I’m Christina Tondevold, the Recovering Traditionalist. And today, we’re looking at The Key to Developing Young Math Problem Solvers in our quest to build our math minds so we can build the math minds of our students. 

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog.

The Counting on Number Sense course will be opening for registration on April 30th.  Get more information here:  https://buildmathminds.com/counting-on-number-sense 

Without further ado, I’m going to hand it over to my guest this week: Sue Looney.

Hi, I’m Dr. Sue Looney of Looney Math Consulting. Thank you for being here today. Today, we are going to tackle a myth.

MYTH: Young children are not capable of complex problem solving.

This is actually not true. And so today we’re gonna learn why this isn’t true. We’re going to take a look at some of the work and how that builds on a foundation of understanding counting. 

Often, people believe that students can’t start doing story problems until they’ve mastered their basic facts. That we first have to do some skill and drill practice before we can add in the context of a story problem. But it turns out it’s the exact opposite. 

Actually the context of a story helps a child visualize what’s going on and it gives them a purpose for making sense of the mathematics that’s involved. So without context, we might be able to manipulate and play with numbers, but why? What’s the purpose? What is it attached to?

It turns out that children as young as age 3 are able to start solving problems that have to do with addition and subtraction and patterning. Once they understand the cardinal meaning, they understand that when I count a collection (how many objects are there), they’re able to start reasoning about problem solving.

How Counting Links to Problem Solving

I’d like to unpack further now this myth of young children not being able to solve problem solving and how counting is what links to this ability to solve problems.Here’s a story problem that I presented to a preschool student. If you take a moment and look at the context of this problem, you’ll see that what’s required here is the ability to put 3 amounts together. 

Specifically they’re putting together a 2, a 2 and a 1. 

If we think about this from a standards based lens, we might think, ‘oh, this is a 1st grade problem.’ You’re putting together three addends. A child needs to be able to add. But actually, if we understand counting, we can make sense of this situation. 

You can see how interested this child was in figuring this out. So I sit with this child, who is 4.  We have this conversation and they say to me quite clearly, “yes, there were 5.” I say, “how do you know?” They say, “well 2, 2, and 1 make 5.”

As they’re saying that to me, they’re putting up all of their fingers. They’ve got a full handful of 5.Then further, they’re so interested in thinking about putting amounts together. They say, “I want to know what 2, 1, and 5 equals.” 

So they want to know more. They now know and feel powerful that ‘I can use counting to figure out cool things.’ And they know the word ‘equals’, which is interesting information.

Here’s a kindergartner with a task. If we look closely at this task, Buttons for Snowmen, we might think that this is a story about multiplication. We have a story about building 3 snowmen and getting rocks for the eyes and nose. But we don’t explicitly have: ‘there are 2 rocks for eyes and there’s 1 rock for a nose’ or have the word each, which tells us something, right?

We just have a story. We’re having a conversation around a story. We have a child who can solve this with counting.

So in this story, you can see that the child counts…we can see the numbers. They are able to write their numerals. We can see on the top of their hats, 1, 2, 3 – 4, 5, 6 – 7, 8, 9. Then at the bottom, we can also see the rocks for each snowman. 

There’s an awful lot going on in this problem. And in order to solve this, they’re using counting. They’re becoming powerful mathematicians, building on what they know and using drawings. 

I love this example here, because what you can see is this child is not interested in making detailed drawings like the last child. Again, we have a story problem here that’s about putting 3 amounts together.

This four-year-old student knows how to do that by counting. We can see here, first, Max counts 3 cars. And so they go, “Boom, boom, boom.” 3 cars. They don’t even need to draw cars. Dots will do just fine. Max counts 1 car. And then last, he counts 2 cars. They count them all up and decide that there’s 6. 

So using counting and the ability to represent thinking on paper, but a bit abstractly here at four years old. Powerful, complex problem solving

Back to our snowman problem. This student here is in preschool. So they are using their fingers. 

They draw this picture of this hand. I let them draw that out. I see that they’ve kind of highlighted the first 3 fingers and almost scribbled out the other 2 with black. Then they focused on those three. 

So I say, “I see that you’ve drawn this hand here. How many are there?” 

They say, “oh, 9.”

I say, “well, how do you know?”

