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2 Ways to Encourage Reflection on Math Concepts

Updated: Jul 8, 2021

Open-ended questions guide students to participate and to think mathematically, which cements their learning.

For many students, math is a subject where every question has one (and only one) correct answer. If a student is asked, “What is two plus two?” the only acceptable response is “Four.” What if students were also asked, “Why does two plus two equal four?” Reflection questions like this, which are purposely open-ended, do not have a single correct answer. Instead, these questions remove the fear of being wrong and encourage mathematical thinking, participation, and growth. “Reflection questions are important for students and help move the focus from performance to learning,” says Stanford professor Jo Boaler, who believes that “assessment plays a key role in the messages given to students about their potential, and many classrooms need to realign their assessment approach in order to encourage growth instead of fixed mindsets among students.” In addition to performance-focused questions and assessments (“What is the total sum of the interior angles of a triangle?”), you can ask open-ended reflection questions that encourage mathematical thinking and participation (“Why do you think the total sum of the interior angles of a triangle always equals 180 degrees?”). The second question shifts the focus from performance toward thinking, learning, and engaging with mathematics without the fear of being wrong. How can you incorporate reflection questions into your math lessons? Try these two useful strategies.

WHICH ONE DOESN’T BELONG? If you grew up watching Sesame Street, you probably remember the “One of These Things Is Not Like the Others” segment, where viewers had to identify one object out of a set of four that did not belong. This simple activity helps children to identify similarities and differences, and this type of thinking can be extended to learning math. Which One Doesn’t Belong? (WODB) math activities present students with four different visual graphics that are all similar and different from each other in some way. This four-quadrant activity is my go-to for getting whole-class participation, as each option can be argued as the correct answer.


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