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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was higher at 5^th than 8^th grade. The mean score of improving pupils’ cohesiveness for
5^th grade teachers was 3.30 (SD=. 88, median = 3.0). 5^th grade teachers were divided
into those who scored at least 4 (40.4%) or below 4 (59.6%). The mean score of
improving pupils’ cohesiveness for 8^th grade teachers was 2.95 (SD=. 86, median = 3.0).
However, 41.5% of 8^th grade teachers scored 3. Therefore, it was difficult to divide them
into equivalent sized groups. 65.9% of 8^th graders scored at least 3 and 34.1 % scored
below. These groups were used for the analysis.

Difficulty - Most teachers indicated moderate to high attempts to reduce pupils’
difficulties, although the percentage was higher at 5^th grade than 8^th grade. The mean
score for reducing pupils’ difficulty for 5^th grade teachers was 3.68 (SD=. 78, median =
4.00). 5^th grade teachers were divided into those who scored at least 4 (61.7%) or below
4 (38.3%). The mean score for reducing pupils’ difficulty of 8^th grade teachers was 3.52
(SD= .80, median = 3.00). 8^th grade teachers were divided into those who scored at least
4 (42.9%) or below 4 (57.1 %).

Friction - Overall, teachers perceived little friction in their mathematics classes. The
mean score of 5^th grade teachers’ perceptions of friction in mathematics classes was
2.00 (SD=. 73, median = 2.00), and 8^th graders 1.88 (SD=. 71, median = 2.00). Teachers
of both age groups were divided into two groups, those who perceived friction at least
sometimes (21.7% of 5^th grade teachers and 19.0% of 8^th grade teachers) and those
who perceived friction never or hardly ever (78.3% of 5^th grade teachers and 81.0% of 8^th
grade teachers).

Competitiveness - The mean scores of 5^th grade teachers’ responses to using
competition for promoting pupils’ motivation was 2.70 (SD= 1.06, median = 3.00). This
indicates moderate agreement. The mean scores of 8^th grade teachers was 2.86 (SD=.
93, median = 3.00). 50 % of 8^th grade teachers responded that they were neutral about
using competition for promoting pupils’ motivation. Teachers were divided into two
groups; those expressing at least neutral feelings (59.6% of 5^th grade teachers and
71.4% of 8^th grade teachers) and those expressing disagreement or absolute
disagreement (40.4% of 5^th grade teachers and 28.6% of 8^th grade teachers).

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