4

I was just reviewing a chapter on integration defined through step functions, and was wondering how would you explain the concept of an integral of a step function to a child ?

  • 4
    Just sum of area of rectangles. In fact, integral can be viewed as the "limit" of these sort of sums. – achille hui Nov 08 '13 at 17:22
  • 2
    Define "child." – Rocket Man Nov 08 '13 at 17:22
  • Child : 10 year old –  Nov 08 '13 at 17:23
  • Then I would go with what @achillehui said. – Rocket Man Nov 08 '13 at 17:24
  • If that child was Gauss, I think there is no such concern. :P And I am curious about the relations between Gauss and "Gauss" functions. – awllower Nov 08 '13 at 17:27
  • 1
    You won't. A ten year old child will not have a solid notion of a function. So: cui bono? There gazillion math related topics to keep those children stunning. – Michael Hoppe Nov 08 '13 at 17:28
  • @MichaelHoppe I didn't mean defining an actual integral but the idea behind it. –  Nov 08 '13 at 17:33
  • Don't do it. A ten year old child isn't interested in such things for a lacking background. Also regard that a ten year old child is hardly to be supposed to know what a variable is. Consider also their capability to calculate. I'ld go for something different. – Michael Hoppe Nov 08 '13 at 17:41
  • 2
    Michael, maybe this child is from India or China? My cousin was doing derivatives at age 12. He got done with Bsc in engineering at age 20, whereas I at that age, well never mind... – imranfat Nov 08 '13 at 17:54
  • 2
    @MichaelHoppe: I think you severely underestimate the thinking ability of a child... If the question is whether to present an abstract notion of how to find area of a figure, and an option is presented as taking a sum of decreasing-size increasing count of rectangles, I would say that approach would be well-received by a child interested in the topic. – abiessu Nov 08 '13 at 17:58
  • 1
    @MichaelHoppe: as for interest, how many children play games like SimCity or The Sims? One of the basic properties of such games is that applying something like carpet or industrial zoning to an area comes with a cost proportional to the area, which means that at some point it is helpful to know the area to know how much a thing will cost. That's just an example I can think of, I'm sure there are others... – abiessu Nov 08 '13 at 18:02
  • Maybe this gives some intuition:

    http://math.stackexchange.com/questions/543176/what-situations-models-require-calculating-the-area-under-a-curve/543269#543269

     – Christian Blatter Nov 08 '13 at 19:29

0 Answers0