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

6.1.38

8^w

Pupils who could present original ideas and clear proof of their ideas often
impressed me. It is important to encourage them to develop their
mathematics ideas. I think that developing pupils’ mathematics ideas can
enhance pupils’ interest, motivation, sense of accomplishment and
confidence.______________________________________________________________

6.1.39

8^tn

Although many pupils cannot see progress without improvement in test
results, I can observe pupils’ progress from the way they develop solutions.
Pupils who have progressed, became accustomed to thinking through
problem logically and presenting their views clearly. I can observe much
change from not only the examination but also from presentation in class
and ways of taking notes. Therefore, I want to have opportunities to elicit
pupils’ views in a class and examine pupils’ notebooks as many as
possible. It is not a true sense of progress and obtain right answers. It is
important to encourage pupils to find solutions by themselves and come to
a conclusion. I want to emphasise the process when I think what pupils’
sense of progress is._____________________________________________________

6.1.40

8^m

Pupils set up goals such as the extent to which they need to improve their
mathematics attainment for the requirement of the high school of their
choice. They reflect on their learning by examining the extent to which they
achieve their goals in the tests. They observe their improvement from the
test results easily. I myself do not think this is a wrong measure. I
encourage my pupils to set up the optimum level of goals and make an
effort to achieve their goals.___________________________________________________

6.2.1

"^i≡Γ^fr~"

I don’t think that explaining the content through drawing pictures on the
blackboard is enough to promote my pupils’ understanding. It is especially
useful for pupils to learn volume and capacities through observation.
Observation is effective in promoting pupils’ understanding of not only
shapes but also numbers better than verbal explanation can achieve.______

6.2.2

^5^tfr^

Pupils are more likely to be able to keep the learning content in long-term
memory when they learn it through experience than when they memorise
the formula. Pupils can remember the experience itself. They may forget
the formula easily, but they are less likely to forget the experience._________

6.2.3

~5^er~~

I always try to employ a problem-solving learning style. Firstly, the pupils
think individually or in a group. Practical activities are quite often employed
at this stage. Afterwards, the pupils share the ideas in class and this leads
to a conclusion with my support. The child finds his or her ideas first. The
teacher can plan the lesson based on an understanding of the individual
pupil’s ideas and attainments. Therefore, this teaching method is effective
in promoting pupils’ mathematical ideas, I believe.__________________________

6.2.4

^5^tr~

Adopting a trial and error learning style through activities is better for
developing pupils’ mathematical ideas than explaining the concept to the
pupils on the blackboard. Pupils can note their misunderstanding, adapt
what they have learned before to the new problem and link existing
knowledge and new findings, through manipulating materials and
experiences__________________________________________________________

6.2.5

8^tn

Adoption of practical activities can avoid evaluation and comparison
between pupils based on their performance. So such activities can promote
the pupils’ individual interest and learning preferences. Naturally, pupils feel
able to take part in the activities and learn mathematics.____________________