Abstract
This paper demonstrates how semiotic-conceptual analysis (SCA) can be applied to an investigation of mathematical language and notation. The background for this research is mathematics in higher education, in particular the question of why many students find mathematics difficult to learn. SCA supports an analysis on different levels: pertaining to the conceptual structures underlying mathematical knowledge separately from and in combination with the semiotic relationship between the representation and the content of mathematical knowledge. We believe that this provides novel insights into the structure of mathematical knowledge and presents a method of decoding which lecturers can employ.
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- 1.
The object concept of an object is the smallest concept which has the object in its extension. Vice versa an attribute concept is the largest concept which has an attribute in its intension.
- 2.
For example, definitions of “set”, “\(\Longleftrightarrow \)” or the Peano axioms for natural numbers are challenging for first year students.
References
Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2
Goguen, J.: An introduction to algebraic semiotics, with application to user interface design. In: Nehaniv, C.L. (ed.) CMAA 1998. LNCS (LNAI), vol. 1562, pp. 242–291. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48834-0_15
Presmeg, N., Radford, L., Roth, W.-M., Kadunz, G. (eds.): Signs of Signification. ICME-13 Monographs. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-70287-2
Priss, U.: A semiotic-conceptual analysis of conceptual learning. In: Haemmerlé, O., Stapleton, G., Faron Zucker, C. (eds.) ICCS 2016. LNCS (LNAI), vol. 9717, pp. 122–136. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40985-6_10
Priss, U., Riegler, P.: Automatisierte Programmbewertung in der Mathematik-Ausbildung. In: Automatisierte Bewertung in der Programmierausbildung, Waxmann (2017)
Priss, U.: Learning thresholds in formal concept analysis. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 198–210. Springer, Cham (2017a). https://doi.org/10.1007/978-3-319-59271-8_13
Priss, U.: Semiotic-conceptual analysis: a proposal. Int. J. Gen. Syst. 46(5), 569–585 (2017b)
Priss, U.: A semiotic-conceptual analysis of conceptual development in learning mathematics. In: Presmeg, N., Radford, L., Roth, W.-M., Kadunz, G. (eds.) Signs of Signification. IM, pp. 173–188. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-70287-2_10
Puchalska, E., Semadeni, Z.: Children’s reactions to verbal arithmetical problems with missing, surplus or contradictory data. For Learn. Math. 7(3), 9–16 (1987)
Schleppegrell, M.J.: The linguistic challenges of mathematics teaching and learning: a research review. Read. Writ. Q. 23(2), 139–159 (2007)
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Priss, U. (2019). Applying Semiotic-Conceptual Analysis to Mathematical Language. In: Endres, D., Alam, M., Şotropa, D. (eds) Graph-Based Representation and Reasoning. ICCS 2019. Lecture Notes in Computer Science(), vol 11530. Springer, Cham. https://doi.org/10.1007/978-3-030-23182-8_19
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