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Acknowledgements

Exuberant thanks are due to our partners for their patience and encouragement during the writing process; and to those of our children who were about while the work was in progress.

In the construction of many of the graphs in Sharpening Understandings, we used Autograph: dynamic software for teaching coordinate geometry and statistics. We are grateful for the permission granted by Douglas Butler of Autograph-Maths, through Eastmond Publishing Ltd PO Box 46, Oundle, Peterborough PE8 4JX, UK. 

Image credits - these are under Creativecommons licence 2.0
Inspiration, cropped from an image by Thomas Leuthard
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