Bill Jackson, the Scarsdale Singapore Math coach who is making waves nationwide, wrote an interesting series for The Daily Riff. The first article lays out how he got interested in Singapore Math. Here is a quote from his experience working with Japanese math teachers:
When I began working with the Japanese teachers, I soon realized three important reasons why they were such good math teachers:
(1) They had a high level of math content knowledge. In fact, I felt that their first grade teachers knew more about math than I did as an 8th grade teacher!
(2) They used thin, lightweight paperback textbooks that were much more focused and coherent than our heavy hard cover books.
(3) They continually worked to improve their teaching throughout their careers by conducting lesson study.
The next article describes a lesson that uses problem solving and model drawing to bridge children’s thinking from concrete to pictorial to abstract. I really like the way he describes the differences in approach between Singaporean lessons and traditional American textbooks:
Problem solving and mathematical thinking are two big ideas behind Singapore math. To understand this better, let’s look at an example that many American elementary students struggle with, long division. As noted in part one of this blog, word problems are often the last thing on the page in U.S. mathematics textbooks. Often times teachers never even get to these problems or if they do, usually only the advanced students have the opportunity to tackle them while struggling students continue to practice procedures. The third grade Primary Mathematics textbook, however, introduces long division with a word problem. The description below is one way how the concept of long division might be introduced in Singapore math.
After a brief warm up with multiplication and division flash cards, the teacher introduces a problem by saying, “Our friend Meihua has some toy soldiers. She wants to put them equally in some tents.” (Note that no numbers are mentioned and there is no question asked yet.) The teacher then asks the students to try to imagine the situation and discuss what it means to put the soldiers in tents equally. Students share examples such as, “If she has 15 soldiers and 3 tents, she could put 5 soldiers in each tent,” and “If there were 10 soldiers and 5 tents she could put 2 soldiers in each tent.”
I highly recommend a visit to these articles; he has much of value to say about teaching math.