Word problems in math textbooks often give much of the information needed to solve them. There is no mystery. Students walk away from a math course with the only skill acquired being the ability to decode the textbook. They are just swapping numbers and plugging in different information. As a result, the so-called problems are no longer problems. They are routine and predictable. The problems are too scaffolded and the students realize that it’s an exercise in futility. An insult to their intelligence. While practice is indeed a fundamental part of math, when problems are variations of the same one, the motivation to complete them is lost. They don’t see the point of it all.
How can we make problems interesting and challenging?
Look to Enrico Fermi. The Italian physicist had a gift for making accurate estimates of seemingly unsolvable questions. Given little information, he was able to provide educated guesses that came very close to the actual answer. His most famous question, “how many piano tuners are in Chicago?” seems to make no sense, but through a series of questions, estimations and assumptions, he arrived at a reasonable answer. Legend says that Fermi calculated the power of an atomic explosion by looking at the distance his handkerchief travelled when he dropped it as the shockwave passed. He determined it within a factor of 2. For a discipline that is always looking for realistic applications, math class would do well to use Fermi problems. It doesn’t get more real-life than that!
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Using Fermi questions in our math classes will remove the pseudo-contexts of much of the problems. They are actually used in real life, unlike many of the questions from a math textbook. Companies use Fermi problems during job interviews as they offer a window into a person’s ability to think on their feet and their creativity. Scientists, economists and engineers use them in their work to get a ballpark idea of the feasibility of their projects. This power of estimation is a key aspect of mathematical thinking. Without it, all the math in the world won’t mean a thing.
Fermi problems emphasize the mathematical processes and help students practise estimation and reasonableness when solving problems. They strengthen number sense, dimensional analysis, and are important in developing a quantitative understanding of the world around us. They allow students to ask the right questions and break down complex problems into smaller, solvable ones. The problems don’t have a definite solution, providing room for interpretation and multiple approaches to problem-solving. The questions are not grade specific and can be used in a range of classes. The open-ended quality of Fermi problems is one of their strengths.
Encourage intuition in math class through Fermi questions. Give students something meaningful to solve. Tired, old word problems should be a thing of the past.