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: new tutor here
Replies: 151   Last Post: Jul 17, 2013 4:09 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Hansen

Posts: 7,527
From: Florida
Registered: 6/22/09
Re: new tutor here
Posted: Jun 21, 2013 7:57 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (9.8 K)


On Jun 21, 2013, at 12:46 AM, Joe Niederberger <niederberger@comcast.net> wrote:

> R Hansen tries attempts gambit:
>> I guess I should have been more specific. I meant to say that the other 9 pictures also relate those quantities, but not in a way that would make an argument that e^pi is greater than pi^e.
>
> Oh! Please show me those 9 OTHER pictures!
>
> (Or, in my paranoid conspiracy theory moments, might I suspect Robert may come up with 9 non-nonsensical pics and only one that rings true, just to prove his point?)
>
> Stop right there, mister! Suppose I ask you you to picture a nice 5 dresser drawer Chippendale cabinet, made of walnut. Will you call up in your mind's eye a hairy amoeba?


Let's cut the chase. You cannot visualize a mathematical proof without connecting the dots. It is impossible. I don't think any mathematically minded individual will agree with you that you managed to pull off a proof without connecting the dots.


> Or maybe vision is a fundamental sense that factors
> into much of our thinking. Fundamental sense belonging to perhaps the majority of humans, by virtue of their genetic inheritance, and grounding our thought processes. The ability to picture a Chippendale dresser drawer, or a picture relating pi, ln(pi) and 1/e, not so. To suppose the two are at all alike, is a category error.



Virtually every living animal, human or otherwise, possesses the sense of vision, with pretty much equal acuity and resolution (within their species), yet very few humans (and no animals) could make sense of your picture. Thus, vision is obviously not the key ingredient. Mathematical reasoning is the key ingredient. Connecting the dots is the key ingredient.

I don't see a world of algebrists and world of geometers, just like I don't see a world of arithmetic and world of mathematics. How many students of algebra would be stumped by your visual proof and how many students of geometry would be stumped by a symbolic proof? Hardly any. Note, "students" = "students successfully progressing through the art".

Telling me that the algebrist possess a different sense of mathematics than the geometer is like telling me that the pianist possess a different sense of music than the violinist or that the sculpturer possess a different sense of art than the painter. Each pair is using the same sense. They will have to develop strategies unique to their medium but they are feeding the same sense. Musicians generally play more than one instrument. Artists generally work in more than one medium. Mathematicians generally understand visual proofs as well as symbolic ones. And they all know arithmetic.:)

I give you credit for not connecting the dots when you presented your picture, even though you claim (foolishly imo) that there aren't any dots to connect. That is the problem when teachers use visualizations poorly. There is no math left. They will work through algebra problems from start to finish and say "See? X = 3." and the students will nod their heads. Then, when the students fail their algebra exams, the teachers throw their hands in the air and say that it is the X's and Y's fault. So they proceed to use visualizations instead and repeat the same mistake all over again. They will work through the problem from start to finish and say "See? Segment A is longer than Segment B." and the students will nod their heads, then fail their visual algebra exams.

I know you are a believer in Dehaene, and by analogy, the "Chariots of the Gods" was a damn interesting story, and if it were true, it would be pretty cool as well. But open your eyes (PUN INTENDED) and look around you. Vision cannot be a key ingredient to mathematics any more than breathing can. If it were, we wouldn't have any trouble teaching it. These theories that share the common theme that there is some dark force suppressing the innate mathematical genius of our youth are getting old and absurd. My comparison to "belief in psychics" wasn't that far off.

