Re: New Math

1

Look, the pope of SWPL viewpoints, Louis CK, has laid down the law on the "common core," and who are you to question the wisdom of the pope?


Posted by: Robert Halford | Link to this comment | 07-27-14 10:10 AM
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SPouse (who is one of the math coaches for a local district) says that is actually in the fourth grade curriculum. 4.OA.A.3


Posted by: SP | Link to this comment | 07-27-14 10:20 AM
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It's always a little odd for me to discuss CC because it's not been implemented in Texas, but basically, wow do people have a very poor understanding of what's actually CC and what's textbook writers and what's Race To The Top and so on and so forth.


Posted by: heebie-geebie | Link to this comment | 07-27-14 10:21 AM
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2: Huh. It seems like a really abstract concept for fourth grade. In her opinion are the kids able to wrestle with it?


Posted by: heebie-geebie | Link to this comment | 07-27-14 10:23 AM
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Yes, if they are exposed to it early enough.


Posted by: SP | Link to this comment | 07-27-14 10:23 AM
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Well good!


Posted by: heebie-geebie | Link to this comment | 07-27-14 10:23 AM
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Also she said that:
1) Things are in fact taken out of standards fairly regularly, at least moving them to later grades. CC in fact is much more focused on mastery in each grade instead of making kids do a little of everything in one grade, then a little of it again in the next grade, etc. It requires more mastery in each grade of fewer subjects per grade.
2) You should be careful about interchanging curriculum and standards which is about 95% of what the arguments over CC are about. CC is a set of standards, and individual curricula that address those standards may or may not suck. Most of the examples you see on FB of ridiculous "CC" things are just bad curriculum, not a reflection of problems with the standards.
For some reason I am sitting here transcribing her comments, she won't comment herself.


Posted by: SP | Link to this comment | 07-27-14 10:27 AM
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3 to 7.2, apparently.


Posted by: SP | Link to this comment | 07-27-14 10:27 AM
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For point 2, I'm not in a CC state, so it's slightly moot. But I don't have a bad impression of the math CC standards.


Posted by: heebie-geebie | Link to this comment | 07-27-14 10:29 AM
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I really liked my kid's first grade math homework worksheets, which I believe are in some way related to an implementing common core curriculum. They did things like introducing "x" and "y" notation and basic algebra at the same time as teaching arithmetic, which seemed to make sense to me. I shouldn't really comment though since I barely mastered counting.

Also my own first grade math teacher permanently screwed me by saying that greater than/less than signs are like a big fish eating a little fish. What the fuck? To this day, I still have to mentally adjust to the greater than/less than sign thing because the "less than" sign totally looks like a BIGGER fish eating a smaller fish.


Posted by: Robert Halford | Link to this comment | 07-27-14 10:33 AM
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Everyone knows they're greedy alligators who want to eat the bigger thing. I used to actually draw little teeth inside them.


Posted by: SP | Link to this comment | 07-27-14 10:35 AM
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I never understood why that notation needs a mnemonic device. The bigger side of the symbol goes with the bigger item. It's its own mnemonic.


Posted by: heebie-geebie | Link to this comment | 07-27-14 10:53 AM
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11 is right. However they first tried to explain it to me, it didn't take. I still use the alligator thing.


Posted by: Moby Hick | Link to this comment | 07-27-14 10:55 AM
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Math is the one with all the lines and stuff, right?


Posted by: Flippanter | Link to this comment | 07-27-14 11:57 AM
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1: Louis CK was, IIRC, mostly targeting the emphasis on testing. I'm midway through season 4 of the Wire where Simon seems to be making the novel case that what's needed is separating the good kids from the bad and then connecting each groups interests (gambling odds and the rules of the street, respectively) to academic subjects.


Posted by: Eggplant | Link to this comment | 07-27-14 12:09 PM
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14: That's the airport.


Posted by: Moby Hick | Link to this comment | 07-27-14 12:19 PM
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I have a similar story where I was messed up by a young idealistic algebra teacher who taught us a new way to factor quadratic equations. This was great at the time, but then when I moved on to other classes, my math teachers assumed we knew the old, traditional way and taught based on that. When I tried to use the new method, they were basically like what the hell are you doing?

I don't know which way is taught nowadays. Needless to say, I don't think I remember how to do either.


