{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T19:29:26Z","timestamp":1772652566278,"version":"3.50.1"},"reference-count":82,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T00:00:00Z","timestamp":1603152000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T00:00:00Z","timestamp":1603152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Artif Intell Educ"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s40593-020-00223-1","type":"journal-article","created":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T16:02:27Z","timestamp":1603209747000},"page":"668-700","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Stat-Knowlab. Assessment and Learning of Statistics with Competence-based Knowledge Space Theory"],"prefix":"10.1016","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8474-0724","authenticated-orcid":false,"given":"Debora","family":"de Chiusole","sequence":"first","affiliation":[]},{"given":"Luca","family":"Stefanutti","sequence":"additional","affiliation":[]},{"given":"Pasquale","family":"Anselmi","sequence":"additional","affiliation":[]},{"given":"Egidio","family":"Robusto","sequence":"additional","affiliation":[]}],"member":"78","published-online":{"date-parts":[[2020,10,20]]},"reference":[{"key":"223_CR1","doi-asserted-by":"crossref","unstructured":"Albert, D., & Hockemeyer, C. (2002). Applying demand analysis of a set of test problems for developing adaptive courses. In International conference on computers in education, 2002. proceedings. pp 69\u201370.","DOI":"10.1109\/CIE.2002.1185866"},{"issue":"2","key":"223_CR2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1207\/s15327809jls0402_2","volume":"4","author":"JR Anderson","year":"1995","unstructured":"Anderson, J.R., Corbett, A.T., Koedinger, K.R., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The journal of the learning sciences, 4(2), 167\u2013207.","journal-title":"The journal of the learning sciences"},{"issue":"4","key":"223_CR3","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1007\/s11336-012-9286-0","volume":"77","author":"P Anselmi","year":"2012","unstructured":"Anselmi, P., Robusto, E., & Stefanutti, L. (2012). Uncovering the best skill multimap by constraining the error probabilities of the gain-loss model. Psychometrika, 77(4), 763\u2013781.","journal-title":"Psychometrika"},{"issue":"2","key":"223_CR4","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s11336-016-9498-9","volume":"81","author":"P Anselmi","year":"2016","unstructured":"Anselmi, P., Robusto, E., Stefanutti, L., & de Chiusole, D. (2016). An upgrading procedure for adaptive assessment of knowledge. Psychometrika, 81(2), 461\u2013482.","journal-title":"Psychometrika"},{"issue":"3","key":"223_CR5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1111\/bmsp.12095","volume":"70","author":"P Anselmi","year":"2017","unstructured":"Anselmi, P., Stefanutti, L., de Chiusole, D., & Robusto, E. (2017). The assessment of knowledge and learning in competence spaces: The gain\u2013loss model for dependent skills. British Journal of Mathematical and Statistical Psychology, 70(3), 457\u2013479.","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"issue":"3","key":"223_CR6","first-page":"1","volume":"4","author":"LG Barbara","year":"1996","unstructured":"Barbara, L.G., & William, L.H. (1996). Enhancing statistics education with expert systems: more than an advisory system. Journal of Statistics Education, 4(3), 1\u201319.","journal-title":"Journal of Statistics Education"},{"issue":"1","key":"223_CR7","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s11092-008-9068-5","volume":"21","author":"P Black","year":"2009","unstructured":"Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability (formerly: Journal of Personnel Evaluation in Education), 21(1), 5.","journal-title":"Educational Assessment, Evaluation and Accountability (formerly: Journal of Personnel Evaluation in Education)"},{"key":"223_CR8","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1017\/CBO9780511840975.004","volume":"1","author":"S Chaiklin","year":"2003","unstructured":"Chaiklin, S., & et al. (2003). The zone of proximal development in vygotsky\u2019s analysis of learning and instruction. Vygotsky\u2019s educational theory in cultural context, 1, 39\u201364.","journal-title":"Vygotsky\u2019s educational theory in cultural context"},{"issue":"4","key":"223_CR9","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1023\/A:1021258506583","volume":"12","author":"C