When two things are related…

…does one cause the other?

Hello all. Welcome to the 188th edition of TEPS Weekly!

A Grade 7 Mathematics teacher shows students a graph comparing the hours they spend studying each week with their test scores. Each dot represents one student.

The teacher asks, “What can we conclude from this graph?”

One student responds, “The more you study, the higher your marks will be.”

Another disagrees. “Not necessarily. My friend studies much longer than I do, but I usually score higher.”

A third student adds, “Maybe students who already understand the topics better are more interested in studying for longer and therefore score higher.”

Which student would you agree with?

The first student's answer seems to match the graph. But does studying longer really cause higher marks? The second student points out an exception, but does one exception make the overall pattern wrong? And could the third student's explanation also be possible?

The students are looking at the same graph but are reaching different conclusions. Does the graph really show that spending more time studying causes students to score higher?

To answer this, we need to understand the difference between correlation and causation.

Correlation and causation

Correlation means that two things are related: when one changes, the other tends to change too. For example, our graph shows that students who study longer generally score higher (as opposed to saying that studying longer causes students to score higher). When one thing increases, and the other also tends to increase, this is called a positive correlation.

But the two things do not always move in the same direction. When one increases while the other tends to decrease, it is called a negative correlation. For example, students who miss more school days may tend to score lower on tests.

Sometimes, there may be no clear relationship at all. For instance, a student's shoe size is unlikely to have any meaningful connection with their Mathematics score.

These graphs help us see how two things are related – but even when we see a clear pattern, we still do not know whether one thing is causing the other.

This is where causation comes in. Causation means that one thing actually produces a change in another. For example, as winter temperatures fall, sweater sales increase.

But does our graph prove that studying longer caused the higher scores?

Remember what the third student said in the classroom discussion. Perhaps students who already understand the topics well are more interested in studying for longer and also score higher.

There could be other explanations too. For example, students who receive more support at home might study for longer and also score higher. Here, support at home could influence both study time and test scores.

When a third factor influences both things we are comparing, it is called a confounding variable. This makes it harder to know whether study time itself caused the higher scores.Notice something important here. The pattern is visible in the graph, but the causes behind it can be invisible. Studying longer might genuinely improve scores, or other factors might explain the relationship. We cannot tell which explanation is correct from the graph alone.

However, this does not mean that studying longer cannot cause higher scores. If it really does improve performance, the relationship would be both correlated and causal. Correlation and causation are not opposites. A correlation can suggest a possible cause, but it cannot prove that cause on its own.

Why is recognising a pattern easier than explaining it?

Finding a pattern is often easier than explaining it because a pattern tells us what happened, while an explanation requires us to think about why it happened.

One of the first skills a student learns in foundational years is to recognise patterns. They know that pushing a door makes it open or that dropping a glass can make it break. In these examples, the action and the result are easy to connect. But this is the “what” of the relationship (or correlation), not why it happens. 

The discussion between the students at the beginning showed this difficulty. Each suggests a different causation, but none has enough information to establish the cause.

Research by developmental psychologist Deanna Kuhn and other researchers has shown that children can find it difficult to consider several possible causes at once. They may also pay more attention to information that supports what they already believe.

For example, a student who strongly believes that studying longer always improves marks may focus on those who studied longer and scored higher. They may overlook students who studied for several hours but still scored poorly.

What does research suggest about teaching this crucial difference?

Helping students distinguish between correlation and causation is an important part of developing critical thinking. In an age where students regularly encounter information through social media and AI, they need to learn to question claims, consider other explanations and check whether the information supports what is being said. These skills are useful across subjects, not just in Mathematics and Science.So, if students find it difficult to consider different explanations, how can you help them decide which explanation is supported by evidence?

One way is to teach students how to make fair comparisons. In 2016, Martin Schwichow and colleagues reviewed 72 studies examining how to understand what fair experiments are and how fair experiments are designed. The review found that demonstrations and practice helped students develop these skills. An earlier study by David Klahr and Milena Nigam involved 112 children in Grades 3 and 4. More children learnt how to design fair experiments through clear, direct instruction than through unguided discovery. Children who learnt the method could also use it to judge other experiments.

