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GhostStalker posted:I feel like I'm a terrible math major because I had no problems with using algorithms to calculate things when given actual numbers, but I pretty much fall apart when it comes to doing proofs. I mean, I head a hell of a time during Abstract Algebra, because while I could see where my professor was going with proofs done as examples and could follow it then, when it came time to take the exam, I'd be pretty lost on a bunch of problems. The Numerical Analysis course I took this past semester wasn't much better. Like I understand that proofs are pretty much the thing you have to do when it comes to higher level math, and I just can't help but feel like I made a terrible mistake deciding to be a math major. i hope u find what u are looking for
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May 28, 2014 12:03
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Lightanchor posted:The best word defined on that page is rekenrek Common Core: Now, what is your name? If you say abacus again I'll start cutting pieces off of you! Abacus: Rekenrek....my name...is Rekenrek...
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May 28, 2014 14:01
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i'm permabanned poster numberstomper58. i first started studying common core when i was about 5. by 7 i got really obsessed with the concept of "algorithms" and tried to channel them constantly, until my thought process got really bizarre and i would repeat things like "math situation" and "hidden partners" in my head for hours, and i would get really paranoid, start seeing things in the corners of my eyes etc, basically prodromal schizophrenia. im now on antipsychotics. i always wondered what the kind of "algorithmic" style of common core was all about; i think it's the unconscious leaking in to the conscious, what jungian theory considered to be the cause of schizophrenic and schizotypal syptoms. i would advise all people who "get" common core to be careful because that likely means you have a predisposition to a mental illness. peace.
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May 28, 2014 14:57
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gary oldmans diary posted:i really wish we could throw a government dime into research on head start fade instead of just disregarding it This, a million times this. Al Borland posted:Holy gently caress discrete math to high schoolers though? That's gonna be like trying to teach a westboro church member gay rights. Counting, finite series, basic graph theory, and finite automata would be easy enough. I've personally taught cryptography and graph theory to high-school students as part of various outreach programs I've been a part of. I am not saying we teach it as we teach it in college. Example: Geometry at the college level is all about studying isometries. We talk about reflections, rotations, translations in high-school without having to do things like prove the isometries form a group, or are really just functions from the plane to the plane that preserve the metric. GhostStalker posted:
You are a representative case of over half of my math majors. I had the pleasure of teaching Abstract Algebra for the first time this year, and I had a student say they hate proofs because "in math there is only one right way to get the answer!". When asked where he learned that, he said he learned it in high-school. This is because our freshmen/high-school courses are about following a canned procedures, and major courses are about proofs (for which no canned procedure is going to help). Intro to proof in some form should be taught to everyone at some point (probably in HS Geometry). I hate that people typically do not get to see the coolest part of my field unless they already decided to be math majors. Pure Mathematicians prove stuff. That is it. All the way down. Proofs are not easy, and they take a long time to be proficient at. If you like them, don't give up. If you hate them. then applied math is likely a better place for you. Although you had better get your Numerical Analysis and Differential Equations down if you plan to go the traditional applied math route. Alternately you could learn Operations Research or Statistics. Also, they actually do put most of the field axioms in standard algebra texts (they explicitly mention commutativity, associativity, and distributivity). They also tell you that the reals is an integral domain without actually saying the words integral domain (kinda important if you want to solve (x+2)(x-1)=0 as x+2=0 or x-1=0). Most teachers just do not mention them, or do so once and then never again. You can teach distribution without being axiomatic about it. Doing examples for kiddos is a good idea. Example: Multiply 53 by 34 using the standard algorithm. Now break up 34 as 30 + 4. Multiply 30 by 53, and 4 by 53. What should we do with these two numbers when we are done to get 53*34? Maybe draw simpler pictures with boxes "cube sticks" to give them the general idea.
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May 28, 2014 16:14
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Gulzin posted:No Chemist has to constantly hear "I hate Chemistry". Bullshit we don't
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May 28, 2014 17:04
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Irradiation posted:Bullshit we don't The day I got my Ph.D. two people told me they hated math. Every time I meet someone new, they tell me they hate math once they learn what I do. Is this your experience with Chemistry?
