One of the first things that pops up in chemical education at the high school level is stoichiometric equations where a student is supposed to determine such things as yields, coefficients, and amounts of substance on a purely theoretical basis. This quickly becomes old hat for many students. In high school, my stoichiometric technique (if you could call it that) left a lot to be desired. I tended to “divine” my answers on tests and quizzes by playing with numbers until an answer made sense- then using it. It worked surprisingly well- and I got through classes learning very little but with decent grades. At the time, I wasn’t terribly interested in chemistry, and the class really was boring up until the end, where we got to learn about electrochemistry. I didn’t realize at the time that the subject matter wasn’t being done any justice. To me a mole was a mole was a mole. I just knew there were these numbers that I used to divine answers.
I didn’t know that Avogadro’s constant has changed slightly. IUPAC and IUPAP were embroiled in controversy over whether to consider the mole to be the number of oxygen atoms in a sample of oxygen-16 or as the physicists preferred, the number of atoms in a fixed sample of carbon-12. By adjusting the standard, the atomic mass unit slid a little, so that hydrogen was no longer 1.0000 amu, but became 1.0083 amu. To me, Avogadro’s number was a constant, an unvarying and mysteriously established number in the universe like pi or Euler’s number. In reality, it’s nothing more than the definition of an arbitrary unit of measure unvarying only so long as the units chosen to measure it. Technically so are approximations of pi and Euler’s number, since they are written in the base 10 system we use for counting.
The physicist Richard Feynman, arguably well known for his antics as much as his science, wrote of “fragile knowledge” in his book, “Surely, You’re Joking Mr. Feynman”. I’ve only recently read it, I sort of happened upon it at the bookstore. He recounts how he capriciously got some people to look in astonishment over a french curve and note how the lowest point at any of its curves was designed to have a horizontal tangent, no matter which way it was turned. The trick was of course, that it wasn’t designed that way, the lowest point of any curve has a slope of zero! Yet here were a bunch of students who had taken calculus and were all using pencils to establish for themselves this peculiar whim of french curve makers. The story struck a chord with me, since it set the lower bound for the harm caused by fragile knowledge: Looking like a fool.
Yet this is the way I was taught the number–as a number–not as a relationship or standard. When you think about it, this is the way we’re taught many other things, like pi as 3.14, instead of “the ratio of the circumference of a circle to its diameter”. My question is, why insist on this sort of teaching? So that students can focus on calculations and thereby “learn what they need to know?” That’s foolish and short-sighted, as demonstrated by my experiences fooling teachers into believing I knew anything about stoichiometry and getting Bs (which stood for Better than I deserved). So what if the time available in a semester or school year is limited, isn’t the measure of how well something is “taught” the extent to which it is “learned” (as in- not simply memorized)?
In fact it was only after reading Asimov on Chemistry a long time ago, that I was able to finally get a handle on constants, the real tragedy being that this information is not something I could have gotten from a class or even my college level chemistry textbook. I could not have even developed an interest an chemistry (or math- another story) were it not for my readings outside the classroom. It’s easy to understand why it’s important for students to learn to manipulate numbers in chemistry, but what is the point if they’re doomed to be obsolete calculating machines who can give you the recipe for 1M sodium acetate, but have no clue what that information means?