysis, CAI Coaching Test (C.C.T.) will be used; (C.C.T.) is a self-constructed question paper based on the perceived topics to be used in the research; it will be constructed and administered to the sample population of the 49 research. It will consist of two sections A and B each comprising of 15 objectives questions from two selected topics in algebra (geometry and trigonometry) which will be marked and the scores will be used to determine the results of both the experimental group and that of control group. The test questions will be carefully designed. The test will be administered as pre-test and post-test before and after couching the students using CAI in teaching the selected mathematic topics. 3.5.1 Validity of the Instrument This is the extent to which the research instrument measures what it intends to measure. Thus, to establish the validity of the instrument, the instrument will be given to some experts in test, measurement and evaluation within or outside the department of Science and Vocational Education, Faculty of Education and Extension Services, Usmanu Danfodiyo University, Sokoto before it will be administered. Usage or otherwise of the instruments for the research will be based on the judgement of this experts thereby confirming its suitability and validity to be used as instrument for conducting this research. 3.5.2 Pilot study To establish the reliability of the instrument, it will be pilot tested; the instrument will be administered to a non-selected sample not within the target population. The result obtained from the pilot testing will be used to establish the reliability of the instrument before it will finally be administered in the field. 3.5.3 Reliability of the Instrument In order to ascertain the reliability of the instrument, it will be administered to a sample of students within the target population outside the selected samples. The reliability of the instrument will be established using the scores obtained from pilot testing 3.6 Method of Data Collection 50 The research instruments will be administered to the respondents in a class with the help of mathematics teachers to be drawn from the sample schools. Each respondent will be served with a copy of the instrument. Considering their age and schedules, the respondents will be given free time to go through them and respond appropriately. 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(2003), 'ICT implementation and school leadership Case studies of ICT integration in teaching and learning', Journal of Educational Administration Vol. 41 No. 2, Pp;158-170. 59 Appendix I List of Public Senior Secondary Schools and Number Students in Sokoto State S/No 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. Name of Schools Government Technical College, Binji Government Day Secondary School, Binji Government Day Secondary School, Danchadi Government Day Secondary School, Takatuku Government Day Secondary School, Badau Government Day Secondary School, Bodinga Government Day Secondary School, Sifawa Government Girls Unity Secondary School, Bodinga Government Secondary School, Dingyadi Army Day Secondary School, Sokoto Government Day Secondary School, Dange Government Day Secondary School, Shuni Government Secondary School Gada Government Secondary School, Wauru Ahmed Adamu Muazu Science Secondary School Goronyo Government Secondary School, Shinaka Government Science Secondary School Gwadabawa Government Secondary School, Gigane Government Day Secondary School, Illela Government Girls Model Secondary School, Illela Government Girls Arabic Secondary School, Isa Olusegun Obasanjo Technical College Bafarawa Government Secondary School, Isa Government Day Secondary School, Kuchi Government Secondary School, Kebbe Federal Science College Sokoto Government Secondary School, Kware Gamji Girls College Rabah Government Day Secondary School Rabah Government Day Secondary School, Kurawa Government Day Secondary School, Makuwana Government Secondary School, Gatawa Government Secondary School, Sabon Birni Aminu Ginga Day Secondary School, Shagari Government Day Secondary School, Dandin