Mitchell, A. & Clarke, D. (2004). When is three quarters not three quarters? Listening for conceptual understanding in children's explanations in a fraction interview. Ian Putt, Rhonda Farragher, Mal McLean. 367-373. Townsville,Australia: James Cook University.
Twelve students across Grades 2 to 6 were interviewed individually using a range of tasks, where the mathematical focus was a conceptual understanding of fractions. Careful listening established that despite giving a correct answer and appearing to have conceptual understanding, further probing sometimes revealed that the child had only a faulty procedural understanding. Similarly, success on one task did not guarantee success on a different but related task. Conversely, a task involving a continuous quantity enabled a child to move between discrete and continuous interpretations of fractional parts. This study supported the claimed advantages of one-to-one interviews over pen and paper tests, but also highlighted the importance of careful listening and the need for multiple tasks in the one mathematical domain in eliciting understanding.
School of Education
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