Research on experts as a resource (rather than a tool) in mathematics education
The underlying assumption of the expert-novice paradigm is that findings on experts in a particular field (e.g., mathematicians, expert teachers, gifted students) can be applied for advancing novices in the same field (usually "regular" students and teachers). The paradigm blossomed over the ‘70ties and ‘80ties, when mathematics education research was concerned with mathematicians' problem-solving approaches. However, the recurrent attempts to employ these approaches to novices did not result in a significant improvement of their performance. In particular, while experts' behaviors appeared to be teachable to novices, students and teachers struggle with selecting the potentially productive approaches, employing them and avoiding errors. Accordingly, the paradigm faded in the recent years.
I suggest that research on experts provides insights on the nature of expertise in a particular field, rather than tools for its advancement among novices. Developing these tools is a research process of its own that can be approached with the design-based methodology. In this research process, the findings on experts serve as an intellectual resource of ideas. These ideas should take into account the necessary adaptations of findings on experts to the practices of the novices. In addition, our expectations from novices' performance should be refined and moderated.
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