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.
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