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   1  CHAPTER ONE INTRODUCTION Background of the Study Mathematics is considered by many people, institutions, and employers of labour, among others, as very important. Mathematics is considered indispensable because it has substantial use in all human activities including school subjects such as in Introductory technology, Biology, Chemistry, Physics including Agricultural science. Its unique importance explains why the subject is given priority as a school subject. Infact, the International Association for the Evaluation of Educational Achievement (IEA) (2004) has also associated the learning of mathematics with basic preparation for adult life. Also, mathematics is used for analysing and communicating information and ideas to address a range of practical tasks and real-life problems (Gray and Tall, 1999). Again, employers in the engineering, construction, pharmaceutical, financial and retail sectors, have all expressed their continuing need for people with appropriate mathematical skills (Smith, 2005). This situation demands that every child should be included in mathematics instruction right inside the classrooms (Sydney, 1995; Hill, 2001), at the secondary school level of education. There is ample evidence to show that all over the world, majority of Secondary School students’ performance in mathematics have been variously reported by individuals and group of persons to be generally poor. For instance, at the international scene, the situation reported by the National Research Council in the late 1980s is of the view that students   2 study of mathematics is getting worse worldwide especially with regard to the enrolment and performance of minority groups in mathematics/science courses (Ezeife, 2002). Locally, similar reports on students’ poor performance on mathematics were noted (Chief Examiners’ report, 1993-2000; Raimi, 2001; Igbo, 2004; Aguele, 2004). It is unfortunate that the general performance of students in mathematics has been observed to be poor (Agwagah, 2000; Ekele, 2002; Kurume, 2004). This situation cannot be allowed to continue escalating without proper check. Several reasons including (Usman and Harbor- Peters, 1998; Harbor- Peters, 2001; Ikeazota, 2002 and Igbo, 2004), have offered reasons for these consistent poor performance in mathematics. Some noted that it was associated with poor teaching of the subject (mathematics) by teachers. Specifically, accusing fingers have been pointed at the way mathematics is taught in schools, and the lack of relevance of mathematics content to the student’s real life experiences (Ezeife. 2002). Some reported that students detest mathematics, suggesting that the students are not working hard enough or learning the subject seriously. For instance, the inability of students to change to a thinking mode suitable for the particular problem, for example, to alter between a numeric, graphic, or symbolic form of representing mathematical ideas deterred them from solving a wide range of mathematical problems (Tall, 2005). Other researchers (Usman and Harbor- Peters, 1998; Unodiaku, 1998; an Aguele, 2004) have also examined the incidence of errors as determinant of students’ achievement in mathematics. Among these errors are the   3 process errors committed by students while solving mathematical problems. Teaches inability to diagnose these process errors among other factors according to Harbor- Peters and Ugwu (1995); and Aguele ( 2004) has contributed to the poor performance of students in both internal and external examinations over the years. Therefore, if poor performance of the students in mathematics is to be halted, these errors or weaknesses relating to the process skills should be identified among JS 3 students for further learning of mathematics in SS1 level. It becomes necessary, therefore to investigate the students specific areas of weakness as indicated by the process errors they committed. The mathematics readiness test (MATHRET) indicates the frequency of these process errors, from which one can find out the extent students entering the senior secondary school possess the knowledge of the Js 3 mathematics curriculum contents in readiness for senior secondary school mathematics work. This situation demands that a mathematics readiness test ( MATHRET) need to be developed with which to know whether the JS 3 students posses the background learning experiences that can enable them cope with SS1 mathematics work. Okonkwo (1998) developed and validated mathematics readiness test for JS 1 students. Also, Obienyem (1998) identified mathematical readiness levels of JS1 entrants. Both studies were centred on pupils of primary six intending to resume new mathematics programme in JS1 level. This and the paucity of instrument for determining the readiness level of JS 3 students intending to resume new mathematics programme in SS1 level and remedying mathematics deficiencies of Nigerian secondary school students and for the improvement of the teaching and learning of the subject motivated this researcher to   4 develop and validate a mathematics readiness test for senior secondary school students. Readiness is a condition, which reflects possession of particular subject-matter knowledge, or adequate subject-matter sophistication, for further or increasingly learning complex tasks (Ausubel, Navok and Harison, 1978). More still, the quality of education received, in other words is a significant determinant of the pupils developmental readiness, as well as of subject- matter readiness, for further learining ( Ausubel, et al, 1978). Lack of readiness in a given task, therefore signals failure in such. Moreso, when a pupil is prematurely exposed to a learning task before he is adequately ready for it, he not only fails to learn the task in question (or learns it with undue difficulty), but also learns on this experience to fear, dislike, and avoid the task (Ausubel, et al, 1978). Thus, readiness becomes an essential factor in any learning, which involves acquisition of sequential skills (Gagne, 1967; Zylber, 2000). Lack of prerequisite skills in a given task invariably inhibits acquisition of subsequent related skills. This is particularly so with Mathematics (Igbo, 2004) because of the nature of its structure (Piaget, 1979), the sequential procedure used in its instruction (Gagne, 1962; 1968) and the hierarchical pattern of its organization (Igbo, 2004). Thus, effective teaching and learning of Mathematics may achieve with reliable assessment of readiness as based on diagnostic information (the process errors students commit in solving mathematics problems). Readiness test has been defined as test that determines the possession of prerequisite knowledge for further learning task (Ausubel, et al, 1978). Diagnostic test has been defined as test
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