Many LINCS members have taken and benefited greatly from the course, "Deeper Learning Through Questioning." The basic activities in that course investigate the following ideas:
- Why do teachers ask questions?
- How can instructors encourage learners to self-question?
- How can instructors motivate discourse in the mathematics classroom?
- How do instructors model self-questioning?
- What effective questioning strategies promote mathematical thinking and discussion?
Whether you have taken the "Deeper Learning Through Questioning" course or not, you are invited to share your successes (failures, too) with using questioning to promote deeper learning in mathematics. What ideas do you have? What are the challenges? What are the rewards? For what do you need help or encouragement? How has effective questioning changed your teaching/your students' learning?
I've found questioning in math to be very important, especially about process and multiple strategies to solve problems. We use math minutes at least once a week as a way to review some basic computation. We go over answers and then target questions that people don't know how to do or had trouble with. I always ask for volunteers who got the correct answer to share how they solved the problem. What did you do? What did you do next? Why did you do that? This allows me to understand what they are getting and what is missing. People who say, "I just knew it." are not quite understanding something, but the ones who can explain their reasoning have a deeper understanding. Sometimes I can probe a bit more with the "knew its" and can get an explanation out. This is valuable for the students who were confused, too. And then, I ask, "Is there another strategy to solve this problem?" So if someone else heard the first explanation and did it another way, this is their chance to explain.
I preach that there are multiple ways to solve problems in math, just like in life. So for me, some of the best math questions are: What's another way? What other strategy will work?
I think this also answers your third question about discourse. My students do a lot of practice in pairs or groups so that they can ask each other questions, too. As there is only one of me, they have to ask each other a question before asking me. Often, the group can figure it out, sometimes explaining it in a more manageable way for the person with questions. If they are really stuck, the whole class will look at the problem when we come back together.
Your comment about the "I just knew it" response is very on-target! What a great idea it is to have students ask another person in the class before asking you!