Conati","year":"2002","unstructured":"Conati, C., Gertner, A., & Vanlehn, K. (2002). Using bayesian networks to manage uncertainty in student modeling. User modeling and user-adapted interaction, 12(4), 371\u2013417.","journal-title":"User modeling and user-adapted interaction"},{"key":"223_CR10","doi-asserted-by":"crossref","unstructured":"Conati, C., & VanLehn, K. (1999). Teaching meta-cognitive skills: Implementation and evaluation of a tutoring system to guide self-explanation while learning from examples. In Artificial intelligence in education, pp 297\u2013304.","DOI":"10.1007\/978-3-7091-2490-1_32"},{"key":"223_CR11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.endm.2013.05.143","volume":"42","author":"D de Chiusole","year":"2013","unstructured":"de Chiusole, D., Anselmi, P., Stefanutti, L., & Robusto, E. (2013). The Gain\u2013Loss Model: bias and variance of the parameter estimates. Electronic Notes in Discrete Mathematics, 42, 33\u201340.","journal-title":"Electronic Notes in Discrete Mathematics"},{"key":"223_CR12","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.endm.2013.05.144","volume":"42","author":"D de Chiusole","year":"2013","unstructured":"de Chiusole, D., & Stefanutti, L. (2013). Modeling skill dependence in probabilistic competence structures. Electronic Notes in Discrete Mathematics, 42, 41\u201348.","journal-title":"Electronic Notes in Discrete Mathematics"},{"issue":"4","key":"223_CR13","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1037\/met0000050","volume":"20","author":"D de Chiusole","year":"2015","unstructured":"de Chiusole, D., Stefanutti, L., Anselmi, P., & Robusto, E. (2015). Modeling missing data in knowledge space theory. Psychological Methods, 20(4), 506\u2013522.","journal-title":"Psychological Methods"},{"key":"223_CR14","doi-asserted-by":"crossref","first-page":"503","DOI":"10.3758\/s13428-019-01248-8","volume":"52","author":"D de Chiusole","year":"2019","unstructured":"de Chiusole, D., Spoto, A., & Stefanutti, L. (2019). Extracting partially ordered clusters from ordinal polytomous data. Behavior research methods, 52, 503\u2013520.","journal-title":"Behavior research methods"},{"issue":"4","key":"223_CR15","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1007\/s11336-013-9325-5","volume":"78","author":"D de Chiusole","year":"2013","unstructured":"de Chiusole, D., Stefanutti, L., Anselmi, P., & Robusto, E. (2013). Assessing parameter invariance in the blim: Bipartition models. Psychometrika, 78(4), 710\u2013724.","journal-title":"Psychometrika"},{"issue":"4","key":"223_CR16","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.3758\/s13428-016-0780-7","volume":"49","author":"D de Chiusole","year":"2017","unstructured":"de Chiusole, D., Stefanutti, L., & Spoto, A. (2017). A class of k-modes algorithms for extracting knowledge structures from data. Behavior research methods, 49(4), 1212\u20131226.","journal-title":"Behavior research methods"},{"key":"223_CR17","doi-asserted-by":"crossref","unstructured":"Deonovic, B., Chopade, P., Yudelson, M., de la Torre, J., & von Davier, A.A. (2019). Application of cognitive diagnostic models to learning and assessment systems. In Handbook of diagnostic classification models, pp 437\u2013460. Springer.","DOI":"10.1007\/978-3-030-05584-4_21"},{"key":"223_CR18","doi-asserted-by":"crossref","unstructured":"Doignon, J.-P. (1994). Knowledge spaces and skill assignments. In Fischer, GH, & Laming, D (Eds.) Contributions to mathematical psychology, psychometrics and methodology, pp 111\u2013121. New York: Springer-Verlag.","DOI":"10.1007\/978-1-4612-4308-3_8"},{"key":"223_CR19","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0020-7373(85)80031-6","volume":"23","author":"J-P Doignon","year":"1985","unstructured":"Doignon, J.-P., & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175\u2013196.","journal-title":"International Journal of Man-Machine Studies"},{"key":"223_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58625-5","volume-title":"Knowledge spaces","author":"J-P Doignon","year":"1999","unstructured":"Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. New York: Springer."},{"issue":"1-3","key":"223_CR21","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0012-365X(96)00095-7","volume":"173","author":"J-P Doignon","year":"1997","unstructured":"Doignon, J.-P., & Falmagne, J.