Abstract
This paper views Formal Concept Analysis (FCA) from an educational perspective. Novice users of FCA who are not mathematicians might find diagrams of concept lattices counter-intuitive and challenging to read. According to educational theory, learning thresholds are concepts that are difficult to learn and easy to be misunderstood. Experts of a domain are often not aware of such learning thresholds. This paper explores learning thresholds occurring in FCA teaching material drawing on examples from a discrete structures class taught to first year computer science students.
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Notes
- 1.
Because FCA is the topic of this conference, this paper does not provide an introduction to FCA. Further information about FCA can be found, for example, on-line (http://www.upriss.org.uk/fca/) and in the main FCA textbook by Ganter and Wille (1999).
- 2.
In just-in-time teaching, students read textbook pages and submit exercises, comments and questions before each class session. The lecturer then prepares each class session so that it addresses exactly the questions and problems the students are having. This method provides a wealth of continuous feedback both for learners and for teachers about the learning process.
References
Almstrum, V.L., Henderson, P.B., Harvey, V., Heeren, C., Marion, W., Riedesel, C., Soh, L.K., Tew, A.E.: Concept inventories in computer science for the topic discrete mathematics. ACM SIGCSE Bull. 38(4), 132–145 (2006)
Amalric, M., Dehaene, S.: Origins of the brain networks for advanced mathematics in expert mathematicians. Proc. Natl. Acad. Sci. 113(18), 4909–4917 (2016)
Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)
Edwards, B.S., Ward, M.B.: Surprises from mathematics education research: student (mis)use of mathematical definitions. Am. Math. Mon. 111(5), 411–424 (2004)
Eklund, P., Ducrou, J., Brawn, P.: Concept lattices for information visualization: can novices read line-diagrams? In: Eklund, P. (ed.) ICFCA 2004. LNCS, vol. 2961, pp. 57–73. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24651-0_7
Goguen, J.: An introduction to algebraic semiotics, with application to user interface design. In: Nehaniv, C.L. (ed.) CMAA 1998. LNCS, vol. 1562, pp. 242–291. Springer, Heidelberg (1999). doi:10.1007/3-540-48834-0_15
Kaminski, J.A., Sloutsky, V.M., Heckler, A.F.: The advantage of abstract examples in learning math. Science 320(5875), 454–455 (2008)
Lyons, J.: Introduction to Theoretical Linguistics. Cambridge University Press, Cambridge (1968)
Meyer, J.H.F., Land, R.: Threshold concepts and troublesome knowledge 1 - linkages to ways of thinking and practising. In: Rust, C. (ed.) Improving Student Learning - Ten Years On. OCSLD, Oxford (2003)
Moore, R.C.: Making the transition to formal proof. Educ. Stud. Math. 27(3), 249–266 (1994)
Presmeg, N.C.: Research on visualization in learning and teaching mathematics. In: Handbook of Research on the Psychology of Mathematics Education, pp. 205–235 (2006)
Priss, U.: Associative and formal concepts. In: Priss, U., Corbett, D., Angelova, G. (eds.) ICCS-ConceptStruct 2002. LNCS, vol. 2393, pp. 354–368. Springer, Heidelberg (2002). doi:10.1007/3-540-45483-7_27
Priss, U.: A semiotic-conceptual analysis of conceptual learning. In: Haemmerlé, O., Stapleton, G., Faron Zucker, C. (eds.) ICCS 2016. LNCS, vol. 9717, pp. 122–136. Springer, Cham (2016). doi:10.1007/978-3-319-40985-6_10
Priss, U.: Semiotic-conceptual analysis: a proposal. Int. J. Gen. Syst. (2017, to appear)
Rosch, E.: Natural categories. Cogn. Psychol. 4, 328–350 (1973)
Spangenberg, N., Wolff, K.E.: Datenreduktion durch die Formale Begriffsanalyse von Repertory Grids. In: Scheer, J.W., Catina, A. (eds.) Einführung in die Repertory Grid Technik. Klinische Forschung und Praxis 2, pp. 38–54. Verlag Hans Huber (1993)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)
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Priss, U. (2017). Learning Thresholds in Formal Concept Analysis. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds) Formal Concept Analysis. ICFCA 2017. Lecture Notes in Computer Science(), vol 10308. Springer, Cham. https://doi.org/10.1007/978-3-319-59271-8_13
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DOI: https://doi.org/10.1007/978-3-319-59271-8_13
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