CHAPTER ONE
INTRODUCTION
Background of the Study
Education is one of the most important factors that distinguish human beings from animals, since it is one of the principal outcomes of human beings’ rationality. Okafor (2006), defined education to include all the experiences of the individual through which knowledge is acquired, the intellect enlightened and the will strengthened to choose and do the good. Consequently, education fosters the worth of the individual, trains his character and engenders his development. (National Policy on Education,2004). Through education also, the individual is appropriately prepared and suitably equipped for living in the community. Hence, Eliot (1964) in Okafor (2006), maintained that education is the process by which the community seeks to open its life to all the individuals within it, enabling them to take their part in it, attempting to pass on to them its culture and making available to them the standard by which it will have them live. To be able to guarantee all these, the curriculum content of education is usually well planned and various subjects are taught. These subjects help to equip students with knowledge, skills and attitudes necessary for their development and for their suitable living in the society. In schools, one of the subjects taught is Mathematics.
Mathematics is a subject that teaches various concepts like; relationships of quantities, sets, properties, measurement, use of numbers and symbols. It also studies such concepts as structure, space and change. It is regarded as the science of numbers. As the science of numbers, mathematics is an indispensable foundation to all physical sciences and technology (Olagunju, 2001). It is usually instrumental in aiding the formulation and development of many scientific and technological laws and theories. Mathematics has many branches, which majorly include; simultaneous equation, arithmetic, analysis, quadratic equation, combinatories, euclidean and non-euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, construction, small and great circles, trigonometry and algebra. Algebra as one of the major branches of pure mathematics, concerns itself with the study of the rules of operations, relations, constructions and the concepts arising from them, including terms, polynomials, equations and algebraic structures. (American Heritage Dictionary, 1999). According to Brian (2010), algebra is the branch of mathematics which is concerned with structure, relation and quantity. It is also one of the branches that many secondary school students find difficult to learn (Martin, 2000). Studying mathematics in general, as well as algebraic concepts, variables, processes and equations have many advantages.
It appears to be quite impossible to live meaningfully, without mathematics in ones daily life. This is because according to Cockcroft (1982), one needs mathematics skills to plan and organize the home well and to achieve so much in the office or in the workshop. No home or office functions well without a programme or time table. Mathematics skills help to organize the activities well. Furthermore, no home, office or workshop is self sufficient, such that it does not need to buy from, sell to or transact any business with another company, or home. In the context of buying, selling or transacting any business, mathematics skills are indispensable. That was why Kilpatrick (2001), opined that mathematical technique is needed as a management tool in commerce, industry, workshop and home. He further noted that mathematics proficiency is necessary for visual processing, visual memory and visual-spatial relationships. Equally, Mazzocco & Thompson, (2005), reported that ignorance of mathematics makes adaptive reasoning difficult. Adaptive reasoning means the capacity for logical thought, reflection, explanation and justification (Garnett, 1998). Mathematics is also needed for proficiency in engineering, technology and science (Lee, Grigg & Dion, 2007). As such, it is clearly one of the subjects which have practical necessity for every human being and that is why it appears to be difficult for anybody to live meaningfully without mathematics. In the same vein the importance of algebra, as a major branch of mathematics for the student cannot be over emphasized. In addition to the usefulness of mathematics generally, Brian (2010), maintained that algebra, which is a major branch of mathematics, is important for the cognitive, critical and analytical skills of the brain. It sharpens the critical thinking skills of the students and enables them to solve real life problems logically as well. Also, studying algebra creates mental discipline. It teaches people to think and reach solutions to various problems in a well structured and logical way. Furthermore, it helps students to learn how to sustain reflection. Yet, many Nigerian secondary school students are observed to have problems with mathematics, especially, in the area of algebra (Amoo,2001).
To have problem with mathematics disadvantages the students. In the opinion of Fuchs and Fuchs, (2002), lack of sound knowledge of mathematics, can affect the students’ overall strategic competence, which involves the ability to formulate, represent, solve, discriminate and generalize facts. According to Wallace & McLoughlin (1988), mathematics is a very important subject and adequate performance in it is usually considered fundamental to school success. In view of the above, Eze, (2003) maintained that it may really be difficult for any student to advance meaningfully in science and technology without good foundation in mathematics, especially at the secondary school level. This is because students require mathematics for basic calculations in science, angle formulation and constructions in basic technology, critical thinking, creativity in arts and humanities, and the secondary education is the stage where these foundational principles are laid. Consequently, learning mathematics becomes imperative for every student in the secondary education level.
The Secondary education is the level after the Primary Education. It is a sensitive period because it is the time when most of the foundational concepts in most subjects including, mathematics are laid and attempts made to clearly explain them. It is also the time when the students are exposed to variety of subjects in the bid to ascertain their interest and inclination, and know how best to guide them so that their potentials and capabilities would be maximally developed. Yet, it is at this stage that many students find mathematics difficult.
