Greater than, less than, equal to

A flash from the past: First grade. Mrs. Jorgenson, a round grumpy woman who always wore her hair in a bun. Once she made me sit in the thinking chair* for trying on Carleena Buchanan's glasses during listening center. (Why can I remember Carleena's last name...and I can't remember what I ate for lunch today?) It's math time, and Mrs. J has just showed me how to do "greater than/less than." I was so thrilled. No one else in the class got to do this math! I proudly whipped through my paper and brought it to Mrs. Jorgenson, glowing with pride and accomplishment because I'd had so much fun doing something new.

(Her) "Some of these are wrong."

(Me) "Oh."

(Her) "Which ones are wrong?"

I stared at that paper for an eternity. They all looked correct to me. I wanted to cry because I'd felt sooooo smart and now...I couldn't for the life of me figure out what I'd done wrong.

Then she took out the pen. In my mind's eye that pen is huge, a red pen bigger than the whole world. She quickly, impatiently slashed a red mark on every single problem. I started to cry (quietly, I didn't want to be a crybaby) on the way back to my seat. I stared at the paper once I got there. I had no idea why I'd gotten them wrong....after all, in every single problem, the arrow was pointing to the larger number.

I corrected them all by turning the arrow to face the other direction. But I had no idea why. Mrs. J didn't bother to actually explain it to me.

As an adult I know that it has to do with reading from left to right, and that I had learned the concept but that my teacher had forgotten to make sure that I understood the expression of the concept. As the adult, she should have understood that when I got every single problem wrong. I had the same teacher in fourth grade. She really wasn't a bad teacher. But I still vividly remember her berating the entire class because we'd all gotten "F"s on a math test. Even then I knew there was something wrong with that. When the entire class fails or when a student gets every single problem wrong, there is a teaching problem instead of a learning problem. But I didn't know how to articulate that then, I just knew that I was going to have to go home and show my dad that I'd gotten my very first "F" ever. (Mom said she wouldn't tell. I don't know whether she did or not, but I never heard about it so if she did tell she made it clear that I was devastated. I should never make fun of my mother again.)

The lesson I learned: It is my job as a teacher to teach the task along with the concept. If a child doesn't understand something it's my job to rectify the problem, not the student's. And, most important, try not to be hasty.

Back to "greater than" and so forth. For second grade, I had Mrs. Buck. I still remember her as one of the nicest teachers I'd ever had. We reviewed "greater than/less than." Alex (or Andy or Al or some such, just go with me here) the Hungry Alligator wanted to eat more fish. So he opened his mouth as wide as he could go toward the larger group of fish. AHA!! That was why the arrow pointed the wrong way. Because it wasn't an arrow at all, it was an alligator! (It would have taken all of what, five seconds?, for my first grade teacher to explain this, by the way.) For the rest of that second grade math unit, all of my > and < had eyes and teeth.

Yesterday the fine young gent and I took a break from Miquon math and paged through a different math book until we saw something that looked like fun. And I showed my fine young gent the hungry alligator.

Look at those eyes and teeth! That's my boy, all right.

*My sister had Mrs. Jorgenson for first grade too. She never had to sit in the thinking chair, not even once. She always reminds me of that when we talk about first grade. So I thought I'd save her the trouble of posting a comment to that effect. So there!