What Is Fluency & My Thoughts On TouchMath

Recently, I received an email from a follower asking me about my thoughts on TouchMath®. I hope you’ll stick around while I go off on a little rant about why I hate TouchMath® as I hope to build your math mind as we are on our quest to build the math minds of our students.

Watch the video below or read the transcript.

What is Fluency

Let me take a moment to talk about the background on how children learn mathematics and then I’ll connect it back to TouchMath®. This is a little chart from our state standards about the fluency expectations around addition and subtraction.It starts in kindergarten and works all the way up through fourth grade. As you can see, every grade level has a fluency expectation. And your standards may be a little different than this, but typically most states are around the same idea. It has some kind of fluency component at each grade level. Now, if we look a little bit deeper into it, they are talking about letting kids use objects, drawing pictures, and having strategies along with that fluency expectation.

I want to talk for just a minute about what fluency is. One of the questions I get is, “how many in a minute should kids be getting?” To me, a kid who is fluent is not determined by how many answers they get right on a timed test. That is not fluency to me, the research backs me up, it’s not just my opinion.

When Common Core came about, there were these progression documents. And so I dug a little deeper into what did they mean by “fluent”.Their expectation of what fluent means is kids need to be fast and accurate, it involves a mixture of just knowing some answers, knowing some answers by using patterns and knowing some answers through the use of strategy. So, even if your standard doesn’t specifically say strategies, it’s implied by what they are saying fluency means. Kids need strategies.

Another definition that I’ve used a lot are these three pieces that were put out by Susan Jo Russell in an article in 2000. She said there are really three parts to determining fluency.

Kids do need accuracy. They need to be accurate, they need to be fast and efficient, but they also need to be flexible. Way too many of our kiddos are accurate and efficient, but they are not flexible. So I’m going to use this definition and come back to it again after we talk about what TouchMath® is and talk about if we feel like it helps kids build all three of these pieces or not. Hint, not!

TouchMath® Keeps Kids In The Counting Phases

The other thing that I want to talk about is the Cognitively Guided Instruction (CGI) Progression. I’m a firm believer in Cognitively Guided Instruction. Their research showed us that kids will go through four stages as they start to develop strategies for addition. Those stages are the same for subtraction and multiplication and division. These show up when kids are learning all four of the operations.

The first way is that kids will Direct Model what the problem says. So, if the problem is “Sierra has 4 dollars, she earns 3 more dollars. How much money does she have now?” They would count out 1, 2, 3, 4 fingers and they would count out 1, 2, 3 fingers. Then they have to come back and recount all of that and count every single finger that they put up.

As kids start to progress more and they start to learn more about numbers, they get to a stage called Counting On or in subtraction it’s Counting Back. This is where they can hold one of the numbers in their head and then count on. So they might be able to hold the four in their head and then go 5, 6, 7. To get the 7 as their answer of how much money she has.

Now, the piece that tends to be lacking is we will jump to the next stage and we go straight to the Fact stage. But, if they don’t remember it, their fallback is to go back down to counting on their fingers. That’s why the number one complaint I hear from teachers is that kids are still counting to be able to add and subtract. It’s because if they don’t have it memorized, they fall back to those counting stages.

The in between stage is what they call Derived Facts. This is when a kid can use something they know to help them with something they don’t know. They’re deriving the fact. So, when the problem was 4 plus 3, that might be a kid who says, “well 4 plus 4 is 8, just take 1 away from that and that gives me 7.” Or another kid might say “well if it was 3 plus 3 it would be 6, but it’s 1 more than that.” So Derived Facts are those strategies, those thinking strategies, that we wanna help kids develop.

Now, that I’ve talked about those TouchMath® stages and Susan Jo Russell’s definition of fluency, let’s talk about TouchMath®. With TouchMath® they put a touch point at certain spots on the numbers. So on 5, you see 5 touch points. On 2, there are 2 touch points.

So then when they go to add, they can touch each one of those touch points and count to be able to determine the total. Because there’s 5 touch points, then 2 touch points, they can come back and count each one of those. And that’s what kids will do, they’ll touch each one of those to figure out that the answer is 7. As they get into larger amounts past five, they have these kinds of circles which are a double tap. If it has the circle within a circle, that means you tap it twice in order to tap seven times.

I will give them credit, it does encourage kids to count each set. When beginning addition, they’re counting the 8 things and then they’re counting the 5 added onto that to get their 13. Then they encourage kids to stop touching the first number and work on touching the second number, which is the Counting On stage.

So, if we come back to the CGI progression, TouchMath® keeps kids in that Counting On and Direct Modeling phase. The reason I really dislike TouchMath® is that it doesn’t allow our students to work up into those higher level strategies.

And, according to Susan Jo Russell’s definition of fluency, the only one that it hits is accuracy.

Kids will get the correct answer, but they’re not efficient, they’re still sitting there counting the dots, and they are not flexible

The only way they can solve the problem is by using those touch points. I have seen adults who still use the touch points. TouchMath® even puts it on their website. This is a direct statement I screenshot of their website. Look at the first line.

They say TouchMath® works because it is “based on counting.” Yes, they are counting and they’re adding and subtracting just by counting.

To me, that is not learning addition and subtraction. That is counting. Counting is the foundation that builds our understanding of addition and subtraction, but it’s not where we want kids to stay.

When TouchMath® Works

For the majority of our kids, TouchMath® should not be the place that we start. Where TouchMath® gets it right is if you have kids that just can’t get it.

If you have spent time trying to build their number sense and build their understanding of addition and subtraction and you are at your wits end and you don’t know what else to try, then I’m okay with you trying TouchMath®.

If it were my child who was struggling, I would try anything and everything. My problem is that TouchMath® has become the first thing that we teach, not the last resort for children who are really struggling.

So, I want to really encourage you to work on building kids’ number sense and their understanding of how numbers work together to get them up to that Derived Fact and Fact stage.

If you can get your kids to a Derived Fact stage, they will become more accurate, more efficient and they will have flexibility.

So, I hope this has helped you build your math mind and to evaluate a system that’s been used for a while but may not be the best thing for the majority of our students.