This week I have been reading with great interest a discussion in a chemistry teachers' Google Group. It started with a post about whether or not teachers find it acceptable when students give answers as 3.6e-4 instead of 3.6 x 10-4. There were a couple of back and forth ideas about whether or not this is acceptable practice on its face value:
Then the conversation shifted away from that and to a more important idea: does writing an answer as 3.6e-4 tell a teacher something about a student's understanding of the math and/or the chemistry?
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
When we begin the mole, we have to use scientific notation because the numbers of atoms in a small sample of matter will be so large. Until then, has there really been a point in their mathematical education where they really needed scientific notation? I argue that even though it is probably taught in middle school math, it isn't really needed and, after that initial treatment, it also isn't revisited or practiced. Am I wrong? Why teach it in 8th grade if students don't need it?
What I observe when I teach this is that a lot of students want to use, and persist against my advice, to use the buttons for "x 10^" instead of EE, but shouldn't we expect that? They see 3.6 x 10-4 and that looks like the operations they have been putting into a calculator for many years, so they do what they know. Maybe what is missing is a conversation about when that will work (when they multiply) and when it will not (when they divide without parentheses) because that gets at mathematical understanding too. Eventually, most students become adept at punching the designated buttons into their calculator, but in March and April when we have been using it for months, I still have students who ask what they did wrong to get 0.00036 when I give an answer as 3.6 x 10-4, so I know the understanding isn't there.
Chemistry creates the headache that requires scientific notation to be the aspirin. Too often, though, perhaps my focus has been on getting us over the math hurdles so that we can be successful on the chemical ones. This same Google Group debates the merits of significant figures about once a year. Every year by May I make the same threat: Next year I am not teaching the sig fig rules. Instead I will require students to write down every digit they see in their calculator. After a few days of that torture, when they start begging to have some rounding rules and then I unpack the sig fig rules. Would it work? Is there something there that could help with scientific notation?
In short, how can I simultaneously help students be successful in chemistry and better understand math? Do you have ideas? I am all ears. Please comment!
Related aside: There are two iOS apps that I like for helping students see the magnitude of the powers of ten: TickBait's Universe and Universal Zoom. While they won't necessarily help students understand what a number in scientific notation represents, I love the conceptual way they represent it.
Related aside #2: Funny that it's called scientific notation, right? Not mathematical . . .