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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the respondents) and nine 8^th grade teachers (28% of the respondents) perceived that
meeting pupils’ individual needs would promote the their sense of progress. Most of
these teachers suggested that consideration of individual differences in attainment was
needed to promote pupils’ sense of progress (ap.5.4.1.5^th T), especially at 8^th grade, as
wide individual differences existed in pupils’ attainment within a class (ap.5.4.2.8^th T).
However, few 8^th graders agreed (N=17, 4%). Some mentioned that they felt a sense of
progress when they learned mathematics at their own pace (ap.5.4.3.8^th P). Others
mentioned that they felt progress when individualised methods were used, because they
could focus on doing exercises according to their needs (ap.5.4.4.8^th P).

Secondly, eight teachers from each grade (23% at 5^th grade; 25% at 8^th grade) thought
that promotion of pupils’ understanding of the curriculum would promote their sense of
progress. These teachers thought that practical activities, which allowed pupils to learn
mathematics through experience (ap.5.4.5.8^th T), and teacher explanation, whereby
teachers could explain accurately what the pupils had not mastered (ap.5.4.6.5^th T),
promoted pupils’ understanding of the curriculum, and subsequently, pupils would feel
more progress. Other teachers considered that pupils’ sense of progress ∞uld be
enhanced by improving their understanding of the curriculum through doing exercises
repeatedly or reading a textbook. Some teachers mentioned that adopting a range of
teaching methods would be beneficial to promote pupils’ understanding of the
curriculum. One 5^th grade teacher mentioned that the combination of practical work and
teacher explanation would be most effective in promoting pupils’ understanding of the
curriculum and hence sense of progress, because pupils need to be taught knowledge to
support their experiences obtained through practical activities (ap.5.4.7.5^th T).
Approximately three out of ten 122 8^th graders (29%) indicated that promotion of their
understanding of the curriculum would enhance their sense of progress. Promotion of
such understanding was perceived by many 8^th graders to relate to all of the four facets
of affective attitudes towards mathematics learning. One student wrote that doing
exercises after listening to the teacher’s explanation was effective in promoting
understanding of the curriculum (ap.5.4.8.8^th P), while another student wrote that reading
a textbook repeatedly after listening to the teacher’s explanation was effective
(ap.5.4.9.8^th P).

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