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The Teacher Tip

Eliciting Students’ Mathematical Thinking

January 11, 2018

Adapted from Children’s Mathematics: Cognitively Guided Instruction, Second Edition by Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, and Susan B. Empson

Asking students, “Can you tell me how you solved that?” is a central feature of CGI classrooms. This question is a productive way to start engaging students in explaining the strategies they used to solve a problem. More specific follow-up questions support students to elaborate the details of their strategy. Having a student share more details of her thinking engages the student in articulating, explaining, and justifying her thinking and enables the teacher and other students to understand the strategy the student used.

Keep in mind these principles for eliciting students’ mathematical thinking:

  • Consistently ask students to share their thinking.
  • Find ways for each student to explain his thinking to you or other students.
  • Follow up with specific questions drawing from what the student shared or did.
  • Support students to work all the way through the details of their strategies.
  • Ask about correct, incorrect, and incomplete strategies.
  • Watch for students to tell or show you that they are ready to be supported to adapt their strategy or try a new one.
  • Listen, observe. Try to not impose your ideas on students.

To learn more about Children’s Mathematics: Cognitive Guided Instruction and download a sample chapter, visit 

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