Today on the *mumble*th anniversary of my birth, I break from my studies to reflect on one of the few good memories from math class.
I mentioned in my first post Algebra II brought me both a C and a good friend: +Betsy White , mathematical mind extraordinaire. She has umpteen places of pi wrapped around her office as a border, finds four leaf clovers with ease, and shares a love of froggy boots with my kid. She's taught calculus to high schoolers and currently teaches college engineering. I am green with envy at her ability to make sense of math problems with so many Greek letters I think they're actually directions to the Oracle of Delphi. Maybe they are and she's helping the math world keep it a secret from me.
Betsy and I already knew each other from marching band as fellow flute players, but we did not get off to a good start. Why? I don't remember. Even if I did, rehashing everything 15+ years later seems sort of tacky. Probably normal teenager/high school/"we're still learning who we are and screwing it up all over the place" type stuff. I can say that last one definitely applied me more than her. Actually that still holds pretty true for me.
*pause for introspective moment*
Betsy was a year behind me. Usually Algebra II is taken sophomore year. She had some sort of schedule snafu between first and second semester. Since she'd already taken (and I'm sure got an A in) Geometry, she wound up not only in my class but sitting right behind me in the Band Geek Corner of the classroom. Call it fate, divine intervention, a life lesson, but somehow it was Algebra II that made us close. Just as I don't remember the specifics of our initial feud, I also don't remember how that changed. That part should be revisited now. I hate that I forgot it. Metaphorically dragging me through the class by my hair definitely changed things. She burned the quadratic formula so deeply into my brain I remembered it until childbirth and parenthood wiped what little RAM I had left. I bet she carved it into the cheese of those Lance crackers she shared with me. All I know is we exited the class as friends despite the fact we were -- and still are -- pretty different people. Somewhere in that semester we found a way to understand one another.
We grew pretty close throughout my last two years of high school and stayed in touch into my junior year of college. And then we drifted. No catalyst, just life happening I guess. It didn't help I had recurring issues with depression and went down a hidey hole for several years. That's stuff for a different blog on a different day.
Three years and one day ago (I looked it up) we reconnected on Facebook. She still lives out of state but her parents are local to me. That summer we met for lunch. I won't speak for her, but I know on my end it was falling off a log. We were older, definitely smarter, debatably wiser, and while it took a bit to find our old rhythm it was still there. The then two year old that tagged along with me had a way of delaying things. Still does at five. Since then we've stayed in touch mostly through Facebook with a luncheon here and there when she's in town and our schedules mesh. Sadly they often don't. There's that real and complex life again.
I've been trying to wrap this post up for an hour with some deep insight wrapped in wit. It keeps eluding me so I'll end it sincerely. Thank you, Betsy, for both literally and figuratively prodding me through Algebra II. I got something besides a headache out of it after all.
Do you have anymore of those crackers?
Monday, January 7, 2013
Diving in Head First, or Equations I Did Not Miss Thee
Backtracking a bit to the beginning of my reintroduction to algebra. I can't get any work done on weekends.
With great enthusiasm and apprehension I opened Idiot's Guide to chapter four, the first appearance of basic equations. Surely I could start here, right? I flipped to the end for a test problem.
With great enthusiasm and apprehension I opened Idiot's Guide to chapter four, the first appearance of basic equations. Surely I could start here, right? I flipped to the end for a test problem.
Solve the equation 9x + 3y = 5 for y
Perhaps the time honored adage "begin at the beginning" was in order. Back to pre-algebra.
Chapter one was filled with dusty concepts.
Mathematical classification systems: Both books went through the whole number hierarchy, but Everything had a Venn diagram nightmare implying all numbers were real numbers. Idiot's Guide defined real numbers as "all rational and irrational numbers" but didn't comment on the existence of "unreal" numbers. Thankfully there is now Google to tell me the counterpart to real numbers is complex numbers. It will be a hot minute before I feel like dealing with i.
Absolute value: Totally forgot about this. Whatever is inside the lines will be positive. Okay.
