Mathematical learning models that depend on prior knowledge and instructional strategies

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Title: Mathematical learning models that depend on prior knowledge and instructional strategies
Creators: Pritchard, David E.; Lee, Young-Jin; Bao, Lei
Issue Date: 2008-05-20
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
DOI: 10.1103/PhysRevSTPER.4.010109
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.
ISSN: 1554-9178
URI: http://hdl.handle.net/1811/48818
Rights: ©2008 The American Physical Society
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
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