mathematical and cognitive –
via the epistemic actions model for abstraction in context
Tommy Dreyfus, Tel Aviv
The emergence of a new mathematical knowledge construct may be
considered as a process of abstraction. In order to help researchers
analyze such processes of abstraction, as they occur in specific
learning contexts, Hershkowitz, Schwarz and Dreyfus (2001) have
proposed the RBC-model for abstraction in context. The model is based
on the idea of epistemic action, and specifically on the three
epistemic actions of Recognizing, Building-with, and Constructing
(whence its name: RBC-model).
Examples of knowledge constructs include fraction as a number, the
distributive law, algebra as a tool for proof, 2-dimensional sample
spaces in probability, rate of change as a function, the equivalence of
infinite sets, and bifurcation in dynamic systems. Contexts include
historical (students’ personal and common learning experiences), social
(interaction with others such as another student or group of students,
a tutor, or a teacher) and material (computer tools, books, worksheets)
In the talk, I plan to present the basics of the RBC-model, using the
example of the distributive law as constructed by an interacting pair
of junior high school students. I will then concentrate on a number of
modifications of the model that were found relevant when using it for
analyzing processes of abstraction in advanced mathematics,
specifically for the topic of bifurcations in dynamic processes. For
example, I will show how constructing actions may go on in parallel and
interact, and more specifically how they may bifurcate, thus giving a
double meaning to the idea of bifurcation.
Hershkowitz, R., Schwarz, B., & Dreyfus, T. (2001). Abstraction in
Context: Epistemic Actions. Journal
for Research in Mathematics Education, 32 (2), 195-222.
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