Associative and commutative properties: Order doesn't matter in addition and multiplication. One can cheat subtraction by changing 5 - 7 to (-7) + 5.
Identity and inverse properties: Adding 0 and multiplying by 1 do nothing. Adding the inverse negative gets 0, multiplying by the reciprocal gets 1. Forgot the fancy names but did remember the concept.
Chapter two was a skim through. All about fractions. Never had a problem with them. I did have to re-read the paragraph on division (multiply by the reciprocal). I wish I'd remembered that two weeks ago when I was struggling to divide 2/3 by 2 in my head. Yes, I felt dumb when .3333... popped up on the calculator. Very, very dumb.
Chapter three had the first appearance of the dreaded variable x. With exponents attached. Real and complex life awaited me, so I closed the book for the day.
The next day I took a deep breath and went back to chapter three. Idiot's Guide puts variables in a cross-disciplinary form I wish somebody had told me at the beginning.
Variables are pronouns.
Variables are pronouns!
Mind blown.
Does this make numbers nouns, operations verbs, and coefficients adjectives? Hold on, this metaphor is getting way more involved than I want it to. For now. Give me six weeks and I'll come up with a way to diagram a (very simple) math problem like a sentence. Or I'll Google around and find a meme where someone else did it. I can't be the first person to have this thought.
The rest of the chapter didn't have such strong epiphanies. Exponents were familiar but rusty.
Perhaps the time honored adage "begin at the beginning" was in order. Back to pre-algebra.
Chapter one was filled with dusty concepts.
Mathematical classification systems: Both books went through the whole number hierarchy, but Everything had a Venn diagram nightmare implying all numbers were real numbers. Idiot's Guide defined real numbers as "all rational and irrational numbers" but didn't comment on the existence of "unreal" numbers. Thankfully there is now Google to tell me the counterpart to real numbers is complex numbers. It will be a hot minute before I feel like dealing with i.
Absolute value: Totally forgot about this. Whatever is inside the lines will be positive. Okay.
Associative and commutative properties: Order doesn't matter in addition and multiplication. One can cheat subtraction by changing 5 - 7 to (-7) + 5.
Identity and inverse properties: Adding 0 and multiplying by 1 do nothing. Adding the inverse negative gets 0, multiplying by the reciprocal gets 1. Forgot the fancy names but did remember the concept.
Chapter two was a skim through. All about fractions. Never had a problem with them. I did have to re-read the paragraph on division (multiply by the reciprocal). I wish I'd remembered that two weeks ago when I was struggling to divide 2/3 by 2 in my head. Yes, I felt dumb when .3333... popped up on the calculator. Very, very dumb.
Chapter three had the first appearance of the dreaded variable x. With exponents attached. Real and complex life awaited me, so I closed the book for the day.
The next day I took a deep breath and went back to chapter three. Idiot's Guide puts variables in a cross-disciplinary form I wish somebody had told me at the beginning.
Variables are pronouns.
Variables are pronouns!
Mind blown.
Does this make numbers nouns, operations verbs, and coefficients adjectives? Hold on, this metaphor is getting way more involved than I want it to. For now. Give me six weeks and I'll come up with a way to diagram a (very simple) math problem like a sentence. Or I'll Google around and find a meme where someone else did it. I can't be the first person to have this thought.
The rest of the chapter didn't have such strong epiphanies. Exponents were familiar but rusty.
- Add powers when multiplying
- Subtract powers when dividing
- Multiply exponents when the exponential expression is raised to another another power
- Negative exponents are considered bad grammar and must be written in reciprocal form.
Scientific notation: Positive exponents = Big number. Negative exponents = small number.
Distributive Property: This was where I got myself in trouble a lot in Algebra I...and II...and Precal. It's a wonder now I even made it so far in math. 5(x + 1) = 5x + 5 not 5x + 1. I now rewrite that expression as (5)(x) + (5)(1) in my work so I don't keep making that mistake.
