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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Fourthly, four 5^th grade teachers (11%) and six 8^th grade teachers (20%) pointed out that
promoting pupils’ understanding of the curriculum would promote pupils’ enjoyment of
mathematics classes. The teaching methods were considered to support this varied, and
included practical activities with observable materials (ap.5.1.29.8^th T), clear teacher
explanation (ap.5.1.30.8^th T) with replication according to pupils’ needs (ap.5.1.31.8^th T),
and group discussion providing opportunities for peer tutoring (ap.5.1.32.8^th T).
Approximately three out of ten, 136 8^th graders (29%) pointed out that their enjoyment of
mathematics learning could be promoted by teaching methods which promoted their
understanding of the curriculum. However, the teaching methods which 8^th graders
perceived as promoting enjoyment of mathematics learning by improving their
understanding of the curriculum content varied across all of the teaching methods
explored in this study. Some students commented that practical activities promoted
understanding of the curriculum and helped maintain the lesson content in long-term
memory (ap.5.1.33.8^th P). Learning ‘shape’ through using a ∞mputer appealed to the
visual sense (ap.5.1.34.8^th P). Reading a textbook provided pupils with schemata for
what they were learning (ap.5.1.35.8^th P). Pupils also developed understanding of the
curriculum by listening to a clearly presented teacher’s explanation (ap.5.1.36.8^th P).
Doing exercises individually helps pupils to construct thinking abilities through trial and
error independently (ap.5.1.37.8^th P). Pupils also reported clarifying uncertain points by
receiving individual support from the teacher (ap.5.1.38.8^th P). Discussion in a class
(ap.5.1.39.8^th P) and learning mathematics with peers (ap.5.1.40.8^th P) were also
reported as developing understanding.

Fifthly, six 5^th grade teachers (17%) and two 8^th grade teachers (6%) wrote that pupils
would come to enjoy learning mathematics by developing mathematical thinking abilities.
Some teachers recommended the adoption of practical activities to promote pupils’
enjoyment of mathematics learning by activating children’s mathematical thinking
(ap.5.1.41.5^th T), while others believed that sharing ideas with their peers in a class or a
group must be enjoyable (ap.5.1.42.5^th T; ap.5.1.43.8^th T). Twenty-three 8^th graders (5%)
wrote that developing mathematical thinking abilities was linked to enjoyment in
mathematics learning. Some students thought that practical work was enjoyable
because they could develop their thinking through observation (ap.5.1.44.8^th P). One
student mentioned that she enjoyed finding various solutions with many friends through
whole-class discussion (ap.5.1.45.8^th P), while another mentioned that group discussion

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