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Piaget’s proposal that children find it easier to learn mathematics using concrete
materials. Piaget (1969) stated that this condition continues until the formal-operational
stage begins around the 11th year, when children begin to create mental structures using
abstract thinking. Katz (1997) showed that project work provided opportunities to apply
skills, addressed children’s proficiencies, and encouraged intrinsic motivation. Adoption
of problem-solving and the discussion of findings were also perceived to reduce pupils’
mathematics anxiety by promoting pupils’ understanding through helping them construct
concepts (Greenwood, 1984). In contrast, rote-memorisation (Newstead, 1998) or the
‘explain-practice-memorise’ teaching paradigm (Greenwood, 1984; Skemp, 1986) were
perceived as increasing pupils’ anxiety in mathematics learning, because they did not
help pupils to accommodate new knowledge into existing conceptual structures (Skemp,
1986).
In contrast, some have recommended a transmission model of teaching. Vinner (1994)
suggests that the use of procedures and rules, which are cognitively simpler, clearer and
easier to handle than concepts, and the focus on procedure rather than emphasising
reasoning may provide pupils with a sense of security. A strong teacher presence in a
transmission-type classroom can lessen discomfort and already-formed anxiety for some
students who lack confidence in their own thinking skills (Clute, 1984; Norwood, 1994).
Overall, different teaching methods are perceived to have an impact on learning
outcomes. A transmission model of teaching is likely to be adopted where the curriculum
is overloaded. For instance, Gipps et al. (1999) reported that some teachers in England
adopted a transmission model Ofteaching after the introduction of National Curriculum in
1988.
Recently, a position which is a compromise between teaching methods based on the
constructivist view and the transmission model has been studied in the UK. Askew et al.
(1997) reported in the Study of Effective Teachers of Numeracy that better results were
found, irrespective of the organisation of learning situations, when teachers adopted a
Connectionist position valuing pupils’ discovery and the transmission of knowledge
based on pupils’ understanding. Teachers adopting a Connectionist position were
reported as taking time to share their positive attitudes towards mathematics learning
with their pupils (also see, Brown, 1999a). The concepts of the Connectionist position are
theoretically the combination of Piagetian perspective and Vygotsky’s (1981) ‘social
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