How Transition Students Relearn School Mathematics to Construct Multiply Quantified Statements

Autor/in	Schüler-Meyer, Alexander
Titel	How Transition Students Relearn School Mathematics to Construct Multiply Quantified Statements
Quelle	In: Educational Studies in Mathematics, 110 (2022) 2, S.291-311 (21 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Schüler-Meyer, Alexander)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-021-10127-z
Schlagwörter	Learning; Mathematics; Mathematics Instruction; Mathematical Concepts; Semantics; Pragmatics; Syntax; Concept Formation; Students + Suchen Sie Ihr Suchwort? Lernen; Mathematik; Mathematics lessons; Mathematikunterricht; Semantik; Pragmalinguistik; Concept learning; Begriffsbildung; Student; Schüler; Schülerin; Studentin
Abstract	Understanding the intricate quantifier relations in the formal definitions of both convergence and continuity is highly relevant for students to use these definitions for mathematical reasoning. However, there has been limited research about how students relearn previous school mathematics for understanding multiply quantified statements. This issue was investigated in a case study in a 5-week teaching unit, located in a year-long transition course, in which students were engaged in defining and proving sequence convergence and local continuity. The paper reports on four substantial changes in the ways students relearn school mathematics for constructing quantified statements: (1) endorse predicate as formal property by replacing metaphors of epsilon strips with narratives about the objects [epsilon], N[subscript epsilon], and \|a[subscript n] - a\|; (2) acknowledge that statements have truth values; (3) recognize that multiply quantified statements are deductively ordered and that the order of its quantifications is relevant; and (4) assemble multiply quantified statements from partial statements that can be investigated separately. These four changes highlight how school mathematics enables student to semantically and pragmatically parse multiply quantified statements and how syntactic considerations emerge from such semantic and pragmatic foundations. Future research should further investigate how to design learning activities that facilitate students' syntactical engagement with quantified statements, for instance, in activities of using formal definitions of limits during proving. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01