Purposeful Math Questions Help Students Thrive

If you are a regular reader of this blog, then you know that I’m a big advocate of asking questions, lots of questions, in the math classroom. After all, math is a field where we pose and answer questions. Some may take only seconds to answer, for many we already know the solution (although we may arrive at the answer through different paths), and others have challenged mathematicians for years. It’s by asking and answering questions, those we pose to students, and those they ask themselves that students own their learning. I have often said that if I could wave a magic wand and change one thing about how math is taught in elementary school, I would make sure that we (both teachers and students) more frequently ask questions that help elucidate student thinking and reasoning.

Why Are Questions Important?

As I noted above, math is all about asking and answering questions. Getting students to reflect upon and justify their thinking, strategies, process, and reasoning, either via teacher-posed questions or through self-inquiry, is key to true learning. Unfortunately, too many students start erasing their work when questions are asked, thinking that a question indicates that they’ve made an error. And students are often reluctant to ask questions, thinking it signals not an inquisitive mind, but rather a lack of knowledge. So, we need to convince students that a math class where questions are routinely posed, particularly those asked by the students themselves, is one in which learning thrives.

Research shows that there are many benefits to incorporating questions into your mathematics instruction and centering student learning around rigorous inquiry.

• Student engagement and participation improves in classrooms that encourage and reward questioning.
• Student motivation and learning increases when students are given the opportunity to ask questions of each other and the teacher.
• Students can monitor their own learning when they know how to pose thoughtful questions that encourage them to consider multiple strategies and approaches and to challenge their thinking and that of their classmates.
• Students who actively engage in asking and answering questions are more likely to understand and retain complex concepts.
• Students who learn in an environment that encourages and celebrates questioning improve their academic performance.
• Student willingness and ability to ask questions better prepares them for college and for the workplace.

Thoughtful questioning is also an essential formative assessment tool for teachers. Purposeful questions, both those posed by teachers as well as those from students, can help teachers determine what students know and don’t know, and then decide how best to move forward with whole-class, small-group, and independent instruction. Additionally, questions often uncover student misconceptions and gaps in student learning, thus allowing teachers to focus on areas where student knowledge is unclear, only partially formed, or simple incorrect.

A word about wait- or think-time. It’s critical when asking questions that students are given the time to reflect upon their answer. But research shows that typically teachers give students one second or less to answer. That just isn’t enough time for students, particularly EL students, to frame a response. Research indicates that we need to provide students with at least three to five seconds (more for particularly complex questions) to contemplate and prepare an answer. The consensus is three to five seconds after the question is asked and an additional three to five seconds after the student’s answer provides most students with enough time to think about their response.

And a word about equity. We’ve all fallen into the trap of calling on those students most eager to answer or those we think will move the discussion in the direction we want to head. And sometimes this may be necessary. But to have a math classroom where questioning leads to deep learning for everyone, everyone needs to participate. By cultivating an environment where questioning is part of the learning process, we let students (all students) know that we value their thinking. Convincing students that when we ask questions, we’re not fishing for the right answer and that mistakes lead to learning takes time but is well worth the effort.

Questions that Promote Deep Learning

In an earlier post on how to support rigorous math discourse, I discussed the types of questions we ask in the math classroom and the purposes of each. Here’s a quick recap.

Closed questions help you check if students are fluent with particular math facts or if you want a single correct answer. These questions are an essential assessment tool, but don’t lead to deep learning, so they shouldn’t dominate

Open questions lead to multiple strategies and solution paths and help students understand that there are different ways to solve a particular problem. Open questions not only support rich discourse, but also help students dig more deeply into the math behind the equation.

Funneling questions help students follow your train of thought and steer them to a particular strategy or solution path. These questions help students when they are frustrated and at risk of moving into unproductive struggle.

Focusing questions help students clarify their own thinking and move forward. These questions are a great way to promote productive struggle and show students how questioning their own reasoning moves them toward a deeper understanding of math concepts.

Recall questions, which are often close-ended, help students show what they know. Similar to funneling questions, recall questions can help students get unstuck.

Probing questions help students make important connections as they explain and justify their thinking, whether their reasoning if correct or not. Probing questions are particularly important in highlighting that mistakes are a pathway to deeper learning.

Process questions allow students allow students to clarify their choices and showcase their solution path, in essence to showcase the how behind their thinking.

Developing questions on the fly can be very difficult, so we recommend that you have a bank of questions which you can use throughout your lessons. To help you get started, we’ve put together a list of questions to help spark student thinking. I recommend that you post this list prominently in your classroom and give older students a copy to keep. You might also want to send a copy home to parents as one way in which parents can help students with their math homework is by knowing the questions that get their kids thinking in creative and diverse ways.

Have fun as you transform your math classroom into a place filled with students who recognize that asking and answering questions is not a badge of shame, but simply how they learn math.

References

Berger, W., & Foster E. (2020). Beautiful questions in the classroom: Transforming classrooms into cultures of curiosity and inquiry. Thousand Oaks, CA: Corwin Press.

Engel, S. (2015). The hungry mind: The origins of curiosity in childhood. Cambridge, MA: Harvard University Press

Ostroff, W. L. (2012). Understanding how young children learn: Bringing the science of child development to the classroom. Alexandria, VA: ASCD.

Ostroff, W. L. (2012). Understanding how young children learn: Bringing the science of child development to the classroom. Alexandria, VA: ASCD.

Berry, J. W., & Chew, S. L. (2008). Improving learning through interventions of student-generated questions and concept maps. Teaching of Psychology, 35(4), 305–312.

Conley, D. T. (2005). College knowledge: What it really takes for students to succeed and what we can do to get them ready. San Francisco: Jossey-Bass.