Studying concept elements as a way to trace students’ conceptual understanding
Abstract
The understanding of mathematical concepts has been described in terms of concept definition and concept image. We suggest an elaboration of these constructs, the concept element, to find a way to theoretically describe students’ understanding. The concept element construct was tested in a setting with students working with linear functions at the secondary school level. Our empirical findings reveal traces of students’ concept elements regarding linear functions. Some concept elements appeared early in the process while others appeared after a cognitive conflict (e.g. evoked by the task construction and setting). The detailed grid on which concept elements are defined was a useful tool, yielding new insights into students’ knowledge and understanding.
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