To engage students in productive mathematical conversations, teachers can orchestrate discourse and structure learning environments to deepen engagement and support learning. Using effective strategies will support students as they learn to participate in mathematical discourse.
Below are six strategies from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom. For more, please download Dr. Kersaint’s new whitepaper: Orchestrating Mathematical Discourse to Enhance Student Learning.
Dr. Gladis Kersaint
Strategy 1: Help students work with and rely on one another.
Rules such as “Ask three before you ask me” can help establish classroom expectations by encouraging students to seek assistance from peers before defaulting to the teacher.
The teacher can also designate student experts (students who have demonstrated depth of understanding about a particular problem, concept or procedure) whom other students can consult before approaching the teacher.
Strategy 2: Allow students to work independently before sharing in small or large groups.
Students need time to gather their thoughts and identify what they know or do not know before they are exposed to the influence of other students. Then they can compare and contrast their approaches and solutions with those shared by others during the mathematics discussion.
Strategy 3: Use questions strategically to engage students in mathematical discourse.
Teachers can engage students in mathematical discourse by posing questions that encourage discussion and debate. Strategic prompts and questions require students to attend to particular aspects of the learning process, explain and justify their thinking, and deepen their understanding in the process.
For strategic question examples, see Talking Math: 100 Questions That Help Promote Mathematical Discourse.
Strategy 4: Acknowledge the importance of mistakes in learning and understanding by:
Learning mathematics is not just about getting the right answer. It is also about learning from previous mistakes. Encourage students to take risks in mathematics by:
- Recognizing that students will make errors because they are exploring and making conjectures.
- Reminding students constantly that errors are expected and natural and that they can be a good thing because they lead to enhanced learning.
- Helping students recognize what they have learned by analyzing their mistakes and identifying misunderstandings.
- Encouraging students to ask questions to clarify and critique the reasoning of their peers and establish the correctness of solutions.
- Empowering students to reach and justify conclusions based on their own mathematics knowledge without relying on the authority of the teacher.
Strategy 5: Use collaborative learning strategies.
When students work with peers or in small groups, they are able to take risks and build confidence on a small scale before they present solutions to the whole class. Strategies include:
- Think-pair-share. This approach can be used in a variety of instructional circumstances to encourage students to engage in mathematics independently and then share their results with a partner.
- Numbered heads. When students are working in groups of three or four, each can be assigned a number. Students know that any member of the group may be called on to provide a response, so everyone must have the same level of understanding.
Strategy 6: Take a creative approach to engaging all students in whole class discussion.
Teachers can use a variety of methods to gather information from the whole class or individuals that simultaneously allow them to assess individual and collective student understanding:
- Thumbs up/thumbs down. Teachers pose a question or problem that has a dichotomous answer (yes/no, true/false, X or Y) and ask students to respond, using thumbs up to represent one choice and thumbs down to represent the other.
- Response sticks. Teachers write each student’s name on a Popsicle stick or similar item, place the sticks in a container, and randomly select students by choosing a stick.
- Classroom response systems or other digital tools. Teachers can use classroom response systems to gather immediate feedback from students by asking them to respond using a clicker, website or text message and display results as a chart or graph.
We hope you’ve enjoyed our Mathematical Discourse blog series and are ready to begin this journey in your classroom. We strongly feel everyone benefits from mathematical discourse in the classroom: teachers are better able to access, monitor and evaluate students’ mathematical understanding and development; and students can reflect on their own understanding while making sense of and critiquing the ideas of others in a collaborative and supportive learning environment.
This blog is part of a three post series on the importance of mathematical discourse from Curriculum Associates, a Getting Smart Advocacy Partner, and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy here.
For more on mathematical discourse and Curriculum Associates, check out:
- Talking Math: How to Engage Students in Mathematical Discourse
- Talking Math: 100 Questions That Promote Mathematical Discourse
- Curriculum Associates: Leveraging For-profit Power With a Nonprofit Purpose
Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of South Florida.
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