-C. (1997). Well-graded families of relations. Discrete mathematics, 173(1-3), 35\u201344.","journal-title":"Discrete mathematics"},{"issue":"1","key":"223_CR22","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1006\/jmps.1993.1003","volume":"37","author":"CE Dowling","year":"1993","unstructured":"Dowling, C.E. (1993). On the irredundant generation of knowledge spaces. Journal of Mathematical Psychology, 37(1), 49\u201362.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR23","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1111\/j.2044-8317.1995.tb01047.x","volume":"48","author":"I D\u00fcntsch","year":"1995","unstructured":"D\u00fcntsch, I, & Gediga, G. (1995). Skills and knowledge structures. British Journal of Mathematical and Statistical Psychology, 48, 9\u201327.","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"key":"223_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2044-8317.1988.tb00884.x","volume":"41","author":"J-C Falmagne","year":"1988","unstructured":"Falmagne, J.-C., & Doignon, J.-P. (1988). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 1\u201323.","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"key":"223_CR25","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/0022-2496(88)90011-9","volume":"32","author":"J-C Falmagne","year":"1988","unstructured":"Falmagne, J.-C., & Doignon, J.-P. (1988). A Markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232\u2013258.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-01039-2","volume-title":"Learning spaces","author":"J-C Falmagne","year":"2011","unstructured":"Falmagne, J.-C., & Doignon, J.-P. (2011). Learning spaces. New York: Springer."},{"key":"223_CR27","first-page":"204","volume":"97","author":"J-C Falmagne","year":"1990","unstructured":"Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P., & Johanessen, L. (1990). Introduction to knowledge spaces: how to build, test and search them. Psychological Review, 97, 204\u2013224.","journal-title":"Psychological Review"},{"key":"223_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-35329-1","volume-title":"Knowledge spaces: Applications in education","author":"J-C Falmagne","year":"2013","unstructured":"Falmagne, J.-C., Albert, D., Doble, C., Eppstein, D., & Hu, X. (2013). Knowledge spaces: Applications in education. Berlin: Springer Science & Business Media."},{"issue":"10","key":"223_CR29","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1080\/01443410.2018.1495829","volume":"39","author":"Y Fang","year":"2019","unstructured":"Fang, Y., Ren, Z., Hu, X., & Graesser, A.C. (2019). A meta-analysis of the effectiveness of aleks on learning. Educational Psychology, 39(10), 1278\u20131292.","journal-title":"Educational Psychology"},{"issue":"2","key":"223_CR30","first-page":"null","volume":"2","author":"I Gal","year":"1994","unstructured":"Gal, I., & Ginsburg, L. (1994). The role of beliefs and attitudes in learning statistics: Towards an assessment framework. Journal of Statistics Education, 2(2), null.","journal-title":"Journal of Statistics Education"},{"key":"223_CR31","unstructured":"Gamboa, H., & Fred, A. (2002). Designing intelligent tutoring systems: A bayesian approach. Enterprise Information Systems III. Edited by J. Filipe, B. Sharp, and P. Miranda. Springer Verlag: New York, pp 146\u2013152."},{"key":"223_CR32","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1348\/000711002760554516","volume":"55","author":"G Gediga","year":"2002","unstructured":"Gediga, G., & D\u00fcntsch, I. (2002). Skill set analysis in knowledge structures. British Journal of Mathematical and Statistical Psychology, 55, 361\u2013384.","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"issue":"1","key":"223_CR33","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1111\/j.1745-3984.1984.tb00221.x","volume":"21","author":"E Haertel","year":"1984","unstructured":"Haertel, E. (1984). Detection of a skill dichotomy using standardized achievement test items. Journal of Educational Measurement, 21(1), 59\u201372.","journal-title":"Journal of Educational Measurement"},{"issue":"4","key":"223_CR34","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1745-3984.1989.tb00336.x","volume":"26","author":"EH Haertel","year":"1989","unstructured":"Haertel, E.H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26(4), 301\u2013321.","journal-title":"Journal of Educational Measurement"},{"issue":"3","key":"223_CR35","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF02294762","volume":"55","author":"EH Haertel","year":"1990","unstructured":"Haertel, E.H. (1990). Continuous and discrete latent structure models for item response data. Psychometrika, 55(3), 477\u2013494.","journal-title":"Psychometrika"},{"key":"223_CR36","doi-asserted-by":"crossref","unstructured":"Heller, J., \u00dcnl\u00fc, A, & Albert, D. (2013). Skills, competencies and knowledge structures. In Falmagne, J.