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In geometry (and life), sometimes the theorem proves something other than what you expected

I slinked into the geometry classroom with a nasty attitude. That year began my third year in the terrible town and horrible school district that I had grown to hate. Each day I plotted how I would be able to escape. At the library---no Internet back then, friends---I looked up information about boarding schools, and mailed weekly inquiries to get brochures. I researched different schools in the area, and even called a few to find out if I could transfer. My mother scuttled each plan. She was sure it was simply typical teen angst; nobody actually enjoyed middle or high school. I was sure anywhere was better than there. So, stuck there another year, I began the year with a surly demeanor.

Geometry, I thought, another math, another waste of time, another horrid teacher.

The previous year I'd had a newbie teacher for algebra and had learned nothing. The truth is she was actually a mathematician, not a teacher. She began the year with the goal to make us all stellar math students who adored algebra. She'd wax enthusiastically about X and Y and draw enormous equations on the board. She'd look at the problems and expect us to see what she did, as easily as she did. She was quickly disheartened and took it personally when we didn't. She had no control over the class. Before our mid-year exams, she had a meltdown in our class---yelled, cried, and eventually ran from the room. She took a six week mental health leave. During that time we got a substitute who expected us to already know the subject and require no teaching, so we spent day after day individually struggling through problems in our textbook. When our teacher came back, she was quieter, and her goal was simply to get to summer as quickly as possible.

The year before that, my math teacher had been Miss Love, who liked to perch her hip on the corner of her desk and swing her leg. This was significant only because she wore very short and very tight skirts that rode further and further up her leg as it swung. She had her desk in the corner of the room rather than the center, and had arranged students in a fan outwards from there. We appeared to be arranged by our social status, rather than anything else, such as alphabetically by name. This was significant only because she had the cute athletic boys front and center, with cheerleaders flanking them. It went down the cute and popular scale from there. Those on the far edge---including me---were largely ignored. Miss Love shuffled her ballet-flat clad feet when she walked and had a soft, wistful sort of voice. She was tall, slender, and probably attractive to men in their late 20s and 30s, her age range. That just made her flirtation with 13 and 14 year old boys that much creepier---and even they felt creeped out, eventually. Each day she shuffled to the far corner of the room, perched on her desk, and began swinging her leg. She'd tip her head sideways, smile beguilingly at the boys, and ask them what was up. I don't remember learning anything about math that year, but I did learn a lot about inappropriate teacher behavior, flirtation styles, and how some adults never left adolescence or middle school.

So I walked into geometry with low expectations and slumped into a desk, ready for whatever horror show of a teacher I'd have that year.

When the teacher walked in, a veteran, an actual teacher, and stated her hard and fast rules upfront, then softened it a bit with how each one of us would walk out of her classroom having learned something significant, I knew this year was going to be very different, and I sat up straighter.

For the first time in my experience, this math teacher actually taught math. She seemed to intrinsically understand each place where kids would hit the "I don't get it spot," even though it varied by student. Class wasn't a place she lectured and showed all she knew, it was a place where she taught, and had us work it out, with her guidance and support. She never sat down. She didn't speak for fifteen or so minutes, then give us exercises, and go sit at her desk and grade or flip through a magazine. Instead, she walked up and down the rows, checking in multiple times, individually, with each student.

I had the courage, in her class, to raise my hand and say, "I don't get it, I need help," and it never bothered her to have to explain it once, twice, three times to me.

One day, as I struggled with a theorem, and she kept hitting a roadblock with me, she said, "I'll tell you the problem here and it's ignorance," My face must have crumpled because she quickly added, "Which is not your fault. For some reason..." and here her lips got very, very tight, "You haven't been taught the essentials---the basics---that come behind being able to do this sort of math."

"It's because I'm dumb at math, just can't do it," I told her, "I never have been able to. I'm the despair of math teachers," I tried to joke.

"You are not dumb. Not even at math, and I don't know how or why anyone has convinced you that you are. You are unlearned, which is very different," she said, "I'm going to teach you this, and when you leave this class you will understand geometry."

She called my mother and told her to get a tutor. With that individualized instruction and attention, plus a teacher who actually taught with the goal of me "getting it," the fog began to clear, and I felt, for the first time the warm rush of success in math.

By the end of the school year I loved geometry---I didn't actually love geometry, I loved that I got it. I loved that I could do it, and get good grades, and not feel stupid. I loved that teacher---I actually loved her, was ridiculous in my gratitude that she made me feel smart and capable.

She taught me a lot more than geometry. She taught me that learning involves two people, and failure isn't a failure solely on the part of the learner; it's also a failure on the part of the teacher. Success is the same, a credit to both student and teacher.

On the final day I loitered in the classroom. I was reluctant for my year with her to end, worried about the next math and teacher. My confidence in my math ability had blossomed, but was still fragile, and could still easily wilt under the wrong circumstances.

"Did you need anything, Julie?" she asked.

Yes, I needed to tell her how much she'd meant to me, what a great teacher she was, how grateful I was. I needed to let her know how much her support and guidance had brought to me. I wanted to let her know how valuable this year had been for me.