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May 28, 2014 17:09
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Yeah kinda. I probably hear it less since math is a more important in everyday use, but anytime someone tries to make small talk with me like at the dentist or doctor I get to hear about it.
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May 28, 2014 17:14
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That really sucks. I take it back then. I thought shows like Breaking Bad and Cosmos would have at least helped the sciences in regards to public opinion.
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May 28, 2014 17:16
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Gulzin posted:The day I got my Ph.D. two people told me they hated math. Every time I meet someone new, they tell me they hate math once they learn what I do. If it makes you feel any better, I don't dislike what you do but I'm sure I understand very little of it.
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May 28, 2014 17:21
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Just kidding, lol nerd.
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May 28, 2014 17:21
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i kinda get why math and chemistry get so much hate. they are both tough classes a lot of unrelated major had to take and both generally feel arcane to most ppl
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May 28, 2014 17:22
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But for real, I don't hate math and am glad you can do it because its probably important for something and someone has to get around to do.
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May 28, 2014 17:22
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People on GBS having problem with basic arithmetic? Why am I not surprised?
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May 28, 2014 17:30
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Gulzin posted:That really sucks. I take it back then. They probably help on a superficial level, but I've noticed once people learn that sciences aren't really what you see from pictures in a buzzfeed list and that it sometimes involves countless hours of frustration just to produce a single data point people start changing majors real quick.
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May 28, 2014 17:34
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I won't claim to have read all 18 pages of this thread because, well....gawddamn. I think one complaint to common core is what we run into here in Virginia. Virginia doesn't do Common Core because we have a similar system called Standards of Learning. The problem with SoL (poo poo outta luck) is that the SoLs dictate what is taught, no more and no less. Teachers here in VA teach to the SoLs and after that they give up. You're not getting ahead, you're not learning new things. You get SoL and that's that. SoLs control funding and school accreditation. How your school performs on these tests is all anyone cares about. Little Johnny will be a poet but sucks at math? He's an idiot and threatens the well being of the rest of the school. These sorts of educational standardization really does just produce standardization. Instead of this becoming the minimum acceptable level of educational performance it's the whole and complete target.
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May 28, 2014 17:40
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GhostStalker posted:Advanced classes in middle school (plus some help from an Asian test prep school) helped me get into the best public high school in New York, with the year's credit of Algebra I that's practically a requirement to get in there, and then I really had no problems with math in school afterwards except for failing to hand in some research assignments in an "advanced" Algebra II class Sophomore year that had a research component. Oh hey, sup fellow Stuy grad. Read the Math Team comment and I immediately knew what school you were talking about. GhostStalker posted:I feel like I'm a terrible math major because I had no problems with using algorithms to calculate things when given actual numbers, but I pretty much fall apart when it comes to doing proofs. I mean, I head a hell of a time during Abstract Algebra, because while I could see where my professor was going with proofs done as examples and could follow it then, when it came time to take the exam, I'd be pretty lost on a bunch of problems. The Numerical Analysis course I took this past semester wasn't much better. Like I understand that proofs are pretty much the thing you have to do when it comes to higher level math, and I just can't help but feel like I made a terrible mistake deciding to be a math major. Yeah higher level math classes can be brutal. Most people don't get the context of pure math (I know I didn't as an applied math undergrad) and will view proofs really rigidly. The best way to think like a pure mathematician is to put yourself in the shoes of someone like Cantor or Godel. You're seeing ideas/algorithms applied to novel situations that only exist in your head and you have to try to prove it to the mathematical community. Developing intuition plays a huge part in grounding yourself in these types of proof classes. The very first thing to do is understand what you're trying to prove and have examples and counter-examples help you limit the search space. Or else you're just staring at the page going WTF because you have an 'infinite' search space (yes this is a fuzzy concept, maybe the better idea is combinatoric to the tools that you have to mash together to prove a concept.) Intuition 'grounds' the 'degrees of freedom' so you're not performing an insane exhaustive search. For Abstract Algebra in college, the context is that you're working with regular algebra but generalized so you relax constraints (assumptions) and get new generalized results. So extra cases could come to mind and help you visualize what you're trying to solve. For Real Analysis, I tried to 'brute force' the class and it was not pretty. Rudin is a hell of a book to learn from starting out. Also definitely branch out to other sources/intuition/diagrams when the book just doesn't make any sense. In the end of the day, you're objective is to get the material and that's the goal to not lose sight of. Tezzeract fucked around with this message at 18:12 on May 28, 2014 |
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May 28, 2014 18:08
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Lightanchor posted:i'm permabanned poster numberstomper58. i first started studying common core when i was about 5. by 7 i got really obsessed with the concept of "algorithms" and tried to channel them constantly, until my thought process got really bizarre and i would repeat things like "math situation" and "hidden partners" in my head for hours, and i would get really paranoid, start seeing things in the corners of my eyes etc, basically prodromal schizophrenia. im now on antipsychotics. i always wondered what the kind of "algorithmic" style of common core was all about; i think it's the unconscious leaking in to the conscious, what jungian theory considered to be the cause of schizophrenic and schizotypal syptoms. i would advise all people who "get" common core to be careful because that likely means you have a predisposition to a mental illness. peace.