Order of Operations: I sort of remembered it but sort of didn't. Parentheses first? Yup, still got it! Exponents? Uh, yeah sure. That totally came next. I did remember multiplication and division came before addition and subtraction, however by now I'd fallen into a very common trap that you do the multiplication and division in the order you encounter them, not all the multiplication first followed by all the division. I'm sure I knew this when I was actually in math class. Now not so much.
Thursday, January 3, 2013
In Which I Connect Algebra to Schoenberg
Time to find equations based on perpendicular and parallel lines. It's easier than I thought but not as simple as I tried to make it.
The rules:
- Perpendicular lines have opposite reciprocal slopes. Idiot's Guide explains this as if line g is perpendicular to line h, m = a/b for g and m = -(b/a) for h. That wonked my head. I need an example I can process easier. Hello there, twelve tone row matrix! Opposite reciprocal = retrograde inversion. (Why, oh, why did I not have this connection to make the first time around?)
- Parallel lines have the same slope. Of course they do! They're parallel! Otherwise they'd intersect at some point. Maybe not on the part of the graph you're looking at but eventually.
My practice problem for perpendicular slopes is
Write the equation of line k in slope-intercept form if k passes through (2,-3) and is perpendicular to the line with the equation x - 5y = 7.
I can do this, right?
First solve for y.
x - x - 5y = -x + 7
-5y = -x + 7
(5y/5) = (-1x/-5) + (7/-5)
y = (1/5)x - (7/5) = slope-intercept of the line perpendicular to k
Now I need to take the retrograde inversion opposite reciprocal to get the slope of k.
(1/5)(-1) = -5 = m of k
On to point-slope form
y - (-3) = -5(x - 2)
y + 3 = -5x + 10
y + 3 - 3 = -5x + (10 - 3)
Which leaves me with slope-intercept
y = -5x + 7
Self-assigned extra credit -- write in standard form!
5x + y = 7
I am so proud of me. :)
*************************************************************
Then we come to parallel lines.
Write the equation of line j in standard form if j passes through (-6,1) and is parallel to the line with the equation -2x + 6y = 7
I can figure this out on my own. I don't need no stinkin' book!
...switch the signs? *check answer* I am un-proud of me.
Put in slope-intercept form to solve for y
-2x + 6y = 7
6y = 2x + 7
(6y/6) = (2/6) + (7/6)
y = (1/3)x + (7/6)
Plug the point given in the problem into point-slope
y - 1 = (1/3)[x - (-6)]
y - 1 = (1/3)(x + 6)
y - 1 = (1/3)x + 2
y - 1 + 1 = (1/3)x + 2 + 1
y = (1/3)x + 3 = slope intercept of j
Convert to standard form
-(1/3)x + y = (1/3)x + -(1/3)x + 3
-(1/3)x + y = 3
[(3/1) * -(1/3)x] + [(3/1) * (y/1)] = 3(3)
-x + 3y = 9
(-1)(-x) + (-1)(3y) = (-1)(9)
x - 3y = -9
Note to self: always read the directions.
*****************************************************************
I've already done the chapters on inequalities, but I will write about those over the weekend. Maybe I'll be able to finally sit down and write the 3 chapters I did pre-blog as well. Monday starts my descent into the matrix sans Neo. Wish me luck!
Tuesday, January 1, 2013
Graphs, graphs, graphs...
I was going to do a play by play of the chapters I've already done, but I'm afraid of forgetting my current epiphanies. I'll just back date those entries.
Today I covered chapters 5 and 6. Chapter 5 is the basics of graphing and graphing equalities. In a nut shell I learned graphs represent all possible solutions to an equation. I'm sure at one point I knew that, but today it was an "a-HA! My math teachers had a reason for this other than torturing me!" Basically instead of randomly choosing an x or y and plugging them in an equation -- my time honored method -- you can graph the equation and see which x and y work together. I only see intercepts easily. Maybe that's all I really need to see well. Absolute value was a looooooooooong forgotten concept. Use it to find the vertex of a V-shaped graph. Got it. Only one of the example problems made me head tilt.