Posted by: pasdquoi | Link to this comment | 07-27-14 12:34 PM
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17.1: I've heard stories like that a bunch, and I never understand what's wrong with the teachers. Anyone competent should be able to figure out what a kid using an alternative method to solve a problem is doing, and if the alternative method is valid, what's the point of objecting?


Posted by: LizardBreath | Link to this comment | 07-27-14 12:47 PM
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It's probably not easy to get competent and giving a shitetent on what most schools pay.


Posted by: Moby Hick | Link to this comment | 07-27-14 1:04 PM
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I remember learning how to translate word problems into equations in seventh grade.


Posted by: Blume | Link to this comment | 07-27-14 1:20 PM
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Moby has either made a joke beyond my ken in 19 or has been at The Cage for longer than I'd have thought at this point in the afternoon. Or maybe autocorrect.


Posted by: Jesus McQueen | Link to this comment | 07-27-14 1:25 PM
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It's a new coinage I'm trying out.


Posted by: Moby Hick | Link to this comment | 07-27-14 1:28 PM
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Probably should spell it "give-a-shitetent."


Posted by: Moby Hick | Link to this comment | 07-27-14 1:39 PM
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I've heard stories like that a bunch,

Does this locution mean you don't remember this happening to you, repeatedly? You are fortunate, if so.

We moved several times, and I went from progressive to mainline schools and back, in two different countries, and had this experience just as described, and also earlier when I used a different way of doing long division.

I experienced math instruction as an organ of arbitrary discipline, conformity and humorlessness.

That I learned it well enough to always do well on standardized tests, despite bombing individual classes, kind of amazes me now.


Posted by: idp | Link to this comment | 07-27-14 1:41 PM
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I experienced math instruction as an organ of arbitrary discipline, conformity and humorlessness.

That's how I experienced P.E. I had a very good math teacher. Back when he was teaching, I knew he knew quite a bit and that I was one of his better students, but mostly I noticed that he hadn't bought any new clothes since 1973.


Posted by: Moby Hick | Link to this comment | 07-27-14 1:53 PM
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I also wasn't totally thrill with the non-arbitrary discipline.


Posted by: Moby Hick | Link to this comment | 07-27-14 1:55 PM
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+ed.


Posted by: Moby Hick's Copy Editor | Link to this comment | 07-27-14 1:55 PM
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I actually don't remember ever having any particular desire to use an unconventional method for doing math. Battles I had with math teachers were pretty tightly focused on whether I actually needed to (a) do my homework or (b) abstain from crossword puzzles in class.


Posted by: LizardBreath | Link to this comment | 07-27-14 1:57 PM
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(Which were both, strictly speaking, things that counted as non-arbitrary discipline, but I still didn't take to it well. I still resent Mrs. Barn/hard attempting to keep me from enrolling in BC Calculus simply because I'd slacked through her class five years before, and enjoyed the 5 I got on the AP just a little bit more because of her being completely, entirely wrong about everything.)


Posted by: LizardBreath | Link to this comment | 07-27-14 2:01 PM
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I think you're supposed to call it BCE Calculus now.


Posted by: Moby Hick | Link to this comment | 07-27-14 2:05 PM
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Anyone competent should be able to figure out what a kid using an alternative method to solve a problem is doing, and if the alternative method is valid, what's the point of objecting?

There's valid reasons for them to quibble and invalid reasons for them to quibble. It's sometimes possible that the kid is able to do the problem using some shortcut because the problem is sufficiently simple, but it will help the kid more to understand a more general procedure for the kinds of problems coming up.

But other times the teacher can't follow what the students has done and shuts them down, which isn't okay.

One thing to keep in mind, though, in calling this "competence" or "incompetence" is that if you've got five classes of 25 students, you're going to have some really fucking smart kids in there, and the teacher may be be a middle-of-the-pack math major who is really excellent with the bottom 90% of the class, but has trouble keeping up with a really innovative, smart kid. That doesn't make them an incompetent teacher, exactly - math is hard, and kids don't explain themselves well.


Posted by: heebie-geebie | Link to this comment | 07-27-14 3:08 PM
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Also, a lot of times the kids and teachers are talking at cross-purposes where the teacher is saying "show your work" and the kid is saying "I'm doing it a different way (ie in my head)". The teacher is ok with the different way, but wants the kid to write down the steps. The kid may not have any clue how to write down the different method in their head.

