How do you teach students to hang in there when learning gets difficult? We talk about the importance of perseverance all the time these days; it’s akin to growth mindset but not precisely the same thing. The ability to persevere in mathematical work relies on a set of skills that some students have and others do not yet have. Many students who struggle with mathematics have not yet developed the ability to stick with learning when it becomes tough; because of their history of failure in school they do not see their own capacity for academic learning. They probably have plenty of perseverance when it comes to non-school-related learning but they don’t believe that perseverance in mathematics will result in success. Unconsciously perhaps, they think that continuing to work hard on challenging problems is a waste of time; it will just confirm their lack of innate ability and their unworthiness. Additionally, they may not yet know how to persevere in academic settings – the specific strategies they can draw on to push through cognitive dissonance in search of understanding.
At the TeachingWorks Elementary Mathematics Laboratory* I witnessed Dr. Ball teaching her students how to persevere in working on a highly challenging math problem. It was eye-opening!
Dr. Ball had introduced the students to the mini-computer, a fascinating low threshold – high ceiling problem set created by Belgian mathematician Frédérique Papy. The class solved some basic problems with the mini-computer (e.g., What are all the ways you can make 7 on your minicomputer?) and then for homework they taught an adult about the mini-computer.
The next day Dr. Ball posed this problem:
| If you have just two checkers, what’s the smallest number you can make? What’s the largest? What numbers in between are possible?” |
Things started off smoothly enough. The class agreed that 2 was the smallest possible number and that 16 was the largest option. Dr. Ball asked students to explore the second part of the problem independently. Some students dove right in, quickly discovering solutions for 3, 4, 5, and 6. Others struggled to understand the problem and asked Dr. Ball or each other for help. I was focused on taking notes when I heard a sudden shift in the sounds of the classroom. For an instant things became quieter – frequently a sign that thinking is taking place. I looked up and watched in amazement as multiple students simultaneously gave up on thinking and on themselves. Emotional distress was evident in the students’ behavior and voices. Off task behavior erupted. Several students lashed out at each other verbally over trivial matters. One student began arguing with Dr. Ball, in essence accusing her of not being fair by giving them a problem that was so difficult. Across the classroom, I heard a tone of agitation in voices. I realized that this transformation had been triggered when students tried to find a solution for the number 7 (which is impossible with two checkers). I thought to myself, “This is what it looks and sounds like when student don’t yet know how to handle cognitive struggle.”
Through it all, Dr. Ball remained calm and focused. She ignored the off-task behavior and non-critical conflict and continued working with individual students to help them gain a foothold with the problem. She focused initially on what a student had done right: “I noticed that you figured out ___. How did you do that?” She called the student’s attention back to the conditions of the problem. She encouraged students to ask themselves questions. Gradually the emotional distress dissipated. Students became calm and thinking resumed.
During the class’s reflection on their experience, Dr. Ball wrote the word “perseverance” on the board. The class was silent as Dr. Ball explained this term and its importance to learning. My sense was that each student was making connections from his or her experience to the concept of perseverance. I felt that this new understanding would boost the students’ confidence in tackling future problems and would also re-shape their identities as learners.
In the end-of-day exit ticket, Dr. Ball gave students a sentence frame to respond to: Today I persevered by ___. One student called Dr. Ball over and whispered that he hadn’t persevered today. Dr. Ball responded, “You can write that. And tomorrow I’ll help you to learn how to persevere.”
What could be more important to our students’ future success in school and in life?
*The TeachingWorks Elementary Mathematics Laboratory (EML) at the University of Michigan is both a summer math program for students and a professional learning experience for educators interested in learning about effective mathematics instruction. More information about the EML can be found at http://www.teachingworks.org/training/LaboratoryClasses.
Reference:
Ball, D., & Shaughnessy, M. (2017). Lab class #2 lesson plan. TeachingWorks, University of Michigan Ann Arbor.
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