I had lots of pimples in eighth grade. It wasn't horrific but it certainly wasn't good as practically all of my peers were still baby-faced and unblemished. I took my share of abuse for it, too.
I wasn't particularly good at school; I had more than my share of Cs though I was "gifted." I was a mess at eighth grade math; fractions, decimals and percentages were not my friends. In fact, I had to talk my math teacher into recommending me for regular, ninth-grade Algebra class. She wanted to place me into the "college prep Algebra" class, which was a nice way of saying the math class for people who can't do math but needed to pass Algebra in order to qualify for a four-year college. My English teacher didn't think I was too sharp, either, and moved me down to "regular" English for ninth grade while all of my friends were placed in "honors."
More below.
The diary continues in a moment.
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My family pediatrician decided to experiment with a new product just coming on the market for acne: Retin-A, which now seems to be in all of the anti-wrinkles stuff. He wished and wished he'd taken "before" pictures of me because my face cleared up just in time for the first day of high school. He could have published my results in a journal.
I got my first dose of straight-As in ninth grade, including my Algebra and English classes. How did that happen? I haven't a clue except that my face cleared up.
In fact, my Algebra teacher pulled me aside in early November and told me to stop coming to class except for tests. I could go hang out in the Science Department storeroom or the library but I was to not be in class. My understanding of equations, inequalities and graphs was so far beyond my classmates that my teacher couldn't get them to try problems; they all went dumb, so to speak, waiting for me to just answer everything. Because of a schedule change, I had a different teacher for the second semester. He kept me in class because I could tutor the other students about quadratics. I suspected at the time that I knew more about them than my teacher did.
Why could I not figure out "lowest common denominator" in eighth grade but I could solve any equation in ninth grade? Why could I not figure out the mean, median and mode of some data in eighth grade but I could figure out the x- and y-intercepts and slope of a graphed line; in fact, I didn't even need to see the line because I could calculate those things from the equation? Why did I confuse perimeter, circumference and area in eighth grade but I could calculate the vertex and solutions/roots/zeroes/intercepts of a quadratic equation in ninth grade?
At thirteen, I could not figure out concrete, practical math. At fourteen, I understood communicating an abstract thought. I see this happening; how do I say it? There's a pattern here; how do I show it? How can I express something that's true so that it includes only what is true and denies everything false? I see a graph or an equation; what is true that they show or express?
During the summer before high school, somehow, in some way, my brain grabbed a hold on the concept of equivalence. I know no teacher explained it to me and I'm sure the only time the word "equivalent" appeared in the textbooks was in the chapter about fractions. Nevertheless, my mind was ready to see how adding four to one side of an equation required me to add four to the other side. The two sides looked different but I had to maintain their balance. I couldn't change one without changing the other. And I understood that I was changing what I was seeing; the soft meat of the nut was hidden within a removable shell.
I can remember, distinctly though it has been more than thirty-five years, that I began to ask myself, "How does it go?" every time something new was introduced in math class. What was the order, what was the pattern, what was the formula, how did the numbers affect the letters? "How does it go?" suggests math as music or poetry. "How does it go?" hints at language. "How does it go?" implies a harnessing of power, a directing of flow, a conservation of effort. Elegance, in a word.
Math stopped being about cups of sugar. I didn't care anymore about how many tickets to the dance the band sold. What mattered was every time I learned something that let me do something else; I was writing the notes to a piece of music from beginning to end.
It was after I understood Algebra that I understood Arithmetic, not the other way around.
Consider this: I did not learn that a fraction simply shows division (In my classes, students are trained "You don't like fractions?" is followed by "Don't do them! Multiply!"). I learned "part of a whole" all the way up to Algebra. The books in use today still teach it that way.
For that matter, the books teach that when two numbers multiply each other, they are called factors. Students are told to "break down" numbers into factors, particularly prime factors. Nowhere is a student told that factors are numbers (let's just start there) that divide something else without a remainder. Factoring means dividing.
Any questions?