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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enabled pupils to learn mathematics with a small number of peers, could build closer
interactions between pupils than whole-class discussion, and in turn, promote pupils’
understanding. Such interaction was perceived as beneficial for both high and low
achievers. Teachers thought that higher achievers could deepen their understanding
through the process of explaining the content to other members, through thinking
through the justification for the solution and seeking ways to explain their solution to
other members in plain language. One 5^th grade teacher mentioned that this process
would facilitate mathematical development of those higher achievers who tended to rely
on the formula and procedure (ap.6.2.58.5^th). Teachers also perceived that learning
through peer explanation might be easier than by teacher explanation for pupils who
were poor at mathematics. Teachers perceived that children might feel able to ask their
peers to clarify their uncertainty, and in turn, promote not only their understanding but
also their positive affective attitudes such as enjoyment, motivation and a sense of
security (ap.6.2.59.5^th). Five 5^th grade teachers (25%) mentioned that pupils learned to
build good relationships with peers through taking part in discussion in a group. 5^th grade
teachers who valued children’s personal development particularly supported this view
(ap.6.2.60.5^th).

Some teachers judged that discussion had disadvantages. Six 5^th grade teachers (25%)
suspected that the adoption of whole-class discussion in mathematics classes would be
beneficial for only a limited numbers of pupils, who felt able to put forward their views,
although the teachers attempted to encourage all of the pupils to contribute
(ap.6.2.61.5^th). Pupils might feel more comfortable about raising their views in a small
group rather than in front of the whole class, and would also have more frequent
opportunities to raise their views (ap.6.2.62.5^th). Four 5^th grade teachers (20%) and two
8^th grade teachers (17%) pointed this out. However, four 5^th grade teachers (20%) and
three 8^th grade teachers (25%) doubted the extent to which pupils could profitably share
views with peers in a group. One 5^th grade teacher mentioned that dividing pupils into
groups so that as many pupils as possible felt able to raise their views was difficult
(ap.6.2.63.5^th). Some teachers perceived that pupils’ competencies to share views with
their peers in a group had not always developed, even by 8^th grade (ap.6.2.64.8^th). Four
5^th grade teachers (20%) and two 8^th grade teachers (17%) indicated that teachers’
supervision would not be available to each group all the time. One 5^th grade teacher
stressed that teachers would be unable to take up pupils’ good ideas in the whole class

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