Rogers and Edwards have been working together to engage students in “math conversations” in an effort to encourage students to think past the answer and focus on the process of getting the answer.
“It goes back to math practices. Some of the practices require kids to be able to have conversations with each other. For example, math practice three is to justify and critique the reasoning of others,” Edwards said. “And so, kids have to be able to know how to talk with each other in order to be able to justify and critique, but also anytime you have kids talk, the learning becomes deeper. And then that focus shifts to the thinking.”
The students agree.
“When you talk about it, it makes more sense,” said sixth-grader Kennedy Brown. “You can take what you think, then see what someone else thinks about the same problem and put them together to come up with new ideas or different ways to do things.”
Rogers, who teaches sixth and eighth grade math at HCMS, trains students from the beginning of the school year on how to engage in effective discourse with each other. Students need to know how to respect and be appreciative of each other’s ideas and opinions and how to constructively disagree or critique another student’s work.
“We want them to be able to look at math problems and be able to talk about them and be able to work on them together as a community, and that happens as part of that math conversation,” Rogers said.
Generally, students are provided a math problem to solve. They are given time individually to formulate a strategy to solve the problem, then attempt to answer the problem using that strategy or “pathway.” Then, students form small groups to share their ideas, decide whose strategy might work best and attempt to solve the problem together.
“At first I thought it sounded a little silly,” Shane Raisor, another sixth-grader, said. “But when we started practicing it, it really helped us. If you’re not sure about the answer, you can talk about it. It gets your mind thinking.”
Getting students to think about how they got their answer is exactly the outcome Rogers and Edwards hope for.
“Having the conversation allows the kids to transfer their thinking into words, to each other, on paper through a drawing, an illustration, whatever it may be, and by them having that conversation they’re allowed to talk with each other and problem solve together and collaborate as a group to get to a solution,” Rogers said.
Math conversations help students understand the processes, which deepens their comprehension of a particular concept and leads to their ability to apply what they’ve learned in a variety of situations, including real world scenarios.
“With conversations, kids learn multiple strategies to get to a solution. In the real world, we all collaborate and build off each other’s ideas and work together,” Rogers said “In math, we make mistakes all the time and the kids may try a pathway that doesn’t lead to the right solution. Hopefully they’ll be able to use their logic and their number sense to look at it and say, ‘Oh no, there’s no way that could be the right answer.’ They learn from their mistakes and re-try solving a problem a different way.”
Getting students to understand there could be more than one way to find the right answer opens students up to a process of problem-solving that includes room for different solution pathways.
“Even if you take a math fact like 3x5, I know that equals 15, but one kid might see that as three groups of five, another kid might see that as five groups of three, another kid might say well I know that 3x10 is 30, so then I could half it to get 15,” Edwards said. “Kids need to be able to manipulate that number and see that there’s some fluidity. It’s not just here’s the right answer, it’s a procedure.”
Because Rogers and Edwards have seen first-hand the success students experience using math conversations, the two will be presenting their concept to other educators from across the state at the annual Kentucky Center for Mathematics conference this spring. Rogers was teaching class when he learned their proposal, “Math Conversations Matter!” was chosen by conference organizers.
“Of course I started jumping up and down and screaming like a crazy person, and so the kids got excited too because their teachers are going to go present at a statewide conference,” Rogers said. “They took pride in that and I’m personally excited to see Henry County represented at a state-level conference. HCMS has incredible things going on at our school and I want others in the Commonwealth of Kentucky to know it.”
Edwards echoed that sentiment.
“We’re doing good things here, and we want to share that with other people across the state so they can see this is how we’re incorporating discourse into our instruction,” Edwards added.
Edwards pointed out that she and Rogers will be showcasing the students’ work as well, providing examples of math conversations, discussing improvements in test scores, and providing examples of the students’ opinions of how talking about math has helped them succeed in the class.
“We just really believe that math conversations are important. We’ve done a great deal of research about discourse in the classroom and have attended several trainings and it all points to the power of collaboration and discourse between kids,” Edwards said. “We learn better when we learn together.”