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.
As an aside, one of my friends and coworkers who reads this blog (and has forgotten most of her algebra -- and she made it to Calculus II before getting lost) went through the same school district. Different middle schools, same high school, mostly same courses but not actual classes. The only class we were in together was marching band. We recently talked about how a teacher can make such a difference. Not only in how you do in a subject, but how you feel about it. Math wasn't something I was ever at home with, but I felt capable until algebra. I can't help but think if I'd had a different teacher for Algebra I, I wouldn't have dreaded every math class after that. Maybe algebra was something I wasn't quite ready for at 13. Maybe I still would have struggled with it -- and everything to follow. Maybe I should've paid more attention, asked to be moved from the back of the class, not written absolutely horrible teenage slop Star Wars fanfiction before I knew fandom was a thing instead of taking notes (some geek traits start early). Honestly by that time I was so lost it probably wouldn't have made a huge difference.
To say it was all my teacher's fault isn't fair. There was more I could've done. But much as I've forgotten about middle school and algebra, I clearly remember that teacher's attitude and carried it with me through the rest of my mathematical studies. I'm not saying I'd be the nuclear physicist my mother always wanted in the family. Just not scared of math. Although if I ever get to have a George Bailey moment and it turns out I would be on Neil deGrasse Tyson's staff now, I will punch Clarence in the gut and ring bells in his face as he stands there still wingless. And oddly my difficulty in math wasn't a major obstacle in science class. I don't remember what grade I got in chemistry, but apparently I was good enough at it my teacher (who was known as the teacher you did not want) couldn't understand why I wasn't signing up for AP Chem. Chemistry is a LOT of math. Obviously I could hack it there. Why couldn't I do it in my actual math classes?
I said I would start matrices Monday, but I forgot it's my birthday. Don't have any plans (birthdays after 30 chill out until the next decade rolls around), but I may not feel like tackling a "new" algebraic concept. We'll see. If not there will be new insights and confuddlement on Tuesday.
As an aside, one of my friends and coworkers who reads this blog (and has forgotten most of her algebra -- and she made it to Calculus II before getting lost) went through the same school district. Different middle schools, same high school, mostly same courses but not actual classes. The only class we were in together was marching band. We recently talked about how a teacher can make such a difference. Not only in how you do in a subject, but how you feel about it. Math wasn't something I was ever at home with, but I felt capable until algebra. I can't help but think if I'd had a different teacher for Algebra I, I wouldn't have dreaded every math class after that. Maybe algebra was something I wasn't quite ready for at 13. Maybe I still would have struggled with it -- and everything to follow. Maybe I should've paid more attention, asked to be moved from the back of the class, not written absolutely horrible teenage slop Star Wars fanfiction before I knew fandom was a thing instead of taking notes (some geek traits start early). Honestly by that time I was so lost it probably wouldn't have made a huge difference.
To say it was all my teacher's fault isn't fair. There was more I could've done. But much as I've forgotten about middle school and algebra, I clearly remember that teacher's attitude and carried it with me through the rest of my mathematical studies. I'm not saying I'd be the nuclear physicist my mother always wanted in the family. Just not scared of math. Although if I ever get to have a George Bailey moment and it turns out I would be on Neil deGrasse Tyson's staff now, I will punch Clarence in the gut and ring bells in his face as he stands there still wingless. And oddly my difficulty in math wasn't a major obstacle in science class. I don't remember what grade I got in chemistry, but apparently I was good enough at it my teacher (who was known as the teacher you did not want) couldn't understand why I wasn't signing up for AP Chem. Chemistry is a LOT of math. Obviously I could hack it there. Why couldn't I do it in my actual math classes?
I said I would start matrices Monday, but I forgot it's my birthday. Don't have any plans (birthdays after 30 chill out until the next decade rolls around), but I may not feel like tackling a "new" algebraic concept. We'll see. If not there will be new insights and confuddlement on Tuesday.
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