Knowing and Teaching Elementary Mathematics (1999) by Liping Ma
This book has made a deep impression on me
It demonstrates in many different ways that Chinese Elementary teachers have a more profound understanding of maths fundamentals that their American counterparts
When I talk to people about this they are surprised (as I was) and normally express the view that Chinese teachers teach by rote and that Chinese students do better in maths competitions because they have a better work ethic (but not better understanding)
Well, if you believe this then all I can say is read this book and I'm confident you will change your mind
She also has the solution to the maths wars, the so called dichotomy between transmission and inquiry based teaching methods. That is usually surface appearance. The degree of meaningful understanding that occurs in the classroom depends mainly on the depth of the teachers conceptual understanding
Please read this book, she is brilliant.
Related: Long Multiplication
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