A Comparative Study of Cognitive Units in Mathematical Thinking
نویسندگان
چکیده
In this paper we consider the theory of ‘cognitive units’ introduced in ‘Cognitive Units, Connections and Mathematical Proof’ (Barnard and Tall, 1997) and compare it with other theories of cognitive construction. We find that it includes a theory of ‘cognitive compression’ to reduce the cognitive strain involved in thinking about more complex concepts that is related to the ‘varifocal theory’ of Skemp. It generalises the notion of process-object and schema-object encapsulation to give a broader theory of rich cognitive units, with connecting links that minimise cognitive strain and maximise thinking power.
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