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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The marks were converted into standardised z scores to enable comparison of ratings
between the pupils at 5^th and 8^th grade. Comparison of the z scores of the general-self
scale of both grades were not statistically significantly different (t=. 000, df=3522, p>.
05).

Mathematics self-concept

The mathematics self-concept scales of SDQ-I and SDQ-II were adopted to measure the
mathematics self-concept of 5^th and 8^th graders, respectively. Marsh (1990) explained
that the mathematics scale measured the child’s self-concept regarding his or her ability,
enjoyment, and interest in mathematics. If 5^th graders selected the highest point 5 for all
eight questions on the scale, they would get a s∞re of 40. If 8^th graders expressed their
absolute agreement for statements supporting a high self-concept for all ten questions,
they would get 50.

The mean score for the mathematics scale for 5^th graders varied between 2.82 and 3.16,
the overall mean being 3.00. For 8^th graders the scores varied between 2.12 and 3.51.
The overall mean was 2.71. The standard deviation was greater than 1.0 at both grades.
The total mean score of 5^th graders was 24.01 (SD=8.38). The total mean score of 8^th
graders was 27.07 (SD=8.94). Z scores of the mathematics scale at both grades were
not statistically significantly different (t=1.158, df=2391, p>. 05).

Perceptions of being good or poor at mathematics

Pupils’ perceptions of being good or poor at mathematics were measured by a five-point
rating scale with 5 for very good and 1 for very poor. The mean score of 5^th graders was
3.27 (SD=. 96), while the mean score of 8^th graders was 2.70 (SD=1.02). Overall, 5^th
graders reported that they were average at mathematics, while 8^th graders reported that
they were poor at mathematics. This difference was statistically significant (t=17.122,
df=3305.06, p<. 01).

Pupils’ mathematics self-concept and their perceptions Ofthemselves as good or poor at
mathematics were highly correlated at both grades (see Table 7.1.1), although pupils’
perceptions Ofthemselves as being good or poor at mathematics might not reflect actual

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