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I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of

• CalChris 10y ago
  Berkeley EECS grad. I didn't go the device physics route but I used calculus about twice in 4 years except in physics classes.
  • supahfly_remix 10y ago
    Circuit analysis turns differential equations into algebra, so you might have been using calculus more than you realize.
    • CalChris 10y ago
      Yeah, I might have been guilty of some hyperbole. I remember a nasty integral on the Linear Systems midterm. It probably would have taken an hour or so if I didn't make any mistakes; but you could transform it and solve it as a linear equation in 10 seconds. That was the point of the class, that there area two kinds of problems, linear problems and problems you can't solve. I'm not in the least suggesting that an engineer shouldn't go through three semesters of Calculus, Linear Algebra+DiffEq and a Discrete Math course.
  • dboreham 10y ago
    That really makes no sense, unless the "EE" part was optional in your case.
    • thatswrong0 10y ago
      There are different "tracks", and some of them have very little EE (with way more CS focus). I think I only took two EE courses IIRC..
  • baldfat 10y ago
    The beauty of calculus is that you actually understand the Real World. For example I taught my daughter factions this way. Me: "These factions you see them? Now see these decimal points?" Her: "Yeah I hate factions they are stupid!" Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333." Her: "I always thought it was the otehr way around."
    • fao_ 10y ago
      ... Ohhhhhh. I wish you would teach me calculus =)
      • fao_ 10y ago
        This... might have come out wrong. What I meant was something along the lines of: You should teach, have you considered mentoring?
    • yequalsx 10y ago
      The first sentence in Your last statement in your conversation to your daughter is profoundly wrong. Your daughter was not in any way made to better understand fractions by this interaction. By the way, .3333 is a rational number and therefore equal to a fraction.
    • thesimpsons1022 10y ago
      is there a reason you call them factions and not fractions?
    • deleted 10y ago
      [deleted]
    • gohrt 10y ago
      Your idea did not translate into English. I think you are trying to say that most decimals we see in real life are approximations, not exact measurements, while fractions are exact? This has nothing to do with calculus, though.
    • 10y ago
  • surrey-fringe 10y ago
    Berkeley's a really good university.
    • eanzenberg 10y ago
      lel
  • wfo 10y ago
    Berkeley lets you skip learning asymptotic runtime analysis of algorithms if you're doing EECS? Weird. FYI: infinite sums are calculus.
• kj01a 10y ago
  >BUT people are always afraid of anything past 4th grade math! Then the solution is simple! We teach calculus to 3rd graders, then no one will be afraid of it! But seriously, I agree that calculus is taught way to late. I wasn't introduce to calculus until college, and if I had been even by senior year of high school, I would probably be a mathematician right now.
  • dboreham 10y ago
    In the US, problem #1 is that it is very hard to find people who understand Mathematics sufficiently well to teach it effectively, who are willing to work for the salary typically paid to a teacher. For example, my 8th grader is being taught "Higher School Algebra" by a teacher who last year taught 5th grade and by all accounts has to leave the classroom often to get tips on the material from the 7th grade math teacher.
    • sokoloff 10y ago
      Spot on. Both of my parents were high school math teachers (for most of their career). They essentially forbade me from going into public education, which is what I thought I wanted to do when I was in high school. Boy, am I ever glad! I am much more financially comfortable, enjoy the hell out of my job, and don't have to deal with the annoyances and politics of being a high school teacher. Would I be technically capable? Absolutely. Would I be good [enough] at it? Probably. Would I do it for a mid (or even high) five-figure sum, even with the good retirement package? Not on your life...
    • sigstoat 10y ago
      the other criteria that kicks some people out are the requirements for a K-12 "teaching certificate". if you don't get a degree in education, it can be difficult and time consuming to get a teaching certificate. a friend of mine some years back desperately wanted to teach high school math, and had a bachelor's in pure math, tutored for years and was well loved, but couldn't surmount the teaching certificate hurdles. so now he works in software QA.
    • sdenton4 10y ago
• rhizome 10y ago
  I would have done much better in math if the class after Geometry was something other than pre-trig.
  • jameshart 10y ago
    As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.
    • jhbadger 10y ago
      The idea of a "pre-" course is that you cover ideas needed for the later course. For example, a "pre-calc" course typically covers the sort of algebra that you would need in calculus but not actually integrating or differentiating anything. It's a matter of naming. You could call it "Algebra II" or "pre-calc".
    • greendragon 10y ago
      They're not always required, but they try to bridge what you already know (or are supposed to know) with what is to come and move at a slower pace. It's also sometimes like an extra option for the less mathematically inclined who are still required to take such a number of math courses. On the other hand the only 'pre-' course I ever took (I tested out of pre-algebra somehow) was 'pre-calculus with honors'. I don't remember it much but I think it was mostly reviewing the harder topics from intermediate algebra aka 'algebra 2', which included trig (no separate trig course in my system), introduction to limits, and toward the end differentiation and maybe discrete summation. The 'honors' variant was also geared toward students who were planning on taking the more comprehensive 'AP Calculus BC' variant rather than the 'AB' variant.
