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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Thirdly, five 5^th grade teachers (14%) and six 8^th grade teachers (19%) suggested that
encouraging pupils’ involvement in mathematics learning promoted a sense of progress.
Autonomous and active learning activities, such as discussion whereby pupils could
raise their views positively, was perceived to promote a sense of progress (ap.5.4.10.8^th
T). The same issues were raised as in the previous sections. Sixty-nine 8^th graders
(17%) indicated that positive involvement in activities was important. Pupils saw
involvement in activities in terms of self-reliance. They perceived that accumulation of
individual effort (ap.5.4.11.8^th P) and cultivating individual competencies by individual
effort (ap.5.4.12.8^th P) was important in promoting their sense of progress.

Fourthly, four teachers from each grade (12% at 5^th grade; 13% at 8^th grade) considered
that developing mathematical thinking abilities promoted pupils’ sense of progress. Most
of these teachers recommended adopting discussion-style teaching methods, either
whole-class discussion or group discussion, to develop pupils’ sense of progress (e.g.
ap.5.4.13.5^th T). The percentage of 8^th graders considering that they felt a sense of
progress as they were developing mathematical thinking abilities was low (N=14, 3%).
One 8^th grader wrote that he felt a sense of progress when he was aware of developing
abstract thinking abilities through finding different perspectives through having
discussions (ap.5.4.14.8^th P), while another wrote that she felt progress when she could
putforward her views in individual or group learning (ap.5.4.15.8^th P).

Although promoting pupils’ interest in mathematics learning was perceived by teachers
to promote pupils’ enjoyment and motivation, teachers did not seem to think that this
aspect was important for promoting pupils’ sense of security and sense of progress.
Fourteen 8^th graders (3%) pointed out that teaching methods which inspired their interest
were important. Only one student mentioned that learning mathematics through a new
method enhanced their sense of progress (ap.5.4.16.8^th P).

Eleven 8^th graders (3%) suggested that interaction with peers developed a sense of
progress, because peers could be asked about areas of uncertainty and provide
clarification (ap.5.4.17.8^th P). More pupils pointed out interactions with the teacher rather
than peers as important in giving them a sense of progress; 95 8^th graders (23%) did so.
Some of them mentioned that receiving help from the teacher encouraged them to learn
mathematics to repay the teachers’ kindness, and as a result of this effort, they

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