“Curiosity is great fuel for motivation... let students sit with their curiosity before attempting to solve.”

Asking effective questions to spark critical thinking in math is as much an art as a science. And if you’re anything like me, you like to have a roadmap to take the guesswork out of it. Young learners are just building up their foundational skills in math that will carry them through their elementary years and beyond. And equally as important – they are beginning to build up their confidence in themselves as mathematicians!

Here are 5 concrete strategies for effective questioning to help build curiosity, collaboration, and critical thinking in math. Remember, the ultimate goals are to help your students truly understand the content AND develop the courage to take risks!

Notice + Wonder

Starting a math lesson, problem, or activity with “What do you notice?” and then moving on to “What do you wonder?” is an easy entry point for all students to share their thinking and helps to build curiosity around the problem or activity. Curiosity is great fuel for motivation, which is why this is such an effective routine to incorporate at the beginning of a math lesson. Students may surprise you with their observations, and it will help you to see where their focus is and what really stands out for your students. This is the lowest lift strategy to incorporate as it requires very little time and planning on the teachers part. Try to stick just to the noticing and wondering without diving into the why of the problem (yet) to let students sit with their curiosity before attempting to solve.

Partner up

Before explicit instruction, allowing students the chance to attempt a problem gives them the opportunity to figure it out for themselves and try out various strategies. After allowing students to grapple with it for a bit, asking these questions about strategies can help to get the discussion rolling:

“What’s one strategy you used?”

“What’s one strategy your partner used?”

“What worked?”

“What didn’t?”

A quick tip is to highlight “when you got stuck” stories to build grit and resilience in problem-solving. When students hear about others struggling with a problem and finding a way forward, it can help inspire a growth mindset and comfort with uncertainty. This could sound like, “Did you hear that? When Malia and Cesar tried adding the numbers together and got 12, they knew that wasn’t right because the balloons are popping in the problem, so the numbers should be getting smaller. When they felt stuck, they grabbed some counters to act the story out and were able to figure it out.”

Start with what, then why, then how questions

This is a general rule to help you think about the level of complexity of the questions you’re asking and build from simple to more complex.

What? Starting with recall questions helps students orient themselves to the problem and understand it fully before starting to solve. Examples are: “What are the kids eating in the problem?” “Cupcakes.” “What do you notice about the numbers in the story?” “They are the same, like a doubles fact.” A little caveat is that “How many” questions are equivalent to “What” questions in their complexity - they require little thought and are simple recall questions.

Why? These types of questions get to the heart of the strategy work and challenge students to think about their process of problem-solving. “Why did you choose to subtract this from that?” “Why do you think there are 7 leftovers?” These require more lift and critical thinking and may require some extra think time or scaffolded questioning.

How? This type of question generally requires the deepest level of thinking and can push students to think about the question more broadly and enter into the theoretical stage. “How did you know to group those into tens?” “How does this pattern grow?” “How does this rain collection problem remind you of the sticker problem we did yesterday?” This type of questioning can help students see their math thinking on a higher level, comparing and categorizing strategies they’ve used previously.

Pattern center list of guiding questions for kindergarten and first grade teachers to help students build critical thinking skills and determine what comes next in the repeating pattern.

Wait time

This sounds simple, but teachers are often uncomfortable with silence and end up moving on before students have time to process the question. Studies show that the average length teachers pause after asking a question is .9 seconds. Less than just one second! I try to count to 15 in my head after asking a question that requires some deep thinking, and usually I get responses in 10-12 seconds. If I don’t, that may mean I need to reteach, rephrase the question, or have students share first with a partner (this can be helpful to give those internal thinkers a chance to share in a less public format).

“Can you see it?”

If students get stuck solving or continue using an incorrect strategy, stop them and ask if they can really “see” the problem. Have them close their eyes and visualize what is happening in the problem or put some math manipulatives in front of them to help make it more concrete. This is especially helpful when you’re working on story problems and students get to the stage where they’re solving using derived facts. Students at this stage can quickly manipulate numbers and have the urge to solve, so oftentimes they will jump to familiar strategies that have worked in the past before fully understanding the problem. Slowing them down by using visualization can be very helpful.

There is so much to cover each day that as teachers, we can get caught up in the hustle and end up just getting our students to surface level understanding. Luckily, these intentional questioning strategies only require a brief slowing down to go deeper and strengthen understanding! Check out this list of questions from this Growing Pattern Task Cards resource and try out the progression from What? to Why? to How? questions with a concrete, visual activity.

Bonus: students LOVE solving these and beg to do them, even at indoor recess and choice time. Win-win!