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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tended to set their level of aspiration at an intermediate level where there was moderate
risk. People who had strong avoidance motives, greater than their achievement motives,
tended to choose either the easiest or the most difficult task and avoided choosing the
optimal level of task so that they could minimise the expected pain of failure. In contrast,
Eccles et al.’s (1983) expectancy-task value model proposed that task value is positively
correlated with expectancy. In addition, Eccles et al.’s (1983) model does not include the
stable and enduring personality constructs of motives. While Eccles et al’s (1983) model
proposed that task value is positively correlated with expectancy, Atkinson’s (1964,
1966) model proposed that it is positively correlated with task difficulty. However, the
optimal level of the task could motivate the person to initiate action in both models.

The optimal level of task has also been perceived as contributing to people’ affective
attitudes. Harter’s (1974, 1978, 1981) ‘intrinsic motivation’ model added optimal
challenge as a determinant of intrinsic pleasure. Harter (1974, 1978, 1981) developed
White’s (1959) ‘effectance motivation’ model, which postulates that only success
determined intrinsic motivation. Harter et al. (1984) suggested that children are most
likely to have perception of their competence through success in optimally challenging
activities. Piaget (1977) in his equilibration model suggested that optimal challenges,
which contain information relevant to structures already stored and mastered but are
discrepant enough to generate accommodation, promote children’s feelings of
competence or interest. Csikszentmihalyi (1985) postulated that the concept of flow, i.e.
the situation where the individual feels total involvement in the activity combining positive
affect and activation (Csikszentmihalyi, 1982) where there is the equilibrium between the
individuals’ perceived action opportunities (challenge) and action capabilities (skill). Lack
of action opportunities compared to action capabilities may produce boredom, while
excess action opportunities may cause anxiety; in both situations, motivation decreases.
This seems to be the case for children. Danner et al. (1981) showed that children felt the
most interesting tasks were one step ahead of their pre-tested skill level. Japanese
mathematics textbooks are reported as systematising mathematics learning into a step-
by-step procedure (Duke, 1986), which reflects this need.

The Ministry of Education in Japan (1999) has proposed that informing pupils of the
meaning and purpose of learning mathematics will also motivate them to learn
mathematics. What do the theories suggest can increase the value of the task? Eccles

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