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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findings obtained through observation of a small sample would have been difficult.
However, the findings of this study suggest a need for observation studies to follow up
the data on teacher practices. Many teachers reported using several teaching methods.
How this is implemented in practice is important for determining future developments.
Generalisability

The current research, which adopted a questionnaire survey, enabled a large sample to
be studied. This may assist in the extent to which findings can be generalised. However,
the study was conducted in schools, which expressed their willingness to take part. In
other words, the sample was ‘opportunistic’. This may limit the extent to which
generalisations can be made.

Most of the teachers taking part were very interested in developing teaching practices
which promoted their pupils’ affective attitudes towards mathematics learning. Thus, the
findings ofthis study might not be applicable to all schools in Japan where teachers may
be less committed.

While the study was carried out within Japanese culture which has been extensively
reported as differing from Western cultures (e.g.Befu, 1986), improving pupils’ affective
attitudes in mathematics learning and adopting a diversity of teaching methods in
mathematics classes appears to be central to the policies of other countries as well
(Robitaille, 1997; DES, 1992; Commission on Standards for School Mathematics, 1989;
Alexander et al., 1992). While some of the findings here may not generalise to other
cultures some may enable an increased understanding of how external factors influence
teaching and learning.

Reliability and validity

This study depended largely on quantitative data assessed by five-point rating scales
with a large sample. Statistical analysis using large samples tends to produce more
easily statistically significant results and there is also an increased risk of Type 1 errors
where multiple analyses are undertaken. Therefore, the probability p<. 01 was used
rather than p<. 05. Multivariate analysis of variance could have been used in some
cases but the data and the analysis required were not always well suited to this
particularly where there were differences in sample size.

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