5th and 8th grade pupils’ and teachers’ perceptions of the relationships between teaching methods, classroom ethos, and positive affective attitudes towards learning mathematics in Japan

6.1.31

5^ffi~~~

I think that promoting pupils’ feeling able to understand’ is more important
than their feeling able to manage tasks. It is important to enable them to
understand the reasoning of the formulas and procedures.________________

6.1.32

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 the area of many triangles and then made a formula [the base x
the height x ½]. This is inductive thinking. Then, 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._________________________________________

6.1.33

~5^πτ~~

I think educational aims may differ in the units on number and shape. I
would like to emphasis the acquisition Offundamental knowledge and skills
in the unit of number, while I would like to promote pupils’ motivation and
interest in the unit on shape. In other words, I think pupils need to master
the way of solving problems accurately and quickly in the unit on number,
while they need to learn to examine a problem in various ways with wide
ideas in the unit on shape.__________________________________________________

6.1.34

~5^tr^~~

Children are likely to feel progress in mathematics learning when they get
higher marks in tests, express their views in discussion and get approval
for their views. Especially, children take approval and praises from
classmates, parents and the teacher seriously as indicators of progress.
Such approval and praise gives the child confidence in mathematics
learning. Getting good marks in tests becomes a clear aim for the children
and promotes their motivation to study. I do not think such a goal in itself is
wrong. But children put too much stress on better results, as a result, they
tend to neglect processes such as trial and error learning.__________________

6.1.35

8^ttl

A sense of progress in mathematics classes is indicated when pupils can
understand the explanation in the textbook rather than memorising the
formula.____________________________________________________________________

6.1.36

8^tn

In my view, a sense of progress in mathematics is indicated by the extent
to which individual pupils can understand in the class and the extent to
which they absorb that understanding.__________________________________

6.1.37

8^tn

It is important for pupils to proceed in their mathematics learning by
understanding why they got a wrong answer. I let my pupils write down
why they got wrong answers after examination in order to encourage them
to find out what their weakness was. Many pupils wrote they made
mistakes due to their carelessness in the examination setting. I suppose
that they believed that they failed to apply the formula, which they had
memorised for the examination, due to carelessness. I observed that pupils
who had tried to understand the principles could find out why they got a
wrong answer through rereading the explanation in the textbook. But these
pupils were few and they are normally the better performers at
mathematics._________________________________________________________