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

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thought that pupils could confirm from the textbook findings obtained through exploratory
learning; six 5^th grade teachers (30%) and one 8^th grade teacher (8%) expressed this
view. These teachers did not plan lessons around the textbook. Instead, these teachers
used an exploratory learning method, with discussion, and after such exploration, used
the textbook to confirm the appropriateness of findings and understanding through
checking with the formulae written in textbooks (ap.6.2.32.5^th). An additional advantage
was, as two 5^th grade teachers (10%) mentioned, that using the textbook as the main
resource in mathematics classes released teachers from preparation of materials and let
them manage their time better. One 5^th grade teacher mentioned that she preferred to
use time for individual support rather than preparing extra teaching materials
(ap.6.2.33.5^th).

Five 5^th grade teachers (25%) and five 8^th grade teachers (42%) indicated that textbooks
were sometimes difficult for pupils to understand. These teachers considered that some
children had not developed sufficient vocabulary or comprehension competencies to
understand the textbooks, while the textbooks were not appropriate for pupils to learn
independently. For instance, they did not contain detailed explanations. One 5^th grade
teacher said it was necessary to explain the content of the textbook in plain language to
promote pupils’ understanding (ap.6.2.34.5^th). Similarly, many teachers of 8^th graders
thought that learning mathematics by reading a textbook, which was supposed to be
used with the teacher’s guidance, was not easy for the pupils by themselves
(ap.6.2.35.8^th). In contradiction to this view, six 5^th grade teachers (30%) and two 8^th
grade teachers (17%) mentioned that the mathematics textbook contained too much
explanation, which might hinder pupils from thinking through the problem by themselves.
These teachers thought that pupils might rely on memorising formulae or procedures
without thinking of the principles underlying each formula or whether the procedures
were valid (ap.6.2.36.5^th). Many teachers, especially at 5^th grade, used textbooks to
encourage pupils to confirm understanding obtained through exploratory learning, in
order to avoid methods relying on formulae and procedures written in the textbook, as
described above (ap.6.2.37.5^th). Five 5^th grade teachers (25%) thought that reading
textbooks was not an enjoyable way to learn mathematics for the pupils, because of the
monotonous description and unfamiliar topics presented in them (ap.6.2.38.5^th).

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