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developed a sense of progress (ap.5.4.18.8th P). Forthese students, the interaction itself
rather than the enhancing of cognitive development through interaction promoted a
sense of progress. Interaction with the teacher and peers was, thus, perceived by
students to promote their affective attitudes towards mathematics learning, although
teachers did not take this point very seriously. Thirty-six 8th graders (9%) pointed out that
concentration on the tasks provided was important to a sense of progress in
mathematics learning. Many perceived that they could concentrate better in individual or
small group sessions than in whole-class sessions (ap.5.4.19.8th P).
Six 8th graders (1%) suggested other factors as promoting their sense of progress in
mathematics learning. Ofthese, five wrote that their sense of progress was enhanced by
methods, which they were familiar with. They had confidence that they had made
progress in learning mathematics by the methods used so far (ap.5.4.20.8th P).
Although the number of the pupils stating this was small, it was larger than the number
of the pupils considering that learning mathematics through new methods could promote
a sense of progress. One student mentioned that competition with peers promoted their
sense of progress.
Six 5th grade teachers (17%) and five 8th grade teachers (15%) suggested multiple
factors as contributing to promoting pupils’ sense of progress; most of them mentioned
pupils’ understanding of the curriculum and one other factor. Some teachers perceived
that a particular teaching method could achieve several goals necessary for promoting
pupils’ sense of progress. For instance, one 8th grade teacher mentioned that
individualised teaching methods could meet pupils’ individual needs in mathematics
learning, while promoting pupils’ understanding of the curriculum, both of which were
perceived necessary to promote a sense of progress (ap.5.4.21.8th T). Others believed
that the combined adoption of several different teaching methods was necessary to
promote pupils’ sense of progress. For instance, one 5th grade teacher believed that
combination of practical work, to promote pupils’ understanding of the curriculum, and
discussion, to develop pupils’ mathematical thinking abilities was necessary
(ap.5.4.22.5th T). There were contrasting views as to whether a particular teaching
method could satisfy all of the requirements for promoting pupils’ affective attitudes, or
whether several different teaching methods should be adopted for the purpose.
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