“If two wrongs don’t make a right, try three.” ~Author Unknown
I think often teachers forget how important discussion in any subject is but especially in math. I believe many educators don’t always realize the benefits of discussion and see it as a ‘time waster’. Math discussion to me is one of the most important things to be taking place in the classroom. When students discuss math they are able to clarify their own thinking and learn from others. The teacher can also informally assess if the student’s truly under stand the concept or just walking through the steps to solve it.
Asking students to talk about mathematical concepts and problem solving doesn’t happen over night. The educators need to make a safe learning environment so the students feel comfortable to share their thoughts. This includes showing and allowing the students to solve math problems in more than one way. The classroom needs to have clear, high expectations and the students need to treat each other as equals through respect.
Once you have a safe learning environment math discussions will flow and the students will start to hold each other accountable by asking each other ‘how did you get this or that’ etc. This is also a great way to infuse the 21st century skill of communication. The key to great math discussions is asking the students to explain their mathematical thinking which also incorporates the 21st century skill of critical thinking.
When I was visiting a math classroom this week, 2nd grade, the students were working on finding the missing addend in math problems. A little girl, Jessica*, was showing the class how she solved the math problem. The teacher was doing a great job of asking her guided questions of getting her to explain her work. I was watching and walking around looking at other students work as well and saw many students got it right but solved it multiple ways. Once Jessica was done showing the class the teacher was ready to move on to there math workshop time. I jumped in (I don’t do this in all classrooms, but with this teacher I knew that I could) and said, “I see Frank* has a different way of solving this problem. Frank can you go up to the board and show us what you did. I also see that Sam* did a different way as well, can you show us what you did too.” The students went up to the board and showed and explained their work all getting it right. I then asked, how many of you solved it the way Jessica did, 10 hands went up. How many of you solved it Franks way, 6 hands went up. How many of you solved it Sam’s way, 4 hands went up. I then asked who solved it the right way? No one raised their hands. I waited (one of the hardest things a teacher has to do-30 seconds feels like 10 minutes some times!) after a few seconds of their little brains turning, Steven* said, ‘all of them, as they all got the same answer.’ I then asked, “Is there more than way to solve a problem?” Most of the class shouted out yes.
Here is just a snip it of one classroom and how the discussion lead to understanding there can be more than one answer. It also showed the students that didn’t do it Jessica’s way that it was okay; where if we didn’t have that discussion they could of thought they had done the problem wrong. This did take about 8 minutes off of their workshop time but the benefits were priceless.
Teachers need to realize the benefits of math discussion and the only way to do that is making more teachers aware. Facilitating math discussions involves engaging students in sharing and listening, questioning and responding, and agreeing and disagreeing. It also gives us, the teacher, an opportunity to really understand the students thinking. This should be occurring within and through the teaching process. Students will also benefit from hearing what others say and see that there is more than one way to analyze and solve a problem. Classroom math discussions also give you the chance to clear up any misconceptions the students may have.
Do you allow time for math discussions in your classroom?
*names changed to protect identity.