Getting kids to show their work and communicate math accurately is super important, but an entirely different, more rhetorical language-based skill, which doesn't necessarily go hand-in-hand with math ability.


Posted by: heebie-geebie | Link to this comment | 07-27-14 3:12 PM
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On the topic of math pedagogy, I've been meaning to ask heebie what she thinks of Danica McKellar's books. (They're basically math textbooks written in the style of teen girl magazines.) I see them at my local used bookstore a lot, and it seems like an interesting concept but I have no idea if they're actually any good.


Posted by: teofilo | Link to this comment | 07-27-14 3:31 PM
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31.1 and 32 both make sense.


Posted by: LizardBreath | Link to this comment | 07-27-14 3:33 PM
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31 and 32 are way too reasonable and informative. We're not going to get anywhere with comments like that.


Posted by: Robert Halford | Link to this comment | 07-27-14 3:35 PM
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There's a fascinating site called quadrivium dot info and it goes through why we have the particular math curriculum we do. Why geometry and calculus and trigonometry? And he traces it back to the Puritans and making bombs and Cromwell and some other stuff. Anyway, the point is that nobody, not the teachers and certainly not the students, knows why we are still learning this particular curriculum, and his proposal is to teach the curriculum in such a way that teachers are prepared to answer the question "why are we learning this?" Key to his proposal is using lots of computer animation of curve drawing machines, which connect the algebra and geometry together in a more intuitive way. Who knows, it might work.


Posted by: bjk | Link to this comment | 07-27-14 3:43 PM
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You actually have to have dedication to the idea that not all important topics should be covered - that it is crucially important to omit key ideas, because there are too many key ideas to cover them all effectively.

This, I found interesting. I've never had anything to do with developing math curriculum, but the impression I got both in school myself and watching my kids was that the actual volume of math to be taught in grade school was very small. I mean, it's hard to teach, so all the repetition is necessary, but it seemed to me that there wasn't that much stuff.

Arithmetic, decimals, fractions (number lines go in here). Geometry: perimeter and area of various shapes, angles in different kinds of polygons. Very simple algebra. Some stuff with graphs and charts.

I must be missing all sorts of stuff, but I can't think of what would be a key idea that you could run out of time to cover. What kinds of things were you thinking of?


Posted by: LizardBreath | Link to this comment | 07-27-14 3:46 PM
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33: Someone gave one of them to me, once, and I thumbed through it. Basically I was on board - my impression was that it's full of cutesy teeny bop language to access actual math, and general enthusiasm for how much fun we're having about math. I didn't connect with it much because it was more basic than the math I ever teach, and I was reading it as a potential resource, but it seemed like it probably does mostly more good than harm.


Posted by: heebie-geebie | Link to this comment | 07-27-14 3:52 PM
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37: I don't know much about K-8 curriculum, but my knowledgable friend says that at every level - college, high school, middle school - the teachers feel that the students failed to be exposed to key concepts at the previous level.

At college, my colleagues are horrified that high school students aren't familiar with conic sections, complex numbers, trig identities, geometry proofs, etc.

One problem is that teachers often spend the first month of school covering what they consider to be the remedial topics, as rushed and fast (and ineffectively) as possible. Often times the kids probably were exposed to the topic, but they need to see it a few times before it sticks, and when teachers are rushing through it to get to the "real" material, they reinforce a whole lot of "JUST FOLLOW THE DAMN ALGORITHM" teaching.


Posted by: heebie-geebie | Link to this comment | 07-27-14 4:04 PM
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Furthermore, from what I understand in Singapore Math, you spend like two months playing with Zero before ever getting to One. To compare the pace.


Posted by: heebie-geebie | Link to this comment | 07-27-14 4:08 PM
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Shite tent is British slang for cob house.


Posted by: Todd | Link to this comment | 07-27-14 4:11 PM
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In a topic like "polynomials" there is so much excessive shit covered in textbooks which is completely stupid. The coefficient rule to narrow down candidates for roots. Memorizing end behavior based on the leading coefficient sign and highest power. Rules for whether or not certain roots cross the x-axis or are tangential to the x-axis. Endless techniques for locating roots and then using polynomial division to find the other roots. In a college class, those are probably all covered in a single day.

The students who is just trying to survive the damn class is not left with any sense that a polynomial can be factored into irreducible roots, and how both forms tell you useful information about the polynomial. They're just overwhelmed with procedures, where if you pick the right procedure you can answer the specific question.


