Abstract
A longitudinal study is being undertaken into the question of whether or not discussion in the mathematical classroom is an aid to understanding. Preliminary analysis shows that, while the hypothesis that discussion aids understanding is very attractive, evidence to support the hypothesis has been limited. Classroom observations during the first year of the study have led to a method of classification of mathematical talk in the classroom which we expect will prove useful in investigating links between mathematical discussion and mathematical understanding.
The ability to ‘say what you mean and mean what you say’ should be one of the outcomes of good mathematics teaching .... Pupils need the explicit help, which can only be given by extended discussion, to establish these relationships (between different mathematical topics); even pupils whose mathematics attainment is high do not easily do this themselves. (Cockcroft, 1982, England)
In all other topics, we saw teachers there (Kitamaeno School in Tokyo) using peer group dialogues ... (they) justified their use of group dialogue because of their large classes (35–43) and the unusually independent spirit of many of the 600 pupils. Mathematics achievement was very high by American standards. (Easley, 1984, on a Japanese project)
We need to recognise the importance of verbalisation. Putting thoughts into words requires students to organise their thinking and to confront their incomplete understanding. Listening to others affords them the opportunities to contemplate the thinking of others and to consider the implications for their own understanding. (California State Department of Education, 1987)
This article is based on the first year of a longitudinal study intended to shed light on the question of whether or not discussion in the mathematics classroom is an aid to mathematical understanding. Before looking further at the research context in which this project is set, we wish to offer our definitions of the two notions in the title.
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Pirie, S.E.B., Schwarzenberger, R.L.E. Mathematical discussion and mathematical understanding. Educ Stud Math 19, 459–470 (1988). https://doi.org/10.1007/BF00578694
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DOI: https://doi.org/10.1007/BF00578694