Effects of Grounded and Formal Representations on Combinatorics Learning

Abstract

Two experiments examined the differential effects of grounded and formal representations on learning of mathematics. Both involved combinatorics, using outcome listing and combinatorics formulas as examples of grounded and formal representations, respectively. Experiment 1 compared performance on near and far transfer problems following instructions involving listing or formulas. Instruction in formulas led to more near transfer, while far transfer performance did not differ by condition. Experiment 2 compared performance following four types of instruction: listing only, formulas only, listing fading (listing followed by formulas), and listing introduction (formulas followed by listing). The listing fading condition led to performance on par with the formulas only condition, and for near transfer problems, significantly higher than the listing introduction and pure listing conditions. The results support the inclusion of grounded representations in combinatorics instruction, and suggest that such representations should precede rather than follow formal representations in the instructional sequence.


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