Posted by: heebie-geebie | Link to this comment | 07-27-14 4:12 PM
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38: Thanks!


Posted by: teofilo | Link to this comment | 07-27-14 4:23 PM
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I got to use Descartes Rule of Signs in a paper, so that section isn't totally useless for at least one person.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 07-27-14 4:55 PM
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When I write a paper, I still check the direction of the less than signs using the Rule of Alligators Eating.


Posted by: Moby Hick | Link to this comment | 07-27-14 5:00 PM
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44: me too


Posted by: Turgid Jacobian | Link to this comment | 07-27-14 5:04 PM
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"shitet ent" is elvish for "fertilized tree"


Posted by: Turgid Jacobian | Link to this comment | 07-27-14 5:06 PM
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What most impressed me in the OP article was the discovery that people learned and applied complex math on the job which they couldn't replicate on paper, because their mis-education got in the way.


Posted by: idp | Link to this comment | 07-27-14 5:33 PM
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If you can't replicate the math on paper, how do you write the methods section?


Posted by: Moby Hick | Link to this comment | 07-27-14 5:35 PM
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48: I thought that part was poorly explained, actually. I'm totally willing to believe that badly taught math leaves you in a much worse place than intuitive, on-the-job thinking from the ground up problem solving. But in another sense, the situations aren't at all comparable, because the classroom setting has this whole symbolic reading comprehension and writing aspect, which is hugely important for any technical field that requires communicating technical things to other people, but which is not very important when you're doing complicated fractions word problems in your head, in the warehouse.


Posted by: heebie-geebie | Link to this comment | 07-27-14 5:41 PM
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But I do think that's key to thinking about the problem with math teaching -- that what people usually run into problems with really isn't, on some level, the math itself, it's something about how they've been taught to put math on paper. One of the earlier threads on this, I remember talking about how ordinary people don't have any trouble figuring out, e.g., if they do the speed limit and their car gets about 32 mpg, what time they're going to get to Grandma's and whether they're going to need to stop for gas, but equivalent 'algebra' in a classroom setting would often stymie them.


Posted by: LizardBreath | Link to this comment | 07-27-14 6:16 PM
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I think I'll ask my math ed expert whether or not symbolic rhetoric pedagogy is taught to future teachers. Or if there's much pedagogy on it in the first place.


Posted by: heebie-geebie | Link to this comment | 07-27-14 6:26 PM
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Is there any pedagogy on the pedagogy of pedagogy?


Posted by: Cryptic ned | Link to this comment | 07-27-14 6:38 PM
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It's called "metagogy."


Posted by: teofilo | Link to this comment | 07-27-14 6:39 PM
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Those who can't pedagogy pedagogy, pedagogy pedagogy pedagogy.


Posted by: heebie-geebie | Link to this comment | 07-27-14 6:39 PM
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This does sound, actually, like a problem that the You-Y'all-We pedagogy described is really useful for dealing with. If you could get students to solve problems, I'm not sure what word to use, naively? As if they actually wanted to know the answer, rather than needing to learn the right method, the way they do at work or getting to Grandma's, anyway. Then they'd be approaching learning how to appropriately communicate the answer in a standard way from a position of understanding already how to find it.


Posted by: LizardBreath | Link to this comment | 07-27-14 6:40 PM
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More seriously, yes! People think hard about how best to train teachers. Cf the article about how well japan incorporates ongoing teacher training.


Posted by: heebie-geebie | Link to this comment | 07-27-14 6:41 PM
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Pedagogy pedagogy pedagogy Buffalo buffalo.


Posted by: teofilo | Link to this comment | 07-27-14 6:42 PM
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they reinforce a whole lot of "JUST FOLLOW THE DAMN ALGORITHM" teaching.

SO YOU ADMIT THAT SCHOOL THESE DAYS IS FULL OF WARMIST PROPAGANDA


Posted by: OPINIONATED GLOBAL WARMING DENIALIST | Link to this comment | 07-27-14 6:47 PM
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56: I'd buy that.


Posted by: heebie-geebie | Link to this comment | 07-27-14 7:16 PM
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||

LB, since you've commented in this thread but not the Snowflake one, did you see my comment in that thread re: flaking on Piketty chapter 11? Basically, I'm flaking on chapter 11. Sorry.

|>


Posted by: fake accent | Link to this comment | 07-27-14 7:40 PM
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I got it -- just finished the summary and it's about to go up. Given the length of the chapter, I can see why you flaked if you had anything at all going on.


