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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individual needs should be considered in terms of the pupils’ interests as well
(ap.5.3.6.5^th T). Forty-three 8^th graders (11%) considered that teaching methods which
met individual needs could promote their sense of security. Most referred to pace in
managing the task (ap.5.3.7.8^th P) and pace in understanding of the problem
(ap.5.3.8.8^th P). In this sense, they preferred individualised teaching methods.

There were contrasting perspectives regarding whether pupils felt more secure in
learning mathematics individually or in interaction with others. One teacher from each
year group believed that pupils could enhance their sense of security in learning
mathematics by satisfying their individual needs through interaction with the teacher and
peers (ap.5.3.9.5^th T). Some teachers, however, believed that avoidance of peer
interaction would ensure pupils’ sense of security, and that individualised learning
methods were beneficial in this sense. Teachers suggested that such methods could
reduce anxiety for children who were not skilled in peer interactions (ap.5.3.10.5^th T). In
addition, individualised learning methods, which protected pupils from the fear of making
mistakes in public (ap.5.3.11.8^th T) and being compared with others (ap.5.3.12.8^th T),
were perceived to ensure pupils’ sense of security in mathematics learning. Some
students wrote that they felt secure in individual learning because they could avoid being
observed by others, as they felt nervous of being watched by others when they were
learning mathematics in a whole-class session or group session (ap.5.3.13.8^th P). Some
students indicated that their sense of security in learning mathematics was threatened
as the learning group became bigger (ap.5.3.14.8^th P). In contrast, 22 students (5%)
considered that interaction with peers made them feel more secure. One 8^th grader said
that they avoided the fear of being left behind by sharing learning opportunities with
peers (ap.5.3.15.8^th P). Fifty-eight students (14%) thought that interaction with the
teacher ensured their sense of security in mathematics learning. As mentioned in
previous sections, these students emphasised the actual interaction with the teacher
rather than the cognitive growth produced by such interaction. The students believed
that the teacher was sure to help pupils in need (ap.5.3.16.8^th P) and that the teacher
always paid attention to every student (ap.5.3.17.8^th P). This made them feel secure.

Seven 5^th grade teachers (23%) and four 8^th grade teachers (13%) believed that
promotion of pupils’ understanding of the curriculum helped pupils feel secure. 5^th grade
teachers were more likely to recommend practical work, which promoted pupils’ concrete

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