Fake News: Why patterns aren’t always what they seem

What does a psychology experiment from the 1960s have to do with maths?

A fascinating study about people's beliefs, and what they hold to be true, has important implications for how we teach one of the biggest concepts in maths: patterns.

Let me tell you about it-

Wason's 2-4-6 study

In 1960, psychologist Peter Wason ran one of the first experiments on confirmation bias. In the study, participants were asked to identify a rule applying to triples of numbers:

2-4-6 fits a rule. What other sets of triples might also work?

Participants were told that 2-4-6 satisfies the rule, and then asked: What other sets of triples might also satisfy the rule?

Importantly, for each guess, they were given feedback on whether their triple was correct in fitting the rule or incorrect.

Take a moment to think about what's going on:

  • What do you think might satisfy this rule?
  • Write down some examples.

If you came up with triples like, 4-8-12, 22-24-26 or 30-34-38, you'd be correct. Yet, here's the catch: the rule has nothing to do with even numbers.

When you only search for examples that fit your hypothesis (i.e. even numbers), finding out that these do in fact fit the rule will reinforce your hypothesis. In other words, the feedback you receive will confirm your existing beliefs, and won't tell you anything new.

Indeed, in his research, Wason found that very few participants tested out triples that might disprove their hypothesis.

Think about: what triples of numbers do you think don't satisfy the rule?

[Want a spoiler? See below!]

What Wason's research means for learning maths (& thinking about patterns)

Wason's study showed how we are susceptible to confirmation bias, i.e. the tendency we have to embrace information that supports our beliefs and to reject information that contradicts them.

Our prior experience can colour what we see – even in maths!

Patterns can help us to find connections. Patterns can also mislead.

So often, maths is presented as definitive, black and white, unquestionable. Through this lens, students learn that maths has set rules, definitions and processes, with patterns that are valuable for finding connections – and can be wholeheartedly relied on.

Yet, even in maths, things aren't always what they seem. The 2-4-6 rule shows us that patterns (or, the patterns we think we see) can be misleading.

By thinking critically about information that's presented – numbers, problems, patterns – students can start to see maths in a new light.

Dig Deeper: Help your students see patterns differently

Try out Wason's experiment with your students. What do you notice about their responses?

Run the experiment a 2nd time, but with a different rule. What do you notice this time?


The rule in Wason's study is: three numbers that are increasing in size.

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