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May 28, 2014 18:13
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Gulzin posted:You are a representative case of over half of my math majors. I had the pleasure of teaching Abstract Algebra for the first time this year, and I had a student say they hate proofs because "in math there is only one right way to get the answer!". When asked where he learned that, he said he learned it in high-school. This is because our freshmen/high-school courses are about following a canned procedures, and major courses are about proofs (for which no canned procedure is going to help). Intro to proof in some form should be taught to everyone at some point (probably in HS Geometry). I hate that people typically do not get to see the coolest part of my field unless they already decided to be math majors. Yeah, what I originally liked about math is that it was just numbers, and there was only one "correct" answer to a problem in most cases, and you just need to show how you arrived at that answer, instead of futzing around with interpretations of stuff like in the humanities. Never really fell out of that mindset until I hit Abstract Algebra, where both my professor and another I had previously in a Cryptography class emphasized that it was going to be pretty much proofs from here on out and that I would need to master them to do well in the class. I learned real basic geometric proofs and how to formally structure them with columns, statements, and reasoning in my Geometry class in 8th grade and again in my Freshman year in high school, but that was around the time that New York State was de-emphasising formal proofs as a thing on geometry exams in favor of more graphing stuff, though you still needed to know how to prove triangles congruent and all that kinda stuff. Never really touched them again until Abstract Algebra, where the structure my professor used tended to be a lot less rigid, but required a lot more writing out of reasoning, or using proofs by contradiction, or proving both parts of an if/then statement via a contra-positive and stuff like that. I got the hang of it when examples were being done to explain theorems and stuff we covered, and I followed along relatively well when we were doing them together, enough so that I did decently on quizzes, but I just froze up in my final. And once I had gotten comfortable with that, I could apply some of what I learned into my Numerical Analysis stuff, but I couldn't internalize it fast enough and wound up getting lost soon after. Pretty much a lost cause for me this semester... Apparently, my college has no difference between a Pure Math and an Applied Math degree, both are under the same BS in Mathematics. Probably going to do the Applied Math route though. I've gotten better at proofs, but sometimes I just can't work out how I'm supposed to be doing one given the time I have to do it and it all just falls apart on me. I understand that the basics of the field axioms (commutativity, distributivity, associativity, identity, and inverses) are taught in algebra (and that's where I learned them, in 7th grade), they're just not presented as "the field axioms" but instead just as properties of the real number system. I had no definition of the term "field" until it was brought up near the end of my Abstract Algebra course. Of course, one of the first things done in my Numerical Analysis course was proving the existence of the real number system going just off of the field axioms, and then using that to prove the existence of the rationals, the integers, and the naturals, so I guess that was handy. As for teaching things like double digit multiplication to kids using distribution, I can see how teaching like that to kids who currently don't understand how to do it with the algorithm could help them learn how to do it easier. Like I said, I had a Chinese mom who drilled me on these kinds of things to the point where the algorithm was second nature to me and I grasped the concept pretty quickly. Having to do it with "cube sticks" when I already get how to do it using the normal algorithm just sounds like it'd slow me (and pretty much everyone else in most math classes I've taken) down. I dunno, if a teacher sees that their kids get what they're doing using the old algorithm or using distribution to multiply, or whatever method, it would make sense to me that they could be given the option to skip the alternate method presented with Common Core here and move on to the next topic. Tezzeract posted:Oh hey, sup fellow Stuy grad. Read the Math Team comment and I immediately knew what school you were talking about.  Sup. Class of 05, Freshman year began right as 9/11 happened, that was a hell of a year. Did you ever have Mr. Geller for Pre-Calc or Math Team. Man, when you got past an imposing facade and his hysterics when telling you to study before a test, he was a great teacher and I really learned a lot from him. RIP.And yeah, I'm sticking with the math degree since I'm so close to graduating now. I'll keep plugging away at the Numerical Analysis, and maybe try taking Number Theory again now that I have a grounding in Abstract Algebra to help me out in that regard. While I did have problems with that class, I got through it and can basically understand where it's going for the most part and apply it to other things now. Oh, and this was the textbook we were using for Numerical Analysis. It helped me understand some things, but I got lost after a chapter or two in. As I said though, I'm gonna keep plugging away at it and hopefully eventually understand what's going on there enough to get through the course.
