I’ve been reading blog posts about math like this one, in which a common theme is that we need to return to “basic” or “regular” math skills and dispense with the constructivist programs that were so popular in the last decade or two. I’ve read about people who are frustrated with the idea that children should have to reconstruct the math theorems that evolved over the last 2000 years or so, and it makes sense that they shouldn’t have to do this. Some people turn to Saxon Math, which I have taught, or Singapore Math, as the solutions that teach the basics and provide a strong foundation for children to learn math.
All of that is fine, but what I challenge is the idea that you are not involving constructivism or critical thinking when you use Singapore Math. If you are teaching Singapore Math well, or any math program for that matter, it should involve a great deal of critical thinking and metacognition, or thinking about thinking. The children should be asked, and learn to question themselves, questions like, “Why did you choose to solve a problem this way?” or, “Why did you choose this mental math strategy over another?” and, “Why does this math algorithm work? Explain it to me, or explain it to your friend…” and so on. All of which strengthen the math constructs inside a child’s mind and demonstrate conceptual understanding inside themselves and to others.
So to my mind, constructivism and Singapore Math are not at all mutually exclusive. It’s the approach, and the child’s resulting numeracy, that matter in the end.
What do you think?