They show me and you can see that they started the thumb. They do this really cool repeat counting, 1, 2, 3 – 4, 5, 6 – 7, 8, 9. There’s a foundation of multiplication going on here, sitting on the ability to count. 

So we’ve got 3 groups of 3 going on those 3 blue fingers. Really cool.

The last one I want to show you is back to kindergarten. And this is a different problem about how many hats these students have all together. We have Jack and Ann. 

You can see that this child is thinking about tallies and 10 frames. So building on the models that have been used in their instruction, they’re able to take that. Really what we see here is some powerful use of moving between models. 

We’re moving from tallies into a 10 frame, and then filling this 10 frame in in a really interesting way. Taking 5 and then 6, 7, 8, 9, 10, 11, 12, 13.

Different Ways Young Children Count

It’s really interesting how they’re using their tools for counting. We see students that are able to count using drawings, using fingers, using dots as representations of objects. We’ve got tallies. We’ve got an interesting use of 10 frames. We’ve got 3 addends. We’ve got multiplicative thinking…all in 4, 5 and 6-year-old students. 

So when we teach our children to count with deep understanding, they are 100% capable of complex problem solving.

Counting builds Powerful Problem Solvers

Thank you so much to our guest vlogger, Sue.

Now before I jump into my kind of concluding thoughts here, I wanted to share a video of one of my own kids. I loved seeing the strategies and the ways that kids were modeling the problems on paper the way Sue had shown, but it doesn’t have to be on paper.

Here’s a video of my oldest son when he was, I think, let me think about this for a moment. I think he was 4 because we were celebrating the birthday of my third child when he was one. They’re about 3 years apart. So he was around four, four-and-a-half at the time of this video. We had made cupcakes for my one-year-old’s birthday. And I had asked my son how many M&M’s were on the cupcakes. 

Let’s take a listen.

“Each of those cupcakes have 3 M&M’s on them. And we have 5 cupcakes.”

“But then I took 1, 2, 3. That means 1, 2, 3, 4.”

“Only 4 of them have M&M’s now. So how many M&M’s are there total on those 4 cupcakes?”

“1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 12.”

“So how many M&M’s?”

“All 3 makes 12.”

“Good job!”

What I love about that video is it’s a four-year-old solving a multiplication problem. That’s really what he was doing. That problem is 4 x 3. 4 groups of 3. 4 cupcakes with 3 M&M’s on each. As long as a kid can count, they are powerful problem solvers.

Now, many of you have seen my videos about the Cognitively Guided Instruction stages of how kids solve math problems. Just a quick little refresher here: direct modeling and counting.

Counting is the foundation of these two stages. This is where the kids are counting every single part of the problem in direct modeling. That’s what you saw my son do there. In that counting phase for that problem with the cupcakes, a kid would see the group of three and be able to say 3, then 6, then 9, then 12. Or they might have to count one by one some of the ways in between there.

But the counting phase for multiplication is when they’re counting by a certain amount, that they’re seeing those groups there. It still revolves around counting.

Now how all of my work the last many, many years has been on helping teachers move kids out of those two stages by building their number sense and helping kiddos get to the derived fact and fact stages of Cognitively Guided Instruction.

These two stages down here in the bottom, that direct modeling and counting are so, so important and they heavily rely upon kids’ ability to count. And that’s why I’ve teamed up with Sue Looney to bring a brand new course to Build Math Minds.

A New Course from Build Math Minds

Sue’s course, Counting on Number Sense, is for PreK through 1st grade educators. This course will give you an understanding of what it takes to help your students count. Counting seems so easy, but it really isn’t. It’s such an important foundation to build for our kids because everything else we’re gonna be doing around mathematics is built upon that counting foundation. Once kids can count, they are powerful problem solvers.

Registration for that online course is opening up soon. But before it does, we’d like to invite you to a free training that Sue is doing called, The Power of Counting: Three Reasons Why You Need to Focus on Counting in the Early Grades.

I hope to see you there. We’re doing a few different days and times to give you choices on when you can attend. But remember, it’s live. So you’ve got to show up. Come be there live. We will have a recording, but we also offer certificates of attendance if you show up live.

The most important part is, it’s free. It’s a free training we’re doing. So come on over. 

I hope that this video has helped you build your math mind so you could go build the math minds of your students. Have a great day!

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