Together, these studies suggest an important approach: give students a situation where the conclusion seems obvious, help them notice what is wrong with the comparison, and then explicitly teach them how to improve it.

What does this mean for our classroom?

Let's return to the study-time graph. We know that students who studied longer generally scored higher, but we do not know whether the extra study time caused the difference. The teacher now asks, “How could we check whether studying longer really helps students score higher?”

Students suggest comparing two groups who study for different amounts of time. To explore their idea, the teacher presents an imaginary comparison in which both groups took the same test.

The teacher asks, “Which group scored higher?” 

Students identify Group A. The teacher follows up with, “Can we conclude that Group A scored higher because they studied longer?”

Some students may say yes. Instead of confirming their answer, the teacher asks, “What else was different between the two groups?”

Students may notice that Group A already understood most of the topics before studying, while Group B did not. So, we cannot tell whether Group A's higher scores were due to the extra study time or their existing understanding.

This leads to another question: “If we want to find out whether studying longer makes a difference, what should we keep the same?”

Students might suggest that both groups should begin with similar knowledge, study the same topics and take the same test. The teacher can also explain why students should be assigned to groups fairly, rather than putting all the stronger students together. Having several students in each group would make the results more reliable. This is called the Control of Variables Strategy. It means changing the one thing we want to test while keeping other important conditions as similar as possible. In this case, study time would be the main difference between the groups, making the comparison fairer.

However, even a fairer comparison does not guarantee that the results will prove the cause. We still need to consider whether the difference appears consistently across students and whether other factors could have affected the results. Notice how the discussion has developed. Students began by identifying a pattern in the graph. They then considered other explanations and learnt how to improve a comparison to test one of them.

They are no longer simply accepting or rejecting an explanation. They are learning how to investigate it. This process can become a simple routine for other lessons. You can guide students through three questions:

What about teaching this in other subjects?

The same thinking is useful when students read an article, examine a historical event or come across a claim in everyday life.

In English, for example, you can help students understand how small changes in wording can change what a sentence claims.

Imagine a teacher showing students two headlines:

The teacher asks, “Are these two headlines saying the same thing?”

Some students may say yes. Both connect reading more books with stronger vocabulary. But the teacher asks them to look carefully at two phrases: “tend to have” and “improves”.

Do these phrases make the same claim? Rather than answering immediately, the teacher gives students a short text from which the headlines were written.

After reading, the teacher asks, “What did the survey actually find?”

Students may notice that those who read more books generally scored higher on the vocabulary quiz. But does this mean that reading more books caused the higher scores? There could be other explanations. Perhaps students with stronger vocabulary already enjoy reading more. Perhaps access to books at home also makes a difference.

The teacher then returns to the headlines and asks, “Which one is better supported by the survey? What makes you think so?”

Now the difference becomes clearer. “Tend to have” describes a relationship, or correlation, between reading habits and vocabulary scores. “Improves” makes a claim about causation – that reading more books leads to stronger vocabulary. The survey supports the first claim but does not provide enough information to establish the second.

The teacher can ask one final question: “What else would we need to find out before making the second claim?”

Through this activity, students learn to recognise the difference between correlation and causation in what they read and check whether the information supports the claim being made.

The approach can also be adapted to different learning levels. For students who are new to data handling, you can begin with pictures, classroom observations or simple tables. As students become more confident, they can use graphs, consider different explanations and suggest ways to make comparisons fairer.

Across these examples, students are learning something important: noticing a pattern, explaining it and testing the explanation are different steps. An explanation that sounds reasonable still needs to be tested.

The next time students interpret a graph, read a headline or explain why something happened, help them consider other possibilities and ask: “What would we need to know to check whether the explanation is accurate?”

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Edition: 5.43