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knowledge_assessment:q-matrix [2012/07/11 10:30] jpetrovic [How does a q-matrix look like?] |
knowledge_assessment:q-matrix [2012/07/11 10:35] jpetrovic [What can I do with a q-matrix?] |
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==== How does a q-matrix look like? ==== | ==== How does a q-matrix look like? ==== | ||
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+ | == Matrix elements == | ||
Q-matrix 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. | Q-matrix 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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+ | == Matrix example == | ||
An example of a q-matrix is shown in the following image. | An example of a q-matrix is shown in the following image. | ||
{{ :knowledge_assessment:qm.jpg }} | {{ :knowledge_assessment:qm.jpg }} | ||
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+ | == Understanding matrix values and implications == | ||
From the matrix, one can read that knowledge of concept 1 is required in order to answer correctly questions 3, 4 and 5. One can also read that questions 1 and 2 test only the knowledge of concept 2. | From the matrix, one can read that knowledge of concept 1 is required in order to answer correctly questions 3, 4 and 5. One can also read that questions 1 and 2 test only the knowledge of concept 2. | ||
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==== What can I do with a q-matrix? ==== | ==== What can I do with a q-matrix? ==== | ||
+ | Q-matrix can be used for understanding students' performance. Due to various knowledge and assessment characteristics, students' responses rarely match //ideal responses// generated from the matrix. Still, by assigning the closest //ideal response// to a student's response vector, it can be assumed which concepts the student does, and which he does not know. This information can be used in order to direct him in further learning. | ||
==== How do I create a q-matrx? ==== | ==== How do I create a q-matrx? ==== | ||