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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tried to avoid making pupils nervous about making mistakes by telling them that they
could learn from making mistakes and analysing peers’ mistakes. They also tried to put
the emphasis on bringing out pupils’ ideas rather than seeking the right answer directly
(ap.6.2.44.5^th).

Teachers pointed out different disadvantages of this teaching method according to their
teaching grade. Two 5^th grade teachers (10%) suspected that too much emphasis on
explanation from the teacher might reduce the opportunities for encouraging pupils’
autonomous learning. As a result, pupils’ mathematical creativity would not be
cultivated, and competencies and attitudes deriving from autonomous learning could not
be developed (ap.6.2.45.5^th). Three 8^th grade teachers (25%) mentioned that delivering
an appropriate level of explanation in mathematics classes was not easy because of the
large distribution of pupils’ attainment which existed within a class. They doubted
whether this teaching method could retain the motivation of both high and low achievers
together (ap.6.2.46.8^th).

Individual learning

Teachers perceived the advantages of individualised teaching methods in terms of
meeting pupils’ individual needs. Many teachers believed that individualised teaching
methods could provide pupils with the opportunity to learn mathematics according to
their need; eight 5^th grade teachers (40%) and seven 8^th grade teachers (58%) stressed
this. Teachers believed that pupils could learn mathematics in relation to their prior
knowledge, pace of learning, learning goals, perceptions of own competence, level of
practice and willingness to accept the challenge of difficult problems in individual
sessions (ap.6.2.47.8^th). Many teachers stressed that individualised teaching methods
allowed teachers to provide support according to pupils’ needs (ap.6.2.48.5^th); ten 5^th
grade teachers (50%) and eight 8^th grade teachers (67%) expressed this view. Ofthese,
six 5^th grade teachers (30%) and three 8^th grade teachers (25%) mentioned that they
attempted to support pupils who needed it. Teachers of both age groups thought that at
least one third of pupils needed individual support. Teachers’ support was centred on
particular pupils (see ap.6.2.49.5^th; ap.6.2.50.8^th).

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