An Alternative Method for Division of Fractions: Situations of Contingency and Teachers’ Responses
Keywords:
teacher response, contingency, fraction division, student-invented strategyAbstract
When approaching mathematical tasks, students occasionally introduce unconventional methods, which may be rejected by teachers despite their validity. This paper presents two studies conducted to examine teachers’ responses to an alternative method for division of fractions (AMDF), presented by a hypothetical student, in two different contexts. In Study 1, prospective teachers () wrote about how they would respond to a student’s suggestion to use the AMDF. In Study 2, teachers with various levels of professional experience () were interviewed to capture their responses to a student who uses both the AMDF and a standard division algorithm. The teachers’ responses from both studies were analysed by drawing on components of the Knowledge Quartet framework. The findings suggest additional refinement of the framework and illustrate a difference between teachers’ responses in writing and in an interview.
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