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May 28, 2014 23:21
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GhostStalker posted:I understand that the basics of the field axioms (commutativity, distributivity, associativity, identity, and inverses) are taught in algebra (and that's where I learned them, in 7th grade), they're just not presented as "the field axioms" but instead just as properties of the real number system. I had no definition of the term "field" until it was brought up near the end of my Abstract Algebra course. Of course, one of the first things done in my Numerical Analysis course was proving the existence of the real number system going just off of the field axioms, and then using that to prove the existence of the rationals, the integers, and the naturals, so I guess that was handy. I think when I say we should teach them why things work, I should also say that I am not for just dumping some axioms on kids and having them Moore method math together. We can teach them properties of algebra without getting bogged down in notation. I think we need more proofs in K-12 mathematics, but they don't have to be overly rigorous at that point. Just getting students to realize there are reasons why everything in math is the way it is would be worlds better than what is going on right now. GhostStalker posted:Oh, and this was the textbook we were using for Numerical Analysis. It helped me understand some things, but I got lost after a chapter or two in. As I said though, I'm gonna keep plugging away at it and hopefully eventually understand what's going on there enough to get through the course. Okay, when I said Numerical Analysis, I meant this. What you linked is Intro to Real Analysis, and it seems odd to me they would call that Numerical Analysis (as these subjects are clearly defined by the Mathematics Subject Classification). If you were to go on as an applied mathematician or statistician, you should probably have a good grounding in Real Analysis too.
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May 29, 2014 01:09
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Gulzin posted:Okay, when I said Numerical Analysis, I meant this. What you linked is Intro to Real Analysis, and it seems odd to me they would call that Numerical Analysis (as these subjects are clearly defined by the Mathematics Subject Classification). Technically, the class according to the syllabus is called Advanced Calculus. I think I got mixed up with what to call what we were actually studying, since I've heard it being referred to as just a class on Analysis by my professor. Now I don't know what to make of it...
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May 29, 2014 04:33
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GhostStalker posted:Technically, the class according to the syllabus is called Advanced Calculus. I think I got mixed up with what to call what we were actually studying, since I've heard it being referred to as just a class on Analysis by my professor. Now I don't know what to make of it... Analysis is a general field that comprises topics like Real Analysis, Complex Analysis, and Functional Analysis. Numerical Analysis is actually part of applied mathematics. It is the mathematics of approximation algorithms, typically for Linear Algebra and Differential Equations.
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May 29, 2014 06:16
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Keith Stone posted:I won't claim to have read all 18 pages of this thread because, well....gawddamn. Yeah. My girlfriend teaches third grade for CPS, a big testing year. All management really care about is those tests and the resulting funding for third graders. Third grade is a year the kids can Actually Fail and have to repeat.
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May 30, 2014 19:02
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https://www.youtube.com/watch?v=IRsPheErBj8
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May 30, 2014 19:13
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Frankly, rather than teaching proofs directly, kids might be more receptive to basic Symbolic Logic and then transitioning that into proofs.
