Singapore Bar Model Method - Essential or Nice to Know

[3andme]

We currently use CLE for math and supplement occasionally with other math items including some of the Singapore Process Skills Books. I understand they provide a visual representation and understanding of mathematical problems and this can be helpful but  I can't seem to make up my mind on whether it's really worth it.  

 

For the simpler problems, it doesn't seem to offer much enhancement to my kids. They don't feel the visual model adds anything to their understanding - "I get it - we don't need to draw it, Mom" is the most common refrain. For some of the more complex problems, I understand that this method lets younger students tackle these problems without algebra but I often wonder why that's necessary. Many of these problems are very contrived and not realistic examples and ,in a few years, they will be able to solve them algebraically. Anyway just wondering how much value others have gained by using this method and how much emphasis you feel it deserves.

[KeepItGoing]

I've used the Singapore books since about 2000.

 

You're right, the easy models don't help for someone who already gets it. My kids range in math ability from good at math to extraordinarily good at math, and I never required them to draw a bar model.

 

Having said that, the bar models seemed to make a huge difference in their understanding. They did draw them when it helped. Yes, they could have waited until algebra to learn to solve those problems. But the fact that they could solve them early did seem to make a diference. All three of them can solve problems in their heads that most people need paper and pencil for, and I think the bar models are one of the reasons for that.

 

In fact, my oldest had a hard time being convinced of the value of algebra at all, because she could solve ALL the problems mentally for quite some time. In order to get her to learn algebraic methods, I had to take out all the numbers and use only variables—so instead of finding x, she was solving for x in a big equation like a = by + cx + d. This annoyed her hugely but did get the job done!

 

The most important thing that we got out of the books from Singapore Math, though, was that when you don't know how to solve a problem, you dive in and try things. Does it work to do this? No, that doesn't seem to be helping us, so let's try something else. This looks promising, but no, I can't see how to proceed from here. What about this approach? Because the problems were rich and complex enough to stump me too (at least some of the time), the kids learned a flexible and curious approach. I don't meet a lot of kids with this approach to math, and I think it's extremely valuable.

 

I can't speak to the specific books you mention, because they weren't available when I was buying from them. My kids have moved on to other things (though I still use the books I have with students I tutor). Our favorite resources for brain-stretching were the Intensive Practice books, which aren't for everyone but were wonderful for us.

[sbgrace]

The bar models become more useful as the problems get more complex. I was glad I insisted my resistant son use them for those early books. He saw the value as we moved along in the books (book 3 or 4 especially/I don't remember which was the aha point).

 

CLE, which I use as well, is a really good program. It's weak in word problems, and general challenge, though. By general challenge I mean being faced with a problem that requires you to problem solve and tackle problems that stretch. The word problems we've encountered in 5 and 6 are incredibly simple. Therefore, I think the process skills books are an important addition to CLE. Because the books are short, you can do just one problem a day or recycle through the book twice when the problems get difficult. I went twice through book 4 with one child and twice through book 5 with both. They get more challenging!

[Targhee]

Nice (very nice) to know! I have my kids use them as soon as they are introduced (IIRC end of third).  If they don't need them to solve a series of problems I just have them model how to use it with one example and then let them continue without using the bar model.  I do this because I want them to be familiar with them when the problems become more difficult and the bar modeling becomes more useful.  I also do this, even knowing that algebra is in the future, because it helps them look at problems differently - using reason in addition to mathematical calculations or manipulations.

[Pegs]

I learnt about bar models from seeing folks help each other out with worked solutions here on the boards. They've been really useful to me around the pre-algebra and intro to Algebra levels. For quite a few problems I've encountered, they've led to the quickest, easiest solution.

[Farrar]

I have mixed feelings about them. They don't come naturally to me - I'd much rather use variables. In the simple problems, they're almost a hindrance because they seem like a pointless extra step. For really complex problems of the sort that Singapore CWP or Process Skills has in their 5th or 6th grade books I don't think most kids can solve without them (I'm sure there are a few truly gifted kids who just "see" the answer, but I think that's rather rare) unless they're going to solve them algebraically. The question I have is not whether the bar diagram method is necessary but really whether it's necessary that elementary kids be able to solve such truly complex multi-step problems. I have to say that I don't really know. A lot of them will just be much easier in a few years once they can solve with algebra. I'd almost rather more time be given in algebra to helping kids learn to structure and solve such problems. On the other hand, being able to see the math in a different way is really useful as well - both leading into algebra and just for complex math problem solving in general. And sometimes the solution is much easier with a diagram than with variables. It's nice to be able to find the most elegant solution. But I've seen one of my ds really struggle with them and it seems silly to hold him back when he can do the math and can solve more straightforward problems just fine.

[fdrinca]

My son resists the easy bar models, we keep using them. As problems become more complicated, being able to use a bar model is a big tool in his math toolbox. 

 

While I like the ease of a bar graph, the act of drawing a picture for *any* word problem is so helpful in correctly identifying and solving the problem. 

 

The easy bar model problems are there to practice the skill, not to help in solving a difficult problem. I always point out to my kids that when learning new concepts, the arithmetic difficulty of the problems becomes easier. The challenge isn't remembering to carry or borrow, but in learning how decimals work, for example.