- Episode Highlights
- Transcript
This episode continues our deep dive into questioning in the math classroom by exploring what makes a question truly effective. You’ll learn how open-ended questions can increase engagement, encourage rich discourse, and help uncover deeper mathematical understanding.
Together, we’ll look at the core qualities of good questions, reflect on why planning questions matters, and explore practical ways to shift everyday questioning habits. This conversation offers a strong starting point for anyone looking to increase participation and spark more meaningful thinking during math lessons.
Links Mentioned
- Depth of Knowledge Framework
- Good Questions for Math Teaching by Peter Sullivan and Pat Lilburn
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Hello again, Meaning-Makers! It’s Jillian here from Team Meaningful Math. I am so excited to continue our discussion about asking good questions. Today we’re going to explore the qualities of good questions and also discuss ways we can intentionally plan for them.
Common Questioning Pitfalls in Math Lessons
Before we get started, I want to ask if you can relate to this experience:
You’re in the middle of teaching a math lesson, and the lesson seems to be going pretty well except for the fact that the same 4 or 5 students are raising their hand and calling out answers, while the rest of the students are silent and seemingly disengaged.
Or, here’s another one:
You’re asking a series of questions, and you begin to notice that the questions you’re asking are primarily yes or no questions. Your students are choral answering, “Yeeeesss” or “Noooo”, but it doesn’t seem like they’re really doing any thinking, but rather just yelling out what answer they think comes next.
Do any of these scenarios sound familiar?
If so, you’re in good company because every teacher I know, myself included, have struggled with this.
What Makes a Math Question “Good”?
In order for us to prevent scenarios like these, we need to be asking better questions. But what exactly makes a question “better” or “good”?
Well, let’s dive right in!
Understanding Depth of Knowledge (DOK) in Math Questions
Some of you might be familiar with the Depth of Knowledge Framework developed by Dr. Norman Webb. According to Dr. Webb, instructional questions can be categorized into one of four levels, with a Level 1 question being the most straightforward type of question, and a Level 4 question being the most complex.
It is estimated that 65% – 90% of questions that teachers ask their students are categorized as DOK 1 or DOK 2 questions. So what does this mean exactly? Well, this means that the majority of questions that students answer are only requiring them to recall information or to apply a preestablished rule.
Open vs. Closed Math Questions
While there is a lot of value in the D.O.K. framework, we can simplify categories of questions into just two categories: open or closed.
Closed questions only have one correct answer, and oftentimes, the answer to a closed question can be stated in one, or very few words.
On the other hand, an open question can have more than one correct response and requires a student to think more deeply about a concept.
Teachers are actually pretty skilled at asking open questions in content areas like Language Arts and Social Studies. But for some reason, once we start math class, we stop asking the open questions, and closed questions are a lot more common. It doesn’t have to be this way!
If we want our students to engage in math discourse, participate more, and think more deeply about math concepts, we must shift our questions from closed recall questions to much more engaging open questions.
The Three Qualities of a Good Math Question
Peter Sullivan and Pat Lilburn, who wrote the book, Good Questions for Math Teaching, explain that there are three main qualities of a good question.
Good Questions Go Beyond Recall
First, they note that good questions require more than remembering a fact or reproducing a skill.
For instance, when learning about odd and even numbers, a more typical closed question would be, “Is 23 an odd or even number?” But this question can be altered slightly so that the students have to think a little more deeply about odd and even numbers.
Instead, the question could be: “After all the students in a classroom paired up, there was one student left without a partner. What can we say is true about the number of students in the classroom? And how many students could be in the classroom?”
Notice how a teacher can gauge the depth of a student’s understanding of odd and even numbers much better from the second question than the first.
Good Questions Lead to New Learning
Next, Peter Sullivan and Pat Lilburn claim that if a question is a good question, students can actually learn from answering it. When answering a good question, a student can deepen their understanding of a concept, or identify where their understanding is incomplete.
For example, when learning about measurement, the teacher could pose the following question: “Nick and Sally each measured the length of their notebook. Nick said it was 15 inches long and Sally said it was 16 inches long. “How could this happen?”
When students consider this question, some important concepts about measurement are likely to be brought up. Students will most likely mention ideas related to accuracy, avoiding overlaps or spaces, and the importance of starting at zero. They are developing a strong, foundational understanding of measurement just by answering this question!
Good Questions Allow for Multiple Correct Answers
Lastly, good questions may have several acceptable answers. Most questions teachers ask during a math lesson have only one correct answer. But when we ask good questions, there is more flexibility in how a student can answer the question correctly.
A more traditional closed question about area and perimeter might be, “What is the perimeter of a rectangle that is 8 feet long and 3 feet wide?” but what if this was the question instead?: “The perimeter of a rectangle is 20. What could be the area of the rectangle?”
Not only does this second question encourage higher levels of thinking, but there are many different correct answers!
The other wonderful thing about questions that have more than one correct answer is they are naturally differentiated. Some students may figure out only one possibility while others will try to come up with all the possibilities!
Planning Math Questions Ahead of Time
Educational researchers estimate that roughly 60% of the things said by teachers are questions, and most of them are not planned. So if you really think about it, it’s not surprising to think that if we change our questions, we are changing a great deal of what transpires in our classroom.
But shifting the nature of our questions takes a lot more brain power than one would think, and it takes a lot of practice.
Ultimately, it all comes down to planning. Good questions must be planned ahead of time. For every lesson plan, it’s helpful to write down a few good questions you plan to ask during the lesson. You really only need to plan for the good, meaty questions because those closed, Level 1 recall questions will take care of themselves.
If you find yourself in the middle of a lesson, and you haven’t planned enough good questions, you can always add “Explain why you think so” or “Can you prove your answer” to encourage more discourse.
Working backwards is a helpful strategy when planning good questions. Here’s how this works:
How to Shift a Closed Math Question Into an Open One
First, identify the lesson topic. Then think of a closed question you would typically ask during the lesson and write down the answer to that question. Now think of a more open question that could be asked instead that addresses that same answer.
For instance, let’s say the lesson topic is using a number line to subtract. A closed question that might be asked during the lesson is, “What is the distance between 8 and 14?” and the answer to this closed question is 6.
So now I need to think of an open question that addresses the idea of a distance of 6 between two numbers on a number line. So maybe instead I ask, “The distance between two numbers on a number line is 6. What could the numbers be?” See how that simple shift completely changes things?!?
Changing the Nature of the Questions we Ask
Asking good questions during math class is not easy. But, the more good questions we plan ahead of time, and the more good questions we ask, the better we will become at asking them on the fly.
Meaning-Makers, changing the nature of the questions we ask our students can be transformative. Combine this with access to a variety of math manipulatives and a safe positive learning community, and I think you’ll be amazed by the difference you’ll see in student participation and their quality of thinking.
This is such a rich discussion, and I don’t want it to end! I hope you found this two-part discussion about asking good questions helpful. Until next time, Meaningful-Makers, have a great one!