What I said was, in a typical teen way, from that generation that came before the generation that was taught they could say anything they wanted, any time, "You know, thanks, for helping me get it and stuff."

I think she got it, too.

Note: Remember, tomorrow's Hump Day Hmm topic is about free speech and blogging. What do you think about how courts, employers, and others use blogging against bloggers? Should courts be able to impose censorship on bloggers? Should employers be able to ban bloggers from blogging, or restrict it?

Copyright 2008 Julie Pippert
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le35 said…
Math was truly difficult for me. I was the youngest of nine children. 8 of whom had gone through math at the same school that I had. I passed algebras I, II and Geometry, but I didn't excel. I got into College Algebra, and I was totally lost. My brother got his Master's degree in math. I know now why I couldn't do College Algebra at first. It was because I hadn't learned Algebra I or Algebra II. In three days, I had the crash tutoring session of my life, and I got an A in both College Algebra and in Trigonometry. It gave me the courage to try for Calc. In college I got a B in Calc I and a B+ in Calc II. Honestly, thank heavens for good teachers. You're right. There is a difference between a mathemetician and a good math teacher. It goes the same for all subjects. After having been in teaching classes in college, it is possible to get through them without actually being able to teach. They need to spend more time on teaching how to teach instead of teaching on children's development.
Gwen said…
Is it Old School week at the Pippert place? (lol).

Having been on the other side of that equation, I can guarantee you that teacher still remembers you, too, with great fondness.

And I loved geometry with a white hot passion. Seriously. Loved it.
Sukhaloka said…
:). That's the only decent thing my dad did for me - teaching me maths from the very basics.
He understood my voracious appetite for concepts and my complete dislike for facts. He'd make me sit there and derive theorem after theorem, watch me revel in discovering the answer over and over again until I remembered it so well I got bored.
And yes... if I was mulling over a particular point in a problem, a few seconds later his voice would break in and give me a hint.

Sure, I hate the man, his guts, down to his nail clippings. But he was a GOOD math teacher and I'll acknowledge that.

Talking from the other side of the fence, I was teaching our maid's kids one day. Multiplication. They're in middle school, and supposed to be doing algebra. Heh. They didn't know that multiplication is repeated addition.
What are we supposed to do when no one bothers to teach the basics?
Anonymous said…
For someone who is a visual person, I sucked at Geometry. You'd think it would be the one kind of math I could do,
Julie Pippert said…
Gwen, LOL, I am simply doing as you suggested and providing context.

Actually yesterday I promised to balance with a good teacher story today.


Le, I agree. Teaching is a REAL *skill* and I think it is undervalued. I mean that more than in the usual sense. I relate to teachers a lot because in the same way everyone thinks "eh, writing, anyone can write" I think people think "eh, teaching, all you have to do is know something."

Then there's that nasty cliche about "those who can, do and the rest teach." ICK!

It's a talent, a gift. And people either have it or don't, and if they go into the field and don't, I hope schools give them tools.

Suki, I guess it's always good to find a redeeming quality. :) But yes, that rush when a kid grasps something, and the ability to guide them into discovering it themselves...that's the gift. Real teaching.
markira said…
I'm a mathematician, and I know that there is a serious difference between being that and being a math teacher.

I am so glad that you had at least one *real* math TEACHER. I think there would be far fewer people who "can't do math" if there were more teachers who cared enough to be sure their students really understood what they were being taught.

While everyone may not have the same passion for numbers and equations as we "math geeks," I am truly saddened by those who feel that they "hate math."
Anonymous said…
It's amazing what a difference it can make to have a good teacher. I know that my life would have been very different had I not gotten lucky enough to have quite a few great teachers.

That was a sad story about the algebra teacher, who loved math but couldn't teach it. I think it's all too common at the college level. There are some people who really know their stuff, are really passionate, but are just not teachers. I wish that more PhD programs would place more, or at least some, emphasis on teaching skills, since so many PhDs go on to teach college courses.
Suz said…
First, I had a college Latin teacher like your Alegebra teacher. Brilliant woman. She knew the language backward and forward, but could not explain to us how it worked. Frustrating for all concerned.

Second, it is phenomenal that you found a teacher who took the time to actually fill in the gaps of your mathematical knowledge. I didn't find this teacher until college and, by then, it was too late. To this day, I have a pretty strong math phobia.

I see the same thing with students in writing. They've been told over and over that they can't write. They know they'll fail before they even set pen to paper and it's sad. Because the real reason, of course, is that nobody ever taught them the basics.
Mayberry said…
That teacher sounds so wonderful and in tune -- I am sure she knew you were giving her a high compliment!
SciFi Dad said…
I honestly could not relate to that story. Math was always the one thing that immediately "made sense" when the teacher spoke. When I was in Grade 3, my mother once asked me how I solved a problem, and my explanation was that I "made the numbers dance".

