Students go from class to class and have a million things going on in their lives. So how do I make mathematical ideas sticky for my students? How can I make it so that they still remember a concept a day, a month or even a year later? To answer these questions, my TRC research team and I have been investigating opening up tasks to make them more accessible to students.
At the start of this year, I was thinking of how to make the concept of the definition of a function sticky for lesson 1.2.4 in Core Connections Algebra 1. In the textbook, there is a picture of a soda machine and some questions about what happens in different situations with the soda machine. This typically leads to students developing an understanding of the machine functioning properly – if it behaves consistently and predictably.
In the past when I’ve done it, I’ve drawn a diagram of the soda machine buttons but students still were a little bit confused. As I read the problem this year, I thought about how I could help them see what is going on and hopefully better remember the concept. I realized that I could have my students act out the process, a series of inputs that would cause soda to come out from the machine.
This is my soda machine:
My co-teacher sat behind the machine with the sodas and I narrated different situations and we asked if the machine was functioning properly. The students pressed the buttons and were given cans of soda. As a result, they were able to see and experience what the problem in the book was describing. For example, a student was asked to press Sprite and my co-teacher gave that student a Sprite. Then, another student pressed Sprite and the student received another Sprite. I then asked the class if the machine was functioning properly and many students replied, “Yes.” Then, we had a student press Fanta and they received a Fanta, then another student pressed Fanta and received a Coke. Again, we asked if the machine was functioning properly. This time students replied, “No.” We went through one more situation where the student pressed Coke and kept getting Diet Sprite. This one was a little tricky for the students, but they eventually decided that it was functioning properly. After acting this out in class, we had the students take a minute in their teams and come up with a definition as to whether the machine was functioning properly or not. Teams then shared their definition of a function in a whip around.
During this lesson, I postponed using the text and allowed students to focus on developing the concept. As a result, I noticed more students engaged in learning about the definition of a function and, weeks later, referring to the soda machine experience in subsequent activities. It also made the class a lot more fun with different kids getting hypothetical soda from the machine, and that’s never a bad thing.