This was confirmed by Norman & Zigmond (1980) and McLeod & Armstrong (1982), who in their studies, demonstrated that many students experienced more difficulty in learning mathematics than other subjects at the secondary education level. Supporting their findings, Secada, (1992), held that majority of students under achieve in mathematics when compared with their performances in other subjects. Lee, (2002), also showed that there was a gap between the achievement of students in mathematics and their achievement in other subjects. In the same vein, Steedly (2009), observed that apart from the general problems encountered in achieving well educationally by many students, mathematics appears to be one of the dominant areas where they achieved poorly. According to Wikipedia (2009), mathematics is seen as either a difficult or a boring subject. In his own opinion, Aburime (2007), held that mathematics pedagogy needs a boost at the secondary school level in order to face the challenges of persistent poor performance in mathematics. According to Lassa (1981) and Amazigo (2000), the loud outcry against the frustrating achievement of Nigerian secondary school students in mathematics has been obvious and persistent. Corroborating it, Amoo (2001), demonstrated that failure in mathematics in WAEC rose from 43.3% in 1995 through 52.9% in 1996 to 66.16% in 1997. The poor performance of students in mathematics in secondary schools was also expressed in WAEC by Chief Examiner’s Report (2009). NECO results for 2001/ 2002 sessions showed that students recorded the highest number of failures in mathematics, more than in any other subjects, with over 57.8 % of the candidates failing the subject. Meanwhile, according to WAEC Chief Examiner’s Report (2009), algebra was the area that many of the students found very difficult to handle. Corroborating this Brian (2010), maintained that the problem is that algebra is an abstract area with so many variables and involving a lot of concepts and calculations. Earlier, Martin (2000), had also observed that even when some students manage to perform well in other aspects of mathematics, they always performed poorly in algebra. It becomes then understandable why McLeod and Armstrong, (1982), earlier indicated that large numbers of students require remedial assistance especially, in algebra since many of them experience learning difficulty in it.
Students with learning difficulties in mathematics are those who experience problem with understanding mathematics more than any other subject. A good number of people in this group have problem especially, with algebra. They include those who have mathematics disability and those who are generally afraid of numbers and/or calculation. Those with mathematics disability are those who exhibit one or more deficits in the essential learning processes of perception, conceptualization, language, memory, attention, and impulse control. (Cronin, 1978 in Okeke, 2001). Also, other factors like inattention, difficulty with symbolic language expression, difficulty with understanding of spatial relationships, difficulty with seriation, discrimination, and failure to develop and mobilize cognitive strategies for learning, make the students in this category not to achieve well in mathematics (Okeke, 2001). Furthermore, Howell (2007) opined that some students experience great difficulty in mathematics, which is unrelated to their mathematical intelligence. These students have the potential to learn much more than what they are achieving. They are not experiencing emotional, behavioural or severe environmental issues which prevent their learning, they have a learning difference. There are however, others who experience learning difficulty with mathematics, but who are not having mathematics disability. Meanwhile, it is common practice to group mathematics difficulty into two categories: mathematics computation difficulty and mathematics reasoning difficulty. These categories are based on the students’ performance in class – the outcome of their learning differences (Howell, 2007). There are however those who find mathematics difficult as a result of visual-spatial and organizational difficulties, memory difficulties, language related difficulties, attention difficulties and difficulties with mathematics concepts. So, students with learning difficulty in mathematics include all students who do not find it easy to understand mathematics and even when they attempt to learn it, they do not become proficient in it and as such, they do not achieve well in it.
Achieving well in mathematics, according to Wikipedia (2009), has to do with how students deal with their studies in mathematics and how they cope with or accomplish different tasks given to them by their teachers, bearing in mind the expected standard of performance. Achieving poorly in mathematics then means performing less than the pre-set, or desirable standard that is regarded as sufficient for passing or showing sufficient knowledge of the subject. This means scoring less than 40% in a given test. Achieving well here then means, scoring up to the desirable, acceptable, expected standard and this will be obviously well above 50 percent in a given test.
When students score below the acceptable standard, it presupposes that there may be need for a retraining or the employment of certain learning strategies to help them increase their previous achievement. Learning strategies can be defined as organised approach to achieving a task of learning. They refer to how learners organize and use set of skills to acquire content or to accomplish a particular task more effectively and efficiently either in or out of school (Schumaker & Deshler 1984). Teaching students imply teaching them how to learn, by teaching them learning strategies. Learning strategies give students ways to think through and plan the solution to problems. They also make students become more effective and independent learners. They even help the students to learn more effectively, difficult subjects (Wong, 1993). In fact, learning strategies help to improve the achievement of students. Improving the achievement then means increasing the performances, upgrading it or making it better than it was previously, so that the students achieve more. In this context, in the opinion of Steedly (2008), one needs to ask two questions: what do students need to know how to do mathematically, and what instructional approaches are effective in teaching those skills? Hence, the reason of this study is to examine whether using self-instruction strategy will be able to increase the achievement in algebra of students with learning difficulty in mathematics.
Self-Instruction Strategy is one of the self-regulation strategies that students can use to manage themselves as learners and direct their own behavior, while learning. (Graham, Harris, & Reid, 1992). It is a strategy where students self-tutor and self-monitor themselves. This is quite different from the conventional teacher-dominated strategy of teaching, where the teacher dishes out learning content and the learner merely struggles to learn them(Deborah, 1997). In the conventional strategy, the teacher directs the activities of learning, but self- instruction is learner- directed. Here, the student takes charge of the learning activity, while the teacher merely guides. Self- instruction strategy is therefore, a cognitive learning strategy, in which learning task is broken into steps and the learner himself directs and appraises himself as he goes through the task, step by step. Self-instruction strategy takes place in stages:
