%0 Conference Paper %1 falmagne_2007 %A Falmagne, J.C. %A Cosyn, E. %A Doble, C. %A Thiery, N. %A Uzun, H. %B Annual Meeting of the American Educational Research Association (AERA) %D 2007 %K knowledge_space_theory learning leave-one-out sota_h %T Assessing mathematical knowledge in a learning space: Validity and/or reliability %U http://www.stat.cmu.edu/~brian/NCME07/Validity_in_L_Spaces.pdf %X As implemented in the system discussed here, the assessment of knowledge in a learning space for a scholarly topic, such as beginning algebra, is comprehensive by design, in that the types of problems that can be asked in any assessment come from a large collection encompassing the full curriculum for the topic. The product of an assessment is a knowledge state gathering all the types of problems that the student is capable of solving. Typically, the number of feasible knowledge states is large, on the order of 107. The duration of an assessment is nevertheless tolerable, ranging around 30−35 problems. We summarize the basic concepts underlying learning spaces and report the results of a large scale study (210,102 assessments) investigating whether such an assessment is predictive of the subject’s responses to problems that are not part of the assessment. In each assessment, an additional question was asked, the response to which is predictable from the assessed state. The mean correlation between predicted and observed responses (correct or false) was around .67, and the mean log odds ratio 2.75. This type of analysis resembles the standard item-test correlations computed for the evaluation of psychometric instruments. The essential technical and philosophical differences between the two approaches are discussed.

@inproceedings{falmagne_2007, abstract = {As implemented in the system discussed here, the assessment of knowledge in a learning space for a scholarly topic, such as beginning algebra, is comprehensive by design, in that the types of problems that can be asked in any assessment come from a large collection encompassing the full curriculum for the topic. The product of an assessment is a knowledge state gathering all the types of problems that the student is capable of solving. Typically, the number of feasible knowledge states is large, on the order of 107. The duration of an assessment is nevertheless tolerable, ranging around 30−35 problems. We summarize the basic concepts underlying learning spaces and report the results of a large scale study (210,102 assessments) investigating whether such an assessment is predictive of the subject’s responses to problems that are not part of the assessment. In each assessment, an additional question was asked, the response to which is predictable from the assessed state. The mean correlation between predicted and observed responses (correct or false) was around .67, and the mean log odds ratio 2.75. This type of analysis resembles the standard item-test correlations computed for the evaluation of psychometric instruments. The essential technical and philosophical differences between the two approaches are discussed.}, added-at = {2010-01-03T10:58:43.000+0100}, author = {Falmagne, J.C. and Cosyn, E. and Doble, C. and Thiery, N. and Uzun, H.}, biburl = {https://www.bibsonomy.org/bibtex/2d8e927df7ae6c0caf0e9a24504d41ec8/tobold}, booktitle = {Annual Meeting of the American Educational Research Association (AERA)}, interhash = {46401085027ade06e039ae3d03d2d9a4}, intrahash = {d8e927df7ae6c0caf0e9a24504d41ec8}, keywords = {knowledge_space_theory learning leave-one-out sota_h}, timestamp = {2010-01-03T10:58:43.000+0100}, title = {Assessing mathematical knowledge in a learning space: Validity and/or reliability}, url = {http://www.stat.cmu.edu/~brian/NCME07/Validity_in_L_Spaces.pdf}, year = 2007 }