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Published November 2012. "The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. "

From the abstract: "Studies on creative mathematics conducted in the past decades revealed that the importance of creation of learning and teaching environment favourable to the identification and nurturing creativity in mathematics. Based on psychological, methodological and didactical models created by Krutetskii (2006), Shchedrovtiskii (2008), Brousseau (2007) and Sierpinska (2004), we have developed our challenging situation approach. During 5 years of field study in the elementary grade VII classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical creativity in very young children, keeping and increasing their interest towards more advanced mathematics curriculum. This article is an humble attempt to present our model and illustrate how it works in the mixedability classroom. We will also discuss different roles that teachers and students might play in this kind of environment and how each side could benefit from it."

An encyclopedia of current mathematics knowledge. Interesting recreations.