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--- knowledge_assessment:q-matrix [2012/07/05 14:41]
jpetrovic
+++ knowledge_assessment:q-matrix [2012/07/11 10:59]
jpetrovic [How do I create a q-matrx?]
@@ Line 1: / Line 1: @@
-Q-matrix is a
+==== What is a q-matrix? ====
-   * "//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
-   * originally a binary matrix showing the relationship between test items and latent or underlying attributes, or concepts
-   * 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}}
+Q-matrix is a matrix describing relations of questions and concepts required for their understanding. It is a domain-independent model of knowledge represented by a binary matrix showing the relationship between test items and latent or underlying attributes, or concepts.
-The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions.
+==== How does a q-matrix look like? ====
+== 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.
+== Matrix example ==
+An example of a q-matrix is shown in the following image.
+{{  :knowledge_assessment:qm.jpg  }}
+== 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.
+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? ====
+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? ====
+The goal of q-matrix construction is to extract underlying, or latent, variables, which account for students' differential performance on questions. A q-matrix can be created in two ways:
+   * by having the domain experts analyze assessment items (questions) and define the concept (often referred to as attribute) corresponding to each item and thereby construct the q-matrix. in this case all the concepts in the q-matrix are exactly defined and labeled as elements of the domain. Q_matrix and student's knowledge is therefore easily interpretable.
+   * by automatically extracting the matrix directly from obtaines students' performance on the test items. in this case, the number of concepts is determined by the algorithm (and is usually much smaller than the number of assessment items) and their labels are automatically assigned (and do not reffer to exact domain concepts).
+((see Ham85 for a discussion of item-response theory))
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