-C., Albert, D., Doble, C., Eppstein, D., & Hu, X. (Eds.) Knowledge spaces: Applications in education, pp 229\u2013242. New York: Springer-Verlag.","DOI":"10.1007\/978-3-642-35329-1_11"},{"issue":"4","key":"223_CR37","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.endm.2013.05.145","volume":"42","author":"J Heller","year":"2013","unstructured":"Heller, J., & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42(4), 49\u201356.","journal-title":"Electronic Notes in Discrete Mathematics"},{"key":"223_CR38","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jmp.2017.05.004","volume":"79","author":"J Heller","year":"2017","unstructured":"Heller, J., Anselmi, P., Stefanutti, L., & Robusto, E. (2017). A necessary and sufficient condition for unique skill assessment. Journal of Mathematical Psychology, 79, 23\u201328.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR39","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.jmp.2016.07.008","volume":"77","author":"J Heller","year":"2017","unstructured":"Heller, J. (2017). Identifiability in probabilistic knowledge structures. Journal of Mathematical Psychology, 77, 46\u201357.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR40","doi-asserted-by":"crossref","unstructured":"Heller, J., Hockemeyer, C., & Albert, D. (2004). Applying competence structures for peer tutor recommendations in cscl environments. In IEEE International conference on advanced learning technologies, 2004. proceedings. pp 1050\u20131051.","DOI":"10.1109\/ICALT.2004.1357748"},{"issue":"1","key":"223_CR41","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1027\/1614-2241\/a000035","volume":"8","author":"J Heller","year":"2012","unstructured":"Heller, J., & Repitsch, C. (2012). Exploiting prior information in stochastic knowledge assessment. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 8(1), 12\u201322.","journal-title":"Methodology: European Journal of Research Methods for the Behavioral and Social Sciences"},{"issue":"4","key":"223_CR42","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1007\/s11336-015-9457-x","volume":"80","author":"J Heller","year":"2015","unstructured":"Heller, J., Stefanutti, L., Anselmi, P., & Robusto, E. (2015). On the link between cognitive diagnostic models and knowledge space theory. Psychometrika, 80(4), 995\u20131019.","journal-title":"Psychometrika"},{"issue":"1","key":"223_CR43","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1007\/s11336-015-9494-5","volume":"81","author":"J Heller","year":"2016","unstructured":"Heller, J., Stefanutti, L., Anselmi, P., & Robusto, E. (2016). Erratum to: On the link between cognitive diagnostic models and knowledge space theory. Psychometrika, 81(1), 250\u2013251.","journal-title":"Psychometrika"},{"key":"223_CR44","unstructured":"Hockemeyer, C., & Albert, D. (1999). The adaptive tutoring system rath. In ICL99 Workshop interactive computer aided learning: Tools and applications. Villach, Austria: Carinthia Tech Institute."},{"key":"223_CR45","unstructured":"Hockemeyer, C., Held, T., & Albert, D. (1997). Rath-a relational adaptive tutoring hypertext www-environment based on knowledge space theory."},{"issue":"1","key":"223_CR46","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/ijhc.1994.1006","volume":"40","author":"M Kambouri","year":"1994","unstructured":"Kambouri, M., Koppen, M., Villano, M., & Falmagne, J.-C. (1994). Knowledge assessment: Tapping human expertise by the query routine. International Journal of Human-Computer Studies, 40(1), 119\u2013151.","journal-title":"International Journal of Human-Computer Studies"},{"issue":"1","key":"223_CR47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jmps.1993.1001","volume":"37","author":"M Koppen","year":"1993","unstructured":"Koppen, M. (1993). Extracting human expertise for constructing knowledge spaces: An algorithm. Journal of mathematical psychology, 37(1), 1\u201320.","journal-title":"Journal of mathematical psychology"},{"issue":"3","key":"223_CR48","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0022-2496(90)90035-8","volume":"34","author":"M Koppen","year":"1990","unstructured":"Koppen, M., & Doignon, J.