      • jameshart 10y ago
        There's a difference between AP calculus in Alberta and British Columbia? :)
• M_Grey 10y ago
  We should teach early calculus along with entry-level SR/GTR instead of rehashed Newtonian crap. Unite math and physics for a while, and kids might actually see the point of it.
  • YZF 10y ago
    Exactly. Physics becomes so much simpler with calculus. Once you realize e.g. the relationship between position, velocity and acceleration you don't need to memorize 20 different equations for all the different flavours of problems that are basically down to integrating or differentiating ...
    • spike021 10y ago
      But "you need to learn the hard way everybody else did it before X formula/equation was developed!" I agree it's nice to know the logic and background that is the foundation of how we got _here_, but sometimes the older details aren't really as important and take away time from students learning the modern, more useful techniques and concepts. One of the big things about kids and math these days is that you have less and less of their attention. If they see it's getting too hard, most don't take the challenge and they just put less effort in.
      • rconti 10y ago
        I couldn't disagree more. It gets too hard when you're asking students to memorize arbitrary equations that make no sense to them. It gets too hard when you give them 30 problems that look identical and they do 3 or 4 and figure that's good enough because they know how to run numbers through the meat grinder of a formula. I don't see how students can truly learn if they don't understand the formulas they're applying and their relevance to the real world.
    • learc83 10y ago
      I held off taking physics in college until my senior year because I dreaded the 3 hour labs. By the time I got there I had 3 levels of calculus (and linear algebra, and plenty of proof based CS classes) under my belt, and it turned out to be one of the easiest classes I've taken. Like you said, I didn't have to bother memorizing anything, because everything could pretty much be done with simple integration or differentiation.
• yequalsx 10y ago
  I think that a student not well versed in how to perform calculations will not do well with the theory. Last night in the calculus class I am currently teaching a student could not correctly translate the fact that f is increasing where f' > 0. This on a problem where f' was linear. He just stared blankly at the inequality 2x-3>0. Anyone well versed in this sort of calculation is not going to fumble around at this problem. He thinks calculus is the problem when it's his knowledge of algebra that hinders him.
  • ivan_ah 10y ago
    I'd be very interested to hear your opinion about a book I've been working on. It's a 3-in-1 combo, math+mech+calc, I wanted to teach mechanics and calculus in an integrated manner and I realize, from 15 years of private tutoring, I need to review all the high school math material because many students don't know the basic. Please drop me a line if this sounds interesting. Email in profile.
• rconti 10y ago
  IME the #1 problem is the failure to teach anything WELL. I took AP Calculus in high school, and today, as a 35-year-old, I'm still continually surprising myself with the problems I realize must be related to Calculus-- but nobody bothered to tell me. Things like the 'ol speed vs acceleration vs jerk kind of problems. All calculus ever taught me was to apply these formulas to those problems (for some reason) and that dx/dy meant derivative of x with respect to derivative of y. It boggles my mind that nobody simply bothered to tell us what a goddamned derivative was; what the word meant, and what real-life examples were. The "with respect to" was the most confusing and least useful concept. If we knew what the things were in the first place, the fact that one was "with respect to" the other would have been obvious. And "with respect to" could have been replaced with "relative to" in our minds, because we'd know what the things were. Calculus seemed to be entirely repeating nonsensical mantras and applying impenetrable methods to problem sets and receiving an answer out the other end. I'll also echo calls for more time on algebra. Surely the problem with algebra was that I wasn't a devoted enough student to repeating problem sets ad nauseum, but I just never got the 'knack' for it. I understood what I was supposed to be doing, but I was never satisfied with the answer "you'll start getting a feel for what to simplify to what after you do enough problems" as an explanation. It was frustrating to not feel like there was a concrete process to it all. This made later Calculus and Statistics hard for me, because many exams would simply be 2 enormous problems ; the calculus I could get through but I couldn't simplify the problems quickly enough to be able to apply calculus or statistics at all.
  • eanzenberg 10y ago
    Dude, the "with respect to" clause is a pretty deep idea in calculus that really matters in multi-variate but not so much in uni-variate. I keep seeing how society needs better math education, whether it be statistics or calculus. Well no shit. Unfortunately those are extremely hard subjects to teach in high school. I'd argue statistics is harder to teach than calculus. In calculus you usually derive things by following the formulas. In statistics there isn't always a formula, logic, or path you can follow. I took both AP Calc BC and AP Stats in HS and I'll tell you I learned a lot of calculus then and am learning a lot of statistics now (I'm 32).
• posterboy 10y ago
  This pattern of patterns and structures is the structure of structures While not wrong, that sentence is devoid of meaning, with or without the synonyms swapped out.
• kenjackson 10y ago
  "“Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories." I used to think this until I had kids and started teaching them math. When you know math you can abstract it away and really focus on the concepts. But you don't realize how many simple calculations are done when abstracting these concepts.
• debacle 10y ago
  > BUT people are always afraid of anything past 4th grade math! The problem is that elementary and middle school math teachers can't teach except out of a book. Your child's math teacher isn't teaching your child math, she is just the proctor for their math textbook, which isn't teaching them anything at all really. This is not a dig on (all) teachers. These workbook-driven curriculum are a band-aid for bad teachers, and all they really do is harm good teachers and students.
• deleted 10y ago
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