Equation hunters. You have seen them. This is their method:
- Oh, a projectile motion problem.
- Find projectile motion section in book.
- Find projectile motion example.
- Look for equation with the right stuff in it.
- Plug in numbers. Win.
Only they don't win. Sometimes they don't find the right equation. If they do find a valid equation, they don't know why it is valid. This is a bad idea. I tell my students - if you don't know where the equation came from, don't use it. You wouldn't eat strange candy off the ground, would you? It is much better to cook your own candy. That way you are sure there isn't any high fructose corn syrup in it.
Let me give an example. I have students working on a plain old projectile motion problem. Nothing fancy. A ball starts on the ground and lands on the ground. One of the questions was: how high did the ball go?
So, students are working on this problem. Some in groups, and some independently. A student asks me to check her work. Great. "Ok, what is this equation right here (as I point to her paper)?" Here is the equation.
"That is the equation to solve for the maximum height" she says. "Is it right?"
My favorite reply: "if you are not sure where the equation comes from, maybe you shouldn't use it."
"Oh, but I got the equation from the book. Here on page 88 there is an example that seems the same and they use this equation."
And here is the problem. Here this student found some candy on the ground and she thinks it is ok to eat. DON'T CANDY OFF THE GROUND.
Ok, then what should the student do? My suggestion is to start with very basic ingredients - you know like flour, sugar, and butter. For physics, these are very basic ideas. The two definitions of average velocity are a great place to start.
If you set these two definitions equal to each other, then you get:
Ah ha! So, am I saying that IS INDEED the correct equation to use? No. I am saying with just starting with some more basic ideas, you can get to that equation. Now you baked that equation yourself, you know where it comes from and what it can be used for. Much safer that way.
Really, this "find candy-eat candy" can get even worse. I hate when students find this "range equation candy" on the ground. That stuff has been sitting around for a long time and has ants on it. Yet still students eat it. Really, I blame textbooks for even including the range-equation (the equation that determines the horizontal distance for a projectile shot on level ground) in the summary of equations.
