Different Presentations of a Mathematical Concept Can Support Learning in Complementary Ways

Autor/inn/en	Lampinen, Andrew K.; McClelland, James L.
Titel	Different Presentations of a Mathematical Concept Can Support Learning in Complementary Ways
Quelle	In: Journal of Educational Psychology, 110 (2018) 5, S.664-682 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Lampinen, Andrew K.) Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0022-0663
DOI	10.1037/edu0000235
Schlagwörter	Teaching Methods; Mathematics Instruction; Mathematical Concepts; Adult Education; Adults; Outcomes of Education; Comparative Analysis; Experiments; Hypothesis Testing; Replication (Evaluation); Regression (Statistics); Statistical Analysis; Maximum Likelihood Statistics + Suchen Sie Ihr Suchwort? Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Adult; Adults; Education; Adult basic education; Adult training; Erwachsenenbildung; Lernleistung; Schulerfolg; Erprobung; Hypothesenprüfung; Hypothesentest; Regression; Regressionsanalyse; Statistische Analyse
Abstract	Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of that concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with deeply interconnected concepts and many distinct aspects of understanding of each concept, and we discuss difficulties with the idea that differences among presentations can be ordered on a concrete-abstract dimension. To move beyond this, we explore how different presentations of a concept can affect learning of subsequent concepts and assess several distinct aspects of understanding. Using the domain of elementary group theory, we teach adult participants a group operation using a visuospatial or an arithmetic presentation. We then teach them concepts that build upon this operation. We demonstrate that our presentations differentially support learning complementary aspects of the system presented. We argue that these differences arise from the fact that each presentation supports learning by connecting to different systems of reasoning learners are already familiar with, and that it is these connections to extant knowledge systems, rather than differences in concreteness versus abstractness, that determine whether a presentation will be helpful. Furthermore, we show that presenting both presentations and encouraging participants to recognize the relationship between them improves performance without requiring additional time, at least for some participants. Educational Impact and Implications Statement: The details of how a concept is taught can have far-reaching effects on students' learning. Using abstract algebra with adult subjects, we show that 2 presentations of a concept that connect to different types of students' prior knowledge can have advantages and disadvantages for later learning that builds on the target concept. We show that one possible solution to the dilemma of choosing which presentation to use is giving students both concepts and explaining how they are related to each other. In summary, when designing pedagogical materials, we should consider not only how they affect learning of the present concept, but also how they support learning of future concepts, and use multiple complementary presentations rather than searching for a single ideal one. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01