With that being said, I think math is a very complicated subject to teach and to learn. Non-verbal intelligence and interpretation is so subjective (yet math is considered and taught as an objective course), making it all the more challenging for everyone. Those who "get it" well enough to excel and therefore succeed at a post-secondary level are likely the ones who found it easy, and have well-established non-verbal strengths. An ideal math teacher is someone who struggled with it, as you did, because they can see where the confusion comes from. Unfortunately, most have your perspective (as in, thankfully, it's over) and therefore never teach it.
Magpie said…
Good teacher there.

I got put into algebra in 8th grade, because "they" thought I was smart (you were supposed to take it in 9th grade). I didn't want to be there so I failed it. Big red F.

The following year, I took algebra. Same teacher. Second time around? A+ and a 98 on the regents. I went on to ace geometry and tutor math in high school.

It's all about the circumstances. And the teacher.
Anonymous said…
I have a theory that the people who teach math make it seem more complicated than it actually is. You are so lucky to have had her.
thailandchani said…
She sounds really good.. and you were lucky to have her. I've always had trouble with linear thinking and my spatial stuff isn't so good, either. As you can imagine, math was out of the question. I can still barely balance a checkbook.
Anonymous said…
what a tribute! I had the exact same experience (only a lazy firefighter instead of Miss Love for algebra) and then Mr. Feldt taught me geometry and taught me to love math.
we_be_toys said…
Wow - this could have been MY story about math! It wasn't until I had Geometry that math ever made sense, and all my failures before that were laid only at my door. What you said about teaching and learning being between two people is RIGHT ON!
Thanks Julie!
Kat said…
If only all teachers could be like that.
Anonymous said…
I loved geometry in high school. I had a great teacher who was great at math and also LOVED geometry--so that helped. It also helped that he was drop-dead handsome and charismatic, too (I had just a bit of a crush...). But the thing that was so beautiful about geometry to me was the logic. None of that stupid equation stuff!

I'm glad you got the great teacher. I'm saddened by the algebra teacher--because it's quite true that someone who's in love with a subject doesn't necessarily make a good teacher. I think SciFiDad has a good point: sometimes it takes someone who has also struggled with it (but prevailed!) to be able to show others how to struggle through.
Kyla said…
My geometry teacher was finally the math teacher who made it click for me, too. I also think there is something about geometry that clicks a little better for literary types. It isn't quite so deeply mathematical, maybe.
Unknown said…
I love that teacher! i got my first LIGHTBULB over the head moment in math class- I really do enjoy it, if I approach it like a puzzle, a mystery to be solved and try not to think about the 147 steps I need to take first.
Liv said…
tomorrow's topic?

Aliki2006 said…
I had the worst time ever with math, all through school. I dreaded it, and it ruined my self-esteem. I finally got a good teacher in high school--Mr. Reid. But I so wished he had come into my life earlier.
Jennifer S said…
I liked geometry best of all the math torture devices.

But that has a lot to do with the way I was taught algebra. If only there were more teachers like the one you had.
dharmamama said…
I earned the geometry award at my junior high! *Loved* it. What a great teacher story.

After unschooling for a while now, it's fascinating to me how much the boys (and other unschoolers) get, just by being in the world and playing around with numbers and concepts. They seem to have more of a fundamental understanding of how it works, 'cause no one is telling them how it *should* work. They find what works for them. Such a cool thing to see.
Yolanda said…
Geometry is the only math class I've ever loved, but I didn't "get it," either until I was given one-on-one tutoring sessions with a brilliant, gay, classmate during the final 6 weeks of school. I will never forget that guy, or how happy it made me to score an B- on the final exam. My problem was ignorance, too. A studnet teacher Algebra mishap, just liek yours. And a previous year spent with a teacher so heavily-accented, I tuned out and read rather than trying to decipher what she was saying. But my geometry teacher had us read Alice in Wonderland and related the events in the book tothe geometry concepts we were learning. It is still, hands down, he most brilliant teaching technique I have ever encountered in a math class. No one else I know has been assigned a novel in math.
flutter said…
ugh, I can totally see her in my head and I don't like it.
I had a teacher like that -- Algebra I, Mr. Harber. Like you, I hadn't been prepared by previous teachers -- one of them a coach who spent most of his time joking with his players and flirting with cheerleaders (or napping at his desk). This stupid man told me and my mother that I was hopeless. (this was a pre-Algebra class in junior high)

Mr. Harber undid the damage and while I never did excel in any of my math courses, I learned how to muddle through.
jeanie said…
I was lucky, in that I loved and got maths from a very early age - and it was mainly through a low boredom threshhold in a two teacher school, so the teacher just told me to work ahead - so I did.

It really helped me, especially through those years when I had a crap teacher as I had already done the groundwork - but I realise that I am more a mathematician (if you can be a layman in such a pursuit) than a teacher - watch me knock my head against the brick wall as I try to help my daughter!!!

I am so glad you got someone who taught you what it is to learn understanding.
A truly good teacher is a gem. I hope that everyone gets at least one of them in a lifetime!
Christine said…
i wish i had a teacher like that. math was always so, so hard for me.

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