A Pathway to a Student-Worded Definition of Limits at the Secondary-Tertiary Transition

Autor/in	Chorlay, Renaud
Titel	A Pathway to a Student-Worded Definition of Limits at the Secondary-Tertiary Transition
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 5 (2019) 3, S.267-314 (48 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Chorlay, Renaud)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-019-00094-5
Schlagwörter	Definitions; Foreign Countries; Didacticism; Educational Experiments; Mathematical Concepts; Teacher Role; Student Role; Secondary School Students; Postsecondary Education; Mathematics Instruction; Concept Formation; France + Suchen Sie Ihr Suchwort? Begriffsbestimmung; Ausland; Didaktisierung; Schulversuch; Lehrerrolle; Sekundarschüler; Post-secondary education; Tertiäre Bildung; Mathematics lessons; Mathematikunterricht; Concept learning; Begriffsbildung; Frankreich
Abstract	Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students, which led to the formulation "by the students" of a correct formal definition of the infinite limit for sequences, with minimal background logical prerequisites and in the course of a 2-h session. On a more theoretical level, the teaching project was developed in the framework of didactic engineering, and provides opportunities to contribute to the ongoing work on its adaptation to the specific context of tertiary education. In the a priori analysis, we highlight the didactical potential of tasks of "differentiation" between neighboring concepts as a pathway to advanced mathematical concepts. In the a posteriori analysis, we focus on the nature and extent of teacher intervention in the shaping of a mathematical "milieu" that is conducive to the definition of an advanced mathematical concept. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01