-P. (1990). How to build a knowledge space by querying an expert. Journal of Mathematical Psychology, 34(3), 311\u2013331.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR49","unstructured":"Korossy, K. (1993). Modellierung von wissen als kompetenz und performance. Eine erweiterung der wissensstruktur-theorie von doignon und falmagne. Ph.D. Thesis. University of Heidelberg."},{"key":"223_CR50","first-page":"53","volume":"205","author":"K Korossy","year":"1997","unstructured":"Korossy, K. (1997). Extending the theory of knowledge spaces: A competence-performance approach. Zeitschrift f\u00fcr Psychologie, 205, 53\u201382.","journal-title":"Zeitschrift f\u00fcr Psychologie"},{"key":"223_CR51","unstructured":"Korossy, K. (1999). Modeling knowledge as competence and performance. In Albert, D., & Lukas, J. (Eds.) Knowledge spaces: Theories, empirical research, applications pp 103\u2013132. Mahwah, NJ: Lawrence Erlbaum Associates."},{"issue":"4","key":"223_CR52","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1037\/a0037123","volume":"106","author":"W Ma","year":"2014","unstructured":"Ma, W., Adesope, O.O., Nesbit, J.C., & Liu, Q. (2014). Intelligent tutoring systems and learning outcomes: A meta-analysis. Journal of educational psychology, 106(4), 901.","journal-title":"Journal of educational psychology"},{"issue":"2","key":"223_CR53","doi-asserted-by":"crossref","first-page":"i","DOI":"10.1002\/j.2333-8504.1995.tb01676.x","volume":"1995","author":"RJ Mislevy","year":"1995","unstructured":"Mislevy, R.J., & Gitomer, D.H. (1995). The role of probability-based inference in an intelligent tutoring system. ETS Research Report Series, 1995(2), i\u201327.","journal-title":"ETS Research Report Series"},{"key":"223_CR54","first-page":"1","volume":"43","author":"H Mohamed","year":"2012","unstructured":"Mohamed, H., Bensebaa, T., & Trigano, P. (2012). Developing adaptive intelligent tutoring system based on item response theory and metrics. International Journal of Advanced Science and Technology, 43, 1\u201314.","journal-title":"International Journal of Advanced Science and Technology"},{"key":"223_CR55","doi-asserted-by":"crossref","unstructured":"Ohlsson, S. (1994). Constraint-based student modeling. In Student modelling: the key to individualized knowledge-based instruction, pp 167\u2013189. Springer.","DOI":"10.1007\/978-3-662-03037-0_7"},{"key":"223_CR56","volume-title":"Intelligent tutoring systems: Lessons learned","author":"J Psotka","year":"1988","unstructured":"Psotka, J., Massey, L.D., & Mutter, S.A. (1988). Intelligent tutoring systems: Lessons learned. East Sussex: Psychology Press."},{"key":"223_CR57","unstructured":"Robusto, E., & Stefanutti, L. (2014). Extracting a knowledge structure from the data by a maximum residuals method. TPM: Testing, Psychometrics, Methodology in Applied Psychology."},{"issue":"3","key":"223_CR58","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1111\/j.1745-3984.2010.00119.x","volume":"47","author":"E Robusto","year":"2010","unstructured":"Robusto, E., Stefanutti, L., & Anselmi, P. (2010). The gain-loss model: A probabilistic skill multimap model for assessing learning processes. Journal of Educational Measurement, 47(3), 373\u2013394.","journal-title":"Journal of Educational Measurement"},{"key":"223_CR59","doi-asserted-by":"crossref","unstructured":"Roll, I., Baker, R.S., Aleven, V., & Koedinger, K.R. (2004). A metacognitive act-r model of students\u2019 learning strategies in intelligent tutoring systems. In International Conference on Intelligent Tutoring Systems. pp 854\u2013856.","DOI":"10.1007\/978-3-540-30139-4_98"},{"issue":"3","key":"223_CR60","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.mathsocsci.2009.06.001","volume":"58","author":"A Sargin","year":"2009","unstructured":"Sargin, A., & \u00dcnl\u00fc, A. (2009). Inductive item tree analysis: Corrections, improvements, and comparisons. Mathematical Social Sciences, 58(3), 376\u2013392.","journal-title":"Mathematical Social Sciences"},{"issue":"3","key":"223_CR61","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/S0165-4896(99)00025-6","volume":"38","author":"M Schrepp","year":"1999","unstructured":"Schrepp, M. (1999). On the empirical construction of implications