By Charles Bird, John Hutchison, Mamadou Kante

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Extra resources for Beginning Bambara An Ka Bamanankan Kalan: With Bambara-English Glossary (English and Bambara Edition)

Example text

We’d like to make the claim that our own efforts to understand M4T have not fallen into the trap of over-emphasizing explicit knowledge and under- Knowing and Learning (Mathematics) • Some Game-Changing Insights • 27 addressing tacit knowledge. Such a claim, however, would be somewhat inaccurate. Two earlier, and very unproductive, attempts to investigate teachers’ disciplinary knowledge made precisely this mistake. The first was an effort to develop a formal interview protocol that might be used to assess the range of instantiations of core concepts available to a teacher – by which we did little more than demonstrate that teachers’ capacities to explicitly identify such instantiations paled against their capacities to tacitly invoke them in situations requiring application or interpretation.

System 1 is analogical – associative, metaphorical, impressionistic. In operation it can feel like intuition, given its capacities to take on great amounts of information and present us with immediate interpretations that are relevant and accurate. And we don’t have any intentional control over it. In contrast, System 2 is slow – mostly because it is thinking based. It is what we rely on when confronting a situation that is overly unfamiliar or confusing – that is, when we have no practiced procedures or pre-rehearsed interpretations to call on.

We’d like to make the claim that our own efforts to understand M4T have not fallen into the trap of over-emphasizing explicit knowledge and under- Knowing and Learning (Mathematics) • Some Game-Changing Insights • 27 addressing tacit knowledge. Such a claim, however, would be somewhat inaccurate. Two earlier, and very unproductive, attempts to investigate teachers’ disciplinary knowledge made precisely this mistake. The first was an effort to develop a formal interview protocol that might be used to assess the range of instantiations of core concepts available to a teacher – by which we did little more than demonstrate that teachers’ capacities to explicitly identify such instantiations paled against their capacities to tacitly invoke them in situations requiring application or interpretation.

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