Whether math class is happening online or in person, when kids are encouraged to talk about their math thinking, it can help teachers assess progress, improve students’ math proficiency, and be a “powerful equity strategy” that allows kids to see themselves as “valued math thinkers,” writes Catherine Gewertz for Education Week.
“A well-designed math conversation can make it easier for all students—even those who rarely talk in class—to participate,” writes Gewertz. There are also academic benefits. At Robbins Elementary School in Robbins, California, for example, district superintendent Dawn Carl says that when teachers began focusing on math conversations, the proficiency rates of the school's English language learners improved by 5 percentage points and proficiency rates for native English speakers grew by 7 points.
The benefits of math talks are well-known—Gewertz points to research and publications from the National Council of Teachers of Mathematics dating back 40 years—but the new Common Core State Standards brought the practice back into focus. “Mastery of the common core’s standards for mathematical practice means students must know how to do things like construct viable arguments and critique others’ reasoning.”
Math talk also translates well to online learning. The author highlights four ways teachers can help students improve their math-talk skills.
Encourage rough-draft math thinking
When students share their initial efforts at solving a math problem with their peers, it helps “deepen students’ understanding of math ideas and practices,” says Amanda Jansen, a mathematics education professor at the University of Delaware.
In the classroom, have your students share and comment on each other’s rough-draft solutions to a problem, revise their work based on peer feedback, and then explain how and why their thinking evolved.
Highlight the value of each student’s work
When students have the opportunity to think about how and why their thinking changed, it allows teachers “to call attention to the value each student’s draft brought to the progression of the class’ thinking. … This can really elevate the thinking of their peers. They realize their ideas can help their classmates grow their thinking,” Jansen explains.
Ask your students to examine a math problem together, work on solutions, then agree upon one solution to share with the entire class. Then have a collective discussion about “what’s powerful and what could be improved” about each draft, says Jansen.
It’s a technique that also functions as an equalizer for students—especially those who might not feel comfortable sharing their thinking—once they realize how their individual math thinking contributes to the whole group’s problem-solving abilities.
Set up small-group conversations
Especially for English language learners who might shy away from speaking in front of the entire class, small-group settings can be helpful for tackling word problems. Teachers at Robbins Elementary first model problem-solving to the class, says Carl, the superintendent, then break kids up to work in pairs or small groups.
Teachers observe and ask open-ended questions like “tell me why you believe that, or, let’s think about this,” says Carl. When teachers gently guide the discussion like this without supplying correct answers, kids can start deepening their math thinking.
Model math talk
Kids need help learning how to engage in productive math conversations so teachers at Robbins Elementary use sentence starters—for example, writes Gewertz: “When Robert uses this strategy, it makes me think of…” or, “This makes sense to me because…”—to help get math talks started.
Teachers can also use cartoon-inspired thought bubbles, says Robert Q. Berry, past president of the National Council of Teachers of Mathematics, to help spur math conversations—he suggests modeling a solution, then circling a specific section of it and drawing in a thought bubble. “What do you think I’m thinking here?” a teacher might ask students, indicating the thought bubble. On paper, students can fill in the thought bubble; online this can be done using a text box.