Wednesday, January 23, 2019

My math zipper is misaligned

So, I'm studying for the GRE, which is all kinds of fun and is bringing back lots of, you know, fun memories. And by fun I mean traumatic.

I suffer from a bit of math anxiety, which I've been reading quite a bit about lately. This fear of math can be passed on from parent to child when the parent expresses thoughts such as, "Math is dumb, anyway," or "It's alright if you're not good at math because I'm not good at it either," and things like that. It can also stem from teachers expressing math anxiety in front of their class or, I imagine, from shaming students who are struggling to grasp a particular concept.

Two instances of math shaming stand up readily in my mind. The first is in grade three. We had to do timed multiplication tests weekly in Mrs. Robinson's class and while I did enjoy my time in Mrs. Robinson's class, I did not enjoy those timed multiplication tests. I only ever managed to get through the whole test once at the very end of the school year.

"You must not be as mathematically minded as your brother," I remember her remarking. "He was so quick!"

He had been in her class a couple of years before me and he, of course, finished his timed tests every week. I know this because if you got 100% on the test (which would naturally involve finishing it) then you got to pick a prize. He got a prize every week.

I never got prizes. Until the end of the year. And by that point I don't think I cared any more.

(Except that I am bringing this up again so perhaps I cared a little bit more than I thought).


The second very obvious instance of shaming occurred in grade eleven. When I had moved from Alberta and the school counselor was trying to figure out what in tarnation to do with me, she asked me what level of math I was. I was not sure, exactly, what she meant. I had scored in the top 10%* on the provincial examination in math (in Alberta we take standardized tests every three years and, let me tell you, aside from the diploma exam at the end of grade twelve they are not as big of a deal as the EOG (end of grade) testing they do down here—with kids sitting for exams for a full week and expecting the entire school to be absolutely silent). Was that what she meant?

No. She wanted to know what level I was in—what class had I just taken?

"Math...9," I told her.

"Okay, but what class?" she asked.

"Grade 9 math," I said. "Like, the math class you take in grade 9. I took that class."

"But what was it called?"

"Math 9," I said again.

She was getting frustrated.

"You don't even know what your math class was called?!"

"Yes. It was just math. Grade nine math. There's not really a name for it. Just...math."

"Algebra? Geometry?" she threw out.

I nodded my head.

"Yes."

"Which one?"

"Ummm...both."

"Yes."

"Algebra and geometry?"

"Yes."

If only we had the internet available at our fingertips! I could have told her to look at this. Instead she stuck me in remedial math, so while my peers were taking Algebra II, I was in Geometry. And I never really got back on track, mathematically speaking, because when I was in Algebra II the following year my teacher was very unkind so I dropped the class in the middle of the year and took art instead and then took College Algebra at what was then UVSC to fulfill my high school math (and college math) requirements.

Anyway, I had been doing just fine in Algebra II and my teacher had even nominated me for a few "math student of the week" awards but then one day she was passing back an exam and when she got to me she looked at my paper and said to me—but more to the entire class, "Ooooooweee! You are not going to be happy when you see your grade."

And then she chuckled and handed me back my test and...it wasn't a grade I was happy with (ie. it was not an A (I do not remember the actual score; anything less than an A is an automatic F, right?)) and I was mortified that she would announce such a thing to the entire class. And our relationship just dwindled from there. For example, once I raised my hand to answer a question and she pointed at me as if to call on me and instead said, "Never mind, you probably don't really know the answer."

I think she thought she was "only" teasing me, because when I had her sign the form to drop her class she remarked that she was surprised because she thought I loved math. And I was like, "Uhhhh...bye."

So, math and I have a complicated relationship, complicated further by the fact that I moved in the middle of my foundational mathematical experience.

Anyway, I was telling my Uncle Bruce the other day that I often think back to the very patient tutoring sessions he would conduct for me. I was cry and rage and he would assure me, "Anyone can do math," which I certainly believe to be true now, but then? Oh, boy.

He didn't seem to recall all the tears I shed over math. But my Aunt Sara said something interesting—that there are however many steps to learning multiplication (or what have you) and if your learning is disrupted in the middle of it then that's it. Your learning curve never recovers.

Now, I don't quite believe that learning curves can never recover, but it did make me think about the moves I made in the middle of my learning: I moved from one province to another in the middle of grade four and the curriculum didn't line up well. My class in Alberta was learning things I'd never heard of, while I had, likewise, been learning things in British Columbia that my new peers hadn't yet been introduced to. It wasn't so much that I was behind. It was just...like my zipper got stuck while being zipped up.

My zipper snagged again—big time—when we moved down to the states.

For example, I am just learning about the quadratic equation. Just now. At thirty-three years old.

Because in the states, at least in Utah, it's taught in junior high school, but in Alberta it's not introduced until mathematics 20 (it goes math 8, math 9, math 10 and then diverges into math 20 and 30 because at that point (grade 11 and 12) you finally have a choice about what kind of math you take, rather than continuing in the holistic K–10 math program).