First I solve the equation inside the absolute value for x. (I circle the original operation in my work so I don't confuse which one goes on both sides. Here it's highlighted in red.)
x - 4 = 0
x - 4 + 4 = 0 + 4
x = 4
So now
y = -|4 - 4| - 5
y = -|0| - 5
...what the !@#$ do I do with this negative sign outside the absolute value bars when my answer is 0? There's no negative zero like there's no crying in baseball! My pea brain decided since the 0 disappears I should be left with
y = - - 5
y = 5
The actual answer was y = -5. So the negative sign should've disappeared with the 0. Okay.
But why was that stupid negative sign there in the first place?
Chapter 6 was formula overload. I actually wrote them all in the first page of my fresh new notebook so I could keep track.
Formulas and concepts (re)learned
Slope formula
Point-slope formula
Today I covered chapters 5 and 6. Chapter 5 is the basics of graphing and graphing equalities. In a nut shell I learned graphs represent all possible solutions to an equation. I'm sure at one point I knew that, but today it was an "a-HA! My math teachers had a reason for this other than torturing me!" Basically instead of randomly choosing an x or y and plugging them in an equation -- my time honored method -- you can graph the equation and see which x and y work together. I only see intercepts easily. Maybe that's all I really need to see well. Absolute value was a looooooooooong forgotten concept. Use it to find the vertex of a V-shaped graph. Got it. Only one of the example problems made me head tilt.
What coordinate pair represents the vertex of the graph of the equation y = -|x - 4| - 5 ?
First I solve the equation inside the absolute value for x. (I circle the original operation in my work so I don't confuse which one goes on both sides. Here it's highlighted in red.)
x - 4 = 0
x - 4 + 4 = 0 + 4
x = 4
So now
y = -|4 - 4| - 5
y = -|0| - 5
...what the !@#$ do I do with this negative sign outside the absolute value bars when my answer is 0? There's no negative zero like there's no crying in baseball! My pea brain decided since the 0 disappears I should be left with
y = - - 5
y = 5
The actual answer was y = -5. So the negative sign should've disappeared with the 0. Okay.
But why was that stupid negative sign there in the first place?
Chapter 6 was formula overload. I actually wrote them all in the first page of my fresh new notebook so I could keep track.
Formulas and concepts (re)learned
Slope formula
- (d-b) / (c-a) = m
- m = slope of line
- Positive slopes rise right to left.
- Negative slopes fall left to right.
- Horizontal slope is 0.
- Vertical slope is undefined because you can't divide by 0. Unless you get into that imaginary number stuff and I'm nowhere near the i chapter yet. That might even be a whole other book.
Point-slope formula
- y - y1 = m(x - x1)
- Good: Only one set of coordinates needed
- Bad: More opportunity for me to screw up multiplying all the way across the parentheses.
Slope-intercept formula
- y = mx + b
- b = y-intercept
- Good: x will always be 0!
- Bad: If there's a coefficient with y, there will be division. Must remember to divide on both sides of equation
I did all the practice problems. Most of my mistakes were forgetting to carry negative signs from one step to another, deciding 6/3 = 3, or just plain copying the equation wrong. Concepts solid, second grade math and reading comprehension sloppy. That's what my scientific calculator app is for.
Standard form of a line
This is the part where they tell me slope-intercept form is bad mathematical grammar. Correcting other's grammar in literary form with red ink is way more fun. *sigh* If the slope is a whole number it's golden. If the slope is a fraction I have my calculator ready. I solved this problem all by myself...until the last few steps.
Write the equation of the line that passes through the points (-3,7) and (4,1) in standard form.
This one uses all the goodies in the bag. I really do have to do every single step in the equation or I'll screw up on the shortcut. First calculate m.
m = (1 - 7) / [4 - (-3)]
m = (1 - 7) / (4 + 3)
m = -(6/7)
Now point-intercept. I chose (4,1) because they're both positive.
y - 1 = -(6/7)(x - 4)
y - 1 = -(6/7)x + [-(6/7) * (-4/1)]
y - 1 = -(6/7)x + (24/7)
(7)y -1(7) = [(7/1) * -(6/7)] + [(7/1) * (24/7)]
I am still adept enough with fractions to know when things cancel out.
