My specific book goes:
1.1 Linear equations
1.2 Word problems on linear equations
1.3 Complex numbers (what the fuck? Why do they need this?)
1.4 Quadratic equations (Because we are going to teach quadratic equations including complex solutions. For no fucking reason at all. It just undermines the natural logic of using a graph to guide your intuition about the number of real solutions, and amps of the difficulty of the computations.)
So now, if you skip complex numbers, you have to be very careful for the rest of the book, because all the problems and explanations assume you know about complex numbers. That's actually the essential problem with skipping chapter 1, for that matter, but I should have done it anyway.
It's very possible that high school algebra textbooks are better; college algebra textbooks are just so fucking bad that I want to scream.
Why is there a distinction?
I have no idea. But the covers all say "college algebra", so I'm just admitting that maybe there is a different version out there.
1.3 Complex numbers (what the fuck? Why do they need this?)
Why do they need any of it? I'm not being flippant, I'm wondering who takes the class and what they get out of it. It seems like for people who didn't get this stuff in high school it's pretty late for them to avoid math-phobia and end up in any kind of job where they would actually use these things.
And other departments particularly say that they want us to work on word problems because they need kids to get better at that for the courses that follow College Algebra, but the problems in this book do absolutely nothing to build the skill of translating English to Math and understanding symbolic manipulation for someone who finds this really hard. It's all fun challenge problems for 10th graders who a good at math.
No, "why do they need Algebra" is a very real question, and ISTM one part stupid loyalty to historical tradition, and one part deliberately constructing a bottle-neck course. They should really be taking a gentle statistics course, instead.
In my day, Calc was the bottle-neck course.
Oh it is, too, for the science majors. This is the bottleneck for graduating high school and also for just getting any college diploma.
For example: I would like to teach them (and I will!) that you should only factor quadratics that are easy to factor, and otherwise use the quadratic formula (or a calculator!) But the fucking book specifies a method on each problem, so you're either lobbing complicated override instructions at them, or your available problem set is whittled way down.
Furthermore, it is bad pedagogy to specify a method!
I'm embarrassed to admit that learning algebra when I did and barely using it since the last math class I took in college has made me much more comfortable writing out calculations on paper, and I'm too lazy to take out a sheet of paper so I tend to muddle around using the computer's calculator in the few cases where it would be easier to just solve for x. I guess I should see if there's some scaled down Mathematica type thing I could use. I guess I do put arithmetic in scripts, so that kind of counts.
You're right, we're all doomed.
When I was in high school, our Algebra 2 books (or Algebra 3/4, frigging class nomenclature, the second year of algebra) were called College Algebra, so I'm not sure there's a difference between the two. At any rate, that sucks, but most professors I've taught with hated the available texts. Those that had too much free time ended up writing their own, and I still think theirs are kind of lousy. (One is written in the style of "Imagine you are standing on a hill looking down. You are at a potential energy maximum!")
Students only want algebra if it's torture.
you should only factor quadratics that are easy to factor, and otherwise use the quadratic formula (or a calculator!)
After 2 years of high school algebra that seemed to consist of nothing but factoring quadratics that's the conclusion I arrived at.
Maybe you should write a new book, heebster.
I learned a lot of this stuff LAST YEAR (I guess for the second time) after Khan Academy decided I was a mathematical sixth grader and made me do a bunch of this stuff instead of calculus. And I've forgotten it already.
21: It's odd what things people "think" you need as basics. I was terrible at all things algebraic but fine at most calculus.
Do you not get to choose which textbook to use for the course you teach? Surely there must be one out there somewhere that's set up the way you would prefer.
We used to have logic as an alternative to algebra, but the board of regents decided they wanted everyone to be focusing on arithmetic and statistical reasoning, so logic no longer qualified. It was a shame; it's one of my best courses and students with bad math panic really liked the class.
24: I do, but I wasn't in the mood to search for books when this came up last semester. But at most schools, no - you'll have 30 sections of College Algebra and there needs to be some semblance of interchangeability. I believe a lot of large schools are on the dole from their favorite publisher, as well.
20: You are at a potential energy minimum!
Whats a complex number? Is that like eleventeen, or thirty-twelve?
It's the kind of number that would occur in Ulysses. It's not the simple kind of number that would appear in a Taylor Swift song.
Our students can now (after a long struggle with our Provost and our Curriculum Committee) choose between College Algebra and College Math.
I haven't noticed that it's making them any happier, though. They hate either pretty much equally.
