Knowing and Teaching Elementary Mathematics

I have just finished reading Knowing and Teaching Elementary Mathematics by Liping Ma (none too soon, as my inter-library loan expired yesterday) and I found it a fascinating and challenging read. The book comprises the findings of a study into how certain teachers approach their teaching of mathematics and how the teachers' ability can be deepened and broadened.

As an ex-high school mathematics teacher, it was interesting to read of US and Chinese teachers' responses to four different mathematical situations (subtraction with regrouping, multi-digit number multiplication, division by fractions and the relationship between perimeter and area). I like to think that I would have been able to answer all of these questions correctly, but I would have to acknowledge that I could not come up with the fullness of answers of the best of the Chinese teachers. I have the procedural ability, but the depth of my conceptual understanding is less that of some of these teachers, and I do not necessarily see all the connections from one mathematical idea to the next. From that perspective, it challenged me to wrap my head around the answers that were given, to learn these ways of thinking for myself.

The last section of the book considers at how to increase a teacher's "profound understanding of fundamental mathematics" and this encouraged me to:
1. Obtain my mathematics teaching textbooks (and other curricular tools) early and study the teaching materials intensively.
2. Think through carefully how to teach the topics using the textbooks.
3. Be open to learning mathematics from my children's ideas.
4. Get on with doing mathematics, trying to find several ways of solving any one problem and analysing the strengths and weaknesses of each method.
Now I have a plan, I just need to execute it!