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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• Why do you think particular teaching methods let you feel relaxed in learning
mathematics?

• Why do you think these teaching methods help you to feel that you are making
progress in learning mathematics?

Pupils’ self-concept and mathematics concept

Pupils’ mathematics self-concept was measured through the Mathematics Scale in
Marsh’s SDQ I (1990a) for 5^th graders and his SDQ Il (1990b) for 8^th graders,
respectively. The literature indicates that the pupils’ self-concept and academic concept
are correlated (Harter, 1985a, 1986; Marsh, et al., 1984; Marsh, et al., 1985). Therefore,
the pupils’ self-concept was also measured through the General-Self Scale of Marsh’s
SDQ I (1990a) for 5^th graders and SDQ Il (1990b) for 8^th graders, respectively.

Marsh’ SDQ I (1990a) ∞nsists of eight scales, while Marsh’s SDQ Il (1990b) consists of
eleven scales. These scales were devised according to the theory of ‘a multifaceted,
hierarchical model’ of self-concept proposed by Shavelson et al. (1976). In Shavelson et
al.’s (1976) model, the mathematics concept consists of an academic concept followed
by the general self-concept at the apex. The General-Self Scale measures the child’s
self-worth, self-confidence and self-satisfaction, while the Mathematics Scale measures
pupils’ self-concept regarding their ability, enjoyment, and interest in mathematics
(Marsh, 1988, 1990a,1990b).

Chapter two also reviewed the literature regarding the Perceived Competence Scale for
Children (the PCS) established by Harter (1981). The PCS contains a General self-worth
Scale, which measures the pupils’ self-esteem or self-worth. The PCS measures
children’s competence in an academic domain on a cognitive competence scale, but it
does not adopt subject specific scales. Marsh’s (1986b, 1990a, 1990b) study suggested
that verbal and mathematics self-concepts were almost uncorrelated with each other and
had quite distinct relations to verbal and mathematics achievement s∞res. Therefore,
this study, which focuses on children’s perceptions of mathematics, preferred the SDQ-I
and SDQ-II to the PCS. Another reason for not adopting the PCS was the complexity of
the scales. On the PCS, each item consists of two logically opposed statements. The
child first decides which statement reflects the self more appropriately, and then decides

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