Computational Thinking

Transparent head silhouette with interlocking gold and silver gears inside representing brain function

Connecting Numeracy and CT: The Structure was Always There – Part 3
Transparent head silhouette with interlocking gold and silver gears inside representing brain function

In the last two posts (Part 1 and Part 2), we looked at what fluency actually is and the three structures that sit underneath it. In this post, I want to make a connection that might surprise you.

Those same three structures — place value, properties of operations, and equivalence — are also at the heart of computational thinking.

I know. Stay with me.

What is Computational Thinking, Actually

Computational thinking isn’t about coding. It’s about a particular way of approaching problems — one that computer scientists and mathematicians have always shared. It has four moves:

  • Decomposition — breaking a complex problem into smaller, manageable parts
  • Pattern recognition — noticing what stays the same across different contexts
  • Abstraction — stripping away surface detail to see the underlying structure
  • Logical sequencing — ordering steps where each one depends on the one before

Sound familiar? It should. When a student solves 27 × 4 by breaking it into

20×420\times 4

and

7×47 \times 4

they are decomposing. When they notice that the same move works with 27 × ¼, they are recognizing a pattern across abstractions. When they express that as a(b + c) = ab + ac, they have abstracted. These aren’t separate skills layered on top of mathematics. They are mathematics — the structural kind.

Where Numeracy Fits

Numeracy is what happens when a student can take those structures into the world and use them confidently. Not just in a math class, on a familiar problem type, with a procedure they’ve practiced. But in a grocery store, a spreadsheet, a situation they’ve never seen before.

That flexibility — the ability to deploy structure in unfamiliar contexts — is what separates a student who has memorized math from a student who understands it.

So fluency, numeracy, and computational thinking aren’t three different goals pulling in different directions. They’re three expressions of the same underlying capacity: the ability to reason from structure.

What this Means for Teaching

If the structures are the through-line, then the question worth asking about any lesson, any task, any resource is: does this make the structure visible?

Not just — is it a good activity? Not just — will students enjoy it? But: will students walk away having experienced something about how numbers behave that they can carry forward? Will they be able to use that understanding the next time they encounter something unfamiliar?

That’s the goal. Not fluency for its own sake. Not computational thinking as a trendy add-on. But students who see the structure — in numbers, in patterns, in problems they’ve never met before — and know what to do with it.

And when those students finish a challenging task and they tell you they want to do more — because somewhere along the way, they started asking “What if…?”, run with it. They’re posing rich questions and ideas to explore because they’re curious. Many of their ideas will likely involve some mathematical modeling. Another huge win.

So, the end of the lesson is not, necessarily, the end of a lesson. But it is the beginning of a mathematician.

Connecting Numeracy and CT: The Structure was Always There – Part 1

When students compute, are they executing steps or reasoning from relationships? Most of us were taught the former. But the latter is where mathematical power lives.

Feel the Structure

We all want our students to become fluent with facts. There are many ways we can try to get them there. Some focus on strategy development and building mathematical relationships. Others focus on speed and memorization. One way builds confidence and connections. The other creates anxiety.

To build fluency, we need to understand what it is.

If fluency is represented by this walnut.

When students are able to apply strategies to multiple contexts to solve problems, they are fluent. They are also working their way toward numeracy: having the confidence to use basic maths at work and in everyday life.

Let’s look at some ways to solve 27 x 4:

What’s the underlying structure of each? They all break the factors into friendlier numbers and multiply, then put them back together. Decomposing and Composing. All with the underlying structure of the Distributive Property. One uses the Place Value structure as well (top left). Another also uses Equivalence as a structure (bottom left). But all use the structure of distributive property. Naming the property isn’t something students in grades 3 -5 need to focus on. They just need to understand what’s happing and apply it.

Sometimes teachers go with timed tests rather than focusing on strategies because they think that the strategies are replaced by fluency. It’s not really the strategies, though. It’s the underlying structure of these strategies. And fluency doesn’t replace the structures, it compresses them.

In my next post, I’ll discuss the three big structures that encompass all of K-5 mathematics.