Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » Education » math-teach

Topic: Re: How teaching factors rather than multiplicand & multiplier
confuses kids!

Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Joe Niederberger

Posts: 2,635
Registered: 10/12/08
Re: How teaching factors rather than multiplicand & multiplier
confuses kids!

Posted: Nov 12, 2012 7:58 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Robert Hansen says:
>That "intuition" you speak of is not common sense, otherwise we would see it everywhere. I don't see a shortage of common sense in the world, so why is mathematics so difficult for most? The "intuition" you speak of is the underpinnings of analysis and formal reasoning.

Well, I didn't want to get hung up on this point, but its OK. In the case on "continuity" there is a common sense meaning, that is wide-spread enough - it means no gaps, breaks, sudden jumps. A refined mathematical intuition, on the other, starts there and reasons to further no-so-common or easy to understand observations, correlations, conclusions. All I'm saying is much can be done without
all the various formal definitions from analysis or topology. Euler and Gauss did OK.

But the starting point is pretty much the same for everyone. And Clyde's version was pretty far from the starting point.

Here's a question - how do you get a student to appreciate that a kind of "reversal" is needed in viewpoint to get to a satisfactory definition. What I'm talking about is the common sense viewpoint takes continuity for granted, and merely looks for "gaps" or "breaks" in the otherwise continuous (think of basic functions like 1/x). The formal definitions though, talk about continuity at a point. In fact one can define a function that is *only* continuous at a single point -- a kind of oxymoron.

Joe N

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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.