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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. The reason I chose math as a major is because I was so good with it during middle and high school (advanced classes through the entirely of those years, acing all of my classes), loved all of my teachers (with some exceptions) during those years, and came in to college with the first year of Calculus under my belt. Probably helped that I had a mom who drilled me on math during elementary school, forcing me to memorize the multiplication tables at second grade and constantly drilling me with math problems during summer vacations, which I always complained about at the time, but really helped me when I went back to school for the next year. Chinese moms, gotta love em. 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. Hell, I still love my middle school math teacher who taught us Algebra I and the beginnings of Geometry in 7th and 8th grade (to the point where I was looking to see whether he still taught at my middle school and whether I could go and visit him there sometime in the future) and the Pre-Calc teacher I had in Junior year who was the school Math Team coordinator (Math Team was huge, tons of kids got signed up for it by their parents Freshman year that they had to have multiple first period sections for all the students involved) and died of cancer a couple years back (his obit getting a mention in the New York Times). Hell, I even parlayed my math knowledge (plus a couple of years at aforementioned Asian test prep school on the weekends and during the summer) to get a full 1600 on my SATs (sure, I know that really doesn't mean much in the greater scheme of things, but it's something I'm still proud of). I was originally going to do Engineering in college, but after a bad experience with a Physics class in high school (I mistakenly signed up for AP Physics thinking that it was going to be a research focused class like my previous Biology and Chemistry classes I took Freshman and Sophomore years which I had no real problems with) and not doing much better in it my first year of college, I figured that Engineering was really mostly just math plus physics, so I could drop the physics and stick with the math. And I was fine during my first couple of years when doing Calculus. Linear Algebra was more difficult, but I got most of it. Differential Equations was a bit wonky but I powered through it. Abstract Algebra was harder, but I mostly got it. Number Theory irritated the poo poo outta me, and Numerical Analysis was pretty much a foreign language, albeit one I got the rudimentary beginnings of due to previous experience in Abstract Algebra. Now that I'm just about 2 classes close to being done with my degree, I've been questioning whether it was the right choice ever since more rigorous proofs started showing up... Probably should just stick to Applied Math instead, since I was great working with numbers, but not with those damnable proofs. I can understand why these new teaching standards could help students that have problems with math learn better at the moment, but I can't help but feel that I'd be so slowed down doing this kinda poo poo if I was learning it like this. The lower level stuff especially just looks pretty dumb to me. But now that I'm more experienced with math, I can see how doing addition like in the examples posted is like how one would do math in your head, it's pretty much how I do it now, but I needed a grounding in the addition algorithms with carrying the one and all that in order to understand it in the first place, and then developed the mental arithmetic stiff later. Like, my mom made sure to drill into me why adding works that way, and why you needed to leave a blank space on the second line when multiplying out two digit numbers, so much so that I could explain it to other kids when my teacher asked me to do an example on the board when we did learn it in school. And now I go to a college (City University of New York) where the vast majority of kids who enter Freshman year need a remedial class in basic Algebra, and then never touch math again for their majors besides maybe a Trig or Statistics class, not even Pre-Calc. Hell, Calculus is a goddamn 200 level class rather than the basic 100 level poo poo it should be here... I get that most high schools are dropping the ball when it comes to math education, although I didn't understand that at first because math came so easily to me along with pretty much everyone else I interacted with in my advanced math classes and my high school. Was talking with my brother (who pretty much had the same experience with math during middle and high school as I did, except he only went to the second best public high school in the city) last year about dropping test scores for underprivileged minorities (blacks and Latinos, since test scores basically stayed flat or improved for Asians) after the implementation of the Common Core standards, and he basically said that the two of us never had any problems with math exams, and if we could do it, why can't everyone else? I used to think pretty much the exact same way, but now see why that's such a terrible argument. If Common Core helps bring up these standards, and gets more people to understand math, then I'm all for it. Just wish that it was being implemented better though... Like I don't think that you need to explain the distributive property of multiplication to kids who are just learning how to do double digit multiplication, but I can see how it'd be helpful to some who don't understand how the multiplication algorithm worked. Didn't really cover properties like distributivity, associativity, and commutativity until my middle school Algebra I classes. Stuff like FOIL is also a lot easier to learn if you understand the distributive property, but my class didn't need it when we did so and we understood what was going on. Again, anecdote from an advanced class, but I guess some people need some help in that regard. Don't think you need to start kids on the field axioms and set theory concerning the Reals, Rationals, Integers, and Naturals that early though. Maybe high school before you start touching that kinda stuff. GhostStalker fucked around with this message at 11:09 on May 28, 2014 |
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May 28, 2014 11:05
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| # ¿ Jul 19, 2025 08:48 |
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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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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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