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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Pupils’ perceptions of the frequency of use of different teaching methods and of attitudes
towards learning mathematics in terms of the teaching methods in mathematics classes
were measured adopting closed questions with a five-point rating system. The question
measuring the pupils’ perceptions of the frequency of the use of teaching methods
adopted five ratings: always, nearly always, sometimes, hardly every and never. The
question measuring the pupils’ attitudes towards learning mathematics in terms of
teaching methods adopted five ratings: absolute agreement, agreement, neither
agreement nor disagreement, disagreement and absolute disagreement. One difficulty
with rating scales is that individual participants may interpret differently what each rating
indicates, so objectivity may not be secure (Oppenheim, 1996). However, ratings are, in
this case, used in a subjective way to indicate raters’ perceptions (Oppenheim, 1996) of
the frequency of the use of teaching methods and pupils’ attitudes towards learning
mathematics promoted by different teaching methods. Some researchers prefer to use
an even number of steps, to avoid the tendency to choose the central option
(Oppenheim, 1996). However, in the pilot study, some 5^th graders found difficulty in
responding to a scale with four steps, which lacked the central option. Therefore, a five-
point scale was adopted.

8^th graders were also required to express their opinions, in their own words, as to why
they thought particular aspects of their attitudes towards learning mathematics were
promoted by a particular teaching method. Closed questions whereby the respondents
are offered a choice of alternative replies have the advantage that the respondents
require little time to complete them and that group comparison is easy. However, open
questions provide respondents with the freedom to reply in their own language and
express themselves spontaneously (Oppenheim, 1996). Open questions were not
employed in the questionnaire sheet for 5^th graders, because of their difficulties in
expressing their opinions in this way, as mentioned above in the section on the pilot
study. The questions, which asked 8^th graders why they thought that particular aspects
of their attitudes towards learning mathematics were promoted by the particular teaching
methods, were as follows.

• Why do you think that particular teaching methods allow you to enjoy learning
mathematics?

• Why do you think particular teaching methods encourage you to try hard in
mathematics?

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