Phys. Rev. ST Phys. Educ. Res. 4, 010109 (2008) [8 pages]Mathematical learning models that depend on prior knowledge and instructional strategies |
PRL Celebrates 50 Years
This Week's Milestone Letters are from 1984: |
David E. Pritchard and Young-Jin Lee
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Lei Bao
Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
Received 27 March 2007; published 20 May 2008
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.
©2008 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v4/e010109
DOI: 10.1103/PhysRevSTPER.4.010109
PACS: 01.40.Fk, 01.40.Ha
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