College math can be designed pretty badly, too! Also, haters are going to hate.
As near as I can tell, people are convinced that they will earn more money if they can prevent you from explaining a relatively simple mathematical concept to them. The hell of it is, they may be right.
32 How is College Algebra not a subset of College Math?
35: the prefix "college" is only appended to classes that cover material previously taught at high-school or below. I think "college math" is like repeating junior high school math and "college algebra" is repeating high school math, or something like that. I think "college math" was the one that drove my cousin out of college when she failed it for the fourth time; it involved adding fractions.
Fortunately, every fraction converts to a decimal and you can add those with a calculator.
Even I can add fractions. Are kids still taught how to find a Lowest Common Multiple?
If only they could just call the class College Fractions.
Sounds like someone should become the Stewart of algebra and build a mulitimillion dollar mansion called the FOIL house or something.
They should it call Fraternity Math and all the questions should be about how many pizzas and kegs to order and how to split the bill.
Last night was Math and Reading Night at the kids' school. AB buttonholed Iris' math teacher to get him to tell her how Iris has been taught to do long division, because it is completely beyond us (and sometimes beyond Iris). She hasn't explained it to me yet, so that's all I know.
Long division is just a really awkward fraction.
I think "college math" is like repeating junior high school math and "college algebra" is repeating high school math, or something like that.
There's basically two schools of college math, but it's always math-for-poets. One school is that this should be the most practical math - little bit of how to figure out the interest on your mortgage, a little bit of statistics, etc. That is fine. The textbooks sometimes get hijacked by these people who thing that the questions ought to be gotchas, instead of gentle, but it's still fine.
The other school is that college math should teach students why there is something interesting and beautiful about math. So you study infinity and Hilbert's Hotel, and stretch a donut into a coffee cup, and do fun stuff like that. That is also fine.
In general, college math courses are a big improvement over college algebra. The problem is that a lot of other courses really do need college algebra as a prerequisite, and college algebra does a terrible job teaching the algebra necessary for these other settings.
I am not at all sure what gets taught in College Math. Maybe stats? Finite Math? IDK.
Thank God I never have to take math again, is all I say.
Calculating the interest on your mortgage is easy. They sent you a letter with the answer about this time of year.
A good college math course requirement (presumably for people who are never going to study any math again) seems like it would be a two semester sequence that covered both 45.1 and 45.2. College Math I: Practicalities. College Math II: Inherent Beauty.
Maybe what my cousin took was "college prealgebra" instead of "college math". Whatever it was, it sounded like a train wreck. College really wasn't for her, especially when it was something she was trying to do on the side while working full-time.
I had an idea recently to make an app that would calculate things for sports fans, like how many games out of the next however many your team needs to win to get to .500, or what their magic number is, etc. I guess that's algebra? It took me an embarrassingly long time to figure out the math. Not that I'm making the app.
I was so proud of myself when I figured out the formula for how many games are played in the NCAA Tournament.
The NCAA tournament is a great way to understand why 1+2+4+8+...+2^n = 2^(n+1)-1. The LHS is counting the number of games in each round and the RHS is that every team but the winner loses exactly one game.
The math isn't hard. I don't know what a Gonzaga is.
Semi-on-topic: I always think it would be kind of neat to study math again though I wouldn't have any idea where to pick up. I took high school calculus and did fine and then basically never studied math again, so it's 20+ years. But I do remember HS calc as neat.
Neat neat neat it would be neat to be neat.
I've been getting back into math in order to help the girls with their homework, and yeah, it's fun, but it's also dismaying how much I have to review. I'm still looking forward to reviewing calculus, which I remember really liking in high school even though my teacher was ineffective on account of being nuts.
I don't know what a Gonzaga is.
Northern Italian royalty.
Some of my most effective teachers were nuts.
And speaking of ineffective teachers, my class today looked incredibly bored when I was telling them something I thought was pretty exciting. They looked mildly interested when I was telling them things that are really boring. I don't think I'm very good at this part of my job.
I guess some of mine were too. I should have specified that he was nuts in ways that prevented him from clearly communicating concepts that would have helped me understand math. And he lived part of the time in a friend's car, which was no mean feat in that it was an MG and this was in Vermont, but I think it cut into his organizational capabilities.
We're doing user experience testing for our college algebra software right now and it's just so damned sad. These students are woefully underprepared, especially with (as h-g says) with the manipulation. And some of these students are in majors (e.g. business administration) where comfort with symbolic manipulation is pretty helpful.
