Where Did Quadratic Formula Come From?
by Josh Hostetler
(Richmond, VA, USA)
(I have many stories like this, but this is the easiest one to tell.)
I have pretty profound ADD/ADHD-combined type, but I wasn't diagnosed until I was 32 years old. The reason I am mentioning this is that memorization is not a skill I possess. If there is something I need to remember, I need to know where it came from, or how it came to be, or some curious thing about it, or a pattern, or some other kind of connection between the thing being remembered and the things I already know.
Now, I always had a proficiency for math, (which saved me from complete failure in the year this story takes place), but what I said above regarding origins and connections still applies when I'm learning new mathematical concepts.
So, when I was in tenth grade, I was taking Algebra II with a teacher who, in retrospect, clearly didn't understand the material herself, (a crying shame, and an all-too-common one).
When we got to the subject of solving quadratic equations, the teacher went through all the methods in the curriculum, (like a robot). Of course, the very last method mentioned was the quadratic formula.
As you know, the quadratic formula, while no big deal to the experienced, is a bit complex, at least in appearance, to the novice. So, of course, the teacher presented it utterly disconnected from all that came before, (another crying shame, and another all-too-common one).
When it was presented, despite my general mathematical proficiency, and despite my thorough understanding of completing the square, I was baffled. So, I raised my hand and the teacher called on me.
So I said, "Where did quadratic formula come from?"
To which she answered, "Oh, Josh… I don't know. Some old guy made it up hundreds of years ago."
…and that was that.
I got a C in her
Now, I teach freshman-level math at a University.
When I do, because of this experience and several similar ones involving this teacher and others, I always make sure to explain the origins of everything, and I make doubly sure to always keep things connected, so that no topic seems like it's detached from what came before, (all the way back to 1+1=2), or from what is to come later.
It is my understanding from student feedback that this works very well. I've had several tell me they suddenly "get it" where they absolutely did not before, and I've even had a handful change their major to mathematics after taking my class. I feel I must be doing something right. But, most of all, I feel that my teachers that pulled this stuff on me did something very wrong.
It's a terrible state of affairs, the way math is taught to kids in most schools these days. I hope someday something will happen to fix the situation. Until then, I will do my best to fix the broken students that the system spits out who then land on me.
(Perhaps some day I'll come back and tell another story, which I'll probably call "How I Discovered Algebra." The title is misleadingly positive… Sorry to leave a cliffhanger, but I need to go teach a class now, and who knows when I'll remember to write it. I left the cliffhanger so that, if anyone is dying to read it, they can bug me to write it.)
Thanks for listening.
This is a great story and one in which we can all relate too. Unfortunately, this is the state of affairs and can only be solved with by more experienced, competent teachers...starting at pre-school! Well, we all look forward to hearing how you discovered algebra. Thanks for stopping by.