How do the Chinese do it? Chapter 8 - A vision of much more

Last night I attended an e-seminar with Alexandre Borovik.  I struggled to follow much of it as the conversation was heavily accented and the sound quality poor.  But then, in the last few minutes of the hour, something tremendous.  I opened a draft of his book:
Shadows of the Truth: Metamathematics of Elementary Mathematics
and in it, muddled among many other paths of thought, I could see that he has this incredible insight into the deeper concepts of mathematics that only children and highly eduated pure mathematicians can see.  Insights of which I have only begun to scratch the surface in my teaching.

Thank you Alexandre.

How do the Chinese do it?  Links to my other blogs in this series.

1. Introduction

2. More insights and a first quick starter

3. 30 minutes in.  Reciprocals in calculation.

4. Part 4

5. Part 5

6. Part 6

7. Part 7: The Last Chapter?

8. Chapter 8: A vision of much more