between bi-valued test items. Mathematical social sciences, 38(3), 361\u2013375.","journal-title":"Mathematical social sciences"},{"key":"223_CR62","first-page":"43","volume":"19","author":"M Schrepp","year":"2003","unstructured":"Schrepp, M. (2003). A method for the analysis of hierarchical dependencies between items of a questionnaire. Methods of Psychological Research Online, 19, 43\u201379.","journal-title":"Methods of Psychological Research Online"},{"issue":"4","key":"223_CR63","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1006\/jmps.1995.1035","volume":"39","author":"M Schrepp","year":"1995","unstructured":"Schrepp, M., & Held, T. (1995). A simulation study concerning the effect of errors on the establishment of knowledge spaces by querying experts. Journal of Mathematical Psychology, 39(4), 376\u2013382.","journal-title":"Journal of Mathematical Psychology"},{"issue":"2","key":"223_CR64","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1037\/h0030806","volume":"26","author":"HA Simon","year":"1971","unstructured":"Simon, H.A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American Psychologist, 26(2), 145.","journal-title":"American Psychologist"},{"issue":"4","key":"223_CR65","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.jmp.2012.05.001","volume":"56","author":"A Spoto","year":"2012","unstructured":"Spoto, A., Stefanutti, L., & Vidotto, G. (2012). On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures. Journal of Mathematical Psychology, 56(4), 248\u2013255.","journal-title":"Journal of Mathematical Psychology"},{"issue":"5","key":"223_CR66","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.jmp.2013.09.002","volume":"57","author":"A Spoto","year":"2013","unstructured":"Spoto, A., Stefanutti, L., & Vidotto, G. (2013). Considerations about the identification of forward-and backward-graded knowledge structures. Journal of Mathematical Psychology, 57(5), 249\u2013254.","journal-title":"Journal of Mathematical Psychology"},{"issue":"2","key":"223_CR67","doi-asserted-by":"crossref","first-page":"729","DOI":"10.3758\/s13428-015-0609-9","volume":"48","author":"A Spoto","year":"2016","unstructured":"Spoto, A., Stefanutti, L., & Vidotto, G. (2016). An iterative procedure for extracting skill maps from data. Behavior research methods, 48(2), 729\u2013741.","journal-title":"Behavior research methods"},{"issue":"4","key":"223_CR68","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1037\/a0032447","volume":"105","author":"S Steenbergen-Hu","year":"2013","unstructured":"Steenbergen-Hu, S., & Cooper, H. (2013). A meta-analysis of the effectiveness of intelligent tutoring systems on k\u201312 students\u2019 mathematical learning. Journal of Educational Psychology, 105(4), 970.","journal-title":"Journal of Educational Psychology"},{"issue":"2","key":"223_CR69","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1037\/a0034752","volume":"106","author":"S Steenbergen-Hu","year":"2014","unstructured":"Steenbergen-Hu, S., & Cooper, H. (2014). A meta-analysis of the effectiveness of intelligent tutoring systems on college students\u2019 academic learning. Journal of Educational Psychology, 106(2), 331.","journal-title":"Journal of Educational Psychology"},{"key":"223_CR70","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s11336-008-9095-7","volume":"74","author":"L Stefanutti","year":"2009","unstructured":"Stefanutti, L., & Robusto, E. (2009). Recovering a probabilistic knowledge structure by constraining its parameter space. Psychometrika, 74, 83\u201396.","journal-title":"Psychometrika"},{"issue":"2","key":"223_CR71","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1111\/bmsp.12139","volume":"72","author":"L Stefanutti","year":"2019","unstructured":"Stefanutti, L. (2019). On the assessment of procedural knowledge: From problem spaces to knowledge spaces. British Journal of Mathematical and Statistical Psychology, 72(2), 185\u2013218.","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"issue":"1","key":"223_CR72","doi-asserted-by":"crossref","first-page":"66","DOI":"10.3758\/s13428-010-0036-x","volume":"43","author":"L Stefanutti","year":"2011","unstructured":"Stefanutti, L., Anselmi, P., & Robusto, E. (2011). Assessing learning processes with the gain-loss model. Behavior research methods, 43(1), 66\u201376.","journal-title":"Behavior research methods"},{"key":"223_CR73","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jmp.2017.08.003","volume":"80","author":"L Stefanutti","year":"2017","unstructured":"Stefanutti, L., & de Chiusole, D. (2017). On the assessment of learning in competence based knowledge space theory. Journal of Mathematical Psychology, 80, 22\u201332.