The Place and Purpose of Combinatorics

Hurdle, Zach; Warshauer, Max L.; White, Alex

doi:10.5951/mathteacher.110.3.0216

Cited by 2 publications

(2 citation statements)

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“…Combinatorics has received considerable attention in the mathematics education research literature within the past few decades (Batanero et al, 1997;Coenen et al, 2018;English, 1991;Hurdle et al, 2016;Lockwood, 2013Lockwood, , 2014Lockwood, , 2022Schuster, 2004;Tillema, 2013). It is also included, to some degree, in the curricula of many countries including Israel, Brazil, Germany, Spain, and Hungary; because of its role in the curricula, considerable work has been done in investigating the teaching and learning of combinatorial topics among students at a variety of ages in these and other countries (Batanero et al, 2005;Borba et al, 2011;Hart & Sandefur, 2018;Höveler, 2018;Vancsó et al, 2018).…”

Section: Combinatorics and Enumerationmentioning

confidence: 99%

Teaching and learning discrete mathematics

Sandefur

Lockwood

Hart

et al. 2022

ZDM Mathematics Education

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In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes, topics, and mathematical practices that distinguish discrete mathematics. We then present potential benefits of focusing on discrete mathematics topics for mathematics education; in particular, we discuss the accessibility of topics in discrete mathematics, the connection to mathematical processes and affect, and the relevance of discrete mathematics in our current society. We also emphasize discrete mathematics from an international perspective, highlighting studies from the US, Italy, France, Chile, and Germany, which are across all school levels–primary, middle, and secondary school, and with some implications for post-secondary education. We particularly discuss discrete topics including number theory, combinatorics, iteration and recursion, graph theory, and discrete games and puzzles; we describe and situate these topics within literature. We also suggest the additional topics of game theory and the mathematics of fairness that we hope to see addressed in future studies.

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Section: Combinatorics and Enumerationmentioning

confidence: 99%

Teaching and learning discrete mathematics

Sandefur

Lockwood

Hart

et al. 2022

ZDM Mathematics Education

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“…While these publications did not typically entail research studies, these chapters offered instructional ideas and motivations for incorporating combinatorics practically into the classroom (e.g., Althoen, Brown, & Bumcrot, 1991;DeGuire, 1991;Dossey, 1991;Evered & Schroeder, 1991;Miller, 1991;Schielack, 1991;Spangler, 1991). In addition, Maher and incorporated combinatorics as a key content area in their longitudinal study out of Rutgers University, and their work culminated in a book entitled Combinatorics and reasoning: Representing, justifying and building isomorphisms (Maher, Powell, & Uptegrove, 2011) that highlights particularly important aspects of combinatorics among school-age children, and other teachers and researchers have made arguments for the importance of combinatorics over the years (e.g., Batanero et al, 2005;Hurdle, Warshauer, & White, 2016;Sriraman & English, 2004).…”

Section: Renewing Assertions About the Nature Of Combinatorics In Mathematics Educationmentioning

confidence: 99%

A case for combinatorics: A research commentary

Lockwood

Wasserman²,

Tillema

2020

The Journal of Mathematical Behavior

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In this commentary, we aim to make a case for the explicit inclusion of combinatorial topics in the curriculum -both in K-12 classrooms and in introductory postsecondary mathematics courses -where it is currently essentially absent. To do so, we suggest ways in which researchers might inform the field's understanding of combinatorics and its potential role in curricula. We reflect on five decades of research that has been conducted since a call by Kapur (1970) for a greater focus on combinatorics in mathematics curricula. We offer five assertions about combinatorics, including three existing assertions and two new assertions that relate to increasingly relevant trends in mathematics education. Specifically, we discuss the following in making our case for combinatorics: 1) Combinatorics is accessible, 2) Combinatorics problems provide opportunities for rich mathematical thinking, 3) Combinatorics fosters desirable mathematical practices, 4) Combinatorics can contribute positively to issues of equity in mathematics education, and 5) Combinatorics is a natural domain in which to examine (and develop) computational thinking and activity. As we discuss each of these ideas, we summarize and synthesize existing research and offer new ideas for research. Ultimately, we hope to make a case for the valuable and unique ways in which combinatorics might effectively be leveraged within K-16 curricula, and we hope to elevate its status in the mathematics education research community.

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The Place and Purpose of Combinatorics

Abstract: The union of curriculum goals intersects with math education standards.

Cited by 2 publications

References 0 publications

Teaching and learning discrete mathematics

Teaching and learning discrete mathematics

A case for combinatorics: A research commentary

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