Registers of Semiotic Representations Aiding the Learning of Combinatorial Situations

Montenegro, Juliana Azevedo; Borba, Rute E. de S. Rosa; Bittar, Marilena

doi:10.54870/1551-3440.1537

Cited by 1 publication

(1 citation statement)

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“…In light of such challenges, though, many researchers have attempted to identify ways to improve student success in solving counting problems. This has included identifying productive ways of thinking, identifying potentially useful instructional interventions, and examining ways in which students think about particular ideas and topics in combinatorics, such as Cartesian product problems, multiplication, equivalence, binomial coefficients, combinatorial proof, and symbolization and representations (Coenen et al, 2018;English, 1991;Erickson & Lockwood, 2021a;Halani, 2012;Lockwood, 2014;Lockwood & Purdy, 2020;Lockwood & Reed, 2020;Maher & Speiser, 1997;Maher et al, 2011;Montenegro et al, 2021;Soto et al, 2022;Tillema, 2013Tillema, , 2014Tillema, , 2018Tillema & Gatza, 2016;Wasserman & Galarza, 2019).…”

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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