In this article in Mathematics Teacher: Learning & Teaching PK-12, Kathryn Lavin Brave and Jillian Miller (Baltimore County Public Schools) describe using Fermi questions to get students thinking about key mathematics standards while bolstering their social and emotional skills. Fermi questions were named after the Nobel Prize-winning physicist Enrico Fermi, who was known for his theoretical and practical contributions and for making reasonable estimates from limited data.
Fermi questions are designed to get students working on a challenging problem “by making reasonable assumptions about the situation, not necessarily relying on definite knowledge for an exact answer” (Taggart et al, 2007). These questions are especially helpful, say Brave and Miller, as schools emerge from the pandemic, providing an opportunity to combine math problem-solving with building SEL skills, especially collaboration. Some examples:
- How many times can you say the ABCs in 24 hours?
- How many hairs are on your head?
- How many sticky notes would cover the chalkboard?
- How many pizza boxes would it take to cover our classroom floor?
- How much water is wasted by a leaky faucet in one day?
- How many cars drive by our school building in a day?
- How many plastic containers does the cafeteria throw away each week?
Brave and Miller suggest this step-by-step plan for using a Fermi question in an upper-elementary classroom:
- The teacher gives background information on Fermi and the role of estimation in solving problems.
- Students are presented with a Fermi question that’s appropriate to their grade level and a mathematical skill or concept they’re learning.
- Students are encouraged to make “wild estimates” on what the answer might be.
- The teacher introduces the idea of “outliers” and the class discusses answers that seem too high or too low to be plausible.
- Students discuss which estimates might be closer to the exact answer and why.
- The class discusses a plan for finding the answer, dividing the Fermi question into a series of questions than might be used to get relevant data.
- Students get into groups to find the answer; the teacher fields initial questions like, Can we use a ruler? Can we use a calculator?
- The teacher circulates, guiding students with mathematical questions and prompts and highlighting interesting strategies and insights for the whole class.
- The teacher points out SEL insights on self-regulation, sharing, self-awareness, patience, and persistence.
- The teacher reminds students to evaluate their work and make mid-course corrections.
- Finally, groups present their answers to the whole class for critique and discussion and share what they learned about social and emotional skills.
“Using Fermi Questions to Foster Community” by Kathryn Lavin Brave and Jillian Miller in Mathematics Teacher: Learning & Teaching PK-12, November 2022 (Vol. 115, #11, pp. 801-807)
Please Note: This summary is reprinted with permission from issue #964 of The Marshall Memo, an excellent resource for educators.
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