In many cases, this sounds like the teacher explaining each step and modelling it for the students. While such modelling can be helpful to introduce a new topic, far too often I see math teachers relying on this strategy for all problems they complete during class. If students do not actively force their way into the process by asking a question, they are left to simply observe.
Instead of just showing students what to do, teachers can employ questioning strategies that allow students to become active participants in the solving process. When this shift is made, not only are students more highly engaged as they are being asked questions throughout the solving process but also they develop a deeper understanding of the concepts as they work to justify the mathematical steps.
The questioning strategies below are intended to be used as cold call questions during guided practise in class. While these same types of questions can be answered by volunteers, the goal of the questions is to increase engagement and maintain the pace of the class. I have found a cold calling to be the most effective strategy in this situation. Additionally, when cold calling is used, students develop the understanding that they must always be ready to participate in class.
In order to meet the needs of all learners, teachers must be strategic in what questions they ask of which students; differentiating questions based on level can help all students find success. If you believe that your students are not prepared for cold calls or are worried about particularly introverted students, it can be helpful to instead use the warm call strategy and let them know which question you will be asking them in advance. This is effective if students are completing a problem independently, as you can let each student know which step they will be responsible for explaining when you review.
The first form of questions that a teacher can utilize during math class is “what” questions. These are often best used to start off a problem and can simply sound like “What should I do to solve this problem?” or “What are you thinking when you see this problem?” These “what” questions immediately engage students and can offer them the opportunity to participate whether or not they are highly confident with the material.
For example, while teaching my students how to solve word problems, I often ask them what I should do first. Students who are less confident with the material can easily find a point of access to participate in class by reminding me to annotate the problem. Beyond just providing these students a point of access, this question-and-answer ensures that all students are actively guiding the solving process, which certainly should include annotations.
From there, I can ask what to do next, and my students may state that I need to write an equation, which we then work to solve together. I would proceed with my “what” questions in order to identify the necessary steps to continue solving and to check my work. In this way, my students are the ones who must determine how to approach and complete each problem. If students are unsure about what to do, I am still able to prompt them and offer support, but they have been given a chance to process their thoughts independently first.
Once my students have told me what to do when completing a problem, I begin to shift to asking “why” questions in order to further develop their mathematical language and justification skills. These questions often follow a “what” question and allow me to increase the number of voices I engage on one problem.
For example, if I am working to solve the equation 5x + 2 = 12, I may begin by asking a student what I need to do first. Once they reply that I must subtract 2 from both sides, I can ask why that must be done. By asking this “why” question, I ensure that students are not simply following a set of procedural rules but instead are internalizing the importance of maintaining balance and equality when solving, skills that they can continually apply as they encounter more complicated mathematical problems in the future.
Additionally, as they explain their justifications, they are tasked with utilizing mathematical language, which supports them in meeting the communication goals outlined by the Common Core Standards for Mathematical Practice.
The last type of questions I often use in my lessons is “how” questions, which call on students to explain the process necessary to accomplish a goal or explain their reasoning behind completing a specific step. I find that I don’t necessarily follow a specific structure of asking “what,” then “why,” then “how,” but instead ask “how” when I want to confirm that students understand the process.
Additionally, I find that asking a “how” question offers a student significant freedom in how they plan to answer, as it encourages them to explain how they knew an answer. This, therefore, not only offers them the opportunity to use their mathematical language but also allows them to put the process into their own words. Doing so has allowed my students to deepen their own understanding while simultaneously supporting their classmates by offering a different, and potentially more understandable, perspective.
To see how all these questions work together, click here to read a scripted example.
By Rachel Fuhrman