Although there are many teaching approaches known to educators and a plethora of new scholarly articles on the subject, efforts are continually being made in this regard with the hope of further enhancing students’ understanding and knowledge. This notwithstanding, the various approaches could be categorised as teacher-centred, student-centred or subject- centred.
1.1.3.1 Teacher – centred approach
The ‘traditional instructional mode’ is characterised by teacher-centred instruction where the teacher is supposed mainly to explain procedures and give directions. Teacher-centred focuses on teachers efforts in the classroom system. The curriculum, teaching and learning process radiates around the teacher who uses force, commands, threats, shame and attacks against the personal status of an individual. He remains rigid or inflexible and fails to admit and recognise the psychological inevitability of individual differences. The teacher- dominated class involves force or threats of force or of some other form of the expenditure of energy against the learners. The dominative teacher behaviour however, does not allow him to utilise new data, new information and new experience. She/he puts on an expression of resistance to change. He is autocratic and dictatorial. Since learners are not carried along and does not consider the varying abilities, interests, learning styles and readiness of the students, she/he cannot achieve the desired learning outcome. The teacher is supposed mainly to explain procedures and give directions while the students are expected to listen and remember what the teacher says (Van de Walle, 2007).
The students are rarely allowed to explain their thoughts and reach a consensus on mathematical ideas (Silver & Smith, 1996). Social interaction and communication among classmates are not important to the teacher. The teacher is expected to take responsibility for emphasising and preparing the Mathematics content, but not for making students’ experiences and reasoning about the content visible in a way that enables them to take responsibility for their learning process (Hansson, 2010). Mok & Morris (2001) argue: "...these descriptions fail to capture many salient features of pedagogy". Mok (2003) showed
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in a later study that teacher-centred instruction in East Asian regions was characterised by a conscious teacher intervention together with students active thinking moments. This is however not the case from Nigeria experience. The teacher-centred approach, which is not different from the traditional method of teaching known to be more prominent at both primary and secondary levels of education and lecture method that is predominantly used at tertiary institutions make students to be passive in the class (Mji, 2003). Students dislike for Further Mathematics and attrition of students in the Further Mathematics classroom could be gleaned from the total number of entries and the actual number of students that wrote the Senior School Certificate Examination each year (cf. Tables 1.1 & 1.2).
1.1.3.2 Learner – centred approach
The learner-centred approach is also known as activity curriculum. Activity curriculum consists of things to be done and not things to be known. In learner-centred or activity curriculum, interest is focused on the growth of the learner through visible active experience. Elements of this design are structured with the learners’ felt needs and interests in mind. Learner-centred approach fixes the learner as the starting point, the centre and the end (Hansson, 2010). The development and the growth of the learner is the ideal measure of education. To the growth of the learner, all studies are subservient. They are valued instruments as they serve the growth needs of the learner. Personality or character of the learner is more than subject matter. Self-actualization of the individual learner is the desired goal. The learner determines both the quality and quantity of the learning. Literature (NCTM, 2000) supports teachers’ shift to this approach as the idea that students construct their own knowledge has been replaced by the idea that students should be responsible for their own learning. This is one of the main attributes of the PBL approach.
For the teacher using this design, she/he is of the integrative behaviour, which is consistent with the concept of growth and learning. The teacher behaviour makes the most of individual learner differences, and advances the psychological processes of differentiation. She/he is flexible, adaptive and scientific in his approach. The teacher behaviour is democratic. Her/his indirect teaching approach consists of soliciting the opinions or ideas of learners, applying or enlarging on those opinions or ideas, praising or encouraging the participation of students, or clarifying and accepting their feelings. Educators have long recognised the critical need for restructuring the teaching and learning processes and for helping students to become
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independent thinkers, to explore complex problems, and to apply what they have learnt in real-life situations (Jonassen, 1994).
1.1.3.3 Subject – centred approach
Curriculum could be organised in a way that focuses on the subject matter areas or fields and it is referred to as ‘Subject-centred Curriculum’. In the subject-centred curriculum, the subject matter furnishes the end and it determines methods. The teachers’ emphasis is on the logical subdivisions of the subject matter. Problems of instruction are problems of procuring texts giving logical parts and sequences and of presenting these portions in class in a similar, definite and graded manner. The researcher is of the opinion that this approach on its own could not bring about effective teaching and learning of Further Mathematics except other components such as subject content and pedagogical content knowledge are taken into consideration. This is in line with Shulman (1986) and Ball (2000) submissions that possession of high subject content knowledge, pedagogical content knowledge and curricula knowledge characterise an effective teacher. Several studies have attempted to assess the mathematical competence of mathematics teachers (Harbour-Peters, 1991). The results have consistently shown that Mathematics teachers do not have knowledge of Mathematics expected as a prerequisite to effective teaching. In particular, Obioma (1992) investigated how senior secondary Mathematics teachers assessed the difficulty levels of the Further Mathematics contents. Construction, geometric proofs, locus, computers, analysis, vector geometry and correlations were assessed as difficult to teach by the senior secondary school teachers. This is worrisome, because construction, geometric proofs and locus are also examined in the General Mathematics curriculum that is substantially lighter in content. This approach requires the teacher’s ability to move from the world of life into the world of symbols and moving within the world of symbols according to Freudenthal (1991) definitions of horizontal and vertical mathematisation is that the teacher adopting this approach focuses only on how the curricula contents will be covered within the stipulated time. PBL requires more than this from the teacher for students to have thorough understanding.
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