Mahe Government Day Secondary School, Kajiji Government Day Secondary School, Gande Government Day Secondary School, Silame Government Day Secondary School Gidan Igwai Government Day Secondary School, Kofar Marke, Sokoto Government Day Secondary School, Kofar Rini Government Day Secondary School, Runjin Sambo 60 Male 227 94 107 237 146 978 373 Nil 203 720 391 451 882 380 1095 250 1139 147 837 Nil Nil 602 979 215 195 820 67 Nil 341 392 235 491 1406 477 299 230 366 574 539 Nil 456 510 Females Nil 10 6 61 14 310 278 1232 65 619 64 64 Nil 41 Nil 273 Nil 16 259 473 1014 Nil Nil 35 54 240 16 518 2 10 6 37 Nil Nil 30 35 Nil Nil 255 1181 Nil 375 Total 227 104 113 298 160 1288 651 1232 268 1339 455 515 882 421 1095 523 1139 163 1096 473 1014 602 979 250 249 1060 83 518 343 402 241 528 1406 477 329 265 366 574 794 1181 456 885 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. Gov't Girls Day Arabic Secondary School Nil 643 Government Technical College Runjin Sambo 425 Nil Federal Government College, Sokoto 396 232 Abdul-Rasheed Adisa Raji Special School, Sokoto 982 782 Giginya Memorial Secondary School, Sokoto 1180 Nil Government Day Secondary School, Tudun Wada, Sokoto Nil 598 Government Girls Day Arabic Sec. School, Yar Akija Nil 1016 Hafsat Ahmadu Bello Model Arabic Sec. School, Sokoto Nil 2480 Nana Girls Secondary School, Sokoto Nil 2370 Sheikh Abubakar Gummi Memorial College, Sokoto 2204 Nil Sokoto Teachers College, Sokoto 759 Nil Sultan Atiku Secondary School, Sokoto 890 Nil Sultan Abubakar College, Sokoto 1510 Nil Sultan Attahirun Ahmadu Secondary School, Sokoto 1167 Nil Sultan Bello Secondary School, Sokoto 1785 Nil Nagarta College Sokoto 855 Nil Government Girls College Sokoto Nil 920 Women Centre For Continuing Education, Sokoto Nil 369 Abudullahi Barau Secondary School, Dogon Daji 958 Nil Community Day Secondary School, Tambawal 374 205 Gov’t Girls Commercial Secondary School Tambuwal Nil 602 Federal Government Girls College Tambuwal Nil 375 Government Day Secondary School, Jabo 444 112 Government Day Secondary School, Romon Sarki 218 3 Gov’t Girls' Commercial Secondary School Tambawal Nil 495 Government Girls Day Secondary School, Dogon Daji Nil 225 Government Secondary School Sanyinna 515 Nil Government Secondary School, Tangaza 974 Nil Govrnment Day Secondary School, Gidan Madi 312 35 Government Secondary School, Tureta 312 Nil Ahmadu Bello Academy 506 Nil Government Technical College Farfaru 926 Nil Government Day Secondary School 271 20 Government Day Secondary School Arkilla 835 521 Government Day Secondary School Wamakko 168 48 Sani Dingyadi Unity Secondary School 1432 Nil Sultan Maccido Institute for Quran And General Studies 302 176 Government Day Secondary School, Achida 1146 284 Government Secondary School, Wurno 798 Nil Government Science Secondary Yabo 768 Nil Community Day Secondary School, Yabo 576 Nil Total 41839 20104 Source: Ministry of Basic and Secondary School Education Sokoto (24th October, 2020) 61 643 425 628 1764 1180 598 1016 2480 2370 2204 759 890 1510 1167 1785 855 920 369 958 579 602 375 556 221 495 225 515 974 347 312 506 926 291 1356 216 1432 478 1430 798 768 576 61943 Appendix II Table 3.1: List of Private Senior Secondary Schools and Number Students in Sokoto State S/No Male Females Total Name of Schools 1. Usmanu Danfodiyo University Model Secondary School 120 60 180 2. Blue Crescent Schools Sokoto 300 231 531 3. Success School Sokoto Sokoto 330 221 551 4. Brilliant Footstep International Schools Sokoto 340 274 614 5. Asmau Girls Islamic College Sokoto Nil 368 368 6. Khalil Fodio Islamic Academy Sokoto 350 Nil 350 7. Iman International Schools Sokoto 267 200 467 8. Jagaba Internatinal Schools Sokoto 170 89 259 9. Caliphate Tarbiyya Academy Sokoto 203 65 268 10. Khalifa International Schools Sokoto 160 75 235 11. Kings and Queens Schools Sokoto 180 64 244 12. Unity Comprehensive School Sokoto 480 199 679 13. Bravo International Schools Sokoto 220 100 320 14. Zasshash International School Sokoto 155 105 260 15. Marshal International School Sokoto 112 59 171 16. Global Kids School 250 89 339 17. Nady Academy Sokoto 