4 Questions That Help Math Students Explain Their Answers

“How did you get that answer?” That’s what I used to ask my students as I walked around to check their math work. More often than not, my question was met with a shrug, an “I guessed,” or a vague gesture toward their paper in the hope that I would explain it for them. Even when the answer to the problem was correct, students struggled to find the language to explain their thinking. This made it difficult for me to target intervention or enrichment for individual student needs.

I realized that if I wanted better student responses, I needed better questions. Over time, I have found four effective questions that not only provide me with valuable data for adjusting my teaching, but also help students build independent problem-solving practices, promote metacognition, and practice using academic vocabulary.

‘What tools did you use to find your answer?’

This question shifts the focus from the teacher as the source of guidance and information to the notes, anchor charts, calculators, and other tools the student has available to them. I scaffold this process for students by pointing to similar example problems in their notes or the steps on an anchor chart to help them find the next step in their specific practice problem. After using this question for several weeks, I notice that students bring out their notes or turn to the anchor charts without prompting from me.

Even students who have mastered the problem benefit from this question. Sometimes, what they think of as “guessing” was really using their notes or the anchor chart to piece together the steps needed to work out the problem. Reinforcing this process with them makes them more likely to turn to these tools in the future.

‘What words do you understand? What words are unclear?’

I use this question—which is adapted from the Collaborative Strategic Reading strategy—to reveal gaps in vocabulary that keep students from understanding the problem. For example, a student may know how to plug in a number for a variable and apply order of operations to simplify the expression, but they may not understand what the word evaluate means. A student may be asked to find the area of a parallelogram using a given expression, but if the student does not understand what a parallelogram is, they cannot begin to solve the problem.

Even students who correctly solved the problem might still hold misconceptions that need to be addressed for future problems, especially as the curriculum grows more complex. I address any misconceptions with explicit instruction for the words they don’t know, pointing to context clues or prior knowledge, or providing graphic organizers of key math vocabulary and the operations they correspond to.

‘In this step, why did you...?’

I use this question to drill down into the specific processes students have for solving problems. It often reveals lucky guesses, simple mistakes, misconceptions, or strategies that only work in special cases. Students sometimes hold on to “rules” they were taught in elementary school, such as putting the larger number first in subtraction, that no longer work for higher-level math (in which negative numbers are more common). Or a student might use advice from another student without understanding the reasons behind a certain step.

These conversations allow me to address the gaps in understanding of things like the order of operations or how to treat exponents or fractions with multiple terms in the denominator. They also create a space for students to make observations about the patterns they see in data tables or graphs, which we can validate or refine together, or even pass along to other students who are struggling.

Students also receive practice in using academic language to justify their responses. Even when the step is correct, asking the question allows me to see how students’ vocabulary usage is developing and address any misunderstandings.

‘How reasonable is your answer?’

Serving as a more specific version of “check your work,” this question prompts students to activate knowledge of the real-world context of a problem or what they know about the features of a given function. For example, the square root of a number can be both positive and negative, but a student finding the length of a side of a square would only use the positive answer. Students learn how to interpret the answer they’ve found and explain the meaning of numbers, rather than focusing on “getting to the end.”

Focusing on the reasonableness of an answer helps students find ways to give themselves feedback rather than relying on the teacher to know if they are correct. It also reveals biases students have when assessing their work: Some of my students assume an answer is incorrect if they produce a very large or very small number, regardless of whether this type of answer is expected. This question is most effective if you don’t initially tell them if their answer is right or wrong, so that students can focus on building their confidence and number sense.

These four questions have helped my math students make the change from guessing to engaging in real problem-solving. Try putting these four questions on an anchor chart. This will remind them (and you) what they should be able to communicate as you circulate around the room. Consistently modeling these questions will inspire your students to use the same questions with each other, making the problem-solving process naturally more collaborative.