Making Exponents Powerful

Despite 16 years of formal math education, I didn’t experience powerful math learning until last summer when I attended the math summer institute. In the institute, Kyle and the other presenters focused on a concept I had never heard: discovery learning. They led us through activities that were intentionally structured to allow us (the students) to construct new knowledge based largely off of a combination of what we noticed at different stages of the lesson and our prior knowledge. This experience blew my mind.

I had always loved math because I liked following a strict set of rules that would undoubtedly lead me to the right answer. In college, I struggled with math for the first time in large part because of the abstract nature of it. There was no longer one clear outcome I could achieve, and combined with the subpar pedagogical practices of my math professors, advanced math stopped making any sense to me.

Going into my MAT year, I didn’t want my students to just regurgitate information and plug in numbers to formulas like I did growing up, but I also didn’t want to make them feel as lost and overwhelmed as I felt in my college classes. My experience in the math summer institute showed me a middle ground for the first time, and an extremely promising one at that.

Throughout this year, I have wholeheartedly embraced this idea of discovery learning and designed and implemented a variety of different activities that embody it; as is to be expected, some of them went well while others did not. The element of this sort of learning that makes it so powerful is its student-centered nature. By getting students, instead of the teacher, to do the thinking by asking them what they notice or drawing on their previous knowledge, students can make strides towards, or even reach, significant math conclusions on their own. Through this, students learn to see themselves as constructors of knowledge and capable learners, which is extremely powerful.

The video above showcases a powerful learning experience in which my students discovered different exponent rules in pairs, planned a mini-lesson together based on their exponent rule, and then taught it by themselves to half the class in a jigsaw of sorts. The first powerful part of this came from having students discover an exponent rule for themselves. By noticing patterns in their given examples, drawing on their prior knowledge of exponents and bases, and collaborating with each other, each pair of students was able to write a formal exponent rule. To honor and encourage their ownership over their mathematical discovery, I then asked students to teach their classmates their rule. With their partners, students planned a mini-lesson using a modified version of the Clark LAP. To implement their lessons, the class split in two and each partner taught their exponent rule alone to their half of the class. After each lesson, the class completed a worksheet created by the teachers, which the teachers then graded and handed back.

Throughout this week-long activity, my students worked hard to discover their exponent rule and figure out how to explain it to their classmates. While many of their teaching presentations were shorter than I had originally anticipated, their classmates did a great job of asking questions during the presentations and asking for help as they completed the worksheets. While my students are high-achieving, many of them do not like explaining their thinking. I have consistently pushed my students to provide better explanations throughout this entire year, so it was really powerful to see them act as teachers and take the time to check in with and offer deeper explanations to their “students.” In their post-teaching reflections, over half the class said that they would like to do an activity like this again. I count that as a sign that they found it powerful too!