4 Phases for Students to Work Through When Building a More Statistical Mindset with Data

What does it really mean for students to think statistically?

And no, it isn't that they have to take a statistics class. ;)

In many of our K–12 classrooms, students read graphs, calculate averages, identify patterns, and work with data in all sorts of other ways. But developing a statistical mindset goes beyond being able to execute these individual skills. It requires students to recognize and embrace variability, reason with data, and make informed judgments based on evidence.

One helpful way to think about how this develops comes from research on students' statistical thinking. Mooney (2002), for example, developed a framework for characterizing middle school students' statistical thinking that illustrates something particularly useful for us as K-12 educators: students don't simply "get" statistical thinking all at once. Their thinking develops and becomes more sophisticated over time.

Building from this idea and others' great work in statistical education, we can think about four phases of thinking that we want students to work through as they become more sophisticated users of data, across all subjects and grade levels. 

Phase 1: Describing Data at Face Value

At an early phase, students tend to focus on individual values or surface features of the data.

They might read values directly from a graph, identify the highest or lowest point, or describe what they physically see in it (e.g., color, shapes).

For example:  

• "The tallest bar is 10." 

• “Apples are the red bar.” 

There is nothing wrong with this observation! Accurately identifying what is present in the data is an important skill. But if this is where their thinking stops, students haven't yet begun considering patterns, relationships, or variability within the dataset. In other words, they are just describing what they see, not making sense of what it could mean. This is why we need (even with our youngest learners) to encourage our students to go a bit deeper in their data observations.

An instructional move to try: Once students have described what they see, encourage them to look beyond individual data points:

• What do you notice happening across all the data?
• Do you see a repeating pattern or grouping across all the data?

The goal isn't to skip over describing the data. It is to help students use those observations as a starting place for deeper thinking.

Phase 2: Recognizing Patterns and Trends

As students' thinking progresses, they begin to move beyond individual values and notice patterns across the data.

They might say: 

• “Many of us like apples, oranges, and strawberries.”

• “Most of the values are between 65 and 85.”

• “The data is increasing over time.” 

This is an important shift because students are beginning to think about the dataset as a whole rather than as a collection of isolated points.

Their descriptions, however, may still be fairly general or vague. They may recognize that something is happening without yet being able to describe it precisely or point to the evidence that supports what they see.

An instructional move to try: Instead of confirming the pattern for students, ask them to be more specific:

• What evidence in the data supports the pattern or feature you're describing?
• How do you know it's increasing?

We're starting to move from "I see a ____" toward "Here is the evidence for what I see." That is an important step toward reasoning with data. 

Phase 3: Considering Variability

This is where statistical thinking gets particularly interesting.

Students begin to recognize that data points vary, that not every value fits neatly into a pattern, and—perhaps most importantly—that this variability isn't necessarily a problem with the data. Variability is a natural characteristic of data.

Students might say: 

• “Most values are around 6, but some are higher or lower.”

• “There’s a lot of spread in these data.” 

That may sound like a relatively small shift in language, but it represents an important shift in thinking. Students are no longer looking only for the pattern; they are beginning to pay attention to how the data vary around that pattern.

And this can be hard! 

We spend a lot of time in school teaching students to find the answer, identify the pattern, calculate the average, etc. Statistical thinking asks them to hold onto the pattern and the variability at the same time to determine a takeaway.

An instructional move to try: When students identify a pattern, don't stop there. Ask: 

• How much variability do we see around that pattern?

• Are there data points that don't seem to fit that pattern?

• Does the variability change how we think about the pattern? 

Embracing variability is one of the most challenging—and most important—parts of building a statistical mindset. We dig into this idea further in our Data Literacy 101 article, Why is Variability Worth the Teaching Challenge?

Phase 4: Reasoning with Data to Make Informed Judgments

As students' statistical thinking becomes more sophisticated, they begin putting these pieces together.

They aren't simply identifying a pattern or acknowledging that variability exists. They are considering both as they use the data to make and support a judgment.

For example: "Although the average is higher in Group A, there is also more variability, so we can't be as confident that all plants in Group A grew taller."

Notice how much is happening in that statement. The student has identified a difference between the groups, considered the variability within the data, and used both to qualify a conclusion from the data.

This is the kind of reasoning we ultimately want students to be able to do with data: use evidence to support conclusions while also recognizing what the evidence does—and doesn't—allow them to say.

An instructional move to try: Give students opportunities to compare datasets, justify their claims with evidence, and—importantly—consider the limitations of the conclusions they draw.

Ask questions such as: 

• What evidence supports your conclusion?

• How does the variability affect what you can say?

• What can't you conclude from these data? 

That last question can be particularly powerful. Becoming statistically minded isn't just about being able to make a claim from the data you have. It is also about recognizing when the data actually do not support the claim we'd like to make. 

Why Thinking About These Phases Can Help Us Teach

I don't think the value of these phases is in trying to label every student as a "Phase 1" or "Phase 3" statistical thinker in any particular activity. In fact, the same student may reason differently depending on the data, context, and familiarity of the task.

Instead, the phases give us another way to notice the kind of thinking students are doing with data and consider what might help them take the next step.

A student who can accurately describe individual values may need opportunities to look across the dataset for patterns. A student who readily identifies trends may need prompting to consider variability. And a student who sees both patterns and variability may be ready to wrestle with what conclusions the evidence actually supports.

Statistical thinking develops over time, through repeated opportunities to work with data and make increasingly sophisticated sense of what they see. 

What Can We Do in the Classroom?

Fortunately we don't necessarily need entirely new activities to help students develop this kind of thinking. We can often create richer opportunities within the data experiences they're already having.

Use real, messy data. Clean datasets can make it seem as though data always produce an obvious pattern. Real-world data gives students something much more interesting to wrestle with: variability, uncertainty, unexpected values, and patterns that aren't quite so neat.

Ask questions that leave room for reasoning. Rather questions with one right answer, ask questions like: 

• What do you notice?

• What might this mean?

• What evidence supports that?

• How confident are you?

• What can't we say from these data? 

Revisit data over time. As students develop new skills, return to a dataset they've encountered before and ask: What do you see now that you didn't see before?

That can help students—and us—see how their thinking about data is changing.

Make variability visible. Encourage students to look at spread, compare distributions, notice unusual values, and talk about what the variation might mean rather than treating it as something to ignore on the way to finding the pattern. 

Statistical Thinking Can’t Just be in Math Class

Although frameworks for statistical thinking often come from mathematics and statistics education research, the thinking we're describing happens across our classrooms.

In science, students interpret experimental and observational data to make sense of phenomena.

In social studies, they examine demographic data and consider what those data can—and cannot—tell them about people and communities.

When students encounter statistical claims in the news and media, they need to consider the evidence behind those claims, the variability and uncertainty involved, and whether the conclusion being presented is actually supported by the data.

That's part of why we care so much about this at Dataspire. Building a statistical mindset less about preparing students to do statistics, and more about helping them become more thoughtful users of the data they encounter across subjects and beyond school.

For additional research-based perspectives on statistical education, you can explore resources from the American Statistical Association: https://www.amstat.org/ 

Where Is the Thinking Now—and Where Could It Go Next?

Students aren't going to move from reading a value off a graph to sophisticated statistical reasoning in one lesson. Nor should we expect them to.

But we can pay attention to where their thinking is now: 

• Are they describing individual values?

• Are they noticing patterns across the data?

• Are they considering variability around those patterns?

• Are they using all of that evidence to make—and appropriately qualify—a conclusion? 

And then we can ask ourselves a question that is useful well beyond statistical thinking: What opportunity can I give them next that might move their thinking a little further?