Good question!

Author: Arlene Vinion Dubiel

As mentioned in last week’s blog on teaching math online, we want to use “good” questions to promote student thinking and discussion. As educators we ask questions of our students constantly. But which ones will encourage students to talk with one another? Read on to get some ideas for “good” questions to promote discussion among students.  

Types of Questions

There is a beautiful little 16-page booklet originally published in 1991 by the National Science Teachers Association that is well worth the read. In “How to… Ask the Right Questions,” the late Patricia E. Blosser broke down questions that teachers ask into four types: managerial, rhetorical, closed, and open. 

Managerial questions keep the classroom running. In this day and age, they include questions like “Has everyone muted their mics?” Rhetorical questions are asked in such a way that a response is not expected. We use them to emphasize a point “The answer is x, right?” or sometimes as an introduction to a lesson “Why do we learn inequalities?” We often use managerial or rhetorical questions without much thought to help move a lesson along but otherwise have little instructional value. 

Closed questions are instructional and have a limited number of responses: “Who was the first president of the United States?” Closed questions are necessary to ensure students are on track with their learning. They are often quick and responses are used formatively to make decisions on next instructional steps. Multiple choice poll questions for clicker technology are closed questions.   

Open questions are those with many acceptable responses: “Who was George Washington?” As there is not one ‘correct’ answer, students have to think for themselves and come up with their own answers. Open questions allow students to discover or evaluate information. They are used to begin investigations or as a prompt for discussion. “Good” questions for promoting discussion are always open questions with multiple acceptable responses. 

Content for open questions

When trying to promote discussion, we need to first decide on the outcomes or what we want students to learn from engaging in the discussion. If we want students to know that there are multiple correct ways to solve a particular problem or if we want them to be able to justify a particular strategy, then we can ask students in their groups to explain: “How did you solve that problem?” 

We may want students to be able to explain the meaning of numbers from a mathematical calculation. With complex calculations or with multiple ways to solve a problem, the meaning of the resulting number can be lost. Refocus students’ thinking by asking “How do you interpret your solution?” or “What do you think this solution means in real terms?” Understanding the meaning of a mathematically-derived number is critical for learning science concepts. In next week’s blog, we will talk more about the M of STEM.   

Sometimes a question does not have a single correct answer, rather students need to define concepts for themselves and justify their thinking. One of my favorite examples comes from Physics by Inquiry Volume 1 by Lillian McDermott. Two boxes are displayed with different dimensions. One has more surface area while the other has a large volume. The question is posed “Which box would you say is bigger and why?” (p. 37). The response depends on how you interpret ‘bigger.’ 

There are resources that can help you come up with good questions to promote discussion, particularly for middle grade students. Two such resources for good questions are: “Good Questions for Math Teaching” by Lainie Schuster and Nancy Canavan Anderson and “Good Questions: Great Ways to Differentiate Mathematics Instruction” by Marian Small. Both of these are organized by topic, including algebra and data analysis, and provide ways to prompt students to get started. Marian Small’s text includes K-5, provides links to Common Core State Standards and has good teaching tips throughout. The question phrasing and concepts found in these texts can be modified to fit advanced math content as well.  

Phrasing Questions

““Good” questions for promoting discussion are always open questions with multiple acceptable responses.”

You  have chosen a good topic and have a “good” question in mind that is open in that it has multiple acceptable responses. In practice, how you phrase that question can make or break the discussion. Consider these four items. What are the possible answers to each? Which one would you most like to answer? 

• I wonder why we have seasons.

• Do you know why we have seasons?

• Why do we have seasons? 

• Why do you think we have seasons?

If you think literally, you will notice that the first item is a statement, not a question. There is no question word nor question mark. This item may prompt elementary students to tell you what they think. But older students will likely ignore you or look at you like you are crazy for wondering that. The second question can be answered yes/no. If your students are snarky tweens or teens who are not engaged in the learning, this is probably what they will do. Phrasing questions in these ways will not promote discussion. 

The third question, “Why do we have seasons?” demands an answer. If asked by a teacher, it demands the one ‘correct’ answer. If a student is unsure, they will remain silent for fear of being wrong. Further discussion from this question prompt would rely upon that student who is confident with their response. If the response is correct, discussion ends. If the response is incorrect, then it is up to the teacher to redirect the discussion.   

The last question is phrased in such a way that a student cannot easily be ‘wrong,’ rather it allows for differences of thought. Students could talk about Sun-Earth relationships or the story of Persephone from Greek mythology. Certainly, there is a ‘correct’ answer, but this question allows for students to share their initial thoughts and then go through discussion, research, or investigation to discover the ‘correct’ answer. 

Sidebar: If you do want to know the ‘correct’ answer for the reasons for seasons, there is an excellent teacher’s guide from Lawrence Hall of Science: Great Explorations in Math and Science (LHS GEMS) called The Real Reasons for Seasons: Sun-Earth Connections. The book provides several activities that together allow middle grade students to form a complete explanation for seasons. 

There are several ways to keep classroom discussion going, once it has started. But that is a topic for another time. In the meantime, prompt your students' discussion of math by asking them well-phrased, open questions that prompt them to think and talk with one another. 

When engaging students in a discussion, first decide what you want students to gain from the discussion. Then look for an open question that allows for multiple acceptable responses and phrase that question carefully to ensure students will feel comfortable engaging in discussion with one another. 

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