Bill Carey likens the way we sometimes do or teach math to learning to compose great music but never taking the time to listen to it, or working hard at a task but never having a resulting creation to show for it. How does looking at math as one of the humanities or as a language that expresses beauty change those comparisons?
If you have had a student (or more likely, students) ask you why the class has to learn this math lesson, how do you typically answer? Do students find your answer satisfying? What are some ways Bill suggests that teachers can provide both more compelling answers and more compelling lessons that might answer that question before it is raised?
Does the way Bill uses math in his cartography job surprise you? What about the way professional mathematicians dedicate so much of their time to writing compelling papers? Does either use make you rethink some of the ways you approach teaching math in your classroom? How can you provide more context from “the real world” for the essential mathematical formulas and functions?
When a student asks Bill how it can be fun to work on a math problem for two months, he answers that he has the freedom to take the time to explore and create while aiming to accomplish the larger vision (time stamp 48:30). How does his answer compare with the concept of scholé? How does it contrast? Can you find any inspiration in his answer for your classroom approach, or is it too impractical for day-to-day use?
In what ways can it be helpful to teach the history and drama of mathematics?
How does one balance teaching math as history with ensuring students learn actual content?
Did you learn “pi” as a formula to “plug-in” without any understanding of its origin? What do you think of Bill Carey’s method of requiring students to solve “pi”?
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