“The power of questioning is in the answering.  As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give answers.” — L. Schuster (2005).

Have you ever wondered why our students have difficulty thinking, performing a given task and communicating mathematically? Have you ever wondered why they get bored easily or lose concentration while you are teaching? Have you ever wondered why not all your students are engaged? Could it be that part of the problem is the type of math questions we are asking? Are we lecturing and providing information instead of asking students questions that will challenge them to think and construct meaning? Are we encouraging passive instead of active engagement? How can we generate questions that will advance critical and higher-order thinking? Do you want to know more about your students?

We need to craft lessons that have good questions to promote deeper understanding of math concepts. To do this, we should minimize construction of closed questions that require nothing more than a single number for an answer thereby requiring no further thought or interpretation. Instead, we should ask questions that go beyond the level of simple recall or recognition. We should ask questions that will require students to engage in higher-level cognitive processes, such as comparing and contrasting; applying, analyzing, transferring; making connections; noting relationships and patterns; and making transformations.

It’s essential that we learn how to pose good questions that will capture our students’ enthusiasm and interest. But first we need to know what good questions are.

What are good questions?
According to Peter Sullivan and Pat Lilburn, there are three characteristics of good questions. 1. They require more than remembering a fact or reproducing a skill. 2. Students can learn by answering the questions, and the teacher learns about each student from the attempt. 3. There are several acceptable answers.

How can we make good questions?
Remember, a perfect combination of sound questioning strategies and higher-order questions is essential to promote math reasoning and critical thinking. The questions you ask will have tremendous impact on the learning that occurs in your classroom. Consider all three features of good questions mentioned above and examine the questions in your lessons or core program. Here are some ways to think about asking good questions.

• Give your students some control over the choice of numbers when writing story problems. By doing this, you are giving them the chance to regulate the difficulty level of the questions without compromising the integrity of the problem. Example: Sarah has ____ coins. She has _____ pennies, ______ dimes, and _______nickels. How much money could Sarah have?

• Pay attention to your question structures. Use open-ended questions that have several acceptable answers to encourage discourse and communication. Use the higher level of Bloom’s taxonomy when generating questions (application, analysis, synthesis, and evaluation). Push your students to explain and make connections when necessary. Example, One-third of the class wore sneakers to school today. Half wore leather shoes. How many students were in class today and how many of them wore sneakers? How many wore leather shoes? Explain your thinking. You will have multiple valid solutions to this question because you are giving your students the opportunity to choose the number of students in the class.

• Modify simple questions to create higher-level questions. Example: Instead of asking “What is the area of this square?” ask “What will happen to the area of square ABCD if the length is doubled?” Explain your answer. Instead of asking “What is the perimeter of this rectangle?” ask “Can you draw a rectangle whose perimeter is 20 inches?”

There are two methods to creating good questions: (Sullivan, Peter. 2002. Good questions for math teaching. )

• Method 1: Working Backward
• Step 1: Identify a topic.
• Step 2: Think of a closed question and write down the answer.
• Step 3: Make up an open question that includes (or addresses) the answer.
  
For example:
• Topic: fractions.
• Closed question: What is the sum of ½ and ¾? The answer is 5/4 or 1 ¼.
• Good question: The sum of two unlike fractions is 1¼ . What are some possible pairs of unlike fractions that will give you this sum?

• Method 2: Adapting a Standard Question
• Step 1: Identify a topic.
• Step 2: Think of a standard question.
• Step 3: Adapt it to make a good question.
  
For example:
• Topic: time.
• Standard question: What time is shown on this clock?
• Good question: Talk about your favorite time of the day. Why is it your favorite? Write about it. Show it on the clock.

What are some questioning strategies you can apply?
Here are some suggested strategies in the form of questions that you can use to help enable your students to build meaningful understanding of math concepts. These strategies will help them form connections between procedural knowledge and conceptual knowledge. This will help them become reflective learners.

• Are there materials or manipulatives in the classroom that can help you explain your thinking?
• Will it help you if you apply estimation?
• Will it be helpful to use a list, table, or diagram to illustrate your reasoning?
• Can you draw to show your point?
• Can you use smaller numbers to make it easier for us to understand your thinking?
• What connections can you make in the real world for us to understand you better?
• How can you relate this to real life situations?
• What does this remind you of?
• What did your learning make you wonder about?
• What surprised you?
• What strategy did you make up (invent) that helped you understand the lesson?
• What patterns do you see?
• What are you noticing?
• What will you do next to extend your thinking?

I hope that this article has given you some practical ways to ask your students questions that count to help them become reflective mathematicians. Asking the right questions at all times is one way to provide access to mathematics for all our students. Keep on asking!!!

If you have a question or comment about this article e-mail Luchie.