Back to: Module: Helping Students Do Math
Slide 1: Hello, and welcome to this webinar on asking questions and helping students think out loud. I am Anika Rowe, Research Assistant working for WordFarmers Associates on behalf of the Ohio Partnership for Excellence in Paraprofessional Preparation at the University of Dayton School of Education and Health Sciences Grant Center.
Slide 2: The topic this time is asking questions, and dealing with the answers that students give you. There are a lot of slides here, but the ideas are really simple. Even though simple, the ideas are new to many educators. Because math is about thinking with numbers, questions are very important. Questions get people talking and thinking about the answers they give. This is true of all of us, and it is true of students, too.
Slide 3: So we ask students questions to get them thinking. If we just told them things and then asked them to do things—like divide 5,742 by 53—or find the answer to a word problem, we wouldn’t get a chance to understand how they’re thinking and to help them think.
Slide 4: We could even say that questions are the heart and the brain of teaching. Good teachers ask really good questions and get the class involved in helping each other think. It’s wonderful to see this happening in classrooms. But it’s difficult and, sadly therefore, it’s not that common.
Slide 5: As you work in schools, watch for teachers who ask good questions and watch how the students respond. Many of the videos listed in our activities and toolkits show teachers operating in this way. It’s inspiring to see this sort of teaching! Imagine if your own children and grandchildren and nieces and nephews could have such teachers all the time!
Slide 6: But what can you do as a paraprofessional without a lot of training? Is there anything you can do to ask questions that get students thinking… to get them talking more about what they are thinking in math class? You bet.
Slide 7: These questions are remarkably simple and you can use them all the time. You can use them even if you don’t completely understand the math that is being taught. But you have to know enough to keep the conversation going and the students thinking.
Slide 8: In the typical situation you might be helping a student deal with a math problem and its related ideas. So that’s the context for these questions:
- What does this problem ask for?
- Tell me what you don’t understand.
- How can we find out what you need to know but don’t yet understand?
- Where do you think you should start?
Slide 9: Here are some more:
- What does this part of the problem mean?
- What’s the important idea here?
- Tell me more.
- Why did you make that choice?
Slide 10: And even more:
- Is your answer reasonable?
- Where do you think you went wrong?
- Why do you think that?
- Does that make sense?
Slide 11: Did you realize that the previous slides seemed to group the questions according to the phase of the problem? The first four questions dealt with the beginning, the second four with the middle, and the third set of questions mostly with the end. The next webinar will have more to say about the phases of solving problems.
Slide 12: One of the useful things about this set of questions is that you can use them over and over again—anytime they help students think about what they are doing. Remember, a lot of math instruction has, unfortunately, set up an expectation that students will just follow instructions, not think. They are expected to do it right and get the right answer. But that approach isn’t math. As we’ve said before (and will continue to say), if it’s not thinking with numbers, it isn’t math.
Slide 13: Asking questions and having conversations with students will make your own experience of working with them more interesting as well. It will get you thinking too.
Slide 14: If all this seems strange or scary, think back to learning about “declarative” and “interrogative” sentences. Declarative sentences end in a period and that’s it. They’ve declared something. End of story. But interrogative sentences end in a question mark and they open things up. They start a story.
Slide 15: So the questions on the previous slides help students tell the story of their thinking with numbers. You can invent dozens of similar questions. But you don’t need many such questions—not at all.
Slide 16: The questions are easy to ask, each of them individually. The hard part is keeping the students talking and thinking. And the questions have to lead to satisfying or productive answers eventually. This is where your own understanding of the lesson needs to come in.
Slide 17: When you ask questions, you need to give students time to formulate answers and time to state their answers. This is known as “wait time” and it’s a very simple idea. Questions are supposed to get people talking about their thinking. They need time to do that. Studies of instruction have shown that an emphasis on right answers doesn’t give students a chance to explain their thinking. Explanations take time, especially when students are struggling hard to learn new things.
Slide 18: In fact, the average wait time given by teachers is only around one second. It’s not enough time: not at all. Studies of wait-time recommend wait time of 5-10 seconds before offering any further hints or follow-up questions. It feels awkward at first, but as you see what happens, you should begin to find wait-time interesting. You get to watch students thinking and to help them think.
Slide 19: In each of the next few slides, you will see a pair of questions. Each group of two questions is very similar. But their approach is very different. One question demands wait-time and attempts to open a conversation about thinking, but the other question seems planned to cut off discussion. It’s not a genuine question and it doesn’t, therefore, require wait-time. Which is which? (You may want to pause the video while you think.)
Slide 20: Any idea how we might find the area of a triangle? You remember the area of a triangle, don’t you? (pause)
Slide 21: What is the answer to #3? How did you approach #3?” (pause)
Slide 22: What questions do you have? Do you have any questions? (pause)
Slide 23: The way you respond to students’ answers to your questions is important. Rather than using closed responses such as “That’s right,” “That’s wrong,” or “Almost,” try using open responses like “How did you get that answer?” “Does that answer seem reasonable? Why or why not?” or “How could you check whether that answer is right?” It matters if answers are right or wrong, but not because they are right. The point is the thinking involved.
Slide 24: You don’t need to know everything about the particular problem for which you are asking questions, but you have to be confident in the ideas and procedures dealt with in the lesson. If you aren’t up to speed, you’ll need to prepare. This is something that teachers of all sorts do. And the really good ones do more of it. That includes thinking about and planning questions in advance!
Slide 25: Good questioning starts a conversation about something important, something real. In this case: math (thinking with numbers and space). Good questions invite relevant conversation, but bad ones shut it down. When asking questions, it’s important to wait for—and to encourage—students to answer. Waiting and encouraging answers can actually make a bad question work much better than it otherwise would. And better questions help us teach better in most teaching situations!