My students were not happy with me and they weren't keeping it a secret. After a unit on scientific notation, I gave them a quiz containing a question they deemed terribly unfair:
The mass of a proton is 1.7 × 10–27 kilograms. What is the total mass of 7.2 × 1033 protons? (Write your answer in scientific notation and include the units.)I was told, with exquisite care and patronizing precision, that it was wrong of me not to tell them which arithmetic operation was expected. Addition? Multiplication? Subtraction? Division? How dared I give them numbers without specific instructions!
With professional patience, I waited out their lengthy complaints. Then, without saying a word, I turned back to the chalkboard and wrote out a brand-new problem:
The mass of a nickel is 5 grams. What is the total mass of 6 nickels?With frowns still on their faces, they blurted out, “Thirty grams!”
Another long silence as I waited for their reactions. The faces went neutral. One brave soul ventured a comment: “Were we supposed to know that?”
“Sure,” I replied. “All of you know that you multiply to solve problems like this. You just yelled out the answer to the nickel problem because it was so easy. What I'm trying to get across is that numbers written in scientific notation are still just numbers. You work with them just like you work with other numbers. You're letting your minds shut down because they look different, but you actually already know what to do.”
A smug expression is bad pedagogy, so I maintained a mild and neutral mien. I was quietly satisfied that I had gotten an important point across. My self-congratulation was just a little premature. (You'd think I would know better by now.)
A student in the back row grunted in dissatisfaction and posed a question in an irritated tone: “So on the next exam are you going to tell us what to do with the numbers?”
My spirits fell a notch.
“What do you think?” I asked.
I hope indeed that they do.