Questioning and Vocabulary Supports That Inspire Language-Rich Mathematics

Sue O'Connell

Most of us remember learning mathematics in quiet classrooms. Teachers demonstrated procedures, students silently practiced with worksheets and workbooks, and answers were quickly assessed as right or wrong. In contrast, today's vision of mathematical proficiency blends computational fluency, conceptual understanding, and application, moving math beyond memorization and computations into reasoning and problem solving. As we work to adjust our teaching practice to align with our goal of developing mathematical thinkers, we recognize the importance of talk and writing. Through math talk, our students are able to process their ideas, hear others' thinking, and ultimately revise and refine their own understanding.

Creating language-rich classrooms can be challenging for teachers. Figuring out what questions to ask, determining how to cultivate productive math talk, and finding ways to support precision in communication challenge us as we rethink math instruction.

Questions That Promote Math Talk

What questions do you ask to promote talk and writing in math class and how do your questions foster diverse thinking? Each type of question challenges students to think about mathematics in a different way.

• How questions ask students to explain procedures. They are challenged to identify and communicate the steps they take as they perform math skills or solve math problems. For example:
  • How did you solve that problem?
  • What did you do to get that answer?
    
• Why questions ask students to make sense of math ideas and justify their answers and processes. For example:
  • Can you defend your answer?
  • Why did you choose that strategy?
    
• How does this compare to …? questions ask students compare concepts or methods and make connections between math ideas. For example:
  • How is this like …? How is it different?
  • How is this problem like one you've seen before?
    
• What do you notice? questions ask students to observe data and investigate and identify patterns. For example:
  • What did you observe in the chart, table, graph, or investigation?
  • What patterns do you see?
    
• What is the big idea? questions ask students to use their observations and insights to generalize as they discover rules or shortcuts. For example:
  • What keeps happening? Why?
  • What is the rule?
  • Will it always work? Explain.
    
• What did you learn? questions ask students to rethink lessons and summarize their learning. They reflect on what they learned and ask questions about what remains unclear. For example:
  • What is something new you learned today?
  • What questions do you have?
  • What is easy or hard about this skill? Explain.
    

With careful attention to the questions we ask, we prompt diverse thinking and stimulate rich class discussions that support our students as they test their thinking, refine their skills, build conceptual understanding, and solve math problems.

Cultivating Math Discussions

And who answers these questions? Simple instructional shifts, like asking students to reflect silently followed by partner talk, rather than calling on one student to answer a question, allow all students to process the question and voice their thinking, which yields rich classroom discourse.

Specific questions that encourage student-to-student talk serve to extend discussions and draw more students into the classroom conversations. For example:

• Did anyone solve it in a different way than Liam did?
• What do you think about what Colin said?
• Does anyone want to add to what Bailey shared?

Some students have difficulty diving into conversations, unsure how to insert their ideas into the discussion. Supporting students by discussing and posting possible sentence starters helps them find ways to insert their thinking into ongoing conversations. For example:

• I agree with Blake because …
• That reminds me of …
• I think Molly said …
• I would like to add …
• I don't understand why you …
• Could you explain what you mean when you said …?

And creating a classroom environment that allows students to feel safe to share their thinking, even when it is in a developmental stage, relieves anxiety and leads to more engaging conversations. Some pointers for creating a safe environment for math talk include

• Acknowledge the value of mistakes. Not only are they OK, but they are expected in math class.
• Allow students time to share their ideas with partners and work out their thinking prior to revealing that thinking to the whole class.
• Provide opportunities for students to change their minds as they hear and process others' comments.
• Praise effort, perseverance, and collaboration.
• When possible, deemphasize right or wrong answers and emphasize reasonable procedures, conceptual understanding, and mathematical insights.

Precision

The language of mathematics is extensive and specific, and students often lack the words to adequately express their ideas. Attention to math vocabulary, using any of the strategies below, helps students internalize this technical language and allows them to more precisely share their thinking.

• Introduce new words in context, using pictures, examples, synonyms, and connections to past math ideas. Many teachers record new words on math talk charts, similar to anchor charts. The word is recorded along with pictures, examples, or numbers that help explain its meaning.
• Display words for reference. Regardless of grade level, students benefit from seeing new words as they are learning them. Classroom word walls allow students to locate and use precise language as they are talking and writing.
• Create ongoing opportunities to talk and write using math vocabulary. Classroom experiences like sorting math vocabulary, webbing word associations (e.g., words that go with triangle or decimal), or other interactive vocabulary tasks (e.g., writing and solving math vocabulary riddles) provide ongoing exposure so that students can internalize math vocabulary.

Through the questions we ask, the ways in which we generate math talk in our classrooms, and our intentional focus on math vocabulary, we support students in talking frequently, precisely, and productively about their mathematical thinking. Unlike the silent classrooms in which we learned math, these language-rich classrooms allow our students to make sense of mathematical ideas through their communication.

Sue O'Connell is a former elementary teacher, reading specialist, and math coach. Now a nationally known speaker and education consultant who directs Quality Teacher Development, an organization committed to providing outstanding math professional development for schools and districts across the country, Sue is also the author of Math in Practice: A Guide for Teachers (Heinemann, 2016) and Introduction to Communication (Heinemann, 2007). Connect with Sue on Twitter: @SueOConnellMath

ASCD Express, Vol. 13, No. 22. Copyright 2018 by ASCD. All rights reserved. Visit www.ascd.org/ascdexpress.