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

6.2.37

-ʒnr-

I normally start my lessons with overall explanation to promote my pupils’
understanding of the content. Next, I encourage them to put forward their
views on the topic based on understanding obtained through my
explanation. I conduct the lesson by giving them opportunities to raise their
views as much as possible. I take the role of chairperson. After they reach
a conclusion, I encourage them to use textbooks to confirm their
understanding. Ifwe rely on textbooks from the beginning, I don’t think we
can develop pupils’ mathematical ideas.__________________________________

6.2.38

^5^τfr~

Topics presented in textbooks are not linked with pupils’ experiences in
their daily life. I encourage my pupils to generate problems by themselves.
Taking up a more familiar topic or doing some practical activities will
promote their motivation to think and learn._________________________________

6.2.39

~5^tfr~

Mathematics lessons which emphasise explanation by the teacher can
convey the necessary knowledge and skills to the pupils accurately. I have
tried to adopt exploratory methods, which enable the pupils to discuss the
topic and lead to a conclusion, in my classroom, but I found that this can
cause confusion if the teacher cannot help the pupils to reach the
conclusion well. More teacher-led ways seem safe to avoid pupil confusion.

6.2.40

8^ttl

They cannot enjoy learning mathematics or be motivated to learn
mathematics, if they cannot understand the lessons. So, I want to make
them feel that they are coming to understand something or are doing
something well in each lesson. Taking up the pupils’ views through
questions and answers is effective in making them have such feelings.

6.2.41

~5^πr~

I encourage the pupils, especially those who are not good at mathematics,
to put forward their views. I think they will come to have confidence when
their views are approved._________________________________________________

6.2.42

8^ttl

It is important to take up pupils’ views. Pupils may not be able to read a
correct conclusion directly. But, if they know that their thinking is not in the
wrong direction, they are motivated to rise to the challenge and to solve
other problems as well.___________________________________________________

6.2.43

Pupils who perceive themselves as good at mathematics can concentrate
on learning for one hour. But pupils who perceive themselves poor at
mathematics and need time to understand may lose their motivation to
learn if they cannot understand what they are being asked. It is necessary
to arrange questions in small steps for those pupils. I try to give questions
according to the individual’s current level of attainment. They can answer
my questions, get approval and come to have confidence.________________

6.2.44

^5^m^^

Pupils are motivated to learn mathematics when they feel approval from
the teacher and peers. So arranging the classroom ethos so that pupils
can support each other is important. I tell them not to laugh at classmates
when they make mistakes. I also tell them not to be afraid of making
mistakes. We can learn from making mistakes or analysing others’
mistakes. It is more important to elucidate pupils’ idea through interaction
than leading quickly to a conclusion. The classroom ethos is changing, in
favour of supporting each other.__________________________________________

6.2.45

^5^πr^

I try to avoid putting too much emphasis on explanation. Children are
happy with finding answers from their inspiration. Cultivating their sense of
number is also important. Encouraging their autonomous learning is very
important. If the teacher puts too much emphasis on explanation, it might
make the children dislike mathematics.___________________________________