Watson (Oxford U.) and Mason (Open U.) examine teaching techniques which actively engage learners, enhancing their sophistication and deepening their understanding, revealing their depths, making them accept initiative in finding and applying deeper concepts, and enriching enjoyment of mathematical structures and connections. They give examples used in classrooms, then "example spaces" specifically for learners to explore, then the tools teachers need to help learners develop those "example spaces" and strategies for prompting learners to generate them. They close with a very useful chapter for those seeking to justify expansion of programs that examines the constructive activities of mathematics, including its ability to teach how to learn, how to build evidence, and construct outcomes.

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