This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
knowledge_assessment:q-matrix [2012/07/04 16:21] jpetrovic |
knowledge_assessment:q-matrix [2012/07/05 13:34] jpetrovic |
||
---|---|---|---|
Line 2: | Line 2: | ||
* "//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 | ||
+ | * 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}} | ||
+ | |||
+ | The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions. | ||
+ | |||
+ | 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. | ||
+ | * 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. | ||
+ | |||
+ | Factor analysis: | ||
+ | How to automatically determine concepts? Using covariance matrix. Number of concepts should be smaller than number of questions. Still, this methos has proven to be less fault tollerant. | ||
+ | |||
+ | ==== Q-matrix method ==== | ||
+ | |||
+ | The q-matrix method is a simple hill-climbing algorithm that creates a matrix | ||
+ | representing relationships between concepts and questions directly. The algorithm varies | ||
+ | c, the number of concepts, and the values in the q-matrix, minimizing the total error for | ||
+ | all students for a given set of n questions. To avoid of local minima, each hill-climbing | ||
+ | search is seeded with different random Q-matrices and the best of these is kept. | ||
+ | |||
+ | 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. | ||
+ |