[latexpage]

If there is one thing in particular I dislike about many tests in science and mathematics, it’s how we link the ability to do well on tests with the ability to do science.

The biggest problem I have with this link is that the things we test are not the things we actually care about as scientists, mathematicians, or educators. A great example is the terminology question. This is a question that basically requires a student to know a definition without needing to understand what is important about the concept. Instead, they can “fake it” by knowing the correct definition. These questions don’t actually aid in understanding concepts, they just make sure you know what the proper terms are.

I saw a question like this the other day where I was tutoring a student. It asked, “Write down the above equation in functional form.” The equation was something like $3y -4x = 0$, and I couldn’t immediately understand what the question was. I knew that it involved manipulating the equation, but I didn’t even know what functional form was. Thinking back on it now, I imagine it must be an equation in the form of $y=mx+b$, but I still thought it was strange at the time.

What is the actual value of the question? To me, it only seems like a way of saying, “Write the above equation for y in terms of x.” That makes more sense to me, and it’s only a few words more than “functional form”, yet it is more descriptive. Additionally, I fear it slots the learning of equations and algebra into “archetypes”, which isn’t productive.

Another issue is that science and mathematics (and perhaps other fields, but I am not as familiar with them so I do not know) have serious naming issues. If you were to imagine the body of knowledge science has uncovered as a book in which anyone who has something new to contribute writes their own page and inserts it into the book, you wouldn’t be far off. Science is oftentimes a jumble of confusing terms, with a lot of historical baggage.

For example, I remember learning in my astrophysics class about the different classification of stars. I learnt that we had a whole system of stars: O, B, A, F, G, K, M. At first, I wondered why on earth the classification wasn’t alphabetical, since it classified the brightness of stars. However, I soon found out that the reality was the the original classifications weren’t particularly good, so the names were kept and the order was switched around in order to have them increasing.

Therefore, what could have been an easy process to remember the classifications became a mnemonic: Oh Be A Fine Girl/Guy, Kiss Me. While funny, it isn’t exactly intuitive to learn this classification, and this is something we were indeed testing on. My question then becomes: does being able to remember classifications well on a test really solidify our understanding of which stars are brighter? I’d argue probably not.

This isn’t the only example, either. If you’ve ever been privy to a science or mathematics class, you’ll quickly learn that equations and phenomena aren’t necessarily described in ways that are entirely useful for a person hearing the name. Instead, the concepts will usually carry the name of the person who discovered, invented, or came up with the concept. This is a way for many scientists and mathematicians to stay “immortal” in time. After all, few physics students are ever going to forget who Newton is, just like few biology students will forget about Darwin, or how mathematics students will not forget about Leibniz, Newton, Pythagoras, or many of the French mathematicians. We don’t know these people because we are all fans of the history of science (though some of us are). Really, it’s due to constant barrage of hearing these names in concepts in classes that solidifies these people in our minds.

Unfortunately, this isn’t a great recipe to actually knowing what these concepts means. Saying “Newton’s Laws of Motion” only gives me one real piece of information: the laws will be about motion. But these could have easily been referred to as the three general laws of motion. Except you will almost never hear that. Instead, you’ll hear, “Newton’s Laws”, because it’s a succinct way to describe them. And there’s nothing wrong with describing concepts in concise terms. The problem to me occurs when students get tested on knowing these things, where the names have almost no use.

I’m reminded of some words I’ve heard from Richard Feynman, who described an encounter he had with a kid who criticized his father because he never really explained the names of birds to Richard when they went on walks. However, Feynman shoots back, saying that his father taught him about the birds instead of just what the names were, and that this was much more valuable and interesting. Indeed, this is the sort of thing I imagine. Not that we shouldn’t understand what things are called, but that it’s always more important to know the concept than just the name, and we should be tested accordingly. Personally, I know that it would knock off a lot of stress from remembering how concepts worked, because I wouldn’t have to link a name to a concept. Instead, I could just explain the concept. “Explain Newton’s Second Law” would be asked as “How does motion relate to forces?” The latter question is much more descriptive than simply giving the name of a scientist.

I hope that a shift comes in mathematics and science soon, bringing questions that dig deeper instead of looking at surface-level detail about names.