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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thinking (ар.5.3.18.5^th T), and group discussion, which offered opportunities for peer
tutoring (ap.5.3.19.5^th T) to promote pupils’ sense of security through improving their
understanding of the curriculum. 8^th grade teachers were more likely to recommend
teacher explanation, which gave pupils accurate information (ap.5.3.20.8^th T) and
individual help, which helped pupils have confidence in solving problems (ap.5.3.21.8^th
T). Eighty-nine 8^th graders (22%) indicated that promoting their understanding of the
curriculum would promote their sense of security. Some students mentioned that
receiving help from the teacher when experiencing difficulties helped them to feel secure
because their understanding of the curriculum was enhanced (ap.5.3.22.8^th P). Some
students wrote that they felt secure when they became surer how to manage the task as
their understanding developed. Thus, receiving clear explanations about procedures
from the teacher was perceived as very important for promoting their understanding, and
thus their sense of security (ap.5.3.23.8^th P).

Two 5^th grade teachers (6%) and four 8^th grade teachers (13%) indicated that developing
pupils’ mathematical thinking abilities would promote pupils’ sense of security. Practical
work, which encouraged pupils to think (ap.5.3.24.5^th T), and discussion, which widened
pupils’ mathematical thinking abilities by sharing perspectives with peers (ap.5.3.25.8^th
T) were perceived to promote pupils’ sense of security. The percentage of 8^th graders
pointing out that they felt secure when they found themselves developing their
mathematics thinking abilities was also low (N=20, 5%). However, these students
mentioned that they felt secure in mathematics learning through listening to others’
perspectives (ap.5.3.26.8^th P), raising their own views in a class or a group (ap.5.3.27.8^th
P) and sharing their perspectives with peers (ap.5.3.28.8^th P). In this sense, discussion
was perceived to promote their sense of security.

Teachers of both age groups pointed out that encouraging pupils’ involvement in
mathematics learning would promote pupils’ sense of security as well as their enjoyment
and motivation. However, the number of teachers stressing this element in promoting
pupils’ sense of security was small; three teachers from each grade (9% of the
respondents to this question at 5^th grade; 10% of the respondents to this question at 8^th
grade). These teachers suggested that pupils would feel secure in mathematics learning
when they were actively involved in learning; practical work, where pupils with a wide
range of prior attainments felt comfortable taking part (ap.5.3.29.5^th T), and discussions

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