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accepted, and teachers attempt to use errors effectively as opportunities to promote
pupils’ understanding and rationales (Stevenson et al., 1992a, Stigler, 1998).
In addition, whole-class discussion is perceived as effective to promote pupils’
mathematical thinking by stimulating other pupils’ similar or opposing ideas (Orsolini et
al. 1992). Hatano et al. (1994) found that through interactions pupils could incorporate
discussed and negotiated meanings or understandings. The Cockcroft Report
(Committee of Inquiry into the Teaching of Mathematics in Schools, 1983) mentioned
that extended discussion is assumed to help pupils to understand different mathematical
topics in an inter-related manner. Elaborating pupils’ solutions to problems through
explanation and discussion helps pupils with transferring their procedural memories to
declarative memories, forming mathematics schemata and the processes of
encapsulation of procedures (Davis, et al. 2000). Inagaki et al. (1998) investigated the
effectiveness of whole-class discussion on the performance of Japanese 4th and 5th
graders (10 years of age) and found that children could recognise and remember
reasonable explanations offered by other pupils in the discussion and offer more or less
plausible arguments for or against the alternatives which their classmates proposed,
leading them to change and elaborate their opinions.
Pupils also acknowledge the importance of improving their mathematical thinking. Fujii
(1992) showed that most students at both elementary school and junior high school
believed that there were various ways of reaching solutions to mathematics problems. In
his study, more than 80% of both elementary and junior high school students responded
that the thinking process was more important than finding the answer. This was in
contrast with most parents who believed that mathematics problems had only one
answer. Most of the pupils who liked mathematics, in particular, believed that finding
many solutions was most important in mathematics learning (Kusumoto, 1998).
Thirdly, whole-class teaching is considered to promote pupils’ favourable affective
attitudes towards mathematics learning, building confidence through peer interaction.
Learning mathematics together in a class is seen as beneficial for some weaker pupils
through vicarious learning (Bandura, 1986; Schunk, 1987; Akamasu, et al., 1974),
especially through providing coping models, who overcome difficulties and gain in
confidence through access to new awareness and insights from peers’ practice (Thelen
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