Going a Mile Deep
Last week I attended a workshop on Singapore Math model drawing. I picked the workshop because I am really interested in teaching problem solving to students, and I know that Singapore Math has a great reputation.
Americans have had an Asian math fetish for a while now. We don’t always know exactly what makes Asian math special, but we’ve heard that Asian countries beat us on international tests. The most famous of these tests is called the TIMMS (Trends in International Mathematics and Science Study). I love using questions from the TIMMS because they are very different from state assessment questions and require students to deeply understand the topic. For example, this is a 1995 4th grade question:
This is a 1999 8th grade question:
Primarily, the TIMMS is used to compare different countries. From page 7 of Highlights From TIMSS 2007:
You can imagine that these results spur a lot of debate. It’s important to note that education is not compulsory or even available for every student in every country. Taiwan, Singapore and Hong Kong are also quite small. But, there is always something to learn by studying a different approach, which is why I took the Singapore Math model drawing workshop that I’ll discuss in tomorrow’s post.
As for Asian math instruction, I have often heard it described as “an inch wide and a mile deep” whereas American math instruction is “a mile wide and an inch deep.” Whether or not we can really generalize, it is important for any teacher to struggle with the tradeoff between covering a lot of material and covering it well. I have heard people say that standardized testing encourages teachers to do the former. But that is not a problem with standardized testing, it is a problem with the number of standards.
That is why I encourage every teacher to go through their standards and chunk them together into “power units.” If we think of our many standards as pieces of several large units then students really can delve a mile deep into each topic. We do not need to choose.