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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(ap.6.1.10.8^th) made similar comments. Eight 5^th grade teachers (40%) pointed out that
they could assess pupils’ enjoyment from the extent to which pupils seemed to be
actively involved in the activities. They suggested that:

• Pupils try to understand what they are doing when they are enjoying lessons;

• Pupils make notes tidily, are actively involved in discussion and deal with tasks
autonomously when they are enjoying lessons;

• Pupils ask a lot of questions when they are enjoying lessons;

• Pupils try to find out various ways to solve problems in enjoyable lessons.

Four 5^th grade teachers (20%) pointed out that pupils’ facial expressions reflected their
enjoyment. However, one 5^th grade teacher mentioned that it was sometimes difficult to
assess the extent to which the pupils were enjoying lessons from their behaviour or
facial expressions, because these do not always mirror their feelings (ap.6.1.11.5^th).
This teacher pointed out that teachers might be able to learn to assess pupils’ affective
attitudes from the atmosphere in a classroom. He indicated that he was able to observe
coherence and a common goal in a class where pupils were enjoying learning
mathematics.

Pupils’ motivation to learn mathematics

All of the teachers said that the promotion of pupils’ motivation to learn mathematics was
important. Two main reasons emerged for this: a reduction in disaffection (e.g.
ap.6.1.12.5^th) and an increase in progress (e.g. ap.6.1.13.8^th). One 8^th grade teacher
commented that teachers could recognise unmotivated pupils because their behaviour
was different (ap.6.1.14.8^th). Three 5^th grade teachers (15%) mentioned that pupils’
motivation to learn mathematics was reflected in their positive, autonomous, and careful
involvement with the work. Teachers felt it important to prepare lessons whereby every
pupil was involved in order to promote pupils’ motivation to learn (ap.6.1.15.5^th). Four 5^th
grade teachers (20%) and eight 8^th grade teachers (67%) said that when pupils were
unmotivated to learn, they complained about boredom or difficulties, became less
responsive to the teacher’s questions and were unwilling to put forward their views. One
8^th grade teacher commented that pupils seemed to have lost the desire to master the
content when their motivation to learn mathematics was low (ap.6.1.16.8^th). Pupils’
unmotivated attitudes were more noticeable in the classroom at 8^th grade than at 5^th
grade, and teachers’ concern about pupils’ unmotivated attitudes seemed to increase

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