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Knowing how best to respond to students’ mathematical inquiries is an important skill for all teachers to develop. A class of pre-service teachers (PSTs) was presented with a scripting task in which a student conjectured that 1/6.5 was “exactly in between” fractions 1/6 and 1/7. However, instead of addressing the student’s inquiry directly, many of the PST’s responses contained a variety of explanations for more general information about fractions and their various representations. We offer a classification of the responses using the ideas of attribute substitution along with the availability and representativeness heuristics.

Prospective teachers’ responses to students’ dialogue on fractions: attribute substitution and heuristic approaches