Mathematical learning models that depend on prior knowledge and instructional strategies
Phys. Rev. ST Phys. Educ. Res. 4, 010109 (2008)
David E. Pritchard, Young-Jin Lee, Lei Bao
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.
Showing posts with label Lee. Show all posts
Showing posts with label Lee. Show all posts
2008-05-27
2008-02-11
Lee Palazzo Warnakulasooriya Pritchard - Phys Rev 2008
Measuring student learning with item response theory
Young-Jin Lee, David J. Palazzo, Rasil Warnakulasooriya, and David E. Pritchard
We investigate short-term learning from hints and feedback in a Web-based physics tutoring system. Both the skill of students and the difficulty and discrimination of items were determined by applying item response theory (IRT) to the first answers of students who are working on for-credit homework items in an introductory Newtonian physics course. We show that after tutoring a shifted logistic item response function with lower discrimination fits the students’ second responses to an item previously answered incorrectly. Student skill decreased by 1.0 standard deviation when students used no tutoring between their (incorrect) first and second attempts, which we attribute to “item-wrong bias.” On average, using hints or feedback increased students’ skill by 0.8 standard deviation. A skill increase of 1.9 standard deviation was observed when hints were requested after viewing, but prior to attempting to answer, a particular item. The skill changes measured in this way will enable the use of IRT to assess students based on their second attempt in a tutoring environment.
©2008 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v4/e010102
DOI: 10.1103/PhysRevSTPER.4.010102
Young-Jin Lee, David J. Palazzo, Rasil Warnakulasooriya, and David E. Pritchard
We investigate short-term learning from hints and feedback in a Web-based physics tutoring system. Both the skill of students and the difficulty and discrimination of items were determined by applying item response theory (IRT) to the first answers of students who are working on for-credit homework items in an introductory Newtonian physics course. We show that after tutoring a shifted logistic item response function with lower discrimination fits the students’ second responses to an item previously answered incorrectly. Student skill decreased by 1.0 standard deviation when students used no tutoring between their (incorrect) first and second attempts, which we attribute to “item-wrong bias.” On average, using hints or feedback increased students’ skill by 0.8 standard deviation. A skill increase of 1.9 standard deviation was observed when hints were requested after viewing, but prior to attempting to answer, a particular item. The skill changes measured in this way will enable the use of IRT to assess students based on their second attempt in a tutoring environment.
©2008 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v4/e010102
DOI: 10.1103/PhysRevSTPER.4.010102
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