Friday, October 9, 2015

Math: A Singapore Math primer

Math groups at Summers-Knoll are taught four times a week at 8:55 AM. Almost the entire school (the 7/8s have Math later in the day) has Math at the same time so that kids at different points in math can join math groups that are at an appropriate level. These levels are determined by where each individual student is in their Singapore Math books. 

As I'm sure many of you know, Singapore Math is the backbone of our Math program. You can read a good primer about the program here. It is an article well worth your time, as there are aspects of the program that are unfamiliar to many parents and families. 

For example, the Singapore Bar Model! I've had a number of parents come up to me over the last few years saying, "I tried to help my kid do this problem last night, but I realized that I'd have to teach them algebra to do it." These parents have benefited from learning about the Singapore Bar Model, a useful way of thinking about and taking apart problems. 

Check out this slideshow to see how the Bar Model is taught and used throughout the program. Read through the whole thing. It seems simple at first (because it is!), but it can quickly become confusing if you skip ahead before understanding the earlier steps. 

This is true of the Singapore system in general: As a general rule, racing through the books is ill-advised. Singapore Math strives to teach students why things work in math, rather than just teaching an algorithm to use. It cultivates a deeper sense of understanding, which makes learning higher math concepts more natural later in their education. 

One way that Singapore does this is adding an additional pictorial step, such as the bar models. 

Here are a few other things to keep in mind when working with your child in Singapore Math: 

The 4B Textbook and Workbook. They differ in important ways!

There are two books at each level: A Textbook and a Workbook. They differ in an important way: 

- The Textbook introduces topics, teaches strategies to approach problems, and exercises to practice. 

- The Workbook only provides additional practice problems. There is no instruction in the workbook. 

This means that, on balance, the Textbook is far more important than the Workbook! 

I drew a helpful cartoon to reinforce this in class the other day: 

Here's how the Textbook and the Workbook interact. A child starts out working in the textbook, which introduces a new concept. Here's an example from book 4B, introducing the concept of symmetry:

Most students will work through these two pages on their own (though I will also do direct instruction, depending on student needs and the complexity of the concept). Then, they'll get to a little arrow at the bottom of the page. Here's a close-up: 

This means that the student can turn to Exercise 42 in the Workbook to find more problems of this type for additional practice. 

Here's Exercise 42 in the Workbook: 

Your child's math assignment is very individualized to the work I've seen them do in the classroom. For some topics, I might assign the Textbook lesson, as well as the corresponding Workbook exercises. However, in other cases, I may opt to have a student skip the Workbook exercise if they've clearly demonstrated repeated mastery of the concept in class. (This becomes a useful contract with students: "I won't make you do busywork just because the book suggests it. But that means that when I do think you need to do the extra practice, you'll know that I really feel you need it.") 

If your child is in my math group, you should start hearing about weekly math assignments, usually given in the form of a sticky note placed in their books. 

Of course, we do more than just Textbook and Workbook in our math groups, which we will discuss in a future post! 

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