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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The two main advantages of individualised teaching methods emerged. First, six 5^th
grade teachers (30%) and five 8^th grade teachers (42%) mentioned that doing exercises
individually enabled them to identify the extent to which an individual pupil had mastered
the content. Both teachers and pupils could identify which problems the pupils had not
mastered through doing exercises, and the problems which they had not yet mastered
could be practised (ap.6.2.51.5^th). The other advantage of learning mathematics
individually was that pupils could consolidate their mastery of the curriculum through
doing exercises (ap.6.2.52.5^th); five 5^th grade teachers (25%) and three 8^th grade
teachers (25%) raised this issue.

However, many 5^th grade teachers drew attention to the disadvantages of individualised
teaching methods. First, individualised teaching methods reduced interaction with peers.
Three 5^th grade teachers (15%) believed that too much adoption of individual learning
sessions would reduce the opportunities for mutual growth among the pupils, which
whole-class teaching could achieve. These teachers tried to incorporate mutual learning
through doing exercises (ap.6.2.53.5^th). Secondly, seven 5^th grade teachers (35%)
worried that the provision of tasks according to individual attainment might have a
negative impact on the affective attitudes of low achievers (ap.6.2.54.5^th).

Discussion

Many teachers stressed that the advantage of whole-class discussion was that it could
develop pupils’ mathematical concepts through the sharing of views with peers under the
teacher’s guidance; ten 5^th grade teachers (50%) and five 8^th grade teachers (42%)
mentioned this. Teachers expected pupils to develop competencies through finding
various solutions to one problem and selecting the most effective solution from several
alternatives (ap.6.2.55.8^th). One 8^th grade teacher mentioned that discussion would be
the most effective teaching method to cultivate such competencies (ap.6.2.56.8^th). A 5^th
grade teacher mentioned that this teaching method was especially effective for learning
about shape (ap.6.2.57.5^th).

The advantages of group discussion in mathematics classes were pointed out in relation
to the effects on pupils’ cognitive and personal development. Six 5^th grade teachers
(30%) and two 8^th grade teachers (17%) mentioned that group discussion, which

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