Posted by: LizardBreath | Link to this comment | 07-27-14 7:41 PM
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Is there any pedagogy on the pedagogy of pedagogy?

Oddly, I think it's called the scholarship of teaching and learning.


Posted by: | Link to this comment | 07-27-14 7:56 PM
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At college, my colleagues are horrified that high school students aren't familiar with conic sections, complex numbers, trig identities, geometry proofs, etc.

I don't think we touched any of that until 9th grade and that was on the honors* track, and then some of it wasn't covered until later than that. I certainly felt like math from about 4th-7th grade was pretty repetitive, and K-4th was pretty basic, although changing schools between 5th and 6th skewed my experience.

*You took geometry in 9th grade if you had algebra in 8th grade.** As far as I could tell - I switched districts so I did 8th grade somewhere else - the only people who did this were in honors geometry in 9th grade (about 60 kids at my school). There was a not-honors geometry course, but it seemed to draw from people who took algebra 9th grade.

**This was also the only track that put you on schedule to take the AP Calculus BC test senior year.


Posted by: fake accent | Link to this comment | 07-27-14 8:07 PM
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I misspoke. My colleagues are horrified that their college students don't know those topics, and feel they should have learned them in high school.


Posted by: heebie-geebie | Link to this comment | 07-27-14 8:48 PM
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complex numbers

Why on earth would you learn about complex numbers in high school? I mean, I can imagine a situation in which you learned something like the fundamental theorem of algebra and it came up, or a teacher went down a brief sidetrack explaining what's going on in cases where the quadratic formula doesn't spit out a real number answer, but as a general thing that standard high school students cover?


Posted by: snarkout | Link to this comment | 07-28-14 9:56 AM
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"Dear God -- these children don't know about complex numbers! Weren't they doing discrete Fourier transformations in 10th grade? Are their teachers animals?"


Posted by: snarkout | Link to this comment | 07-28-14 9:58 AM
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I learned about complex numbers in tenth grade!


Posted by: nosflow | Link to this comment | 07-28-14 10:01 AM
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I'm pretty sure we didn't do imaginary or complex numbers at school.

Actual Scottish high school maths questions, from page 8 of this:

http://www.sqa.org.uk/files_ccc/NQMathsHigherSpecimenQuestionPaper.pdf

That's not the most advance level. Second most advanced level. Advanced paper:

http://www.sqa.org.uk/pastpapers/papers/papers/2013/AH_Mathematics_all_2013.pdf


Posted by: nattarGcM ttaM | Link to this comment | 07-28-14 10:03 AM
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Yes, complex numbers in 9th grade.


Posted by: Annelid Gustator | Link to this comment | 07-28-14 10:03 AM
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Or maybe it was ninth grade. I can't remember, actually, I just know that we definitely employed them in my tenth-grade math class, which was ... AP calculus BC.


Posted by: nosflow | Link to this comment | 07-28-14 10:04 AM
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Huh. I remember sort of knowing what they were (neat, negative numbers do have square roots!). But I don't remember doing anything meaningful with them until college.


Posted by: LizardBreath | Link to this comment | 07-28-14 10:05 AM
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Learning about complex numbers was part of learning about imaginary numbers, which I'm pretty sure was in high school. Like "Oh, by the way, now that you know what i is, every number actually is a sum of a real number and an i=something. But for most of them it's i=0."


Posted by: Cryptic ned | Link to this comment | 07-28-14 10:08 AM
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I learned what complex numbers were in high school. Not in AP math, either. Like LB, I don't think we did anything meaningful with them, just learned what they were and how to calculate them.


Posted by: Sifu Tweety | Link to this comment | 07-28-14 10:09 AM
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Yes, we used the equals sign to mean multiplication.


Posted by: Cryptic ned | Link to this comment | 07-28-14 10:09 AM
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I remember learning about them in the context of that an nth-degree polynomial has n roots. I think we learned how to graph complex numbers, in the context of nth roots of unity.


Posted by: heebie-geebie | Link to this comment | 07-28-14 10:17 AM
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Why on earth would you learn about complex numbers in high school? I mean, I can imagine a situation in which you learned something like the fundamental theorem of algebra and it came up, or a teacher went down a brief sidetrack explaining what's going on in cases where the quadratic formula doesn't spit out a real number answer, but as a general thing that standard high school students cover?