I thought business administration was a phoney major, like communications for people whose parents had wised-up to that one.
I think it's different, at least relatively, if you're thirty-five or older and going back to school at a for-profit.
I'd get an MBA and sell out, but I can't figure out who the buyer would be.
Aren't the buyers always suckers?
(If you're saying you can't figure out whot the suckers are, I'm pretty sure that's what you would learn in business school.)
I was thinking I could just make an ethical compromise and be given a ton of money. Lots of fiction seems to imply that.
"two trains leaving, one train travelling 40 mph faster than the other, and when will Joe catch up with Brenda if he left 30 minutes later?"
The better version of this problem has Jeanette MacDonald on a horse and Maurice Chevalier on the train and the answer at the end of Love Me Tonight. Which should be shown to all children.
Although I suppose some of the jokes are a bit louche. But if they're too young for them I don't think they'll understand them. Besides, how louche can Myrna Loy and Charles Ruggles be?
My son has discovered a method of completing sixth grade math homework that may not serve him well in the long run:
Assignment: find the lowest common multiple of 17 and 23.
Son: "Siri, what is the lowest common multiple of 17 and 23?"
I'm not sure whether Siri can handle college algebra.
The better version of this problem has Jeanette MacDonald on a horse and Maurice Chevalier on the train and the answer at the end of Love Me Tonight
"Cary Grant and Eva Marie Saint make out in a train, which then enters a tunnel. Discuss."
Those are both prime. The lowest common multiple is 17 x 23.
Moby has revealed himself as an AI. He had no choice but to answer the question.
Papa was a Proteus
Mama was a library hand
I could use the Chinese remainder theorem before I learned to stand
Home was on the DARPAnet, `make love` was a CLI command
Never got deployed by the boys at RAND
Before you ask me, you should suss:
Papa was a Proteus
76 is the best thing ever. Moby Hick is next.
76 is the best thing ever.
Well, I can't quite see how to make it scan. I think we need to hear an audio recording before voting on how high up it ranks among best things ever. Surely snarkout will indulge us.
this seems like the right thread to mention that Mrs. K-sky awoke from a stress dream and said, "We're going to need to get φ a math tutor," then went back to sleep.
Opinions on Mark Chu-Carroll's blog, Good Math, Bad Math? For his book, he left out the attacks on bad math.
He frequently doesn't seem to have a great grasp on what he's writing about. But maybe that's not so bad if you don't either and just want the gist?
One of my colleagues has written a free, open access college algebra text. I don't know if it avoids any of your problems, but I always promote free textbooks and my colleague's work.
http://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=12
I'm inclined to let some of that slide as a matter of attempting to write in a popular manner. That is, I do not think it's necessarily a matter of his grasp.
They also do precalc and college trig:
Why make your students pay money for a shitty textbook? And they post the LaTeX source code, so you can customize everything!
@70: I'm not sure whether Siri can handle college algebra.
She will, someday soon. It won't be long until we have Watson 4.0 running on our smartphones, and then we'll be in the same situation with algebra, calculus, statistics, PDEs, etc. that we were with long division and square roots when calculators became available. Why teach someone to do vector analysis when he has a machine in his pocket that can listen to him stating a problem and solve it?
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Prim/ordial grav/itational wa/ves have officially turned to dust. Sigh.
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Can I assume that means the world will end soon or do I have to keep working?
Well, what good is your goddamn "science" then.
82-84: It's been a while since I've read Chu-Carroll, but on topics I know about (some bits of pure math, programming languages--that is, closer to his specialities than essear's) I thought he did have a good grasp on stuff, but he would often be more of a jerk about it than I'm comfortable with. I liked his articles on "Cantor cranks", but in retrospect I was probably just laughing at mental illness.
87: at least you no longer have to feel bad about picking the wrong specialization.
86. Siri and Watson won't be real AIs until they can do word problems, especially word problems involving Nelson Eddy and Jeanette MacDonald.
So for now, if you can do word problems you'll have a job.
@93: Siri and Watson won't be real AIs until they can do word problems
I'd be hard-put to come up with a definition of "word problems" that didn't encompass "winning Jeopardy." One can easily imagine "Maytime Sweethearts" as a Jeopardy category. What definition did you have in mind?
I'd have similar problems with the definition of "real AI." I'm agnostic on AI in general.
(Don't want a job; entering my second decade of retirement.)
92: I don't know, after reevaluating all my priors based on last year's announcement I still think they have a decent shot at turning up a signal in the next decade or so.
