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Mathematical learning models that depend on prior knowledge and instructional strategies
Pritchard, David E. Lee, Young-Jin Bao, Lei
Pritchard, David E.
Lee, Young-Jin
Bao, Lei
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Abstract
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.
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2008-05
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The American Physical Society
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Pritchard, David E., Young-Jin Lee, and Lei Bao. "Mathematical Learning Models That Depend On Prior Knowledge And Instructional Strategies." Physical Review Special Topics - Physics Education Research 4.1 (2008). http://link.aps.org/doi/10.1103/PhysRevSTPER.4.010109