We did it at high school, though to be fair until I decided I wasn't going to do double-maths A-level I was in the advanced stream so it probably isn't representative of the "high school" curriculum in England as a whole (and Scotland has an entirely separate education system).

That said, I do think there is at least one good reason to do it. One of the biggest "Aha!" moments I ever had was when a teacher prodded us through the proof of e^i*pi = -1. It had a really profound effect on me, seeing that all these apparently disparate elements were related in a fundamental and elegant way.


Posted by: Ginger Yellow | Link to this comment | 07-28-14 10:17 AM
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Huh, I taught them to my two older kids this past school year (1st and 3rd grades) because I was trying to think of concepts they would find cool.


Posted by: SP | Link to this comment | 07-28-14 10:19 AM
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I just had to say that to make Neb feel neglected by his parents.


Posted by: SP | Link to this comment | 07-28-14 10:20 AM
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One of the biggest "Aha!" moments I ever had was when a teacher prodded us through the proof of e^i*pi = -1. It had a really profound effect on me, seeing that all these apparently disparate elements were related in a fundamental and elegant way.

You got through that in high school? I am impressed.

I found that impressively mindblowing when it showed up kind of casually halfway through a college math class (Complex Variables sounds right -- that was probably it). But I can't picture having reason to understand it in high school.


Posted by: LizardBreath | Link to this comment | 07-28-14 10:25 AM
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There is literally no educational subject as to which at least one Unfogged commenter won't claim to have had unusually precocious knowledge.


Posted by: Robert Halford | Link to this comment | 07-28-14 10:29 AM
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I remember a high school teacher telling us about that (no proof or explanation) in a manner so enthusiastic that I had no choice but to conclude it was completely uninteresting.


Posted by: Eggplant | Link to this comment | 07-28-14 10:30 AM
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I don't think I saw a proof for e^i*pi = -1 in high school, but we saw some consistent facts - look how the roots of unity behave! Doesn't this seem reasonable! and I thought that was pretty great.


Posted by: heebie-geebie | Link to this comment | 07-28-14 10:34 AM
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I think I'd seen the equation before, but not in a way I understood. What blew me away was that it really did make perfect, not terribly difficult, sense, starting from how you graph polar coordinates.


Posted by: LizardBreath | Link to this comment | 07-28-14 10:34 AM
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There is literally no educational subject as to which at least one Unfogged commenter won't claim to have had unusually precocious knowledge.

I know! Math! So obscure and unexpected.


Posted by: heebie-geebie | Link to this comment | 07-28-14 10:34 AM
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You're right, there are a few subjects as to which they'll claim their kids have unusually precocious knowledge.


Posted by: Robert Halford | Link to this comment | 07-28-14 10:37 AM
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My kids have an unusually precocious knowledge of Annie.


Posted by: heebie-geebie | Link to this comment | 07-28-14 10:48 AM
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This is a couple of years later than my era but the same sort of stuff (higher level 2nd paper)
http://examinations.ie/archive/exampapers/2001/LC003ALP200EV.pdf
We generally left out one topic which for my class was vectors. The first paper has a bunch of short questions.


Posted by: emir | Link to this comment | 07-28-14 10:49 AM
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My kid knows nothing about anything. He is quite good at climbing up stuff, bashing things, dancing , and shitting, though.


Posted by: nattarGcM ttaM | Link to this comment | 07-28-14 10:53 AM
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I found that impressively mindblowing when it showed up kind of casually halfway through a college math class (Complex Variables sounds right -- that was probably it). But I can't picture having reason to understand it in high school.

My school was very keen on teaching off-exam (and in my day A-level maths really wasn't very hard for people with any aptitude for maths - further maths is where it starts to get tricky). We'd have regular "circus hours" where someone who wasn't the usual teacher would come in and explain some cool but not immediately useful/relevant bit of maths or history of maths. I can't remember if this was one of those, but possibly. We certainly learned complex numbers as part of the regular course and it seems they're part of the syllabus for AS level and above.


Posted by: Ginger Yellow | Link to this comment | 07-28-14 11:15 AM
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||
Remember kids, don't serve (stand?) pro se/pro per. Lawyers exist for a reason.
|>


Posted by: Josh | Link to this comment | 07-28-14 11:29 AM
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"He who represents himself has a fool for a client."


