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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misunderstandings and construct new concepts more efficiently than explaining the
concept to the pupils on the blackboard (ap.6.2.4.5^th). Thirdly, practical work was
perceived to promote pupils’ interest in mathematics learning. Three 5^th grade teachers
(15%) and two 8^th grade teachers (17%) drew attention to this. Adoption of Practical
work in mathematics lessons was perceived as something new for pupils, which would in
turn, promote their interest. Teachers observed that pupils favoured doing practical
activities rather than listening to teacher’s explanations. Activity-based lessons were
perceived to avoid results-based evaluations and take account of individual interests and
learning preferences. As a result of this, such lessons promoted pupils’ motivation to
learn mathematics (see 6.2.5.8^th).

There were two main advantages of Practical work, which 5^th grade teachers pointed out
but 8^th grade teachers did not. First, 5^th grade teachers perceived that practical work
could link what pupils had learnt in lessons and what they had experienced in their
everyday life. Five 5^th grade teachers (25%) expressed this view. Practical work was
perceived as beneficial for three main reasons. It made new mathematics concept more
familiar to pupils (ap.6.2.6.5^th). It developed pupils’ competencies in applying
mathematics to everyday life (ap.6.2.7.5^th); it made up for a lack of capabilities which
should have been acquired through experience in everyday life. One teacher mentioned
that the children of today especially lack sensory capabilities such as conceptions of
quantity and weight (ap.6.2.8.5^th). The other advantage of practical work which only 5^th
grade teachers pointed out was that it could encourage all the pupils to take part in
activities positively and autonomously, irrespective of their individual current attainment
or their current knowledge of the topic. Three 5^th grade teachers (15%) pointed out this
advantage. Practical work was, as a result, perceived to promote enjoyment, motivation
to learn and the mathematics efficacy of most pupils, including those who might not
succeed through other learning methods. It could also provide opportunities for teachers
to detect competencies which might not be found in test performance, especially of
pupils who were less good at mathematics, and provide opportunities for pupils to get
approval and build confidence. Practical work was also perceived as exciting for pupils
who had already learned the topic outside school (see ap.6.2.9.5^th).

Practical work was, on the other hand, perceived to have several disadvantages. First, it
was perceived as inappropriate for learning abstract mathematical concepts, the need

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