In a post I wrote last month entitled Questioning In Math – NCTM Regionals Minneapolis I talked about the power of questioning in math to promote thinking, problem-solving and foster collaboration and communication among students so they can make mathematical connections. I believe that if you change one simple thing – how you question in mathematics – your students will become better problem-solvers and better mathematicians.
In the Common Core Standards of Mathematical Practices, you will find that all 8 practices are designed to help develop in students this ability to think about mathematics, make connections, communicate their understandings and become problem-solvers. These practices are often overwhelming to teachers, who think they have to completely revamp all their instructional strategies. My advice is always to start small, change one thing at at time, and the best way to start is by changing how you question your students. That simple step can go a long way to addressing the skills & processes the practices set out to develop.
The obvious change is to never accept a students’ answer, right or wrong, but to always ask another question. This is a hard skill to develop, as it is easier to say “That’s right, good job!” or “Not quite – does someone else have an answer?” Something as simple as “Why?” or “How do you know?” or “Can you show me what you mean?” can go a long way in helping students learn to justify their answers and/or rethink their answers, and make connections or corrections in their approach.
Here are some questions to add to your repertoire,. to help foster in students the ability to think, connect, collaborate, justify, persevere and communicate – in short, to become confident problem-solvers. This is by no means an exhaustive list, and comes from many sources and years of experience, but it’s a start.
- Making Connections/Starting the Conversation
- What do you think…..
- What do you wonder about…
- What do you know about….
- Does this remind you of anything….
- What can you tell me about…
- Have you ever heard/seen….
- Exploring, analyzing and persevering
- How do you know…
- Does that always work….
- Why did you do that or say that….
- What would happen if ….
- Can you think of another way….
- Could something else happen….
- Might there be another approach or possibility…
- Conjecturing, Collaborating & Justifying
- Why do you think this is the right approach…
- Are there other ways to show this….
- What will happen next….
- How does your way compare to …. how is it the same? Different?….
- What would happen if….
- Are there other answers/solutions/methods….
- Why do you think that is….
- Can you explain….
- Who can explain what (name) did…..?
- Is this like anything else you’ve done….
- Is this similar to….how so?
- How is this different from…how so?
I use to provide a laminated “book mark” for teachers to keep at the front of their room or on their desk with these type of question starters. As they were teaching, just in case they couldn’t think of a good question on the fly, they had some to pull from. Making a concerted effort to change your questioning takes time & practice. Cheat sheets are okay! Eventually it becomes part of you and your classroom expectations and the conversations where students are learning and engaging in mathematical discourse are worth the effort!