Cognitive Modelling for Predicting Examinee Performance

Cognitive modelling can discover the latent characteristics of examinees for predicting their performance (i.e. scores) on each problem. As cognitive modelling is important for numerous applications, e.g. personalized remedy recommendation, some solutions have been designed in the literature. However, the problem of extracting information from both objective and subjective problems to get more precise and interpretable cognitive analysis is still underexplored. To this end, we propose a fuzzy cognitive diagnosis framework (Fuzzy CDF) for examinees' cognitive modelling with both objective and subjective problems. Specifically, to handle the partially correct responses on subjective problems, we first fuzzify the skill proficiency of examinees. Then, we combine fuzzy set theory and educational hypotheses to model the examinees' mastery on the problems. Further, we simulate the generation of examination scores by considering both slip and guess factors. Extensive experiments on three real-world datasets prove that FuzzyCDF can predict examinee performance more effectively, and the output of FuzzyCDF is also interpretative.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[3]  Fritz Drasgow,et al.  Item response theory : application to psychological measurement , 1983 .

[4]  Konstantina Chrysafiadi,et al.  Fuzzy Logic for Adaptive Instruction in an E-learning Environment for Computer Programming , 2015, IEEE Transactions on Fuzzy Systems.

[5]  Yehuda Koren,et al.  Matrix Factorization Techniques for Recommender Systems , 2009, Computer.

[6]  G. Rasch.  On General Laws and the Meaning of Measurement in Psychology , 1961 .

[7]  Dimitar P. Filev,et al.  Fuzzy SETS AND FUZZY LOGIC , 1996 .

[8]  L. T. DeCarlo.  On the Analysis of Fraction Subtraction Data: The DINA Model, Classification, Latent Class Sizes, and the Q-Matrix , 2011 .

[9]  Carolina Ruiz,et al.  The Composition Effect: Conjuntive or Compensatory? An Analysis of Multi-Skill Math Questions in ITS , 2008, EDM.

[10]  Lee Sael,et al.  Procedia Computer Science , 2015 .

[11]  Michel C. Desmarais,et al.  Mapping question items to skills with non-negative matrix factorization , 2012, SKDD.

[12]  S. Embretson,et al.  Component Latent Trait Models for Test Design. , 1982 .

[13]  Mark D Reckase,et al.  Applied Psychological Measurement , 1977 .

[14]  Jure Leskovec,et al.  Engaging with massive online courses , 2014, WWW.

[15]  Michael Jahrer,et al.  Collaborative Filtering Applied to Educational Data Mining , 2010 .

[16]  J. D. L. Torre,et al.  The Generalized DINA Model Framework. , 2011 .

[17]  S. Embretson.  Test design : developments in psychology and psychometrics , 1985 .

[18]  Ruslan Salakhutdinov,et al.  Probabilistic Matrix Factorization , 2007, NIPS.

[19]  Yi Sun,et al.  Alternating Recursive Method for Q-matrix Learning , 2014, EDM.

[20]  Lars Schmidt-Thieme,et al.  Recommender system for predicting student performance , 2010, RecSysTEL@RecSys.

[21]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[22]  Pierre Sens,et al.  Stream Processing of Healthcare Sensor Data: Studying User Traces to Identify Challenges from a Big Data Perspective , 2015, ANT/SEIT.

[23]  S. Chipman,et al.  Cognitively diagnostic assessment , 1995 .

[24]  Edward Haertel,et al.  An Application of Latent Class Models to Assessment Data , 1984 .

[25]  F. Samejima.  A General Model for Free Response Data. , 1972 .

[26]  Jan Jantzen,et al.  Foundations of Fuzzy Control: A Practical Approach , 2013 .

[27]  Peter Kulchyski.  and , 2015 .

[28]  Vincent Aleven,et al.  More Accurate Student Modeling through Contextual Estimation of Slip and Guess Probabilities in Bayesian Knowledge Tracing , 2008, Intelligent Tutoring Systems.

[29]  原田 秀逸.  私の computer 環境 , 1998 .

[30]  B. Junker,et al.  Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory , 2001 .

[31]  David Engel,et al.  Intelligent Tutoring Systems Evolutions In Design , 2016 .

[32]  Gregory Camilli.  Teacher’s Corner: Origin of the Scaling Constant d = 1.7 in Item Response Theory , 1994 .

[33]  Louis V. DiBello,et al.  31A Review of Cognitively Diagnostic Assessment and a Summary of Psychometric Models , 2006 .

[34]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[35]  Kikumi K. Tatsuoka,et al.  Analysis of Errors in Fraction Addition and Subtraction Problems. Final Report. , 1984 .

[36]  Jeffrey A Douglas,et al.  Higher-order latent trait models for cognitive diagnosis , 2004 .

[37]  P. Fayers.  Item Response Theory for Psychologists , 2004, Quality of Life Research.

[38]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[39]  Sandip Sinharay,et al.  Editors Appointed for Journal of Educational and Behavioral Statistics , 2010 .

[40]  Servicio Geológico Colombiano Sgc.  Volume 4 , 2013, Journal of Diabetes Investigation.