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR74","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.jmp.2017.11.001","volume":"82","author":"L Stefanutti","year":"2018","unstructured":"Stefanutti, L., Spoto, A., & Vidotto, G. (2018). Detecting and explaining blim\u2019s unidentifiability: Forward and backward parameter transformation groups. Journal of Mathematical Psychology, 82, 38\u201351.","journal-title":"Journal of Mathematical Psychology"},{"key":"223_CR75","doi-asserted-by":"crossref","unstructured":"Suraweera, P., & Mitrovic, A. (2002). Kermit: A constraint-based tutor for database modeling. In International Conference on Intelligent Tutoring Systems, Springer (pp. 377\u2013387).","DOI":"10.1007\/3-540-47987-2_41"},{"issue":"1","key":"223_CR76","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1198\/0003130031126","volume":"57","author":"J Symanzik","year":"2003","unstructured":"Symanzik, J., & Vukasinovic, N. (2003). Teaching experiences with a course on \u201cweb-based statistics\u201d. The American Statistician, 57(1), 46\u201350.","journal-title":"The American Statistician"},{"issue":"1","key":"223_CR77","first-page":"1","volume":"14","author":"J Symanzik","year":"2006","unstructured":"Symanzik, J., & Vukasinovic, N. (2006). Teaching an introductory statistics course with cyberstats, an electronic textbook. Journal of Statistics Education, 14(1), 1\u20139.","journal-title":"Journal of Statistics Education"},{"issue":"3","key":"223_CR78","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1037\/1082-989X.11.3.287","volume":"11","author":"JL Templin","year":"2006","unstructured":"Templin, J.L., & Henson, R.A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological methods, 11(3), 287.","journal-title":"Psychological methods"},{"issue":"4","key":"223_CR79","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1080\/00461520.2011.611369","volume":"46","author":"K VanLehn","year":"2011","unstructured":"VanLehn, K. (2011). The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 46(4), 197\u2013221.","journal-title":"Educational Psychologist"},{"issue":"3","key":"223_CR80","first-page":"147","volume":"15","author":"K Vanlehn","year":"2005","unstructured":"Vanlehn, K., Lynch, C., Schulze, K., Shapiro, J.A., Shelby, R., Taylor, L., Treacy, D., Weinstein, A., & Wintersgill, M. (2005). The andes physics tutoring system: Lessons learned. International Journal of Artificial Intelligence in Education, 15(3), 147\u2013204.","journal-title":"International Journal of Artificial Intelligence in Education"},{"issue":"2","key":"223_CR81","first-page":"1","volume":"5","author":"YJ Xu","year":"2008","unstructured":"Xu, Y.J., Meyer, K.A., & Morgan, D. (2008). Piloting a blended approach to teaching statistics in a college of education: Lessons learned. Journal of Educators Online, 5(2), 1\u201320.","journal-title":"Journal of Educators Online"},{"key":"223_CR82","doi-asserted-by":"publisher","unstructured":"Xu, Y.J., Meyer, K.A., & Morgan, D.D. (2009). A mixed-methods assessment of using an online commercial tutoring system to teach introductory statistics. Journal of Statistics Education, 17(2). https:\/\/doi.org\/10.1080\/10691898.2009.11889524.","DOI":"10.1080\/10691898.2009.11889524"}],"container-title":["International Journal of Artificial Intelligence in Education"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40593-020-00223-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40593-020-00223-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40593-020-00223-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T18:12:06Z","timestamp":1772647926000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40593-020-00223-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,20]]},"references-count":82,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["223"],"URL":"https:\/\/doi.org\/10.1007\/s40593-020-00223-1","relation":{},"ISSN":["1560-4292","1560-4306"],"issn-type":[{"value":"1560-4292","type":"print"},{"value":"1560-4306","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,20]]},"assertion":[{"value":"28 September 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}