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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6.2: Teachers’ perceptions Ofteaching methods adopted in mathematics classes

This section presents the results of analysing the data on the perceived advantages and
disadvantages of each teaching method. The study explored eight teaching methods,
Practical work, Using a computer, Reading a textbook, Teacher explanation, Individual
work, Individual help, Whole-class discussion and Group discussion. However, in the
interviews, Individual work and Individual help were combined as Individual learning, and
Whole-class discussion and Group discussion were combined as learning mathematics
through discussion, in order to Simplifythe process.

Practical work

The most notable advantage of practical work which the teachers mentioned was that it
could promote pupils’ understanding of the curriculum. Eight 5^th grade teachers (40%)
and three 8^th grade teachers (25%) perceived that learning mathematics through
experience, observation and practical activities could promote understanding in pupils of
a wide range of attainment. One 5^th grade teacher explained that learning mathematics
through observation was especially beneficial to promote pupils’ understanding of
volume and capacity, which it was difficult to achieve through drawings on the
blackboard or verbal explanation (ap.6.2.1.5^th). Learning mathematics through
experience was also perceived as more effective than memorising formulae in terms of
retaining material in long-term memory (ap.6.2.2.5^th). Secondly, practical work was
perceived to help develop pupils’ mathematical ideas. Seven 5^th grade teachers (35%)
and three 8^th grade teachers (25%) stressed this. Of these teachers, three from each
teaching age group pointed out that pupils could share findings from practical activities
with the whole class to develop their ideas. This method was described as a Problem-
Solving Teaching Method and was described in detail in chapter one. One 5^th grade
teacher mentioned that this teaching method was effective in promoting pupils’
mathematical ideas, because teachers could plan the lessons based on an
understanding of the individual pupil’s ideas and attainments (ap.6.2.3.5^th). Four 5^th
grade teachers (20%) mentioned that learning mathematics in a trial and error learning
style through practical activities was effective in promoting pupils’ mathematical ideas in
a concrete way, especially in relation to shape. This trial and error learning style was
perceived to help pupils adapt existing knowledge to new problems, correct their

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