3.3 Students’ Perceptions of the Learning Environment
3.3.1 Teachers’ beliefs, conceptions of teaching and reflective practice
The significance of exploring teachers’ beliefs, conceptions and perceptions and reflective practices is to uncover how these interfere with classroom practice and eventually how students conceive and perceive mathematics. It follows Konings et al’s (2005:649) argument
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that in teaching, the teacher’s own conceptions and experiences on mathematics are portrayed. The beliefs/conceptions link has been adequately captured by Hudson et al. in quoting Pepin (1999:127) that one’s conceptions of mathematics goes along with one’s conception of how it should be presented and one’s presenting style is an expression of one’s beliefs about what is essential in it. For instance, conceptions that are associated with mathematics are often seen as difficult and threatening and those that portray mathematics as do-able are expressed verbally or through the teacher’s actions. For instance; A teacher who has confidence in his/her students’ capabilities motivates the students to work harder and this leads to the students’ positive perception of mathematics. Conversely, a teacher who lacks confidence in their students acts in ways that confirm his/her beliefs and conceptions and this also affects the way students view the subject.
Jita and Vandeyar (2006:40) argue that teaching is based on the teachers’ prior experiences with mathematics. This includes their experiences as mathematics students at school and at college. The authors argue that RSA mathematics teachers’ experiences and mathematics identities are in the traditional approach to mathematics. That is, although teachers have different views about the nature of mathematics, the aims of teaching mathematics and the ways it could be learnt, “their teaching places more emphasis on content, memorisation, reproduction of knowledge, emulation of problem solving methods and less emphasis on reasoning and problem solving” (Jita and Vandeyar, 2006:40). The authors emphasise that there is a need for teachers to be given an opportunity to learn reformed ideas that are different from their ideas of what entails mathematics teaching practice, if the mathematics curriculum changes in RSA are to be successful. This view is supported by Hudson, Burhenan, Kansenen and Seel (1999:117) in quoting Hansen and Wenestam who argue that classroom practice as carried out by the teacher and what counts as mathematical knowledge, and how students arrive at that knowledge, is nested in the nature of the teacher’s education.
In taking the argument further, Konings et al (2005:649) argue that the teachers’ own perceptions and conceptions of the subjects they teach, including mathematics, are manifested through teachers’ actions and classroom practices. Morrell (2001:292) identifies corporal punishment as one negative classroom practice that is rife in most schools including the mathematics classroom as the study focus. The author argues that “corporal punishment is part of a wider web of violence that fuels antagonisms and hatred”. It is a form of coercion that is characterised by students’ resistance and hatred of the subject they are being punished
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for. This has been endorsed by Morrell (2001 in citing Cherian 1990) who established a link between students’ poor academic performance, low self esteem, anxiety and anti-social behaviours, and corporal punishment.
Naong (2007:284) argues that RSA teachers claim that they had not experienced any harmful effects when corporal punishment was administered to them as students and that they see no reason why they should not administer it to their learners as well. Since the enforcement of the RSA Schools Act (1996) abolished the administration of corporal punishment to students and established that the contravention of the rule amounted to an assault offence, Naong (2007: 284) quotes teachers as decrying their loss of respect by students. The author states that teachers claim that the abolishment of corporal punishment has taken away from them their power to discipline students. This confirms Hudson (1999:129) in quoting Pepin that the teacher has traditionally been responsible not only for the academic but also for the moral development of the child.
The findings of a study by Legotlo, Maaga and Sebego (2002:116) states that poor performance on any subject, particularly in RSA schools is, in part, due to ill discipline among students especially after the abolition of corporal punishment. They are quoted as follows: “Most students abuse the so-called 'rights' and the teachers are unable to curb this situation, more especially after the abolition of corporal punishment” (Legotlo et al 2002:116)
Ability grouping is also another classroom practice for most mathematics classrooms that reflects the teachers’ beliefs as well as conceptions and perceptions of their students’
mathematics capabilities. The popular type of ability grouping in mathematics classrooms is where students are streamed according to their ability range (Reuman 1989:5). Proponents of the ability grouping approach argue that it caters for the students’ individual academic needs as students are grouped according to their high, average or low performance standard.
Critics on the other hand argue that this practice deprives low achieving students of exposure to role models and that it becomes a self-fulfilling prophecy that emphasises their weaknesses rather than their strengths so that students are not challenged to work harder (Zevenbergen, 2005:608). Essentially, this suggests that where the experiences are positive, the greater the likelihood for students to identify with the subject and the opposite is true for negative experiences. The relevance of the ability grouping discussion for the study is to illustrate how
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the teacher’s conceptions and perceptions of mathematical knowledge and how that knowledge is arrived, at informs classroom practice. This is as endorsed by Zevenbergen (2005:608): that the students’ ability is the interpretation made by teachers.