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May 30, 2014 19:59
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Gulzin posted:The day I got my Ph.D. two people told me they hated math. Every time I meet someone new, they tell me they hate math once they learn what I do. Less chemistry generally, and more people complaining about how organic chemistry made them reconsider their life choices/derailed their med school dreams/turned them into an English major.
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May 30, 2014 22:46
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I like the common core math stuff, it feels a lot like how I do math in my head, as others have said. But I also see a lot of "it's important to understand why math works." I don't necessarily agree. As a physics major I use a shitton of math and quite frankly, I don't particularly care why Green's Theorem (or it's 3D counterparts Divergence and Stokes') work, I only care what they can do for me and how to use them. I consider math like a toolbox. I don't care how a wrench was made or who invented it, I care that when I put the boxy end on a bolt and turn it, it tightens the bolt.
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May 31, 2014 02:10
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Hesh Ballantine posted:I like the common core math stuff, it feels a lot like how I do math in my head, as others have said. But I also see a lot of "it's important to understand why math works." I don't necessarily agree. As a physics major I use a shitton of math and quite frankly, I don't particularly care why Green's Theorem (or it's 3D counterparts Divergence and Stokes') work, I only care what they can do for me and how to use them. I consider math like a toolbox. I don't care how a wrench was made or who invented it, I care that when I put the boxy end on a bolt and turn it, it tightens the bolt. And physics is a tool of the engineers. And engineering is the tool of the plumber. We should all just be plumbers! It must not matter why physics works the way it does. I don't care how my wrench is made and all that bullshit. Also, because most Physicists tend to think Math serves Physics. Most real math is used in jobs that have nothing to do with Physics (Financial Quants, Actuary, and Operations Research Analyst). e: Also, if you are using a tool and you don't know how it works, you are a pretty lovely Physicist. Gulzin fucked around with this message at 02:58 on May 31, 2014 |
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May 31, 2014 02:44
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Gulzin posted:And physics is a tool of the engineers. And engineering is the tool of the plumber. We should all just be plumbers! It must not matter why physics works the way it does. I don't care how my wrench is made and all that bullshit. You're a little hostile about this and that's kind of cute. I'm not saying it doesn't matter, period. I'm saying that, for me at least, it's secondary to functionality and applicability. I've done plenty of "this is why it works" in multivariable calc and vector calc, and I think it's fair to argue that it helps (and may even be necessary) for learning how to apply mathematical methods. That said, once I clocked my A and sold the textbook, I stopped remembering or caring about any of the why. You say this makes me a lovely physicist, but I'd challenge you to find anyone in the field not directly involved in education that can, for example, demonstrate derivation of Gauss' law off the top of their heads. As for all the "real math" careers you linked, congratulations on making high speed trading and other wonderful contributions to the sum of human knowledge possible, I guess?
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May 31, 2014 03:16
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I came off as hostile because you didn't say that you didn't care if you didn't understand it. You said:Hesh Ballantine posted:But I also see a lot of "it's important to understand why math works." I don't necessarily agree. which is directly against the main benefit I see of common core. Even if you never remembered a drat thing about math again, just because you wouldn't use it or care why it works is no reason to gently caress over our children's chance of seeing why it works. It would be me suggesting to stop all band programs in the country, because I stopped playing my instrument after high-school. You are suggesting policies that directly gently caress over the discipline I dedicated my life to. A K-12 understanding of math does not mean they have to be able to instantly prove every theorem they learn, but they should spend more time learning why it works than just memorizing and using an algorithm. If you have good number sense, you do better in algebra. If you do better in algebra you do better in Calculus. I hope a physicist would understand why that would be important to their field. Similarly, you don't have to prove Green's Theorem every time you use it, but you do understand it, and were likely enriched by the proof. You understand the physical ramifications, you understand when and how to use it. There are many theorems in my own research field of mathematics I would be pressed to prove off the top of my head. That is not a valid argument for never seeing the proofs, or just not teaching why math works to students. Finally a surface level understanding of math causes poo poo like this.