7y - 7 = -6x + 24
Remember above when I said I circled the original operation in my work? This is the problem that made me start doing it. My original solution was
7y - 7 + 7 = -6x + 24 - 7 etc. y = 17
Flip to the back of the book. Not 17? Wait, 24 + 7 is...argh.
7y - 7 + 7 = -6x + 24 + 7
7y = -6x + 31
6x + 7y = 31
I got there. Wasn't pretty, but I got there.
My brain is a little fried from the endless formatting. My struggle with gleaning equations from lines perpendicular and parallel to the line you're looking for will have to wait until Thursday. My kid turns x - 5 = 0 tomorrow!
Did I just do that? I must be making progress!
Monday, December 31, 2012
Why I Decided to Revisit Algebra
There are lots of reasons, but the ones that gave me the biggest kick in the pants were the YouTube channel on Nintendo Wii and Dr. Neil deGrasse Tyson.
Thanks to the YouTube channel I could watch Dr. Tyson lecture on things from trivial to deep from the comfort of my couch. His love of the universe and science education is infectious. After a month of Tyson lectures I wanted to read some books on basic physics. I went to the public library, opened a book on basic physics, and prepared to expand my knowledge of the universe. There was only one teeny tiny infinitesimal problem. A minor detail, really
Math is an integral part of physics.
I do not have a good relationship with math.
To understand physics, the world, and the best memes on Facebook's I f*cking love science would mean going alllllll the way back to Algebra I. Did I really need to know the answers to the universe so badly? Was I willing to go back to x, y, polynomials, graph paper, the evil f(x), and some of the most miserable academic memories of my life? Was I this much of a nerd?
The answer to every question was yes. Dr. Tyson's scientific fever still has hold on me. He transmits it via StarTalk. One day I'll either thank him for starting this journey or send him some non-Pluto hate mail.
I left the library with two algebra books: The Everything Guide to Algebra (Christopher Monahan, published by Adams Media) and The Complete Idiot's Guide to Algebra, First Edition (W. Michael Kelley, published by Alpha Books). So far Idiot's Guide is the hands down winner. Everything reads like stereo instructions. Monahan covers in one chapter what Kelley splits into three. However Idiot's Guide is light on practice problems despite its "A Plethora of Practice" chapter. Kelley's target audience is probably middle and high school students with an algebra textbook at hand rather than thirtysomething nerds looking to increase their geek cred. Right now I'm keeping Everything as a back up for practice problems.
After a week with these books I feel hopeful. Over the next couple of days I'll post about getting my feet wet, my stupid math mistakes, and how some of those rules my eighth grade math teacher harped on turned out not to be so important after all.
Thanks to the YouTube channel I could watch Dr. Tyson lecture on things from trivial to deep from the comfort of my couch. His love of the universe and science education is infectious. After a month of Tyson lectures I wanted to read some books on basic physics. I went to the public library, opened a book on basic physics, and prepared to expand my knowledge of the universe. There was only one teeny tiny infinitesimal problem. A minor detail, really
Math is an integral part of physics.
I do not have a good relationship with math.
To understand physics, the world, and the best memes on Facebook's I f*cking love science would mean going alllllll the way back to Algebra I. Did I really need to know the answers to the universe so badly? Was I willing to go back to x, y, polynomials, graph paper, the evil f(x), and some of the most miserable academic memories of my life? Was I this much of a nerd?
The answer to every question was yes. Dr. Tyson's scientific fever still has hold on me. He transmits it via StarTalk. One day I'll either thank him for starting this journey or send him some non-Pluto hate mail.
I left the library with two algebra books: The Everything Guide to Algebra (Christopher Monahan, published by Adams Media) and The Complete Idiot's Guide to Algebra, First Edition (W. Michael Kelley, published by Alpha Books). So far Idiot's Guide is the hands down winner. Everything reads like stereo instructions. Monahan covers in one chapter what Kelley splits into three. However Idiot's Guide is light on practice problems despite its "A Plethora of Practice" chapter. Kelley's target audience is probably middle and high school students with an algebra textbook at hand rather than thirtysomething nerds looking to increase their geek cred. Right now I'm keeping Everything as a back up for practice problems.
