The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Education » math-teach

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: techie public school teachers turn to capitalism to improve
bottom line

Replies: 1   Last Post: Sep 12, 2017 2:11 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Joe Niederberger

Posts: 4,657
Registered: 10/12/08
Re: techie public school teachers turn to capitalism to improve
bottom line

Posted: Sep 12, 2017 11:56 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I'd like to call attention to this, again, because I think the claims it makes, that this "approach" to understanding the fundamental theorem of calculus is "made possible by technology" (graphing calculator) and reiterated as "impossible without technology".

"A Conceptual Approach to Calculus Made Possible By Technology"

I like the approach, as I explained before, because, in past times, I simply felt for my own satisfaction, that I should be able to easily see the relation between a rate of flow (water streaming into a container,) a rate of accumulation (total water in container,) and the relation of those things to the symbols on paper (equations an functions) and the numbers they might represent for a given instant of time. I felt it *should* be comfortable intuition, and not a mysterious wonder.

That would seem to be the more or less explicit goals of the documented approach as well. (Yes, Kirby, there are many ways to understanding things, and understanding takes many forms, but I was focusing on this one, because that's what both I and the authors of this paper seem to be after, in this case.)

So I set about it on my own, to complement whatever insights and understandings I was getting for the course proper. in fact, my own musing follow the outline described here, to a surprising degree, though not in its exact mechanics, formulas, or even emphasis (for example, I too was led to approximate an accumulation function as a step function, from first principles, so to speak, and not as a conscious imitation of Riemannian integration.)

But I made no use of a graphing calculator anywhere in my own investigation. So, I think the claims of this paper are either trivially true (you can't take their exact course, as they envision it, without said calculator,) flat out false (you can't achieve the grounding in concepts they are promoting, without a calculator) or somewhere in between (calculator either eases, quickens or enhances, somehow, acquisition of these concepts.)

Of course I'm being kind, the last case still makes their claims false. However, if they could actually demonstrate
that either eases, quickens, or enhances said concept acquisition, then I'd say they have something pretty solid.

How to demonstrate, rather than simply claim, advantage, is something I think they should pursue.

[And of course, having done that (big if,) that still would not show that acquisition of said concepts is itself valuable in any practical sense, though I'm satisfied that that goal is worth something, to me, personally, and wish them well because of that, for making it more easily available to others.]

Joe N

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.