Computational thinking (CT)

CT strategies

The following section is inspired by the principles of computational thinking, an approach to problem-solving that includes decomposing complex problems, recognizing patterns, and designing algorithms to solve them. These strategies are fundamental in both mathematics and computer science.

This perspective builds on Jeannette Wing’s seminal definition of computational thinking, which she describes in terms of three core pillars: abstraction, automation, and analysis. In this context, we place special emphasis on functional thinking as part of abstraction and automation, along with the importance of testing and proving correctness as part of analysis.

For more details, see:

Wing, Jeannette M. “Computational thinking.” Communications of the ACM 49.3 (2006): 33-35

Question 1

Which of the following best shows what abstraction means when solving a problem?

Splitting a big task into smaller steps.

Finding patterns in data to make predictions.

Focusing only on the important parts of a problem and ignoring the rest.

Writing code to do a task over and over again.

Testing different ways to solve the same problem.

Question 2

What does decomposition mean to you? Can you give an example of how you would break down a complex problem?

Question 3

How often do you engage in decomposition (breaking down problems)?

Never

Rarely

Sometimes

Often

Always

Question 4

Why is abstraction useful when writing a math solution or a piece of code?

It guarantees your answer is correct.

It makes your work faster.

It helps you understand and reuse your solution more easily.

It means you don’t need to check your work.

It works for every problem without changes.

Question 5

What is the main idea of automation in computational thinking?

Removing all human effort from tasks.

Building machines that think like humans.

Creating clear steps (algorithms) that a computer can follow to do a task.

Making new problems for people to solve.

Replacing creativity with machines.

Question 6

When should you consider automating a task in math or programming?

If one person can do it by hand.

If it happens often and mistakes are easy to make.

If it involves tricky moral questions.

If the result looks cool.

If it takes only a few lines of code.

Question 7

In computational thinking, what does analysis mean?

Trying random ideas until something works.

Carefully studying different solutions or data to see what works best.

Memorizing answers to common problems.

Only caring about getting the right answer.

Letting AI do all the thinking.

Question 8

You wrote two different programs to solve the same problem. What’s the best way to figure out which one is better?

Ask a friend which one they like more.

Choose the one you finished writing faster.

Test both programs with different inputs, measure how fast they run, how much memory they use, and how reliably they give correct results.

Pick the one with fewer lines of code.

Choose the one that was more fun to write.

Functional thinking

This section explores functional thinking, a key component of the abstraction pillar in computational thinking. Functional thinking involves understanding and solving problems by modeling them as functions—clear, rule-based relationships between inputs and outputs.

In mathematics, functional thinking builds on algebraic thinking but places greater emphasis on how values are transformed. While algebraic thinking focuses on symbolic representations and structures, functional thinking highlights how inputs are systematically mapped to outputs through well-defined operations.

In programming, functional thinking promotes writing code that is modular, predictable, and reusable. It typically involves the use of functions, variables, higher-order functions, and recursion to express solutions in a clear and structured manner.

The following section will assess students’ prior knowledge and intuitive understanding of these concepts.

Question 1

What topics or concepts do you currently struggle with in mathematics, if any?

Question 2

What topics or concepts do you currently struggle with in computer science, if any?

Question 3

In your own words, describe what a variable is.

Question 4

In your own words, describe what a function is.

Question 5

In your own words, describe what a higher-order function is.

Question 6

What does recursion mean to you? Can you give an example or describe how it works?

Question 7

Do you see any similarities between mathematics and computer science? If so, what are they?

Question 8

Has learning programming helped you understand mathematics better? Why or why not?

Question 9

Think about your best experiences learning programming. What made them helpful or enjoyable for you? How do you learn programming most effectively?

Question 10

If there is a concept in math or computer science that still feels difficult, what strategies do you use to try to understand it better?

Multiple-Choice Questions

Question 1

What is a function?

A loop that repeats actions

A named block of code that performs a task and can be reused

A value that never changes

A command to stop the program

An error message returned by the program

Question 2

What is a higher-order function?

A function that returns a variable

A function that runs faster than others

A function that takes another function as input or returns one

A recursive function

A function that only works inside loops

Question 3

What does it mean for a function to be recursive?

It only works in loops

It calls itself within its function body

It contains a syntax error

It uses variables repeatedly

It runs continuously forever

Question 4

Which of the following is likely to be a higher-order function?

const x = 5;

console.log(“Hello”);

setTimeout(sayHello, 1000);

if (true) { return 5; }

let result = x + y;

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