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A Gentle Introduction To Learning Calculus
- dnaquin 18y agoI stopped reading here: How does an equation grow and shrink? Accumulate over time? Equations, don't grow or shrink. Maybe he was confusing equations with functions.
- kalid 18y agoI used the term loosely. But to most people, I think y = x^2 is an "equation".
- abless 18y agoTrue and it's good if people understand it better that way. Nonetheless, I'd advice on introducing a correct grammar as soon as possible.
- create_account 18y agoDon't hate - participate!
- jsmcgd 18y agoYou may be one of the people this article was explicitly not written for.
- euccastro 18y agoFor some level of rigor, functions don't grow or shrink either.
- deleted 18y ago[deleted]
- deleted 18y ago[deleted]
- bridgetroll 18y agoThe author is obviously under the delusion that an introduction to calculus should be gentle and soothing, like slipping into a warm bubble bath. It should not. It should be swift and shocking, like jumping into a river in early Spring. Mathematics requires an exact and expert hand. They are EMTs. This of your Calc 1 mid-term: "Quick, you have two minutes, resuscitate this equation!"
- kalid 18y agoHeh. Unfortunately, a large fraction of the students tend to die of hypothermia :).
- bridgetroll 18y agoThe cold water is harsh, but not necessarily a "bad thing" as it weeds out the weaker ones. The point is, "Do we want to spoon feed sciences?" Looking at what we, western society, boil into pablum to get people to pretend to comprehend, in my opinion, causes more problems than helps. It gives a false sense of understanding, like the solar system model of the atom. Having said that I concede that there is no reason to purposefully obfuscate sciences and higher level math.
- kalid 18y agoYeah, that's a good point. I definitely believe in having rigor when needed. Concepts like calculus, unfortunately, wait until high school or college, so it's being thrown in the river without ever having swum. Sure, some people survive, but most people end up having an aversion to math/science which leads to innumeracy and a host of other problems. Kids could be taught the basic ideas (like the circle -> triangle) just as a way to get thinking. Later, they can cover them more rigorously, but they've had experience doing integrals on their own. Even the solar-system model is "ok" to start with, and later you explain about probability distributions etc. You don't want to jump into quantum mechanics without covering Netwonian Physics (which, technically speaking, is "incorrect but useful").
- vlad 18y ago
- nazgulnarsil 18y agothis is copying the message and style of A Mathematician's Lament
- kalid 18y agoI was definitely enjoyed that essay and want to spread its message; it's why I linked to it and quoted from it :). However, I've been writing about these concepts in this way since 2001, way before I ever heard of the essay (here's my earlier website from school, which was the the precursor to this blog: http://www.cs.princeton.edu/~kazad/resources.htm http://www.cs.princeton.edu/~kazad/resources.htm).
- nazgulnarsil 18y agooh, thought you were just another me too blog. good on you then. :)
- kalid 18y agoHey, no prob -- I dislike me-too posts as much as the next guy :)
- michael_dorfman 18y agoIt's unfortunate that most of the comments so far only engage either with the title of the piece, or with it's (acknowledged) debt to "A Mathematician's Lament". I think the author's main point-- that most teaching of mathematics tends to undervalue the "aha!" types of insights that connect various pieces-- is a good one, and it looks like he has some concrete ideas about how to go about it. I, for one, look forward to seeing the author follow through with additional concrete examples.
- kalid 18y agoThanks :). I don't know what it is, but for a field concerned with abstraction people miss the forest for the trees. I try to catalog insights right as they happen, and try to capture the before-and-after: what, exactly, was the turning point that made it click? Unfortunately that makes articles slow coming, but I think they can be more genuine than explaining something after you're already an expert. Most of us can't remember what it was like trying to learn to read, for example -- it's too hard to relate to that problem.