An Analysis of Statements of the Multiplication Principle in Combinatorics, Discrete, and Finite Mathematics Textbooks

Autor/inn/en	Lockwood, Elise; Reed, Zackery; Caughman, John S.
Titel	An Analysis of Statements of the Multiplication Principle in Combinatorics, Discrete, and Finite Mathematics Textbooks
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 3 (2017) 3, S.381-416 (36 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-016-0045-y
Schlagwörter	Multiplication; Textbooks; Mathematics Instruction; Mathematical Concepts; Computation; College Mathematics + Suchen Sie Ihr Suchwort? Multiplikation; Textbook; Text book; Schulbuch; Lehrbuch; Mathematics lessons; Mathematikunterricht
Abstract	The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of university textbooks in order to explore and identify several key aspects of the various statements of the principle. We characterize the nature of the variety of statements by identifying structural, operational, and bridge statements, and we highlight the respective statements' mathematical and pedagogical implications. We conclude by indicating several directions for future research. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01