Mathematical learning models that depend on prior knowledge and instructional strategies
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Publisher:American Physical Society
Citation:David E. Pritchard, Young-Jin Lee and Lei Bao, "Mathematical learning models that depend on prior knowledge and instructional strategies," Physical Review Special Topics - Physics Education Research 4, no. 1 (2008), doi:10.1103/PhysRevSTPER.4.010109
We present mathematical learning models—predictions of student’s knowledge vs amount of instruction—that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also depend on the type of instruction. We introduce a connectedness model whose connectedness parameter measures the degree to which the rate of learning is proportional to prior knowledge. Over a wide range of pretest scores on standard tests of introductory physics concepts, it fits high-quality data nearly within error. We suggest that data from MIT have low connectedness (indicating memory-based learning) because the test used the same context and representation as the instruction and that more connected data from the University of Minnesota resulted from instruction in a different representation from the test.
Rights:©2008 The American Physical Society
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