Aspects of Predication and Their Influence on Reasoning about Logic in Discrete Mathematics

Autor/inn/en	Dawkins, Paul Christian; Roh, Kyeong Hah
Titel	Aspects of Predication and Their Influence on Reasoning about Logic in Discrete Mathematics
Quelle	In: ZDM: Mathematics Education, 54 (2022) 4, S.881-893 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Dawkins, Paul Christian)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-022-01332-y
Schlagwörter	Mathematics Instruction; Mathematical Logic; Validity; Mathematical Concepts; Concept Formation; Undergraduate Students; College Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit; Concept learning; Begriffsbildung
Abstract	This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of predication are (1) "populating" the way students generate sets of examples of the property, and (2) "testing membership" how one tests whether or not a given object has a specific property. Using data from two teaching experiments in which undergraduate students read proofs of theorems about the discrete concept of multiple relations, we illustrate the nature of these aspects of predication and demonstrate how they help explain student interpretations of the proofs. We argue that these particular properties from number theory likely have correlates in many other discrete mathematics topics because of the role of computation/algorithms for defining and testing properties as well as the role of iteration and recursion in populating examples. We anticipate that these constructs will be useful to teachers and researchers of discrete mathematics to foster and assess student understanding of various mathematical properties. They provide tools for thinking about what it means to understand properties in a rich and coherent way that supports understanding complex lines of inference and generalizations. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01