Good Moment

So this was an exciting moment that happened several weeks ago that I'd like to share with you.

This past semester, a student asked, “Why do we have to learn how to simplify exponents? Will it ever help me when I go to the grocery store?” My immediate response was, “Is the only purpose of education to help you make it through the grocery store?” Many students miss the purpose of education, and schools don’t often do a very good job at responding to their inquiries. We do not educate generation after generation simply for the purposes of survival, but we do want to promote students to ask their own questions and create their own ideas about the world. So another student responded to the question first. He said that it was important to learn math because you don't want to be embarrassed because you can't do a simple calculation when someone asks you. He said that you want to be a smart, educated person. I thought he gave a great answer, and I also added that you need to keep learning math because you don't want to cut out so many options for careers when you're 15 years old. Moreover, the skills you learn from doing math will help you in any field to go into. So I was glad that conversation went as well as it did.

So class went on, and we transitioned to a different topic. We had just started talking about linear functions, so we were reading mini-stories and turning them into equations of straight lines. In one story, someone needed to bake 100 cookies for a bake sale, but that person could only make a dozen cookies every ten minutes. The equation to describe this story is y=1.2x because you begin with 0 cookies and then you simplify 12 cookies divided by 10 minutes to make 1.2 cookies per minute. It seemed equally as straightforward as any other problem we had done, but that same student called out, “Wait, I don’t understand where the 1.2 is from.” So I said, “Well, to find slope, we divide the change in y by the change in x. So 12 divided by 10 is 1.2. You’re simplifying so that it’s like making 1.2 cookies every minute.” The student responded, “But that’s not what’s happening. You’re not making 1.2 cookies every minute. You’re making 12 cookies every 10 minutes. The cookies aren’t finishing gradually; you make them all at the same time.” So I took a minute to think about what he said, and I realized he was right. He was arguing that this problem was not best represented as a linear function. Cookies weren’t being made gradually; 12 cookies were made every 10 minutes. So I had to agree with him. I said, “You’re right. You’re saying that a linear equation isn’t a good model for this problem. So do you think our graph would look more like this?” I graphed a step function (a series of horizontal lines getting higher), which is a function they won’t learn for another year or two. He agreed with me that this graph was better. I was really proud of him for pointing that out, and I was really proud of myself for listening to him. Math can be very complicated, and when we don’t listen to our student’s queries or when we try to make their thoughts fit into our lesson, we restrict their growth and development. I certainly don’t want that. Furthermore, I loved that I could show him that math is actually useful to visually represent real-world problems and that he had the power to figure it out for himself. I only hope I can figure out how to do that every day in my classes.