After a week with these books I feel hopeful. Over the next couple of days I'll post about getting my feet wet, my stupid math mistakes, and how some of those rules my eighth grade math teacher harped on turned out not to be so important after all.
A Brief History of My Mathematical Education
What I remember of it, anyway.
Algebra and I were officially introduced in eighth grade. My teacher was in his last year before retirement. It showed. His idea of checking homework was a file folder with all the homework problems worked out stored at the back of the classroom. We were supposed to get the folder at the beginning of class and check our own homework as the new lesson was going on. If any math teachers are reading, believe me when I tell you this is not a winning strategy. By the time open house rolled around there were a lot of angry parents. I still remember bits and pieces of the showdown. Oh, and he spent a lot of time telling me and my classmates how slow we were compared to last year's class (another strategy that shouldn't be duplicated.) To top things off my father was really good at algebra. He tried to help me, but I was so far behind with the ABCs of algebra none of what he said made sense. Many tears were shed over algebra homework. I got my one and only D on a report card. I think I wound up with a B for the year. Barely. I was downgraded from math and science honors track (the science teacher wouldn't recommend you for honors science if you weren't in honors math) to college prep. My 14 year old self was crushed. How could I not be in an honors class? I wouldn't get the all important honors points! My college chances are ruined!!!!!
Oh, 14 year old self, I want to pat you on the head and tell you this really is the least of your troubles.
My class suffered of a lot of educational guinea pigging. In middle school it was ability tracking. In high school it was block scheduling. Eight classes, four per semester. I didn't have math until second semester. I lucked out, though, because my geometry teacher also taught AP Calculus. She knew her shenanigans backwards and forwards. And I was actually good at geometry. It made sense -- except for proofs. Those made my eyes cross. But I made an A in it! Both my math and science teachers recommended I be bumped back up to honors math and science! Yay! 15 year old self is happy! College isn't derailed forever!
My sophomore schedule once again didn't have me in math until second semester. A whole calendar year between math classes for someone with a shaky algebraic foundation. Honors Algebra II was a trial. I don't remember a specific unit giving me trouble. It was a daily 90 minute root canal without anesthetic. But life has its ways. Thanks to that class I became friends with one of the greatest mathematical minds I've had the pleasure of knowing (more on her later) who also created my short term addiction to Lance snack crackers that were orange with a whitish cheese inside. Algebra II left me with the one and only (final grade) C on my academic record. 16 year old self was once apoplectic. It's okay, 16 year old self.
And for some unknown reason the teacher still recommended me for Precalculus rather than regular Algebra III/Trigonometry. Or maybe I asked so I could get that stupid honors point that has absolutely no bearing on any aspect of my life now.
Precal was a first semester class, so I thought I had a better shot at it. The first half of the term was dismal. I was lost. Even with the then-almighty TI-82 I was drowning. Nothing made sense. My sense of failure was augmented by the fact the girl sitting next to me (not the same person mentioned above) was stomping the course into the mud. She tried to help me out, but she admitted she wasn't sure how she was doing it. It just made sense to her.
After a dismal midterm that left me resigned to accept another final C on my transcript, the material switched from higher algebra to trigonometry. My teacher was shocked when I started raising my hand not to ask more questions but answer them correctly. My neighbor and I traded places in the grade book. I was just as powerless to explain trig to her as she had been to explain algebra III to me. Sines, secants, tangents -- I don't remember a damn thing about them now, but I owned them first semester junior year. I made an A for the second grading period and fled precal with a B. I didn't even consider another math for senior year. The only things left were AP Calculus or AP Statistics.
