The concept of finite limit of a function at one point as explained by students of Non-Compulsory Secondary Education
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Tso, T. Y.
Colloquial languageNon-Compulsory Secondary EducationConceptionsLimit of a function at a point
Fernández-Plaza, J. A.; Ruiz-Hidalgo, J. F.; Rico, L. The concept of finite limit of a function at one point as explained by students of Non-Compulsory Secondary Education. In: T. Y. Tso (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2. Taipei, Taiwan: PME, 2012. pp. 235-242. [http://hdl.handle.net/10481/35923]
SponsorshipThis study was performed with aid and financing from Fellowship FPU AP2010-0906 (MEC-FEDER), project EDU2009-10454 of the National Plan for R&D&R (MICIN), Subprogram EDUC, and group FQM-193 of the 3rd Andalusian Research Plan (PAIDI).
We review various educational studies of the mathematical concept of limit of a function at a point that indicate how colloquial uses of the terms “to approach,” “to tend toward,” “to reach,” “to exceed” and “limit” influence students’ conceptions of these terms. We then present the results of an exploratory study of this question performed with Spanish students in non-compulsory secondary education and analyze the responses they provide to justify the truth or falsity of statements related to the different characteristics of the concept of finite limit of a function at a point when they use these terms. Finally, we organize their answers according to the kinds of arguments made. Using the response profiles detected, we discuss the influence of everyday usage on the students’ arguments.