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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where pupils put forwards their views positively (ap.5.3.30.5^th T). Some teachers
believed that pupils’ autonomy in learning would encourage their positive involvement in
mathematics learning and enable them to feel secure (ap.5.3.31.5^th T). Discussion was
perceived to promote pupils’ sense of security through developing pupils’ autonomy
(ap.5.3.32.8^th T). Fifty-three 8^th graders (13%) pointed out that positive involvement in
activities helped them feel secure. Their views reflected 8^th graders’ reported self-
reliance in mathematics learning. One 8^th grader wrote that doing work through her own
effort rather than relying on others made her feel secure (ap.5.3.33.8^th P).

Only one 8^th grade teacher wrote that promoting pupils’ interest in mathematics learning
would ensure pupils’ sense of security (ap.5.3.34.8^th T), while no 5^th grade teachers
raised this. Overall, teachers did not perceive that promotion of pupils’ interest in
mathematics learning was related to their sense of security. Inspiring pupils’ interest was
perceived by some 8^th graders to promote their sense of security as well as their
enjoyment and motivation. However, the percentage of students perceiving this factor as
promoting their sense of security was much smaller than the percentage perceiving it as
promoting their enjoyment and motivation. Thirty-five 8^th graders (9%) pointed out that
inspiring pupils’ interest would make them feel secure in mathematics learning. They
mentioned that learning mathematics through using a computer (ap.5.3.35.8^th P) or with
new teaching methods (ap.5.3.36.8^th P) would make their learning fun and them curious,
as a result, their sense of security would be enhanced. Perhaps these teaching methods
allow some pupils to escape from the anxiety developed in learning mathematics by
conventional teaching methods.

Several factors were raised by 8^th graders, but not their teachers. Fifty-eight 8^th graders
(14%) pointed out that concentration on work helped them feel secure. These students
said that they felt secure in learning mathematics individually because they could
concentrate on the task in individual sessions more easily than when listening to the
teacher’s explanation (ap.5.3.37.8^th P) or learning mathematics in a group (ap.5.3.38.8^th
P). Six 8^th graders (2%) mentioned other factors such as being accustomed to the
learning methods (ap.5.3.39.8^th P) and previous good experiences with using the
methods (ap.5.3.40.8^th P). These views contrasted with those of students who saw new
methods promoting a sense of security. The numbers of students perceiving that new

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