What Is Computational Thinking, and What Can Puzzles Teach?

In March 2006, the computer scientist Jeannette Wing published a three-page viewpoint in Communications of the ACM (Vol. 49, No. 3) called “Computational Thinking”. Its central claim was bold: “Computational thinking is a fundamental skill for everyone, not just for computer scientists.” She went further. “To reading, writing, and arithmetic, we should add computational thinking to every child’s analytical ability.” (PDF)

Twenty years later the phrase is in school curricula around the world, and it often reaches parents without much explanation. Does it mean learning to code? Being good with computers? In this post I read what Wing actually wrote, look at how Japan’s elementary schools define their version of the idea, and then try to separate what puzzles can build from what they cannot.

What Wing meant

Wing’s essay is short and worth reading in full. A few lines carry most of the weight.

She defines computational thinking as “solving problems, designing systems, and understanding human behavior, by drawing on the concepts fundamental to computer science.” Among the tools she lists are decomposition, breaking a large task into parts, and abstraction, keeping what matters about a problem and setting the rest aside.

She is also clear about what it is not. The first characteristic on her list is “Conceptualizing, not programming.” Thinking like a computer scientist, she writes, “means more than being able to program a computer.” And it is “a way humans, not computers, think.” The goal is not to make children think like machines. It is to give them a way of attacking problems.

Japan’s version: programming thinking

Japan made programming education part of elementary school with the national curriculum that took full effect in the 2020 school year. The Ministry of Education’s guide for teachers, the Elementary School Programming Education Guide, Third Edition (February 2020, in Japanese), uses the term puroguramingu-teki shikō, roughly “programming thinking”. Quoting an expert panel, it describes it as the ability to think logically about which combination of actions is needed to achieve what you intend, how to combine the symbols that stand for each action, and how to improve that combination to get closer to what you intended.

Read slowly, the sentence has four parts:

1. You have an intention, something you want to happen.
2. You break it down into a combination of single actions.
3. You turn each action into a symbol, a command, and combine them.
4. If it does not work, you improve the combination until it does.

The guide’s example is drawing an equilateral triangle on a computer. There is usually no “draw a triangle” command, so you combine “move forward 100” and “turn left 120 degrees” and repeat them three times. Change the angle and you can draw a hexagon.

The guide is direct about one thing. Children may well pick up a programming language along the way, but that is not the aim. It also says something I find important about trial and error. Children should not change commands on a whim or by guessing. When something fails, they should think about where it went wrong, fix it and check the result.

I think that last point is the heart of it. Running something, seeing it fail and changing things at random looks similar from the outside, but it is a different activity. Predict, compare the result with the prediction, look for the cause of the gap. That loop is what “thinking logically” means here.

Japan’s term is narrower than Wing’s. As I understand it, it focuses on the part a primary school can teach: putting actions in order, combining them and fixing them.

What puzzles can build

So can puzzles build this kind of thinking? I believe the answer splits cleanly into what they can and what they cannot.

They can build a sense of order. Adding 2 and then tripling is not the same as tripling and then adding 2. What you combine matters, and so does the sequence. That is parts 2 and 3 of the definition.

They can build the habit of predicting before running. A well-made puzzle cannot be solved by guessing. Reading the board is faster than poking at it, so children start to form predictions on their own.

They can build the habit of looking for causes. When a puzzle fails, the reason is usually clear. Where did it go wrong, and why? That is the loop the guide cares about.

And they can build a taste for shorter solutions. Not only does it work, but could it work with fewer steps? That is the “improve” at the end of the definition.

What puzzles cannot build

Some things lie outside any puzzle.

The first is intention. In a puzzle, the goal is set by the puzzle. The very first part of the definition, “what you intend”, is never the child’s own. Deciding what to make is better practised with an open tool like Scratch, or with paper, scissors and glue.

The second is the experience of making a real computer do something. The Japanese guide accepts that some teaching can happen without computers, but it also says it is not desirable for children to go through programming education barely touching one. A puzzle game does not replace that.

Then there are problems without a single answer, and building things with other people. A puzzle is practice inside a small world with fixed rules. That practice is useful, but it does not cover everything.

Something to try at home

You do not need special equipment. Writing instructions is enough.

Ask a child to write the steps for brushing teeth, and then follow them exactly, doing only what is written. If the steps say “put toothpaste on the brush” but never say “open the cap”, you cannot open the cap. To get an intention across to someone who does only what they are told, the child has to break the task into small actions and put them in order.

When it fails, look together at where it stopped, and rewrite. That is the whole cycle from the guide, done in a bathroom.

Where Math Gates fits

Math Gates is a circuit puzzle game I make. You place gates that change a number and mirrors that turn its path 90 degrees on the empty cells of a board, then press Run. A bit carrying a number travels in a straight line. The port at the end accepts only values that meet its condition.

Because the bit only moves straight, the order in which it meets the gates depends on where you put them and how the mirrors face. In the guide’s terms, gates and mirrors are the symbols and their placement is the combination. As soon as you place a piece, the bit’s path is drawn as a dotted line, so you can check your prediction before you run. When a run fails, it stops with a reason, such as “It hits a wall. Bend it with a mirror”, or a line showing the value the bit arrived with next to the value the port wanted. Stars depend on how many gates you used, and the minimum earns three. The minimum is not shown in advance. After you clear a puzzle, the game only tells you “It can be done with fewer gates”, so there is always a reason to improve.

The limits above apply to Math Gates as well. The goal belongs to the puzzle, and children do not build things of their own design. I would describe it as practice for ordering, combining and fixing.

There are 140 puzzles across seven worlds, from addition and subtraction through fractions and squares to true and false logic. It is aimed at ages 8 and up. It is free to play with ads between puzzles, and a one-time purchase removes the ads.

For more on why the order of steps changes the answer, see Why the Order of Operations Matters. For how Math Gates compares with Scratch and other options, see Math Gates vs Other Math Puzzle Games, Coding Games and Worksheets.

Computational thinking does not need a computer to grow, but puzzles alone will not grow all of it. Order and improvement can come from puzzles. Intention and expression need a blank page. In my view, children are best served by having both.