mathematics is not a pain for them because they learn according to their attainment, the
goal is within their reach. Japanese pupils are encouraged to tackle difficult tasks, and
therefore come to dislike mathematics. But, parental expectations seem to be changing
these days. Parents focused on improvement in their children’s attainments decades
ago, but parents of today seem to encourage their children’s development in forming
their personality and relationships between peers. The social trend also seems to be
changing. The current educational reforms, with the reduction of the curriculum content
and number of lessons may affect pupils’ attainment negatively. But, I think this policy
will work positively to promote pupils’ affective aspects.
I: Next, when do you feel that your pupils make progress in mathematics learning?
T: Progress in mathematics learning for me is different from pupils’ views. I think that
progress in mathematics learning can be measured from the extent to which the pupil
can develop their mathematical ideas. Developing pupils’ mathematical ideas sounds
vague. But, I think developing their inductive thinking competencies is most important.
“Inductive thinking competencies” means the process of collecting as much information
as possible to lead to a conclusion. For instance, children tried to establish many
triangles and then made a formula [the base x the height x ⅓]. This is inductive thinking.
It is important to make them notice that such inductive thinking can be used for
establishing the area of a trapezium. Otherwise, children have to memorise formulas and
how to manipulate them. Learning through inductive thinking gives children inspiration.
Each unit contains opportunities to develop children’s inductive thinking. I value such
opportunities.
I: I think some pupils are accustomed to learning mathematics through memorising the
formula. How do you encourage such pupils to develop their inductive thinking?
T: Actually, it is difficult. Some children have already learned the formula before I take up
the topic in the class. For these children, I try to develop their deductive thinking. I
encourage them to explain why the formula is valid. However, I encourage other pupils
to develop their inductive thinking and make them experience how learning mathematics
through inductive thinking gives them inspiration. Then, pupils come to be fond of using
inductive thinking and avoid memorising the formula.