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

equality but they lose the opportunities to learn inequality. But the concepts used for
inequality and those used for equality are different. This is not just a difference in the
skills needed for solution. So if pupils do not have the opportunities to learn inequality,
they lack the opportunities to build up the concepts of inequality, and this may influence
their abilities to build up the concepts of equality. Adopting various teaching methods is a
good measure to build up pupils’ concepts. But if the acquisition of skills should be
emphasised, teachers do not need to prepare various teaching methods. Making them to
do a lot of practice and making them accustomed to manipulation of the procedure is the
most effective measure to acquire skills. The acquisition of fundamental skills such as
being able to calculate is important for more advanced problem solving. But I think
helping pupils to build up their concepts is very important.

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