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: Of Interest
Replies: 38   Last Post: Nov 5, 2012 7:48 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 1,773
Registered: 11/29/05
Re: Why Dehaene is Wrong
Posted: Nov 1, 2012 2:33 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Sorry. I had to get that off my chest. I realize that even if there is no such textbook a really bad teacher could still teach as you describe. It would be one hell of an accomplishment. I just want to prove that such a method of teaching isn't according to any established method I am familiar with, traditional or otherwise.
>


I agree, no textbooks with just numbers and no other objects.

I like to sort on whether an abacus is shown or mentioned. That tends
to bode well, is one of those early signs we might have a winner.

> So, back to what you were saying. In order to know when to add or subtract you need to know how to add and subtract, correct? So, whether you know just "how" to add and subtract, or both "how and when" to add and subtract, you have to know "how". To know "how" to add and subtract you must understand numbers. When I ask my son "What is the smallest number greater than zero?" and he answers "There isn't one.", by my definition that is number sense, not quantitative sense. He does not get that sense all at once, he gets it over time, by working with numbers. That all begins with counting, adding and subtracting.
>


I would disagree that "to add" and "to subtract" are necessarily
symbolic operations. We may subtract wood from a wood pile and add it
to the stove, add more water to the soup, take carrots from the
garden. Add and subtract have to do with moving objects through
distance (translation) in that we subtract them from a "place" and add
them to another.

Numbers come in when you're tallying a countable number of like type.
By "countable" I don't mean anything fancy, just that pouring rice or
sand is not a matter of counting grains. One goes by volume or,
better, weight. To speak of tiny "atoms" ala Democritus does not
change that fact that we sometimes add in bulk, without precise
integer measurements. The game of "roughly" or "approximately" is
quite rule-bound, meaning no less a language game than one of integers
and abacus adding (with positional notation vis-a-vis a base, a carry
operation, and all the rest of it).

<< snip >>

> My hypothesis is that quantitative sense and number sense are two very different things. One is concrete and physical while the other is imagined and abstract yet can be applied to the first.
>


I get the impression the initial hypothesis was some students will
fail to connect these two, but maybe not in all contexts.

>
> The issue then becomes one of devising *experiments* to follow up on this hypothesis---not, as you seem to think, offering rationalizations for not believing it. Most of those rationalizations can be easily defeated by noting that humans have bigger, more versatile brains---which are capable of extending innate qualities in ways that animal brains aren't.
>


Human brains have a way of filling large tomes with all kinds of
intra-brain traffic such as spy novels and romances.

We don't really know much about the mental life of other animals and
whether these speculations have any utility. What do whales share
about?

> What couldn't be so defeated is evidence from well-defined experiments.
>
>
> Well, I have devised the experiment, and solved the riddle, without even having to perform the experiment. There is the line between quantitative sense and number sense.
>
> Bob Hansen


If I fetch three logs for the fire, subtracting from the wood pile and
adding to the stove, is that quantitative sense or number sense?

If I was asked to "get three logs" and obey, is "number sense" now in
the foreground? Is "counting" alone enough to establish "number
sense"?

When I see two people each have half a load of hay, or half a loaf of
bread, I am seeing that they have copies of "the same thing" (loaf of
bread).

I am able to detect greater than, less than, equal, without having any
names for units or amounts, correct?

Is that quantitative sense, without number sense?

Kirby


Date Subject Author
10/29/12
Read Of Interest
Louis Talman
10/29/12
Read Re: Of Interest
Robert Hansen
10/30/12
Read Re: Of Interest
Louis Talman
10/30/12
Read Re: Of Interest
Robert Hansen
10/30/12
Read Re: Of Interest
Paul A. Tanner III
10/30/12
Read Re: Of Interest
Louis Talman
10/30/12
Read Re: Of Interest
Robert Hansen
10/31/12
Read Re: Of Interest
Louis Talman
10/31/12
Read Re: Of Interest
Robert Hansen
10/31/12
Read Re: Of Interest
Louis Talman
10/31/12
Read Re: Of Interest
Robert Hansen
10/31/12
Read Re: Of Interest
Louis Talman
10/31/12
Read Why Dehaene is Wrong
Robert Hansen
11/1/12
Read Re: Why Dehaene is Wrong
kirby urner
11/1/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/2/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/1/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/1/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/1/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/2/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/2/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/2/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/2/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/2/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/4/12
Read Re: Why Dehaene is Wrong
Wayne Bishop
11/4/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/4/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/5/12
Read Re: Why Dehaene is Wrong
Wayne Bishop
11/5/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/5/12
Read Re: Why Dehaene is Wrong
Wayne Bishop
11/5/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/5/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/5/12
Read Re: Why Dehaene is Wrong
Gary Tupper
11/1/12
Read Re: Why Dehaene is Wrong
Wayne Bishop
11/3/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/3/12
Read Re: Why Dehaene is Wrong
Robert Hansen
11/3/12
Read Re: Why Dehaene is Wrong
Louis Talman
11/3/12
Read Re: Why Dehaene is Wrong
Robert Hansen
10/29/12
Read Re: Of Interest
Robert Hansen

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.