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Scott A. Annin and Kevin S. Lai

Analyzing combinatorics problems involving flags and playing cards presents common pitfalls for students—pitfalls that can be avoided.

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Lawrence E. Spence

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Barbara Britton

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Tim McDevitt and Kathryn Sutcliffe

The Matchstick problem of counting equilateral triangles is modified to allow for additional side lengths and summation formulas, which lead to a result represented with combinatorics.

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Carla Tayeh

The problem appearing in the December 2005/ January 2006 “Problem Solvers” section was stated as follows:

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

In our March editorial (Cai et al., 2019), we discussed the nature of significant research questions in mathematics education. We asserted that the choice of a suitable theoretical framework is critical to establishing the significance of a research question. In this editorial, we continue our series on high-quality research in mathematics education by elaborating on how a well-constructed theoretical framework strengthens a research study and the reporting of research for publication. In particular, we describe how the theoretical framework provides a connecting thread that ties together all of the parts of a research report into a coherent whole. Specifically, the theoretical framework should help (a) make the case for the purpose of a study and shape the literature review; (b) justify the study design and methods; and (c) focus and guide the reporting, interpretation, and discussion of results and their implications.

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Elise Lockwood

A branch of mathematics—combinatorics—is explored through counting problems.

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Janet M. Shiver

A well-known counting problem convinces students that proof is necessary.

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Elise Lockwood

Using sets of outcomes to reconcile differing answers in counting problems.

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Richard A. Edwards

A counting problem in the context of circular seating arrangements extends our understanding of permutations, combinations, and recursions with connections to Stirling numbers and factorial polynomials.