The Point, and the Beginning

So, as a kid (like first grade), I was always one of the "bright kids"--

Point of order: NEVER label your students. It's a cancer that will do horrible things for their self-esteem and/or make them into self-righteous know it alls. Yes, this did both to me. No, it's not a good idea.

-- and I was placed into a gifted-and-talented program. This allowed me to look at math and science, as well as reading and research topics, that were pretty advanced work for someone of my age. I mean, we were doing algebra and actually calling it algebra in first and second grade.

(For those of you that haven't thought about it, you were doing algebra in kindergarten... but no one told you about it till you were in at least seventh or eighth grade. If they ever did. Example: 3 + ? = 7. ... Replace the "?" with "x" and what do you have? 3 + x = 7. Solve for x. MAGIC ALGEBRA GO.)

All my life, I dealt with fractions, counting, and heck, even multiplication at a simple level. Everyone does. Anyone who's used a recipe for basically anything has used all of the above. ("Above" here doesn't include algebra. Usually. I've heard of recipes written in algebraic notation, I just can't find any at the moment.) Anyway, you've got a recipe that calls for 3/8 tsp. of vanilla, but no 3/8 measuring-spoon. So what do you do? You use three 1/8 tsp. measuring-spoonfuls, because 3·1/8 = 3/8. You use algebra and advanced (ish) math techniques, and it's was fairly intuitive.

There were other times in early classes where teachers would outright lie to students about what was "possible" or "allowed". For instance, in my first grade class, we covered subtraction of integers, and we weren't "allowed" to subtract a "big" number from a "small" number. It just wasn't done. But I knew better, and had been told about these shady, "criminal" things called negative numbers.

OOOOOHHH!!

"You're just not allowed to." That was the response. ... .... NO! It's obviously allowed, or the concept wouldn't be named and defined! (Sorry... It just bugged me and still does when teachers outright lie.)

Anyway, the culmination of all of this was in my sixth grade math class. Over the years, I stayed in the gifted-and-talented program and did more advanced math than my peers, and I'd occasionally get frustrated and angry and hate math. (Yes. You read that right. Once upon a long time ago, I actually thought I hated math.) Then Mr. Dye came to me one day in class.

Dye: Colin, why do you hate math?

Me: I dunno. I just do. It's dumb.

Dye: But... You're so good at it. You really are!

Me: It's dumb though!

Dye: Why don't you try not hating it, and maybe even consider liking it? You don't really seem to have a reason to hate it, so maybe if you just stop hating it, you'll enjoy it more.

Me: I... Okay. I guess, I can try that...

And that was the beginning. From then on, I didn't hate math. It wasn't a pain. It wasn't dumb. (It never was any of those things, I was just confused.) I actually started to like it. I got it. Deep down inside of me, it always just made sense and worked the way the teachers said it did. Occasionally (and usually far less obviously than the negative numbers fiasco of first grade) teachers would lie to me, but that would get fixed further down the road. I was just always able to--sooner or later--figure out what was going on, and get things done.

I guess my point is this: Just cause it's not on the list for this grade level, doesn't mean you can't teach it. It might be a little advanced, or a little over some peoples' heads, but lying to students and saying you can't do something that's TOTALLY and COMPLETELY allowed, and possible? Not kosher. Just don't do it.

There's this myth out there that math is hard. It's perpetuated by some teachers, and some of the students. Particularly the students that struggle and get frustrated easily with mathematics. The other kids, the kids who excel there, will hear them, and believe them. The best thing you can do for any kid, is to challenge them to do better. (Believe it or not, reverse-psychology can actually work in some cases.) If a kid is good at--but also "hates"-- a subject, run through the logic of their hatred with them. And if you can, just change the original assumption.

(Here I devolve into the process of proof, don't mind me...) When you're proving a conjecture, you can assume anything, basically. These assumptions lead to other conclusions, some of them contradictory and/or unwanted. But if you pick the right assumption, the proof basically writes itself. Same with kids, as far as I can tell. If you change the "I hate math because I hate math" assumption to something more like "I don't necessarily hate math", then you've done a great service to the child. And a mathematician might just pop out at the end of the logical implications.

Also? Forest fires.