knowledge_assessment:q-matrix
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knowledge_assessment:q-matrix [2012/07/05 13:34] jpetrovic |
knowledge_assessment:q-matrix [2012/07/11 09:59] jpetrovic |
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| - | Q-matrix is a | + | ==== What is a q-matrix? ==== |
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| + | Q-matrix is a matrix describing relations of questions and concepts required for their understanding. It is a M//x//N matrix, where M equals the number of questions in an assessment, and N equals the total number of concepts required for understanding all questions. The matrix element A[i,j] equals 1 if the i-th concept is required for correctly answering j-th question and 0 if the i-th concept is NOT required for correctly answering j-th question. Alternatively, matrix values can be not just {0,1}, but real numbers from the interval [0,1], describing the probability that a student who knows i-th concept will correctly answer j-th question. | ||
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| + | ==== What can I do with a q-matrix? ==== | ||
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| + | ==== How do I create a q-matrx? ==== | ||
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| * "//method, which examines the inputs of many students to automatically extract relationships between questions and underlying concepts, and then uses those relationships in diagnosing and correcting student misconceptions.//" | * "//method, which examines the inputs of many students to automatically extract relationships between questions and underlying concepts, and then uses those relationships in diagnosing and correcting student misconceptions.//" | ||
| * domain-independent knowledge model | * domain-independent knowledge model | ||
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| When forming a correlation matrix, we lose individual student data in favor of calculating average relationships between questions. The q-matrix method is optimized to assign each student the most appropriate knowledge state, using all available response data for each student. | When forming a correlation matrix, we lose individual student data in favor of calculating average relationships between questions. The q-matrix method is optimized to assign each student the most appropriate knowledge state, using all available response data for each student. | ||
| + | As Sellers found in her research, the results obtained through | ||
| + | q-matrix analysis seem to describe relationships among variables in interpretable ways. | ||
| + | Factor analysis and principal components analysis, on the other hand, do not readily offer | ||
| + | interpretable results. | ||
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| + | Later researchers found that, although the q-matrix model was a good way to compare student data to a concept model, expert-constructed q-matrices did not correspond to student data any better than random q-matrices did. | ||
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| + | the findings in Brewer's previous research, which found that the factor analysis method performed poorly in comparison with the q-matrix | ||
| + | method when fewer observations were available. | ||
knowledge_assessment/q-matrix.txt · Last modified: 2023/06/19 18:03 (external edit)
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