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Four Ways to Build Student Motivation and Self-Sufficiency

By Kim Marshall, TIE columnist

“Four Moves to Motivate Students in Problem Solving” by Anjali Deshpande and Shannon Guglielmo in Mathematics Teacher, May 2019 (Vol. 112, #7, p. 510-515), available for purchase at; the authors can be reached at and
In this article in Mathematics Teacher, math educators Anjali Deshpande and Shannon Guglielmo report on four teaching moves that they have found maximize student motivation and foster productive mindsets (i.e., the way students perceive their abilities):
• Deconstructing productive struggle – In her New York City high-school classroom, Guglielmo gave students a challenging problem and walked around taking notes on the strategies they used. After five minutes she paused the lesson and told students the strategies she’d noticed and wrote them on an easel sheet: reading the question again, doing a Google search, talking to a classmate, looking at notes and a previous assignment, looking at the word wall, using a calculator, and asking the teacher. Students could see the wide variety of resources that were available if they were stuck on the problem.
The class got back to work, and this time Guglielmo took notes on students’ facial expressions and body language as they continued to wrestle with the problem. After five minutes, she paused the class again and asked, “So, what does it look like, feel like, and sound like to persist in solving a problem?” and charted what she’d seen around the classroom: deep sighs, putting head in hands, thumping arms, shuffling papers, surprised looks at a breakthrough moment. “To name what productive struggle means in the context of a mathematics classroom is to give students concrete examples of what is acceptable, meaningful, and generative in the school space,” say Deshpande and Guglielmo. They suggest posting easel sheets like the ones generated in this lesson and referring to them often so students will more readily embrace occasional frustration and keep trying.
• Silent think time before collaboration – When a group of students is given a problem and starts discussing it, eager beavers may jump in with a solution, creating a power dynamic about who is smart at math and who isn’t. In addition, some students become freeloaders, relieved of having to do any concerted mathematical thinking. “Speed is often mistaken for intelligence and capacity,” say Deshpande and Guglielmo; “the fastest finishers are usually considered the smartest by their peers.” To counteract this tendency, they tried a partnership protocol for tackling a new math problem:
- Each student reads the problem silently, generates ideas about how to solve it, and jots them down.
- Students ask if their partner or groupmates need a few more minutes or are ready to work together.
- When everyone is ready, students share strategies, ask questions, and support each other.
- When they’re finished with the assignment, students ask themselves if they were persistent, if their solutions make sense, and if they have any questions.
This protocol prevents a few students from hijacking the problem-solving process and gets everyone working at full capacity, with enough time to think through the problem.
• Revise-and-resubmit grading – When students receive a low grade for a test or project, they may take it as an evaluation of their mathematical ability and even of their intelligence, becoming less motivated for future work. Deshpande and Guglielmo experimented with several variations of a revise-and-resubmit policy for students who receive a low grade:
- Students can take an alternative test on the same content and get a new grade.
- Students can revise their answers on the original test and the initial grade is replaced with a new one.
- Students revise their answers on the exam, or take a similar exam, and the new grade is averaged with the initial one.
Students responded very favorably to revise-and-resubmit. One commented that the teacher “doesn’t want to see us fail; she is that type of teacher. She cares, and a lot of people know that.”
• Helping, but not giving too much help – Some students rely heavily on teachers’ hints and rescuing; they need to be weaned from this dependence if they’re going to be self-sufficient down the road. “The keys to using this move successfully,” say Deshpande and Guglielmo, “are to remain neutral in tone, refrain from sharing direct answers to student questions, and paraphrase students’ questions back to them so as to give them a second chance at answering their own questions. End the move by saying, ‘I know you can do this; I’m going to walk away now, OK?’” This approach was helpful in getting students to persist and see themselves as mathematically competent. One student said it was like a parent guiding a child learning how to ride a bicycle and letting go at just the right moment: “She’s basically doing the same strategy but with math, and that feels comfortable.”
All four strategies, conclude Deshpande and Guglielmo, “are about building a risk-tolerant space in which students build confidence and sustain engagement.”

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