Recently I played around with Snagit on one of the class Chromebooks and discovered how easy it was to create a GIF. I then tried to figure out how to leverage this in the classroom. What I came up with was a prompt based on the GIF below.
The prompt essentially asked students to recreate the GIF. To accomplish this they had to “get under the hood” of the mathematics. This required them to generalize (they’re used to finding secant lines at concrete points) and that was very difficult for them. We rarely ask students to generalize and when we do, it’s usually is in context of a “critical thinking” book problem that gets skipped. Worse than that, often the teacher ends up doing the problem for them at the beginning of the next class. And even if a student does try it, unless it’s an odd problem, they usually can’t see if their generalization was correct until the next day.
As we moved through the calculus unit on related rates I searched for a way to bring more meaning to the topic and to make it more exciting. Some students were struggling and I wanted a solid review day before the quiz. I came up with this “Develop and Sell it” Activity. Essentially I gave students 4 related rates problems that were as “real world” as I could find. I had students work in groups of two to four and told them that they could only work with their group. They were told that they worked for a firm that worked out related rates problems for companies. Their task was to “develop” the solution and “sell” their reasoning and solution to the company.
Once they had found solutions that each group member agreed to, I assigned each student in the room a number 1-4. Students who received a number 1, for example, then congregated and compared solutions and methods to that problem. This then allowed students to see different perspectives on the same problem and “argue” about whose answer was right. It was a tremendously engaging activity that the students enjoyed and it relied on one important piece: I couldn’t help at all. I didn’t tell them if their answer was right, if their method was correct, or “what I would do in their situation.” They had to rely on their reasoning and justification. Taking myself out of the equation forced students to analyze each other’s work and critique each other’s reasoning. That was the best part of the activity!
In the future I would love to get actual questions from companies and industry. I’ve also considered video questions and other ways to make the problems more authentic.
As usual, any feedback you can give me would greatly appreciated!
(Here is the Pages Version of the Activity)