Abstract
While technology can enhance learning, ironically, many online systems occlude learners’ cognitive states because instructors do not directly observe students solving problems. In this paper, we show how we utilized an online mathematics homework system where students simply provided final answers to exercises. We then asked, “What can we infer about the cognitive state of the student if they gave an incorrect response?” Through data mining techniques, we found we were able to ascribe a particular type of mechanical error or misconception to 60-75% of the incorrect responses learners made on the subset of problems we analyzed. As such, we illustrate methods for extracting this data to discover knowledge components embedded in an exercise, expose item bias, and reveal learners’ cognitive states.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brown, J.S., VanLehn, K.: Repair theory: A generative theory of bugs in procedural skills. Cognitive Science 4(4), 379–426 (1980), http://onlinelibrary.wiley.com/doi/10.1207/s15516709cog0404_3/abstract
Brown, S., Race, P., Rust, C.: Using and experiencing assessment. Assessment for Learning in Higher Education, 75–85 (1995)
Conole, G., Warburton, B.: A review of computer-assisted assessment. ALT-J 13(1), 17–31 (2005), http://journals.co-action.net/index.php/rlt/article/view/10970
Crooks, T.J.: The impact of classroom evaluation practices on students. Review of Educational Research 58(4), 438–481 (1988), http://rer.sagepub.com/content/58/4/438 , doi:10.3102/00346543058004438
Junker, B.W., Sijtsma, K.: Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement 25(3), 258–272 (2001), http://apm.sagepub.com/content/25/3/258 , doi:10.1177/01466210122032064
Picard, R.W.: Affective Computing. MIT Press (2000)
VanLehn, K.: Mind Bugs: The Origins of Procedural Misconceptions. MIT Press (1990)
VanLehn, K.: The behavior of tutoring systems. International Journal of Artificial Intelligence in Education 16(3), 227–265 (2006), http://iospress.metapress.com/content/AL6R85MM7C6QF7DR
Wang, F., Hannafin, M.J.: Design-based research and technology-enhanced learning environments. Educational Technology Research and Development 53(4), 5–23 (2005), http://link.springer.com/article/10.1007/BF02504682
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
McTavish, T.S., Larusson, J.A. (2014). Labeling Mathematical Errors to Reveal Cognitive States. In: Rensing, C., de Freitas, S., Ley, T., Muñoz-Merino, P.J. (eds) Open Learning and Teaching in Educational Communities. EC-TEL 2014. Lecture Notes in Computer Science, vol 8719. Springer, Cham. https://doi.org/10.1007/978-3-319-11200-8_40
Download citation
DOI: https://doi.org/10.1007/978-3-319-11200-8_40
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11199-5
Online ISBN: 978-3-319-11200-8
eBook Packages: Computer ScienceComputer Science (R0)