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date: 22 February 2020

Abstract and Keywords

Learning to think is about transfer. The scope of transfer is essentially a knowledge representation question. Experiences during learning can lead to alternative latent representations of the acquired knowledge, not all of which are equally useful. Productive learning facilitates a general representation that yields accurate behavior in a large variety of new situations, thus enabling transfer. This chapter explores two hypotheses. First, learning to think happens in pieces and these pieces, or knowledge components, are the basis of a mechanistic explanation of transfer. This hypothesis yields an instructional engineering prescription: that scientific methods of cognitive task analysis can be used to discover these knowledge components, and the resulting cognitive models can be used to redesign instruction so as to foster better transfer. The second hypothesis is that symbolic languages act as agents of transfer by focusing learning on abstract knowledge components that can enhance thinking across a wide variety of situations. The language of algebra is a prime example and we use it to illustrate (1) that cognitive task analysis can reveal knowledge components hidden to educators; (2) that such components may be acquired, like first language grammar rules, implicitly through practice; (3) that these components may be “big ideas” not in their complexity but in terms of their usefulness as they produce transfer across contexts; and (4) that domain-specific knowledge analysis is critical to effective application of domain-general instructional strategies.

Keywords: computational modeling, language and math learning, educational technology, transfer, cognitive tutors, cognitive task analysis, in vivo experiments

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