Elicit and use evidence of student thinking

Teacher Actions

Student Actions

• Identifying what counts as evidence of student progress toward mathematics learning goals.

• Eliciting and gathering evidence of student understanding at strategic points during instruction.

• Interpreting student thinking to assess mathematical understanding, reasoning, and methods.

• Making in-the-moment decisions on how to respond to students with questions and prompts that probe, scaffold, and extend.

• Reflecting on evidence of student learning to inform the planning of next instructional steps.

• Revealing their mathematical understanding, reasoning, and methods in written work and classroom discourse.

• Reflecting on mistakes and misconceptions to improve their mathematical understanding.

• Asking questions, responding to, and giving suggestions to support the learning of their classmates.

• Assessing and monitoring their own progress toward mathematics learning goals and identifying areas in which they need to improve.

Dig in more!

Why Check it Out

Podcast: Rounding Up: What If I Don’t Understand Their Thinking?

Ryan Flessner, What If I Don’t Understand Their Thinking? ROUNDING UP: SEASON 3 EPISODE 15

“What do I do if I don’t understand my student’s strategy?” This is a question teachers grapple with constantly, particularly when conferring with students during class. How educators respond in moments like these can have a profound impact on students’ learning and their mathematical identities.  

In this episode, we talk with Ryan Flessner from Butler University about what educators can say or do when faced with this situation. 

Support productive struggle in learning mathematics

Teacher Actions

Student Actions

• Anticipating what students might struggle with during a lesson and being prepared to support them productively through the struggle.

• Giving students time to struggle with tasks, and asking questions that scaffold students’ thinking without stepping in to do the work for them.

• Helping students realize that confusion and errors are a natural part of learning, by facilitating discussions on mistakes, misconceptions, and struggles.

• Praising students for their efforts in making sense of mathematical ideas and perseverance in reasoning through problems.

• Struggling at times with mathematics tasks but knowing that breakthroughs often emerge from confusion and struggle.

• Asking questions that are related to the sources of their struggles and will help them make progress in understanding and solving tasks.

• Persevering in solving problems and realizing that it is acceptable to say, “I don’t know how to proceed here,” but it is not acceptable to give up.

• Helping one another without telling their classmates what the answer is or how to solve the problem.

Dig in more!

Why Check it Out

Open Middle

Great resource for a quick review or preview to a lesson in a creative way.  Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. 

Podcast: Episode #206 Crafting a Productive Math Struggle in Your Classroom

Kevin Dykema spends time with us to unpack why productive struggle is a necessary part of an effective mathematics program, what we can do now to plan and implement lessons that place students in a productive struggle, and how we might convince key stakeholders that a new kind of math classroom can better serve students.