How to Get Elementary Students to Explain Their Math Thinking

Below is adapted from the video.  If you want the full context PLUS all the visuals I shared, watch the video.

Welcome fellow Recovering Traditionalists!!

Have you ever asked a student, “How’d you get that?” and gotten a shrug? Or the classic, “I just knew”?

We’ve all been there. And here’s the thing: it’s not that first question that decides whether we actually get kids to explain their thinking. It’s what we ask NEXT.

So let’s build our math minds around the questions that get kids to actually explain their math thinking.

Questioning our Patterns of Questioning

This comes from an NCTM article called Questioning our Patterns of Questioning by Beth Herbel-Eisenmann and M. Lynn Breyfogle, which builds on the work of researcher Terry Wood. Their big point is this: the first question we ask does matter, but what happens AFTER it can matter even more.

They describe two patterns of questioning.

Pattern #1: Funneling

A student gets stuck, and we ask a string of smaller and smaller questions that basically walk them straight into the answer. We funnel them directly to it.

It feels helpful. But we’re the one doing the thinking. The student is just filling in the blanks.

Pattern #2: Focusing

A student gets stuck, and instead of leading them, we ask about what THEY are thinking, and then help them make that thinking clear for everyone else.

In focusing, the student is the one doing the thinking.

Funneling feels like good teaching. When we’re doing it, it feels like we’re getting kids to the answer and getting them to explain things. But really, we’re the ones asking all the questions, and we’re leading them (funneling them), often to a particular strategy. Usually OUR strategy.

Now that so many of us are working hard to ask kids to explain their thinking, it’s easy to still be listening for an answer instead of an explanation. A kid gives an answer, we say “good,” and we move on.

Make sure you’ve given them something worth explaining

Before we even get to the questions, we have to start with an issue that happens more often than we think.

If you’re a 5th grade teacher and you ask a kid what 5 + 9 is, they should just know that. No explanation needed. So if we want kids explaining their thinking, we need a problem that requires them to actually think through something.

The examples in the article come from an 8th grade lesson, but these patterns of questioning show up no matter what grade you work with. Even kindergarten. So let’s look at what each pattern sounds like with elementary kiddos.

Example 1: 38 + 25

Let’s say the class has figured out 38 + 25. Everybody agrees it’s 63. We’ve talked about it. But now we want to hear HOW they got it.

So we ask a student, “How did you get 63?” And they shrug. “I don’t know.” A very typical response.

What funneling sounds like

We feel really good about that. But all they were sharing was answers and using OUR strategy, the teacher’s strategy. We still have no idea how they got 63 the first time.

What focusing sounds like

We still ask, “How’d you get 63?” And when they say, “I just knew it,” our follow-up is different:

Now they’re explaining how THEY got it. And once they’re done, we hand it to the rest of the class: “Who can say that in their own words?” Not just repeating it back, but explaining it. And as that student explains, we can model it on an open number line so everyone can see the thinking.

Example 2: A dot image in K–1

Focusing matters even with something we think is simple and straightforward, like a dot image in kindergarten or first grade. We flash the image, kids figure out how many, and now we want them to explain how they saw it.

Funneling

How many were on top? How many on the bottom? So 3 and 4 is…?

That is VERY funneling.

Focusing

How many? What did you notice? How did you see it? Did anyone see it a different way?

It’s not about asking MORE questions

Focusing isn’t about asking more and more questions. It’s about who’s doing the thinking behind those questions.

Here’s a quick check: if you have to think really hard about what to put into your question, you’re probably the one doing the thinking. Focusing questions are a little more open and ask the students to do the thinking.

But not TOO open. We’re still focused on the math. When a question is too wide open, that’s when kids can shut down.

How to turn a funneling question into a focusing question

When a kid is stuck, ask what they’re thinking. Here are some go-to follow-ups:

• What do you notice?
• What do you know about this problem?
• Can you tell me more about what you have right here?
• Restate what they said and hand it back to them.
• Who can say what she did in their own words?
• Do you agree? Do you disagree?

Try this: listen to yourself

If you’re wondering how much you funnel versus focus, here’s something quick to try. The next time you do a number talk or a number string, set up your phone and record it.

Then listen back, and just listen to your questions. Are they basically fill-in-the-blank questions? Or are you helping kids focus on the mathematics and really digging out their thinking?

That second one is the goal.

Want to go deeper?

I recently did a round table with Sarah Schaefer from Mathodology all about purposeful questioning. If you want to keep learning about this, you can find it here: https://www.mathodology.com/videos/purposeful-questioning-guiding-student-thinking/