139 65 204 18. Alheri Schools Sokoto 305 111 416 19. Premier College Sokoto 167 65 232 20. Fomwan Schools Sokoto 60 20 80 21. Nakowa Schools Sokoto 256 102 358 22. Federal Staff School Sokoto 222 104 326 23. Cement Schools Sokoto 300 124 424 24. Royal Comprehensive School Sokoto 87 48 135 25. Al-Hudah Schools Sokoto 168 59 227 26. RHoly Family Schools 66 20 86 27. a Minarat Schools Sokoto 200 122 322 28. NNasara Baptist Schools Sokoto 108 69 177 29. SSautul Haqq Schools 96 48 144 30. Eagle View Secondary Schools 120 78 198 Total 5931 3234 9165 th th Source: Database Offices of the respective schools (25 August to 30 September, 2020) 62 Appendix III Research instrument CAI COUCHING TEST Section A: Trigonometry Instructions: Answer all Questions 1. Given that sin =. , find the value of a. 1 b. 2 c. 4 d. 5 2. In Triangle XYZ, x=2m, y=5m and Z=880, find z. a. 5.3 b. 2.3 c. 3.3 d. 6.3 3. If tan a. 1 b. 3 c. 6 d. 7 4. Given that Sin3 =cos2 , find the value of a. 540 b. 640 c. 740 d. 840 5. In a right angled triangle, one of the angles is 380 what is the value of the other angle a. 520 b. 620 c.720 d. 820 6. The angles of a triangle are 2x, 3x and 4x, find the values of the angle a. 300 b. 200 c. 100 d. 10 7. If tan a. 2 b.1 c. 3 d. 4 8. Express the value of sin600 in surd form a. b. c. d. c. 5 d. 7 9. Evaluate a. b. 1 10. An Isosceles triangle has one of its angles as 560 find the remaining angles. a. 420, 420 b. 620, 620 c. 720, 720 d. 820, 820 11. Solve the equation 5cos -1=0 a. 750 b. 760 c. 790 d. 78.50 12. Solve the equation 2sin a. 750 b. 760 c. 790 d. 300 13. An observer on top of a tower 20m high, views the angle of depression of a point on the ground level, 30m from the base, as a. 300 b. 400 c. 500 d.340 14. The angle of elevation of the top of a flagpole from a point on the ground, 50m away from the foot of the flagpole, is 580. Find the height of the flagpole. a. 670 b. 870 c. 790 d. 800 15. An aeroplane is 800m above the ground. The angle of elevation from a point P on the ground is 300. How far is the plane from point P by line of sight? a. 1600m b. 800m c. 300m d. 400m 63 Section B: Geometry 1. A 3 by 4 rectangle is inscribed at the centre of a circle, what is the circumference of the circle? a. 15.7m b. 31.4m c. 40.4m d. 70m 2. The angles of a quadrilateral are x, 2x, 3x and 4x, find x in degrees. a. 360 b. 780 c. 600 d. 800 3. How many sides have a polygon if the sum of its angles is 1260? a. 9 b. 10 c. 11 d. 12 4. Calculate the sum of interior angles of a pentagon a. 540 b. 1080 c. 2160 d. 4320 5. How many sides have a polygon if the sum of its angles is 3240? a. 30 b. 20 c. 2 d. 22 6. Calculate the area of a circle of radius 7cm a. 154cm b. 154cm2 c. 154cm3 d. 154cm4 7. Calculate to the nearest cm the length of an arc subtended at the centre of a circle of radius 14cm by an angle of 1200. a. 105 b. 102 c. 104 d. 106 0 8. The exterior angles of a triangle are 112 and 980, what is the value of the third exterior angle? a. 130 b. 150 c. 140 d. 160 9. The base angles of an isosceles triangle are y and y, if the opposite angle is 88 0, what is the exact value of y? a. 290 b. 460 c. 560 d. 660 10. Calculate the sum of angles of a regular hexagon. a. 4600 b. 7200 c. 8800 d. 8890 11. Point X and Y are 20km north and 9km east of point O, respectively. What is the bearing of Y from X, correct to the nearest degree? a. 240 b. 1560 c. 1500 d. 1600 12. A man leaves his house and travels 21km on a bearing of 0320 and then 45km on a bearing of 2870. Calculate to the nearest km the distance between the man’s final position and his house. a. 34km b. 45km c. 64km d. 46km 13. The angle of elevation of the top of a tower from a point R on the ground level is 60 0. If the height of the tower is 100m, calculate, correct to one decimal place, the distance between R and the base of the tower. a. 50.0 b. 57.7 c. 57.78 d. 57.67 14. The length of a rectangle is twice its breadth, if the perimeter of the rectangle is 60cm, find the length. a. 10cm b. 20cm c. 30cm d. 38cm 64 15. Calculate the volume of a cube of length 6cm a. 36cm2 b. 216cm3 c. 729cm3 d. 343cm3 65