knowledge_assessment:q-matrix
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knowledge_assessment:q-matrix [2012/07/11 10:02] jpetrovic [What is a q-matrix?] |
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. | ||
| + | == Matrix example == | ||
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| + | An example of a q-matrix is shown in the following image. | ||
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| + | {{ :knowledge_assessment:qm.jpg }} | ||
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| + | == Understanding matrix values and implications == | ||
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| + | 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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| + | Furthermore, one could also say that the //ideal response// of a student taking the test formed of those 5 questions who knows only concept 1 should be "00001". This is so since he does not know concept 2 which is required for questions 1 and 2 (therefore the leading "00"). Yet this concept is also required for correct ansqering of questions 3 and 4 so he can not answer those questions neither (therefore the following "00"). Finally, 5th question requires only knowledge about the concept 1 so the student can answer this question correctly (therefore the ending "1", forming all together "00001"). | ||
| ==== 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? ==== | ||
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| * To build the q-matrix, experts constructed a relationship between test questions and concepts (referred to as attributes) and students taking the test were assigned knowledge states based on their test answers and the constructed q-matrix ((see Ham85 for a discussion of item-response theory)) | * To build the q-matrix, experts constructed a relationship between test questions and concepts (referred to as attributes) and students taking the test were assigned knowledge states based on their test answers and the constructed q-matrix ((see Ham85 for a discussion of item-response theory)) | ||
| - | {{:knowledge_assessment:qm.jpg}} | + | |
| The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions. | The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions. | ||
knowledge_assessment/q-matrix.txt · Last modified: 2023/06/19 18:03 (external edit)
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