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1967 (Fujii, 1992). However, understanding of the curriculum and developing pupils’
mathematical thinking abilities are not orthogonal, rather on a continuum. Developing
understanding of the curriculum depends on increased conceptual thinking, such as
relating new mathematical conceptual structures to existing knowledge. Entwistle et al
(1991, 1992) researching undergraduate students’ perceptions Ofunderstanding' report
understanding in terms of breadth, depth and structure. One possible explanation for the
findings is that the open questions in the survey might have led pupils into feeling that
they had to express their ideas briefly. These short responses allowed the categorisation
of participants’ perceptions of ‘understanding’ into ‘understanding of the curriculum’ and
‘developing mathematical thinking abilities’. These categorisations may be superficial.
Some 8th graders cited interactions with peers and the teacher as contributing to
promoting positive affective attitudes. This supports the earlier finding that Japanese
children think of themselves and accomplishment in terms of relations with others in
particular contexts (Hazel et al. 1991; Befu, 1986, Samimy et al. 1994). This did not
emerge from the teachers’ perceptions as reflected in the open questions. Some
teachers mentioned in their interviews that social dynamics, i.e. relationships with
teacher and peers, affected pupils’ sense of security in mathematics learning. However,
teachers put less stress on enjoyment and sense of security than motivation and sense
of progress. This might indicate that teachers perceived that the effects of interactions in
a class on pupils’ positive affective attitudes were relatively weak.
The teaching methods most frequently adopted at 5th grade were not compatible with
pupils’ preferred teaching methods. However, 5th grade teachers’ perceptions of the
effects of the teaching methods deployed in mathematics classes were similar to the
perceptions of their pupils. Perhaps teachers’ perceptions of the effects of different
teaching methods affect their pupils’ perceptions. 5th grade teachers were likely to
perceive that Practical work and Group discussion positively promoted pupils’ affective
attitudes more than 8th grade teachers. Teachers lacked confidence in their teaching
skills relating to the recently developed teaching methods and stated that lack of
resources prevented them from using these methods.
There were wide individual differences in the extent to which different teaching methods
were perceived to promote pupils’ affective attitudes. Some teachers and pupils
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