One fantastic thing about being a music major is the math requirement is pretty chill. I could either take Math 101 (precal) or Math 140 (ratios and logic based math). I stalled it until spring semester. If p then q, if not p then not q, etc. and I got along very well. I made an A and left the study of mathematics behind me. The closest I came to math over the next nine years were efforts to keep my bank account out of the negative, balance work receipts, and make change. I was more than okay with that.
That all changed around Thanksgiving of 2012.
Algebra and I were officially introduced in eighth grade. My teacher was in his last year before retirement. It showed. His idea of checking homework was a file folder with all the homework problems worked out stored at the back of the classroom. We were supposed to get the folder at the beginning of class and check our own homework as the new lesson was going on. If any math teachers are reading, believe me when I tell you this is not a winning strategy. By the time open house rolled around there were a lot of angry parents. I still remember bits and pieces of the showdown. Oh, and he spent a lot of time telling me and my classmates how slow we were compared to last year's class (another strategy that shouldn't be duplicated.) To top things off my father was really good at algebra. He tried to help me, but I was so far behind with the ABCs of algebra none of what he said made sense. Many tears were shed over algebra homework. I got my one and only D on a report card. I think I wound up with a B for the year. Barely. I was downgraded from math and science honors track (the science teacher wouldn't recommend you for honors science if you weren't in honors math) to college prep. My 14 year old self was crushed. How could I not be in an honors class? I wouldn't get the all important honors points! My college chances are ruined!!!!!
Oh, 14 year old self, I want to pat you on the head and tell you this really is the least of your troubles.
My class suffered of a lot of educational guinea pigging. In middle school it was ability tracking. In high school it was block scheduling. Eight classes, four per semester. I didn't have math until second semester. I lucked out, though, because my geometry teacher also taught AP Calculus. She knew her shenanigans backwards and forwards. And I was actually good at geometry. It made sense -- except for proofs. Those made my eyes cross. But I made an A in it! Both my math and science teachers recommended I be bumped back up to honors math and science! Yay! 15 year old self is happy! College isn't derailed forever!
My sophomore schedule once again didn't have me in math until second semester. A whole calendar year between math classes for someone with a shaky algebraic foundation. Honors Algebra II was a trial. I don't remember a specific unit giving me trouble. It was a daily 90 minute root canal without anesthetic. But life has its ways. Thanks to that class I became friends with one of the greatest mathematical minds I've had the pleasure of knowing (more on her later) who also created my short term addiction to Lance snack crackers that were orange with a whitish cheese inside. Algebra II left me with the one and only (final grade) C on my academic record. 16 year old self was once apoplectic. It's okay, 16 year old self.
And for some unknown reason the teacher still recommended me for Precalculus rather than regular Algebra III/Trigonometry. Or maybe I asked so I could get that stupid honors point that has absolutely no bearing on any aspect of my life now.
Precal was a first semester class, so I thought I had a better shot at it. The first half of the term was dismal. I was lost. Even with the then-almighty TI-82 I was drowning. Nothing made sense. My sense of failure was augmented by the fact the girl sitting next to me (not the same person mentioned above) was stomping the course into the mud. She tried to help me out, but she admitted she wasn't sure how she was doing it. It just made sense to her.
After a dismal midterm that left me resigned to accept another final C on my transcript, the material switched from higher algebra to trigonometry. My teacher was shocked when I started raising my hand not to ask more questions but answer them correctly. My neighbor and I traded places in the grade book. I was just as powerless to explain trig to her as she had been to explain algebra III to me. Sines, secants, tangents -- I don't remember a damn thing about them now, but I owned them first semester junior year. I made an A for the second grading period and fled precal with a B. I didn't even consider another math for senior year. The only things left were AP Calculus or AP Statistics.
One fantastic thing about being a music major is the math requirement is pretty chill. I could either take Math 101 (precal) or Math 140 (ratios and logic based math). I stalled it until spring semester. If p then q, if not p then not q, etc. and I got along very well. I made an A and left the study of mathematics behind me. The closest I came to math over the next nine years were efforts to keep my bank account out of the negative, balance work receipts, and make change. I was more than okay with that.
That all changed around Thanksgiving of 2012.
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