Bob Hansen


Date Subject Author
6/12/13
Read new tutor here
Michael Mossey
6/12/13
Read Re: new tutor here
Wayne Bishop
6/12/13
Read Re: new tutor here
Michael Mossey
6/13/13
Read Re: new tutor here
Wayne Bishop
6/13/13
Read Re: new tutor here
Dave L. Renfro
6/13/13
Read Re: new tutor here
Joe Niederberger
6/14/13
Read Re: new tutor here
Robert Hansen
6/14/13
Read Re: new tutor here
Joe Niederberger
6/14/13
Read Re: new tutor here
Robert Hansen
6/14/13
Read Re: new tutor here
Joe Niederberger
6/14/13
Read Re: new tutor here
Robert Hansen
6/14/13
Read Re: new tutor here
Joe Niederberger
6/14/13
Read Re: new tutor here
Robert Hansen
6/15/13
Read Re: new tutor here
Louis Talman
6/14/13
Read Re: new tutor here
Michael Mossey
6/15/13
Read Re: new tutor here
Robert Hansen
6/14/13
Read Re: new tutor here
GS Chandy
6/16/13
Read Re: new tutor here
GS Chandy
6/15/13
Read Re: new tutor here
Louis Talman
6/15/13
Read Re: new tutor here
Joe Niederberger
6/16/13
Read Re: new tutor here
Robert Hansen
6/15/13
Read Re: new tutor here
Pam
6/16/13
Read Re: new tutor here
Robert Hansen
6/15/13
Read Re: new tutor here
Pam
6/16/13
Read Re: new tutor here
Wayne Bishop
6/16/13
Read Re: new tutor here
Joe Niederberger
6/16/13
Read Re: new tutor here
Robert Hansen
6/16/13
Read Re: new tutor here
Joe Niederberger
6/17/13
Read Re: new tutor here
Robert Hansen
6/16/13
Read Re: new tutor here
Michael Mossey
6/17/13
Read Re: new tutor here
GS Chandy
6/17/13
Read Re: new tutor here
GS Chandy
6/17/13
Read Re: new tutor here
Pam
6/17/13
Read Re: new tutor here
Robert Hansen
6/17/13
Read Re: new tutor here
Pam
6/17/13
Read Re: new tutor here
Robert Hansen
6/17/13
Read Re: new tutor here
Pam
6/17/13
Read Re: new tutor here
Pam
6/17/13
Read Re: new tutor here
Joe Niederberger
6/17/13
Read Re: new tutor here
Robert Hansen
6/17/13
Read Re: new tutor here
Joe Niederberger
6/17/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Robert Hansen
6/17/13
Read Re: new tutor here
GS Chandy
6/18/13
Read Re: new tutor here
GS Chandy
6/18/13
Read Re: new tutor here
GS Chandy
6/18/13
Read Re: new tutor here
GS Chandy
6/18/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Robert Hansen
6/18/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Robert Hansen
6/18/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Joe Niederberger
6/18/13
Read Re: new tutor here
Robert Hansen
6/18/13
Read Re: new tutor here
Robert Hansen
6/18/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Robert Hansen
6/21/13
Read Re: new tutor here
Wayne Bishop
6/21/13
Read Re: new tutor here
Wayne Bishop
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Robert Hansen
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Joe Niederberger
6/19/13
Read Re: new tutor here
Robert Hansen
6/21/13
Read Re: new tutor here
Joe Niederberger
6/21/13
Read Re: new tutor here
Robert Hansen
6/21/13
Read Re: new tutor here
Joe Niederberger
6/21/13
Read Re: new tutor here
Robert Hansen
6/21/13
Read Re: new tutor here
Joe Niederberger
6/21/13
Read Re: new tutor here
Robert Hansen
6/21/13
Read Re: new tutor here
Joe Niederberger
6/21/13
Read Re: new tutor here
Joe Niederberger
6/21/13
Read Re: new tutor here
Dave L. Renfro
6/22/13
Read Re: new tutor here
Robert Hansen
6/22/13
Read Re: new tutor here
Robert Hansen
6/22/13
Read Re: new tutor here
Joe Niederberger
6/22/13
Read Re: new tutor here
Robert Hansen
6/22/13
Read Re: new tutor here
Robert Hansen
6/23/13
Read Re: new tutor here
Joe Niederberger
6/23/13
Read Re: new tutor here
Robert Hansen
6/23/13
Read Re: new tutor here
Robert Hansen
6/23/13
Read Re: new tutor here
Joe Niederberger
6/23/13
Read Re: new tutor here
Robert Hansen
6/24/13
Read Re: new tutor here
Robert Hansen
6/24/13
Read Re: new tutor here
Joe Niederberger
6/24/13
Read Re: new tutor here
Joe Niederberger
6/24/13
Read Re: new tutor here
Joe Niederberger
6/25/13
Read Re: new tutor here
GS Chandy
7/10/13
Read Re: new tutor here
Dave L. Renfro
7/10/13
Read Re: new tutor here
Robert Hansen
7/10/13
Read Re: new tutor here
Joe Niederberger
7/10/13
Read Re: new tutor here
Robert Hansen
7/10/13
Read Re: new tutor here
Robert Hansen
7/10/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Joe Niederberger
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Joe Niederberger
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
GS Chandy
7/11/13
Read Re: new tutor here
Joe Niederberger
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Louis Talman
7/11/13
Read Re: new tutor here
Robert Hansen
7/12/13
Read Re: new tutor here
Wayne Bishop
7/12/13
Read Re: new tutor here
Louis Talman
7/12/13
Read Re: new tutor here
Wayne Bishop
7/12/13
Read Re: new tutor here
Robert Hansen
7/12/13
Read Re: new tutor here
Gary Tupper
7/12/13
Read Re: new tutor here
Wayne Bishop
7/12/13
Read Re: new tutor here
Louis Talman
7/11/13
Read Re: new tutor here
Joe Niederberger
7/11/13
Read Re: new tutor here
Robert Hansen
7/11/13
Read Re: new tutor here
Joe Niederberger
7/11/13
Read Re: new tutor here
GS Chandy
7/12/13
Read Re: new tutor here
Wayne Bishop
7/12/13
Read Re: new tutor here
Joe Niederberger
7/12/13
Read Re: new tutor here
Wayne Bishop
7/12/13
Read Re: new tutor here
GS Chandy
7/12/13
Read Re: new tutor here
Joe Niederberger
7/13/13
Read Re: new tutor here
Robert Hansen
7/13/13
Read Re: new tutor here
GS Chandy
7/13/13
Read Re: new tutor here
Joe Niederberger
7/13/13
Read Re: new tutor here
Wayne Bishop
7/13/13
Read Re: new tutor here
Robert Hansen
7/13/13
Read Re: new tutor here
Robert Hansen
7/13/13
Read Re: new tutor here
Peter Duveen
7/14/13
Read Re: new tutor here
Joe Niederberger
7/14/13
Read Re: new tutor here
Joe Niederberger
7/14/13
Read Re: new tutor here
Joe Niederberger
7/14/13
Read Re: new tutor here
Robert Hansen
7/14/13
Read Re: new tutor here
GS Chandy
7/15/13
Read Re: new tutor here
Wayne Bishop
7/15/13
Read Re: new tutor here
Joe Niederberger
7/15/13
Read Re: new tutor here
Robert Hansen
7/15/13
Read Re: new tutor here
Peter Duveen
7/15/13
Read Re: new tutor here
Joe Niederberger
7/16/13
Read Re: new tutor here
GS Chandy
7/16/13
Read Re: new tutor here
Wayne Bishop
7/16/13
Read Re: new tutor here
GS Chandy
7/17/13
Read Re: new tutor here
GS Chandy

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.