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--- knowledge_assessment:q-matrix [2012/07/11 10:12]
jpetrovic [How do I create a q-matrx?]
+++ knowledge_assessment:q-matrix [2012/07/11 11:01]
jpetrovic [How do I create a q-matrx?]
@@ Line 4: / Line 4: @@
 ==== 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.
-==== What can I do with a q-matrix? ====
+== Matrix example ==
-==== How do I create a q-matrx? ====
+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? ====
-   * "//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.//"
+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:
-   * 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))
+   * 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).
-The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions.
+((see Ham85 for a discussion of item-response theory))
 Approaches:
-   * Hand construction of the q-matrix by experts' assigning concepts to questions and then comparing student answers to closest matrix responses. Problems: a q-matrix is a much more abstract measure of the relationships of questions to concepts. We might assume that the questions designed to test students are a more accurate reflection of the teaching objectives than an abstract construct which relates questions to underlying concepts.
+   * Hand construction of the q-matrix by experts' assigning concepts to questions  Problems: a q-matrix is a much more abstract measure of the relationships of questions to concepts. We might assume that the questions designed to test students are a more accurate reflection of the teaching objectives than an abstract construct which relates questions to underlying concepts.
    * The alternative to this strategy is to design a method to extract a q-matrix, which explains student behavior, and reveals the underlying relationships between questions. Experts can examine the resulting q-matrix 25 to ensure that the extracted relationships seem to be valid, and then use that q-matrix to guide the generation of new problems.

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