Teacher's and students' conceptions of mathematics : a case study of the classroom implementation of three-dimensional geometry in the new key stage 3 curriculum

by Lee, Kin-sum

"3-D Geometry" is a new mathematics topic ill Hong Kong secondary

schools. This paper describes the conception of mathematics in the new content

"3-D Geometry" of a veteran secondary school mathematics teacher and four

students he taught. It was found that the teacher possessed Platonic View in the

nature of mathematics and his views about teaching and learning mathematics

were categorized as a mix view of platonic and problem solving. The findings

supported that the belief structure can influence the teaching and leaning of

mathematics and vice versa (Chapman, 2002), to keep them in equilibrium. The

core beliefs, either central or primary, in the belief structure are the determinant

factors, which shape the teacher's model of teaching and learning. The

curriculum acted as an external catalyst that provokes a conflict between teacher's

own belief in learning mathematics with that embedded in the new mathematics

curriculum. Under the social constraint such as school based curriculum and the

availability of teaching resources, it resulted ill a 'teacher-led with

student-centred' approach. But the teacher's belief in the nature of mathematics

did not change under the same catalyst.

On the other perspective, this study also focused on the students' beliefs and

how they interact with the teacher's beliefs. The result also supports the

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suggestion that students' conceptions in mathematics are mainly underived (Op't

Eynde, De Corte & Verschaffel, 2002). Besides, it is also found that students'

conceptions of mathematics are influenced by the teacher and the implemented

curriculum. It is because we, as a teacher, communicate our beliefs either

consciously or subconsciously to our students through teaching practice.

In this study, data were collected through beliefs questionnaires, video

recorded lesson observations and audio recorded semi-structured interviews.

Through these tools, we can have a clear picture on what happened and why it

happened in the implementation of the new mathematics curriculum. Discussion

on the impact of the new curriculum implementation gives rise to important

implications for mathematics teacher development in the recent reform.

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