Bridging the Gap
Recently at my teaching placement, I introduced the concept of negative exponents during a lesson. This concept always stumps students, and they tend to misconstrue negative exponents with multiplying by a negative number. I think of negative exponents as just notation, they denote an operation that you perform. But where do negative exponents come from? Why would we decide to denote them with a minus sign? Why not a different symbol, like the letter k or the symbol for pi? Asking these types of questions about negative exponents helps me to put myself in my students' shoes, and better empathize with them. One particular student in my class was really struggling to swallow this new idea. I pondered another way to explain the concept, and decided I could relate negative exponents to a concept this student knows well--inverse functions. I asked the student, "Let's go back to what you know. What does it mean to square a number? What does it mean to take a number to the powe...
