Last episode, 112 we talked about doing less. And I’m on that trend with this episode too. I truly believe that we do not need a LONG list of questions to ask students to be prepared to facilitate an engaging math discussion.
Our questions DO matter greatly.
Why do we ask students questions?
To promote their voice, to acknowledge that they have good ideas and their voice matters in the classroom. We ask students questions to get their ideas out and public so that others can think about their ideas. Once students have shared their ideas in response to our questions other are able to consider, respond, and critique those ideas. I like to ask that students can add to their own understanding by listening to their peers.
So, asking questions MATTERS greatly.
However, what might matter even more is LISTENING. So, this episode is about asking 3 questions, but I don’t want us to loose track of the most important part of asking questions… and that is to listen. To USE what students say in response to our questions to further the discussion and understanding of every student in the room.
So what are the 3 questions you need.
#1 What did you do?
This gets students describing their actions and thoughts about solving. This helps students describe their problem solving process. Here you’ll be able to witness students’ math vocabulary and understanding of concepts.
For example, if a student has a problem like, “The White Sox stadium had 1,045 people in the seats in the first inning. By the last inning there were only 709 people in the seats. How many people left between the first and last inning?” If a student answers your questions “What did you do?” by saying, “I took the 7 away from 10 and that was 3 so I knew it was 300.” You will likely notice that the student is not using place value language to describe taking 700 away from 1,000. You’ll have to slow this student down asking them to point to their work (which is a BIG reason why I play the scribe and write their work up as they describe what they did) and explain specifically what they did. Here you might prompt students to use “math words” or talk about the numbers using place value. However, the focus is on what did you do.
#2 Why?
Why? Then, we follow up the what did you do with WHY. I really want to know what the student was thinking about subtracting the 700 from the 1,000. Why did they do that? Why did they do that first? What about the numbers made them think about doing that? WHY!!!! This is the REASONING piece. Reasoning is very important to mathematical thinking and understanding, right. We want our students to know why so that in the future they can apply these ideas to future problems. So, second question to ask WHY?
#3 How can you prove it?
Once your students have described what they did and why they did it, which is really great! They are explaining their process and math moves, along with their reasoning… now we have to add in the justification by asking “How can you prove it?”
Back to our example about the White Sox “The White Sox stadium had 1,045 people in the seats in the first inning. By the last inning there were only 709 people in the seats. How many people left between the first and last inning?” The student may have told us that they subtracted the 700 from the 1,000 because there weren’t any hundreds so they just took the 700 from the 1,000. Then we ask, “Okay. How can you prove that works?”
Then the student shows us their representation by pointing to the place value chart they drew and put their numbers in. They describe how there are no hundreds in the first inning, but a thousand is 10 hundreds so they know there is enough there to subtract 7 hundreds. However they thought about it like, “10 hundreds subtract 7 hundreds because that was easier to subtract in my head.”
This is a great way for you to help students see not only why they did something, but uncover a math truth or make a conjecture about something that might always be true. In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. We can keep track of the conjectures our class comes up with and over time prove if they are true or not. Once we all agree we can move them over to our “math truths” list.
So, you need 3 questions to get students engaged in describing their thinking, reasoning, and providing justification. What did you do? Why? How can you prove it?
As you round out the year I urge you to try adding in these SIMPLE questions that can really lead to deep conversations.
If you want to know more about facilitating math discussions and learn about it more this summer I urge you to check out Word Problem Workshop teacher training where I will show you exactly how to have daily math discussions with your students. Then, in June I’ll be releasing a brand new PD all about facilitating empowering math discussions. Be on the look out for that.
In the meantime, enjoy these last few weeks with your students and celebrate the success of ALL that you’ve done together this year!
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