If you ever do get notice that the world is going to end, you will tell me so that I have enough time to buy liquor before the rush, right?
You can't be too careful; you should buy liquor at every opportunity.
I was asking for audio of snarkout singing "Papa Was a Proteus," not Stephin Merritt singing "Papa Was a Rodeo."
Oh, no. Nobody wants to hear that. You might think you do, but you're mistaken. I'm sure one of the philosophers can explain how that is.
85: you're so right. I'll take a look at that tomorrow.
Why make your students pay money for a shitty textbook?
I think it's called the Principal-Agent Problem.
Here is another answer to a word problem: Nelson Eddy is to Jeanette MacDonald as Jeanette MacDonald is to Maurice Chevalier.
Not clear where Clark Gable fits in here.
103.last: He's an idiot's delight.
The villains: a gang of clowns who want the nutria to thrive as a materials source for their artisanally hand-stretched Fleshlights.
I don't see how 105 could be out of place in any conversation, really.
105 really is a fantastic comment in isolation.
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Puppy sweepstakes time. Voice only or video for the phone interview?
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111: I have never found video to add anything to a phone interview.
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How harshly should I judge an intern for being unable to successfully follow the instructions "Dial 9 for an outside line" without assistance?
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Video seems ok if they're set up so you can see everyone in the room. Worse than voice if they're sitting around a table and connecting through a laptop sitting on the middle of the table and most of the time what you see on the screen is the top of someone's head and a blackboard in the background.
113: the first time, not harshly at all. It's legitimately possible that they've never encountered anything like that before.
If they can't get it after being given assistance the first time? Very harshly.
113. Very harshly. How harshly should I judge you for commenting on two blogs while in the middle of a work crisis?
"It looks like a '6', except upside-down."
A person born in 1995 has never even seen a phone where you had to dial from numbers instead of an exist list of contacts.
Were they just staring at the phone saying "Siri, give me an outside line" and wondering why it wasn't doing anything?
Without even asking if the phone was Android.
112, 114: Thanks for the input. Opting for phone; no need to make gender/appearance/office decor salient.
119 was also my reaction. "Outside number" is probably already going to be unfamiliar to someone who grew up after the point at which "long distance" became an irrelevant (and basically unknown) thing to most phones.
On our work phones, you have to dial a '9' for an outside line unless the number you are dialing ends in '9'. In that case, you have to dial a '7'.
But it actually seems easier to remember that rule than when to use 7 digit or 10 digit numbers during that transition period.
87: There's an interesting thread over at Not Even Wrong that seems to indicate that the announcement wasn't supposed to be made yet. I can't tell if that's correct, but it would be kind of amusing if the announcement that BICEP jumped the gun in announcing their detection of gravitational waves was, itself, jumping the gun.
At some place I worked, there was a problem with accidental dials to 911 so they changed it to 8 for an outside line.
We are such special snowflakes that to get an outside line here one has to dial 99. I think the reason for that is one has to dial 94 to get an internal-external line. So they use two digits as the prefix.
an internal-external line
It is a world-wide private-line telephone network owned by this far-flung federal department. So one can call people at installations in Germany, Korea, etc. without paying international rates or allowing free for all access to international calling. The network is also domestic; most people don't use it for those calls, but they could.
Once in the pre-cellphone era I stayed in room 180 in a hotel. Whenever anyone in the hotel forgot to dial 9 for an outside line, and dialed 1-800, the phone rang in room 180. I didn't get much sleep that night.
Imagine what the person in room 197 must have been going through.
I think the time I accidentally called 911 from work, it was because I was calling Sacramento which starts 1-916, and I flubbed the ordering. Now we have a new phone system where you have to dial 9 first, so it will be 9-1-916 - shudder.
Fortunately, the new system has a desktop interface so I can preferentially just click on a contacts to start a call with them.
129: Their paper is coming out on arxiv next week (Monday, I think). People involved have been publicly discussing the results. But it does seem to be the case that they didn't intend the website to be noticed yet.
When I was a kid I went through a period where I would prank call 911 once a week or so, but I've never called them accidentally or for an actual emergency.
Ironically, being Urple, he was actually near death during each of those prank calls.
I am LB's intern. I have mad computer skillz, but phones, I got nothing.
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I knew puns were a gateway drug to spam.
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Some FPP needs to restore the link in 145! I want to be an ekranoplan magnate!
It's like being a babe magnet but MUCH BETTER.
A superconducting babe magnet. Very chill.