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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observed persons may be affected by their awareness of being observed. The
observers’ attention, encoding, interpretation and memory may be subjective or
selective. Consistency of the analysis of the same behavior may not be maintained in
the results produced by an observer across time or in the results produced by several
observers. Thus, some uncertainty regarding validity and reliability remains, irrespective
of the methods selected (Robson, 1993). In the light of this, the questionnaire method
was selected, which was beneficial for achieving the research aims, while attempting to
minimize biases during the design, execution, analysis and reporting of the findings.

Superficiality is another possible weakness, in adopting a questionnaire method. In this
study, this weakness was addressed through the adoption of the interview method as a
follow-up. Interviews can provide great richness of data and spontaneity in responses by
using effective probes (Oppenheim, 1996). Interviews also offer the possibility of
modifying the line of enquiry, and can help in understanding verbal responses from non-
verbal cues (Robson, 1993). The interviews provided triangulation through employing
different methods with the same aim (Denzin, 1970, in detail Cohen, 2000). This also
aims to increase concurrent validity (Campbell et al., 1959), overcome the problem of
‘method-boundedness’ (Boring, 1953), deepen understanding of the information
obtained in the questionnaire survey and validate information obtained from
questionnaires. As mentioned above, interviews with pupils were not used because of
the difficulties in obtaining permission from schools and parents. However, deeper
insights into pupils’ perceptions were obtained by employing open questions in the
questionnaires.

To conclude, the perceptions of the teachers of two age groups, the pupils of the two
age groups and those of the teachers and pupils of each individual group were collected
through a questionnaire survey. As comparisons were to be made between groups, the
questionnaires were designed to be compatible as far as possible between the pupils of
the two age groups, although they were not identical. The questionnaires for the
teachers of the two groups were identical. The questionnaires for teachers and pupils
were constructed so that a meaningful comparison could be conducted between their
responses.

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