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May 31, 2014 03:31
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give a better example for the argument that common core teaches kids to understand math in ways they otherwise wouldnt than the current example of teaching them to count to and from 0/10 as an intermediary instead of straight to the number theyre going for i gotta know there is more to it than more story problems number lines number statements and this the common core algorithm for addition is not free from being an algorithm that could be plodded through by someone who didnt understand addition its the core of your argument and this thread so lets just get to it
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May 31, 2014 03:47
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gary oldmans diary posted:give a better example for the argument that common core teaches kids to understand math in ways they otherwise wouldnt than the current example of teaching them to count to and from 0/10 as an intermediary instead of straight to the number theyre going for That is fair. Before I provide the two examples below. I do want to say that any part of high-school math could be boiled down to following algorithms, and you certainly could find an algorithm to do any the problems listed below. So let me divorce the standards from their assessment exams. I am doing this because after talking to two of my math education colleagues about common core today, they informed me that they wholeheartedly support the standards (as they are basically repackaged NCTM standards), but there are states writing assessments against the spirit of the standards (they cited New York in specific). That is an issue, and one that is important to address. It is not an issue of the standards themselves. Okay, so here are my two examples (one is against algorithmic learning, the other is how the standards improve general education): Multiplication via multiple forms. the standards, some example worksheets. Edit: To make the example clearer. The standards posted:CCSS.Math.Content.4.NBT.B.5 Basic statistics in elementary school. the standards, some example worksheets. Gulzin fucked around with this message at 04:26 on May 31, 2014 |
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May 31, 2014 04:05
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Quote =/= Edit, so here is my favorite common core image:
Gulzin fucked around with this message at 04:13 on May 31, 2014 |
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May 31, 2014 04:09
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Akumu posted:Everything in those images makes perfect sense, and if you can't understand it you're a god-damned idiot.
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May 31, 2014 06:58
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May 31, 2014 09:06
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and stop naming kids any variety of "jaiden" for fucksake. Your lovely rear end names for kids is ruining this generation faster than your inability to understand math
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May 31, 2014 09:15
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idk what was my actual favourite thing in this thread: 18 pages of grown-rear end adults saying 'well that's how i do math in MY head, seems okay', or that it took that many pages for an actual developmental psychologist to be posted instead of polemic or stories about how MY undergrads were the dumbest it was actually my undergrads, they were the dumbest. this is probably related to why every goddamn idiot in this thread doesn't know jack poo poo about dev psych what a coincidence edit: i guess my third thing is learning that in america even math class is loving partisan, that's probably the Most Hilarious Thing Bleu fucked around with this message at 10:29 on May 31, 2014 |
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May 31, 2014 10:20
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Bleu posted:idk what was my actual favourite thing in this thread: 18 pages of grown-rear end adults saying 'well that's how i do math in MY head, seems okay', or that it took that many pages for an actual developmental psychologist to be posted instead of polemic or stories about how MY undergrads were the dumbest I agree development psychology is just as important in developing standards as mathematicians views. That does not mean my views are invalid. That is why I asked my math education colleagues about it. They are education researchers, not mathematicians. They are heavily rooted in cognition and educational psychology (which also includes a heavy amount of developmental psychology), but they are not research psychologists.. Also, I didn't just post that my undergraduates were dumber. I did link studies that show common core in general helps, and statistics showing that our students are not doing well (even our rich students). I would welcome developmental psychologists views on mathematics in general. However psychological research into learning mathematics has not been a popular area of research for psychologists, and real research into mathematical cognition only started in the mid 1990s. Edit: I did some research into what psychologists think of common core. Aside from crazy Glenn Beck blogs, I did find a large group of them really hate the K-3 standards. I also agree with what they are saying. However, I still support the 4-12 standards. Gulzin fucked around with this message at 19:00 on May 31, 2014 |
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May 31, 2014 18:35
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when i need to multiply or substract some numbers, i just install an npm module and then fire up node on my smartphone. just like everyone else i know. jesus.
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May 31, 2014 18:53
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Gulzin posted:Quote =/= Edit, so here is my favorite common core image: lol What does any of this have to do with socialism?
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May 31, 2014 22:32
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top one was meant for a yakuza kid
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May 31, 2014 22:35
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