Getting students to talk about their thinking process in math can give teachers insight into where they need help. But it鈥檚 also a potentially powerful equity strategy, experts say.
And as teachers learn how to move instruction online because of the coronavirus, they鈥檙e all too aware of the equity issues involved: Some students have computers and good internet connections, and others don鈥檛. Some have parents who can help with schoolwork, and others don鈥檛. In that situation, teachers wonder how they can manage to reach all their students, let alone how they can create a class conversation about students鈥� math thinking.
The good news, according to experts, is that math discourse is a technique that works as well virtually as it does on paper or in face-to-face classrooms. And now, when students and teachers risk feeling disconnected and adrift, there鈥檚 even more reason to consider using 鈥渕ath talk鈥� techniques to help students feel engaged and see themselves鈥攁nd their classmates鈥攁s valued mathematical thinkers.
A well-designed math conversation can make it easier for all students鈥攅ven those who rarely talk in class鈥攖o participate, experts say. And by including all class members, a well-structured conversation can help students feel that their thoughts have value.
Dawn Carl, the superintendent of the Winship-Robbins Elementary school district in Robbins, Calif., started focusing intently on a range of math-conversation techniques two years ago, when the English-language learners at the district鈥檚 one school, a K-8, dropped 12 points on state math tests.
But it turned out that the techniques helped all students in the school. English-learners improved their proficiency rates by 5 percentage points between the 2017 and 2019 test administrations, and native-English speakers increased theirs by 7 points, Carl said.
鈥淚t鈥檚 really made a difference for us,鈥� she said.
The idea that 鈥渕ath talk鈥� can have academic payoffs isn鈥檛 new. of discussing mathematical thinking for decades, and the idea crops up in a stream of publications from the National Council of Teachers of Mathematics dating back 40 years, said Robert Q. Berry, the immediate past president of the organization.
But math discourse got a boost in 2010, when the new Common Core State Standards put a high priority on ensuring that students understood the concepts underlying their calculations. Mastery of the common core鈥檚 means students must know how to do things like construct viable arguments and critique others鈥� reasoning.
鈥淭hese aren鈥檛 new ideas, but they鈥檙e practices many teachers have been working on,鈥� Berry said. 鈥淕ood math talk can help students with math sense-making.鈥�
Here are four ways that experts 澳门跑狗论坛 consulted鈥攔esearchers and practitioners鈥攕uggest you can help your students build their 鈥渕ath talk鈥� muscles.
1. Create a culture that welcomes 鈥渞ough draft鈥� thinking.
Amanda Jansen, a professor of mathematics education at the University of Delaware, argues that can serve two powerful purposes at once: It can deepen students鈥� understanding of math ideas and practices, and it can create an equitable learning environment.
Here鈥檚 one way to do that, and it can work as well remotely as it does face to face, she said. Students write a first draft of a solution to a math problem. They read and comment on their classmates鈥� drafts. Then they submit a revised solution, explaining how and why their thinking changed.
2. Highlight the way students鈥� thinking influenced the outcome.
Asking students to reflect on how their thinking changed, and what changed it, allows teachers to call attention to the value each student鈥檚 draft brought to the progression of the class鈥� thinking, Jansen said.
鈥淭his can really elevate the thinking of their peers,鈥� she said. 鈥淭hey realize their ideas can help their classmates grow their thinking.鈥�
Jansen is using these techniques right now, remotely, with her college students, who are aspiring math teachers. They log into Zoom and review a Google Slides deck that presents one math problem at a time. In small groups in Zoom breakout rooms, they work on solutions to the problem, compare their drafts, and choose one to share via Google Slides when they reconvene. The whole class then discusses 鈥渨hat鈥檚 powerful and what could be improved鈥� about each draft, Jansen said.
This approach fosters equity, she explained, 鈥渂ecause it means we can see the potential in anyone鈥檚 ideas.鈥� The conversation centers not on who has the right idea but how seeds in each person鈥檚 ideas can contribute to the group鈥檚 understanding, she said.
And, importantly, the technique allows more students to contribute to the discussion, Jansen said. In her research, she鈥檚 seen this strategy draw out students who tended not to share their thinking often.
3. Foster small-group conversation about word problems.
At Robbins Elementary, one of the new areas of focus for teachers is helping students tackle word problems. Once teachers model solutions for the class, they let students try on their own, in pairs or small groups, Superintendent Carl said.
The children take turns discussing ways to solve a problem as their teacher circulates and provides feedback. This small-group setting is particularly important for English-learners, who might feel more comfortable asking questions in a small group than in front of the whole class, Carl said.
As teachers listen to students鈥� discussions, they ask open-ended questions, Carl said. 鈥淪aying things like, 鈥楾ell me why you believe that,鈥� or, 鈥楲et鈥檚 think about this,鈥� doesn鈥檛 feed them the answers, and it gets them to think more deeply,鈥� she said.
4. Teach students explicitly how to have math conversations.
鈥淲e find that students don鈥檛 really know how to have mathematic conversations with one another,鈥� Carl said. 鈥淲e have to teach them.鈥�
A popular strategy, in Winship-Robbins and other districts, is teaching students to use 鈥渟entence stems鈥� or 鈥渟entence starters鈥濃�攐pening lines that promote good conversation. The NCTM鈥檚 Berry offered examples.
Learning to say things like, 鈥淲hen Robert uses this strategy, it makes me think of 鈥︹�� or, 鈥淭his makes sense to me because 鈥� 鈥� can help students learn how to 鈥済et mathematical ideas out into the classroom space鈥� and build respectfully on one another鈥檚 thinking, Berry said.
Another technique Berry likes draws inspiration from cartoons. As a teacher models a solution to a problem, he circles a particular section and draws a cartoon 鈥渢hought bubble鈥� next to it, then asks his class, 鈥淲hat do you think I鈥檓 thinking right here?鈥濃�俆eaching online, this can be done through a text box, Berry noted. In a paper version of the exercise, students could fill in the thought bubble.
Whether they鈥檙e teaching virtually or in person, teachers can also harness new technologies to get students talking about math. Tools like FlipGrid or TikTok let students get creative making videos of themselves solving a math problem or explaining their thinking about a possible solution, Berry said.
Maybe, just maybe, when students are having fun, they might not notice that they鈥檙e learning more deeply about math. Research suggests that when students talk more about their math thinking, they are more motivated to learn and they learn more. Talking about math thinking can also serve as a stealth form of assessment, giving teachers insight into what students have mastered and where they still need help.