I was lamenting to Andrew about having to memorize the quadratic equation and he was like, "Oh, but the quadratic formula is much more useful to memorize," he told me.

"There's a formula, too?" I asked with a sigh.

"Yeah. I can't remember it, honestly. There's a song for it. Don't you remember that?"

"A song?" I said.

"Yeah. It's Pop Goes the Weasel. Come on. Everyone knows it!" Then he tried to sing it for me but mostly just mumbled, "Buh-buh-buh-buh-buh-buh-buh-buh, plus or minus the square root of buh-buh-buh-buh buh-buh-buh-buh all over...something!"

"I have never heard that. And clearly it has not helped you remember the formula."

We looked it up so that I could listen to it (and I will probably be listening to it many times so that I can memorize it):



"I have never heard of this," I told him.

After looking up when I would have learned this in Canada and when he learned this in the States, I now know why I had never learned this. And it's kind of a huge hole in my mathematical foundation and makes me a little nervous about what other little things might be lurking in my GRE "review" that I have never seen before.

Not that I don't think I can't learn them. Just that it takes longer to learn something from scratch than it does to review things.

It made me wonder, though, about the American approach to teaching and learning mathematics. In Canada, our math was based on units—we had geometry units, we had algebra units, we had trigonometry units. We did everything, every year (once we got into doing such things after moving on from basic arithmetic of the younger grades (addition, subtraction, multiplication, division and so forth). They don't do that in the States so well, I don't think. They learn it and then don't touch it for years and then expect you to be able to recall it after not using it for a long time.

I'm not saying that the Canadian education system is flawless (it's not) but I think the States could take a good look at how the methods of instruction in the two countries and perhaps adopt some new strategies.

I was shocked to see that in grade four in Alberta students are only learning multiplication and division facts up to 7x7. Miriam is doing up to 12x12 this year! But I think there must be other things grade four students in Alberta are diving into that Miriam is not yet being introduced to.

I think I like the idea of building upon knowledge every year, rather than doing a year of math and saying, "Phew! Good thing we got through that! Now put it on the shelf while we learn something completely different!"

And I think it probably works a bit better, too (PEW research shows that Canadian students score significantly higher on international maths examinations than American students), so I don't think I'm alone in thinking the system could use some tweaking.

For now, I'm going to go study the quadratic formula some more.

Buh-buh-buh-buh buh-buh-buh-buh...all over 2a!

* I remember that because I took an independent study math course, which involved reading and then doing practice questions and submitting them to be graded. There were answers in the back of the book, for all the even questions, I believe, and I would check my work (we were allowed to check our work) and if my answer didn't match the one in the back of the book—which would mean either that it was wrong or that I had done it a different way—I would revise my answers by reworking the problem over and over again until I could do it correctly. (And I still do that with the GRE practice that I'm doing—like, "Huh. I did it this way and got the correct answer. The book did it this way, however, so was my way of doing it a fluke that I arrived at this answer so I should redo it the way the book says to, or does my way always work and is a valid way? Or is there some sort of shortcut that I missed? Or..." 

So I still don't consider redoing a problem over and over again until I understand the answer the book has given as cheating.

Anyway, my teacher once sent back my homework with a note scrawled on it saying, "Your answers are looking more and more like the answers in the back of the book," which, I mean, shouldn't that be the goal if I'm learning from the book and the answers are...you know...correct. "I hope you are not cheating," he continued, "And are actually learning the math. Exams and life will demand it."

And I was so offended. 

And then I scored in the top 10% and was like, "BOOM!"

3 comments:

  1. This whole post made me feel like crying. Over your Grade 3 math (you so very, very, very much wanted to win a prize!), over moving, over quadratic formulas, over how confusing math is!

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    1. It's alright! Math is fine. :) We can't say how difficult it is because that will make children think it is difficult. Instead it's a puzzle that needs to be solved and as they discover more keys they'll be able to unlock more doors.

      I think we really need to redo the whole way we think of math, really, as a society, I mean. When a child is sounding out words we encourage them to work it out, to sound it out, to make mistakes. When we teach them math and they make a mistake we're more like, "WRONG."

      I also feel a little bit like I needed a detailed list of things I had learned so that I could pass it onto my teachers—like a swimming lesson report card. Or something. Maybe I need to make a spreadsheet for my children so that I don't forget what I've taught to whom. I remember you saying you forgot, by the time we got to Josie, which stories you'd told before and so you didn't tell her as many stories (family-history-wise, I'm thinking mainly) as you had to the rest of us, though I'm sure that is rectified by now. :)

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    2. My worst math memory is in Grade 10, and Mr. Baldwin putting his head in his hands and shaking his head back in forth in total I-don't-know-what over something I didn't understand, or a question I asked. (The crying over confusion about math is for me, because I still feel that way.)

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