Getting Students Working on Challenging, Open-Ended Math Problems

            “A good problem-solving task involves students getting stuck, experimenting, and getting unstuck,” say Stephen Caviness (Syracuse University) and sixth-grade teachers Crystal Wallen and Lorraine Stewart (River Bend Middle School, Sterling, Virginia) in this Mathematics Teacher article. “When students approach a problem with uncertainty, they have an opportunity for productive struggle.”

            Using a “Thinking Classroom” format (see Memos 976, 992, and 1013), heterogeneous groups of three students work standing up at vertical surfaces (with one marker) tackling “Open Middle” problems, which have the following characteristics: 

• A “closed beginning” – students get a specific prompt to solve a challenging problem; - Students haven’t been taught a prescribed method for solving the problem; 
• An “open middle” – there are multiple approaches for solving the problem; 
• Problems are designed to be accessible to all students, even those not on grade level;
• Students must approach the problem with their own reasoning and creativity; 
• A “closed end” – there are several possible solutions. 

“The Open Middle structure,” say Caviness, Wallen, and Stewart, “provides ample opportunities for teachers to respond to student struggle and help them to embrace struggle as a norm when solving problems.” 

            They conclude: “These tasks are powerful tools for creating a culture of collaboration in which students acknowledge and embrace the various thinking strategies that their peers have to offer… We believe that Open Middle tasks are worthwhile to implement in your classroom because they help students to embrace uncertainty, persevere through struggle, and be creative with mathematics.” 

 “Embracing Uncertainty, Struggle, and Creativity with Open Middle” by Stephen Caviness, Crystal Wallen, and Lorraine Stewart in Mathematics Teacher: Learning & Teaching PK-12, February 2024 (Vol. 117, #2, pp. 138-141); the article includes three videos of students working on a problem. The authors can be reached at scavines@syr.edu, crystal.wallen@lcps.org, and lorraine.stewart@lcps.org. 

Please Note: This summary is reprinted with permission from issue #1023 of The Marshall Memo, an excellent resource for educators.