I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

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Tag Archives: understanding based teaching

Singapore Math is Thinking Math

Singapore Math is popular because it gives us tools to help with thinking.I’ve been hearing about Singapore Math for years now. Every time I investigate, it just looks like it’s based on pictures.

In some senses, this is true.

It goes deeper than that, though. This “picture math” gives students freedom. It allows them to use paper as working memory!

In my classes, I encourage students to use tons of paper for pictures and math sketching. A professor of mine used to say, “You have to get your hands dirty.” Thinking inside your head is not enough.

Yes, some people do it. And some people are very good at it. But for the vast majority of us, to keep all the thinking inside our head just doesn’t work.

And that’s why Singapore Math (the thinking math) is so cool.

The Standards Require Thinking

I attended a presentation last night hosted by my local school district. They’re moving to Singapore Math to better align with the new Texas state standards (TEKS). Like the Common Core State Standards (CCSS), the new Texas standards ask that students be able to think.

It’s not enough to calculate based on algorithms anymore.

But thinking is hard. And it’s even harder to teach. Especially if the teachers and parents were never taught to think about math when they were young.

Singapore math, or picture math, gives teachers and students a tool to articulate and demonstrate thinking.

More than Just Pictures

Also included in the Singapore Math method is basic numeracy practice. Instead of teaching children rote memorization and algorithms, they encourage playing with numbers.

They call them “number bonds.” It’s decomposing and recomposing numbers in all sorts of beautiful ways.

Like many teachers already do with “number talks,” number bonds encourage flexible thinking.

For example, you can think of adding 8 and 5 in these two ways:

8 + 5
8 + (2 + 3)
10 + 3

8 + 5
(3 + 5) + 5
3 + 10

Of course, there’re many more ways to do this. Singapore math encourages students, and teachers, to do this more – and often!

The Basis of Algebra

The Singapore Math number bonds is a brilliant way to prepare students for Algebra 1, Algebra 2 and College Algebra. And the picture math gets them prepared to tackle any variety of word problem.

The numeracy play allows students to see the algebraic properties at work with regular numbers. Which leads to more comfort and better understanding of algebraic manipulations later.

And the picture math gives them the confidence and perseverance to keep trying new and novel ways to solve problems. Even when they don’t have an example in the book that matches it.

Possible Issues

You might’ve seen the Facebook meme about a crazy subtraction method. This was in an effort to bash the Common Core State Standards, not the new Texas TEKS. But I fear something like this might happen for us with Singapore Math.

In the presentation last night, the teacher showed the decomposition of the problem 52 – 4 as 40 + 12 – 4.

One of the parents asked, “How do you know to change 52 into 40 + 12?” The teacher didn’t explain that 40 + 12 was only one way of decomposing 52 to make this work. That many others were possible.

Hopefully the teacher’s explanation would be clearer to a child. But I worry that teachers won’t get that 30 + 22 would also have worked. Or 50 + 2, then 48 + 2 + 2.

And there’s the problems with the pictures. Again, graphical representation of thinking comes in many forms. My pictures weren’t like the teacher’s. Or the parent next to me.

For many teachers, seeing thinking represented in pictures is new. And some might not see the various ways it could be done.

So we still might end up with a set of algorithms for drawing the pictures. And children getting “points counted off” because they drew pictures wrong.

I certainly hope this doesn’t happen. Especially because I think that this is one of the best ways to teach math.

But we do have to look for it. And encourage teachers to expand their own thinking when we see it.

How about you?

Have you seen Singapore Math? Do you use pictures and number bonds in your class? Share your thoughts in the comments.

And don’t forget to share on Pinterest, Twitter and Facebook!

2 Responses to Singapore Math is Thinking Math

  1. Great post Bon. I can help with this one:
    “52 – 4 as 40 + 12 – 4. One of the parents asked, “How do you know to change 52 into 40 + 12?””

    The teacher/presenter should have shown that when using a place value chart, a student:
    -Starts with 5 tens and 2 ones.
    -Moves a ten from the tens column and regroups it as ten ones, leaving 4 tens and 12 ones on the place value mat.
    -Now they can subtract 4 ones from 12 ones.
    -(Or borrow, as I bet the parent thinks in their head as heir doing subtraction.)

    The manipulatives guide students to the standard algorithm most parents already know! It’s actually quite intuitive for first graders once they work with concrete objects.

    Other methods of decomposing come later.

  2. Thanks so much! That totally makes sense. And parents would understand it (especially when the “borrow” word is used).

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3 Responses to Teaching Processes Destroys a Growth Mindset

  1. Very well said. I just covered solving equations and inequalities, and the whole time the process was thought about in terms of figuring out what was happening to the variable and what should be done to get it by itself.

    What frustrated me to no end was to hear students recite rules related to graphing in equalities on a number line that did not work when the variable is on the right.

    Going to share this article with my department as we have been focusing on transitioning students to a growth mindset.


    • Chris – it sounds like you are doing sort of what I was doing! I did a short video of it here.

      When they start spouting rules senselessly just kills me!

      I look forward to hearing how your transition goes – please share anything, as I’m in that transition too.

  2. This is actually something I’ve been struggling with lately…
    Perhaps a year ago, I would have responded to this post with an enthusiastic “yes”, but right now, a year into grad school, I’m a little less sure.

    I’ve always learned by intuition, and rarely proceed with something until I “understand” it, even if I “know the process”, but lately I’ve seen that sometimes I just need work through something blindly, before going back and understanding what’s “really” going on.

    A particular example is something called “path induction” (or “identity elimination”) in type theory–it’s a notoriously difficult concept (amongst type theorists, anyway), and I beat my head against it for over a month. I then worked through about a dozen exercises and simple proofs blindly using the rule, and then went back to try to understand what it meant, and suddenly, it was almost completely clear.

    Certainly, at school, process is (devastatingly) over-emphasized, but I’m less sure that teaching process is necessarily bad–it has routinely helped me gain intuition for concepts I’m struggling with.

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One Response to Teaching Intuition in Math

  1. I think this has always been my problem with math. I was never taught to use my gut with it, and that’s what I do with just about everything. As an adult I’ve learned, what I like to call, work arounds that make math easier for me, and when I think about them they are all gut things that I do.

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2 Responses to Understanding Math – Let Kids Fake It

  1. Well. I sure wish someone would have realized that I was faking it in high school algebra. I’ve carried that confusion and pain with me all these years!

    Thanks for writing a refreshing and HELPFUL post about it.

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3 Responses to Curiosity Based Learning with 100 Floors iPhone App

  1. Fascinating article. I would like to see my students play with math problems just like they play their video games. I want them to see that they can learn just as much or more from doing something that doesn’t work than from getting it right the first time.

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