achievers, and informing pupils of the value of mathematics learning and reducing
anxiety were important to promote the motivation of lower achievers. On the other hand,
they believed that developing pupils’ mathematical ideas through pupil-centred,
exploratory-based teaching methods in mathematics classes was beneficial for pupils
who were good at mathematics (Ishida et al., 1986; Kajita et al, 1985; Nakano, 1990;
Imai, 1995). The deployment of a wider range of teaching methods in mathematics
classes might believed as effective in promoting pupils’ positive affective attitudes,
especially in Japanese schools where grouping pupils by ability is not the prevailing
practice.
Recommendations to adopt a diversity of teaching methods in mathematics classes
appear in the educational policies of other countries as well as Japan. For instance,
deploying various teaching methods such as practical activities, ICT, and discussion in
mathematics classes is regarded as broadening the students’ learning opportunities in
the UK (Ofsted, 1995a, Ofsted, 1995b). Schools in England and Wales are expected to
select teaching methods which promote high levels of knowledge, understanding and
thinking, and ensure pupils’ engagement with, concentration on and motivation to
complete tasks (DFEE, 1999). Alexander et al. (1992) argued that decisions on class
grouping and teaching methods are not simply a question of mathematical proportion,
but of ‘fitness for purpose’. They suggest that traditional and progressive, direct and
indirect teaching should be balanced. Encouragement for teachers to select appropriate
teaching and organisational strategies were also introduced in the plan for the National
Numeracy Strategy (DfEE, 1998a, 1998b, 1999). Brown’s (1999a) synthesis of earlier
studies suggested that effective mathematics teaching depends on the quality of the
teaching such as the extent to which teachers interact with pupils but not on the
organisational strategy adopted. Educators in the UK have begun to believe that
adopting a diversity of teaching methods in mathematics is beneficial, especially for
promoting pupils’ understanding of the curriculum. However, Gipps et al (1999) reported
that teachers in England felt that they needed to learn which approach was suitable for
particular contexts.
In the UK, the Piagetian Constuctivist model was widely adopted in mathematics
education after the Plowden Report (Central Advisory Council for Education, 1967) was
published. This report recommended the adoption of practical activities based on