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19th century and even before (Okamoto, 1992). Fujioka (1995) showed that elementary
school mathematics teachers and principals, mathematics educators, professors of
education, scientists, mathematicians, and engineers believed that understanding the
system of numeration and fundamental operations, and adopting such knowledge
skilfully were the first priorities in mathematics education. Japanese teachers were
reported as promoting pupils’ understanding by giving small numbers of problems at a
slow pace and avoiding mechanical responses by letting children practise many
problems (National Institute for Educational Research, 1997, 1998). The effects of this
are that children become reflective and accurate on tests of cognitive learning; they are
slow in the early years but gradually speed up as they get older (Salkind et al, 1978).
However, in the current reforms there is an attempt to reduce the time devoted to
repetitive calculation practices, and increase time for developing pupils’ mathematical
ideas (Ministry of Education, 1999). One strategy is the introduction of calculators and
the abacus as a necessity after 4th grade (Ministry of Education, 1999), although the
adoption of calculators has so far been very limited at both elementary and junior high
school levels (National Institute for Educational Research, 1997, 1998). The
development of numerical understanding and competency in calculation is strongly
emphasised at an early stage in elementary schools, as a foundation on which the more
complex and later concepts of mathematics can be built (Whitburn, 2000). This approach
whereby there is an emphasis on mental calculation in the early years and appropriate
usage of calculators after children have mastered master the fundamental calculation
skills, is also seen in the National Numeracy Strategy in the UK (DfEE 1998). Brown et
al. (2000) showed that using calculators for conceptual purposes was associated with
improvement in pupils’ attainments.
Reading a textbook
In Japan, textbooks are considered to be the main material through which children
experience the curriculum, because they are designed to follow the Course of Study and
are approved by the Ministry of Education (DFE, 1992; Whitburn, 1995). Many people
have analysed mathematics textbooks used in Japanese schools. Such analysis
commonly reports that the textbooks are suitable for using in whole-class teaching but
not individual work. Firstly, both elementary school textbooks (Whitburn, 2000) and
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