5th and 8th grade pupils’ and teachers’ perceptions of the relationships between teaching methods, classroom ethos, and positive affective attitudes towards learning mathematics in Japan

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recommendations from others, such as the Course of Study and documents written by
other teachers. Teachers, who are reluctant to adopt practical activities, might have
negative attitudes towards them which may then affect the way they are implemented
and their subsequent success.

In contrast to their teachers, pupils from both grades perceived that the attitudinal
aspects promoted by each teaching method were related, as the literature suggested.
Relationships between pupils’ enjoyment and motivation indicated that their motivation in
mathematics learning ∞uld be internalised as Harter (1992), Deci (1985, 1994), and
Bandura (1997) have suggested and linked to successful learning outcomes. 8^th graders
may find that learning mathematics is enjoyable, even when they are working towards
their entrance examination.

Traditional teaching methods were more frequently adopted and preferred at 8^th grade
than 5^th grade. The provision of ample opportunities for learning mathematics individually
following teacher explanation was the preferred method for older students. They did not
like recently developed teaching methods such as practical work and discussion, which
required them to work together. Perhaps pupils prefer what is familiar to them
particularly as they get older. The teaching methods adopted in mathematics classes
tended to be those methods the pupils preferred particularly at 8^th grade.

Recently developed teaching methods were more preferred by pupils at 5^th grade than
8^th grade. However, overall they were infrequently adopted even at 5^th grade. 5^th graders’
preferred learning methods were not matched with the teaching methods deployed in
their mathematics classes. 5^th graders perceived that practical work could promote their
sense of progress more than enjoyment, perhaps because they (10 year-olds) have not
reached Piaget’s (1969) defined ‘formal operation’ stage. In contrast, their teachers
perceived that practical work could promote enjoyment and motivation more than sense
of security and sense of progress. The difference between pupils’ and teachers’ views of
the effects of practical work on pupils’ affective attitudes might be the reason that this
teaching method was not frequently adopted, despite pupils’ preference for this method.
5^th graders did not perceive that individualised teaching methods positively promoted
their affective attitudes towards mathematics learning; this may be because interactions
with teachers and peers may be more important for elementary school children (e.g.

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