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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Teacher explanation

About a quarter of teachers of both grades perceived that the advantage of teacher
explanation in mathematics classes lay in its effectiveness in promoting pupils’
understanding; five 5^th grade teachers (25%) and three 8^th grade teachers (25%)
stressed this. They believed that teachers could convey knowledge and skills to the
pupils accurately, avoiding pupil confusion, which might occur when learning
mathematics by exploratory methods (ap.6.2.39.5^th). Secondly, some teachers
mentioned that the advantage of teacher explanation was that teacher-pupil interaction
could result in the promotion of pupils’ positive affective attitudes towards mathematics
learning; four 5^th grade teachers (20%) and two 8^th grade teachers (17%) stressed this
point. These teachers believed that improving pupils’ understanding of the curriculum
through teacher-pupil interaction promoted pupils’ enjoyment and motivation to learn
mathematics (ap.6.2.40.8^th). Thirdly, some teachers mentioned that teacher-pupil
interaction could give pupils the opportunity of receiving approval; three 5^th grade
teachers (15%) and two 8^th grade teachers (17%) raised this issue. These teachers
suggested that the experience of receiving approval in class could promote pupils’
confidence, sense of security and motivation. Teachers believed that this was especially
the case for pupils who were not good at mathematics or who might not be able to arrive
at a correct conclusion by themselves (ap.6.2.41.5^th; ap.6.2.42.8^th). Teachers believed
that the extent to which teachers could promote pupils’ positive affective attitudes
towards mathematics learning through interaction depended on the extent to which
teachers prepared the questions, which made pupils feel secure in giving answers. For
instance, teachers of both age groups said that it was necessary to:

• Slow down the pace of lessons so that all the pupils kept up;

• Make the questions clear so that the pupils could understand what they were being
asked;

• Avoid requiring pupils to reach conclusions directly, instead leading pupils to reach a
conclusion gradually through small steps and a series of questions;

• Give appropriate levels of questions to individuals.

One 5^th grade teacher mentioned that such considerations were more necessary for
pupils who were not good at mathematics (ap.6.2.43.5^th). Other teachers thought that
managing classroom ethos, to ensure their pupils valued approval from each other, was
important in promoting their positive affective attitudes towards mathematics. Teachers

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