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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for which increased as pupils proceeded through the grades. Five 5^th grade teachers
(25%) and three 8^th grade teachers (25%) pointed this out. One 5^th grade teacher
mentioned that topics which could not be taught with concrete materials increased in 5^th
grade, especially in relation to number (ap.6.2.10.5^th). Two teachers of each grade, i.e.
10% of 5^th grade teachers and 17% of 8^th grade teachers believed that the construction
of abstract ∞ncepts needed training, and employing practical activities might reduce the
effects of such training (see ap.6.2.11.5^th; ap.6.2.12.8^th). Secondly, some teachers
suspected that Practical work might not promote pupils’ understanding of the curriculum
effectively. Four 5^th grade teachers (20%) and two 8^th grade teachers (17%) expressed
this view. Some suspected that it might confuse pupils if teachers could not provide
appropriate materials or give support effectively, or if pupils were unaccustomed to
learning mathematics by this method (ap.6.2.13.5^th). Some teachers mentioned that this
teaching method was new and not all teachers could adopt it confidently. The
uncertainty of some teachers might prevent other teachers from adopting this teaching
method, because of the need to maintain equality between classes (ap.6.2.14.8^th).
Some believed practical activities might make classes fun but without any benefit to
pupils’ mathematics competencies. Learning mathematics through such activities might
then become a negative experience (ap.6.2.15.5^th). One 8^th grade teacher commented
that learning mathematics through activities did not necessarily link to improved
attainment, because pupils might not be able to transfer what they learned through
activities to other problems (ap.6.2.16.8^th). Fun-based lessons were also believed to
have a negative effect on learning mathematics through other methods, which might
then seem less enjoyable to the pupils. One 5^th grade teacher mentioned that pupils
might come to dislike listening to abstract explanations or avoid practice exercises after
fun-based lessons (ap.6.2.17.5^th).

Thirdly, adopting practical activities frequently was difficult because of the restrictions of
the pressured curriculum in limited class time. Three 5^th grade teachers (15%) and three
8^th grade teachers (25%) raised this issue. One 5^th grade teacher mentioned that
securing the time for mastering fundamental knowledge and skills would be the first
consideration over making classes fun by using practical activities (ap.6.2.18.5^th). Lastly,
two 5^th grade teachers (10%) indicated that not all children were interested in learning
mathematics through practical activities. Some teachers believed that pupils might
experience difficulties with practical activities, irrespective of their mathematics

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