I came across an Algebra I review problem the other day on Classworks. The challenge was to solve a quadratic using the Quadratic Formula. One of the answer choices was “can’t be solved.” *Which I did not notice.*

I was working with three students who did not understand what to do. Once I wrote out the quadratic formula, (actually, all I had to write was the negative b plus or minus!) they began to remember. One boy immediately told the other two how to find a, b, and c. That required a discussion about standard form, so we had to do a little rearranging of the problem given on the screen. Once we got the formula equal to zero, the second student plugged the numbers into the correct places! The third began offering solutions to various parts. I thought we were doing pretty good! Until we came up with a negative under the radical.

Like the music in Jaws… Dum, de dum, dum… They looked at me, dumbstruck.

“What do we do, Ms. Maxcy?”

I asked them if they had learned about imaginary numbers. *(Of course they hadn’t – yet. This was only Algebra I! But sometimes I forget which level I am teaching… Which is another story altogether!!!)*

Still not checking the given answer choices, I blithely proceeded to give them a brief ‘reminder’ lesson on real and imaginary numbers. They continued to look at me blankly.

As I magically (to them) unraveled the answer as 2 plus/minus 2i sqrt 11 divided by 3, they stared at me. Then they stared at their answer choices. They looked back at me.

“It’s not there, Ms. Maxcy.”

At this point, admit it, we teachers think, “it’s got to be there, that’s the right answer; why is it not there? Gosh, did I do it wrong?” And then we doublecheck our answer. And then it hit me. This was Algebra I. We don’t teach imaginary numbers. Yet. It was then that I finally looked at the answer choices…

The correct answer was there, but *it wasn’t the correct answer at all! *

Right there in front of me, there was the answer that the students were supposed to choose: choice “D) Can’t be solved.”

Right there in front of me, there was the answer that the students were *supposed* to choose: choice “D) Can’t be solved.” This is a terrible choice! It’s not the right answer! It’s not a good answer! Okay, so we don’t teach them imaginary numbers in Algebra I, *why don’t we just list the result with a negative under the radical as the answer?!? *

The kids get used to seeing the beast (negative radical) and we teach them how to simplify in Algebra II or geometry, depending on your school system. But, please, NOT *“can’t be solved”!*

That is just setting them up for trouble ahead! Lay the foundations, don’t build a wall that will have to be torn down later. Please!

Rant finished. Thank you for listening.

My daughter fell in love with math when she took high school calculus, continued it at the Naval Academy–even considered a math major. She finally got so far into calculus that they taught theoretic stuff, for situations that don’t exist today. Now that’s problem solving!

That is the mathematical magic.

Problem: Write down the number which when squared gives 2

Can’t be solved !

Never mind, we want it anyway, so we invent a way of writing it down (with a new sign, the square root sign).

But that’s cheating !

No it’s not, it’s mathematics.

What a lot of these there are – pi, e, log, gamma function, infinity, …..