Posted by: Abraham Lincoln | Link to this comment | 07-28-14 11:31 AM
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93

That quote was running through my head the entire time.


Posted by: Josh | Link to this comment | 07-28-14 11:34 AM
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94

I was just going presidential to get anonymity for the time I represented myself in court. I didn't realize it was a quote.


Posted by: Moby Hick | Link to this comment | 07-28-14 11:36 AM
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95

I think it was actually Oliver Wendell Holmes who said it. Or maybe Mark Twain.


Posted by: Josh | Link to this comment | 07-28-14 11:38 AM
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96

Yes but what happened?


Posted by: heebie-geebie | Link to this comment | 07-28-14 11:40 AM
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97

He got shot just after winning the Civil War.


Posted by: Moby Hick | Link to this comment | 07-28-14 11:42 AM
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98

Stop calling me Shirley.


Posted by: heebie-geebie | Link to this comment | 07-28-14 11:45 AM
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99

I think it was actually Oliver Wendell Holmes who said it. Or maybe Mark Twain.

Gomez Addams


Posted by: beamish | Link to this comment | 07-28-14 11:45 AM
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100

I did some summer math thing somewhere between 2nd-4th grade that got into some concepts, presented as fun, that I later associated with more advanced than grade school math. We didn't cover them in depth and I didn't see most of them again for years. It was some educational experimental program, I think, not part of any curriculum.


Posted by: fake accent | Link to this comment | 07-28-14 12:07 PM
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101

They run math camps at the local State U that seem like a ton of fun for 5th-6th graders. And some high school camps. They're great.


Posted by: heebie-geebie | Link to this comment | 07-28-14 12:18 PM
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102

48-50 make me wonder if the people doing complicated work-math can explain it to new coworkers.


Posted by: clew | Link to this comment | 07-28-14 12:23 PM
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103

I wouldn't count on it. (zing!)


Posted by: heebie-geebie | Link to this comment | 07-28-14 12:32 PM
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104

But seriously, I wouldn't.


Posted by: heebie-geebie | Link to this comment | 07-28-14 12:32 PM
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105

66: Why on earth would you learn about complex numbers in high school?

In California, complex numbers are generally taught as part of PreCalculus, along with conic sections, a bunch of trig, vectors, polar and rectangular coordinates and the conversions between them. It seems like a pretty natural fit at that level - here's some stuff you can do with the trig you're learning, including conversions between rectangular and polar coordinates, and here's an extension of the real numbers that also has both rectangular and polar form, and by the way, the polar form is really useful for doing multiplication/division, powers, and roots. If they tied it back by showing how to derive a bunch of the trig identities from the e^(i theta) equation, I think that would help some kids learn a bunch of their trig formulas, but I haven't seen any Precalc course that does that.

Plus this gives the kids some background in understanding their TI-87 calculators, which sometimes show complex solutions in the r*e^(i theta) form.


Posted by: Dave W. | Link to this comment | 07-28-14 12:42 PM
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106

It really makes sense to have differently paced Precalculus classes. The description in 105 is great for kids with some math aptitude, but for quite a lot of students, that is way more material than they can wrestle with. I'm thinking specifically of the college-bound level student who retakes precalculus in college - they do great if you take these topics much, much slower. Like, spend a day making them figure out the graphs of trig functions themselves. Spend another day having them work out the graphs of the reciprocal trig functions, and have them see for themselves why you might have an asymptote at a particular spot. You would not have time for polar coordinates, etc, though.


Posted by: heebie-geebie | Link to this comment | 07-28-14 12:47 PM
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107

103, 104; you would know. Although think how interesting domain-specific descriptions could be. How do the too-much-cited dabbahwallahs (sp?) learn?


Posted by: clew | Link to this comment | 07-28-14 12:49 PM
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108

So, how does this relate to people not understanding that 1/3 is greater than 1/4?

http://www.motherjones.com/kevin-drum/2014/07/great-third-pound-burger-ripoff


Posted by: peep | Link to this comment | 07-28-14 1:23 PM
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109

OP link to 108.


Posted by: SP | Link to this comment | 07-28-14 1:29 PM
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110

I think I'd seen the equation before, but not in a way I understood.

Did it seem like some weird hieroglyphics from an ancient civilization?


Posted by: JP Stormcrow | Link to this comment | 07-28-14 5:16 PM
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