Thanks to the collective pressure from a certain homeschooling forum, I finally got the book *Knowing and Teaching Elementary Mathematics* by Liping Ma. If you’re not familiar with it, Ma, a former teacher of mathematics in her native China, interviewed and observed both American and Chinese teachers of elementary math. She found that the American teachers, while technically better educated than the Chinese teachers, did not seem to understand some of the basic concepts in elementary school math. For example, in the first chapter, she shows how teachers had trouble understanding how to explain to students how to tackle a problem such as 72-18, which would require “borrowing” or “regrouping.” On the whole, the American teachers had methods for teaching the process, but not the reasoning for that process.

It’s a book that’s both depressing and inspiring to me. On the one hand, it’s a depressing look at American teachers and how they know much more about educational terms and methods and less about what they’re actually teaching. In the third and fourth chapters, many of the teachers can’t even get the elementary math problem correct themselves. On the other hand, as someone who is actually teaching elementary mathematics without having received much in the way of higher mathematics education, it’s inspiring to think that if I really understand the concepts I’m teaching, then I’ll be able to give my kids the grounding they really need to do well in math once they get to high school level math. I never made it to calculus in college. I took a class in introductory number theory instead (feel free to roll your eyes). However, I found the questions posed all ones easy to tackle, even if it was baffling that many of the American teachers did not. I was extra pleased when I read the question posed in the second chapter. It showed an issue that I’ve encountered when I briefly taught remedial middle school math. I knew exactly how I dealt with it and it was very close to the approach that the conceptual American teachers used. I know math is a subject that intimidates many homeschoolers, but Ma’s book, at least for the elementary level, can be a positive way to think about what you’re doing without feeling like you need to go back and take calculus at the community college.

Of course, this isn’t just a problem in teaching math. In some ways, while they’re extremely different books, this made me think of *Lies My Teacher Told Me* by James Loewen, which I read many years ago. Loewen’s book is a look at high school American history textbooks and how they are filled with inaccuracies which teachers then go on to reinforce to students. Loewen has a decidedly liberal take on history. However, whether you agree with his rationale for *why* misinformation about Columbus has become so commonplace*, historical record shows that his points are well-founded. Ma’s book about mathematics only looks a little at the teaching materials and focuses on the teachers, while Loewen’s book focuses on the materials and just glosses over the teachers. However, just like in Ma’s book, the teachers he describes seem completely unversed in their own subjects – after all, they can’t even notice what are some glaring errors. It makes you wonder how they can possibly teach what they don’t know. Both books get at an issue that seems at the heart of the problems with American schools – teachers don’t know their subjects and the materials that support them are poorly constructed.

** I personally do agree with Loewen’s opinion that our textbooks have been hijacked by conservative Texas school boards. However, even if you don’t, even if you think that the “great man” approach to history is the right one, I don’t think it’s any excuse for the information about those figures to be untrue.*

I found both of those books depressing and inspiring. Depressing because I just can’t believe that it’s possible to get a Master’s degree in teaching without understanding place value. Inspiring because it puts into perspective that whole question about “what makes you think that you can do better than professional teachers?”