The flipped classroom model of teaching can be an ideal venue for turning a traditional classroom into an engaging, inquiry-based learning (IBL) environment. In this paper, we discuss how two instructors at different universities made their classrooms come to life by moving the acquisition of basic course concepts outside the classroom and using class time for active problem-based learning. Results from student surveys are presented to relate student perceptions of the flipped/IBL classroom model.

Abstract. We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions.

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In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley-Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of type affine C. We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the socalled monomial basis of the Temperley-Lieb algebra of type affine C.

of IBL classrooms from our perspective: upper-division proof-based mathematics courses, the calculus sequence, and mathematics for elementary teachers. Active, student-centered pedagogies such as IBL exist in a dynamic landscape, so describing teaching methods that are constantly evolving is a challenging and slippery task. We are still developing and trying to understand the variety of IBL methods, when and where they are applicable, and identifying best practices. Here we share some of the commonly used examples and core ideas that drive instructor decisions.