Review: Moving Things Around

Moving Things Around by Bowen Kerins
My rating: 4 of 5 stars

...Analysis of in- and out-shuffles of various sized decks exemplifies modular arithmetic and permutations. Returning often to this card shuffle theme, the material brings together number and group theoretic concepts in a truly hands on approach. Problem Set 2 can be used to exemplify the pace and breadth of the problems: After opening with “Can perfect shuffles restore a deck with 9 cards”, #2 asks for the least significant digit of three progressively more complex arithmetic expressions; #13 questions if “… .99999… was equal to 1”; and in #21 the student is challenged to “find all solutions to x2 – 6x + 8 = 0 in mod 105 without the use of technology.” In my experience, roughly two thirds of this material would be new to first-year college students, especially abstract algebra topics such as generators, dihedral groups, isomorphism, etc. While the target is precollege, this advanced material is applicable to many first-year undergraduate programs. The problems have helpful sidebar prompts supplying hints and guidance. The problem sets are laid out as worksheets with permission given to “copy select pages for use in teaching”. The middle section of Facilitator Notes offers presentation and pedagogical advice. This is often drawn from observations with students: “At PCMI 2012, the opener proved difficult to understand for participants. We suggest working through at least one or two examples from both tables…”. The concluding section is Solutions, often multistep and detailed.

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