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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 32   Last Post: Jul 7, 2013 9:03 PM

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GS Chandy

Posts: 7,563
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 5, 2013 6:32 AM
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Robert Hansen (RH) posted Jul 5, 2013 7:52 AM (GSC's remarks precede and interspersed):

I am (quite largely; not entirely) in agreement with Clyde Greeno in regard to the way people (including children) learn. I shall try to make clear in my remarks that follow just how that may be and how that differs to my 'underlying philosophy' about how people learn (if you want to give it such a grand name). [To my mind, it is all a simple matter of applying 'common sense'].
>
> On Jul 4, 2013, at 12:44 PM, "Clyde Greeno"
> <clydegreeno@cox.net> wrote:
>

> > # You take them to a rose bush, and let them smell
> it, and say, "This is how roses smell". If you are
> unwilling to call that "teaching", you have have
> confused "teaching" with "telling" ... as have all
> too many American educators.
>
> Absolutely, that is all you can do, and hope that
> they have a sense of smell.
>

Well, most people DO have a 'sense of smell'. In fact, the whole 'education system' has been built on the premise that the great majority of children who come into and pass through the system do indeed have senses of smell, sight, sound, touch - AND a few other useful/necessary senses (including some basic ideas of modus ponens and modus tollens in their practical lives even thouugh they are unaware of these technical names.

One of the 'senses' that the education system presumes that most incoming students DO have is a basic sense of 'modus ponens' (and 'modus tollens') - and the whole educational system' is (supposed to be) designed to then help them develop, extend,, refine and reinforce these 'senses' in various ways, too many for me to recount. The entire 'Montessori system' (in which you are a firm disbeliever) is founded on this basic concept.
> >
> > # Likewise, you take them to where they can

> experience modus ponens, and say "This is called
> 'modus ponens'."
>
> Absolutely, that is all you can do, and hope that
> they have a sense of modus ponens.
>

In fact, this is just what is done in ALL of 'teaching', of whatever subject. Which is why I had suggested (in various other posts) that what teachers should actually seek to do is to arouse the child's curiosity, excite his/her interest - and then everything flows naturally. From a sizable background of experience and learning, the teacher shows the learner some 'rules' and and 'examples' - the child then 'teaches' him-/herself and THEREBY learns. What the educational system should not forget is that there is no such thing as 'teaching' in isolation. 'Teaching' is, in fact, one part of the dyad 'teaching + learning'.
>
> > And the easiest and most meaningful place for
> learners to encounter modus ponens is within their
> r own routine conversation.
>
> People engage in routine conversation all the time,
> more than anything else they do, yet, without modus
> ponens.
>

WRONG! Modus ponens (and modus tollens) are integrated into a great many of the experiences that people go through, into a great many of the thoughts that people think.

Offhand, I don't believe it is possible to separate the things in our lives that are with/without'modus ponens' (and 'modus tollens')
>
>I guess you meant to say routine LOGICAL
> conversation.
>

Nope. I believe that was NOT what Clyde Greeno had 'meant to say' (at all).
>
>I would agree with that. That is why I
> am distressed when a school lumps everyone together
> and the first thing to go is the routine reliance on
> reasoning (and intelligence). Instead, the class is
> taught as if no one gets it, and no one ever will,
> even if they could, because it isn't there to be
> gotten. Whether you have the sense or not, it will
> not thrive in an environment where it is explicitly
> (or implicitly) prohibited.
>

DEFINITELY, the way most conventional schools 'teach' is profoundly wrong and in fact the whole system contradicts the way people actually learn.

What they (schools) have generally forgotten (except in the cases of a few 'exceptional teachers') is that there is no such thing as 'teaching' in isolation. There IS 'teaching + learning' - and the child mostly teaches him-/herself and thereby learns.

The 'teacher' should be a 'facilitator' for the child's learning. (I am aware of the contempt in which the 'traditional teaching philosophy holds the idea of 'facilitation': it is profoundly in error - probably because most 'reform teaching'/ 'new teaching has not properly understood it either).
>
> > All functional humans naturally use it ... its
> built into the evolution of their thinking processes.
>
> Well, I guess you don't believe that many humans are
> "functional" because you have been trying for decades
> to launch a clinic aimed at fixing this problem. I
> don't see anyone trying to launch a clinic to teach
> humans to talk or to use simple tools.
>

Sorry - there ARE indeed plenty of 'clinics' to 'teach humans how to talk (effectively) and how to use simple tools'. I do not quite understand the sense in which you mean the above.

(The main problem with most of these 'clinics' is that they do not seem to know or care much about the 'teaching + learning' dyad.
>
>The primary
> and natural mode of human thought (for all humans) is
> not reasoning and logic. It is analogy.
>

I would not presume to claim deep or profound knowledge about the "primary and natural mode of human thought (for all humans)". It may well be analogy in sizable measure. I believe the way human beings come to perform 'reasoning and logic' and 'to draw analogies' is generally rather a mystery at present - 'analogy' and 'reasoning and logic' are, in my opinion, inextricably bound together.

If you have successfully resolved the mystery, it may well be worth a detailed paper or even a book.
>
>That is our
> universal edge over the rest of the animal kingdom.
> We can put 2 and 2 together, they cannot. But we
> (universally) cannot put X and X together. And I
> know, you have a video of someone putting X and X
> together like putting 2 and 2 together, but that
> isn't the same thing.
>

I am not able to view videos easily, so haven't looked at Clyde Greeno's videos. As to how a child learns how to "put X and X together" from the (perhaps innate) sense of what '2' and '2' amounts to, I do not know - and I don't believe the most advanced 'learning theories' know either (though they might make a guess at it).

I DO know it happens (because I've seen it happen in/ to several children.
>
> > Any "teaching" of it is merely calling attention to
> it, and giving it a name ... which does, indeed, pave
> the way for further learning more about it.
>
> Partly, yes, but that description doesn't give enough
> credence to the act of coaching and developing the
> sense, which is imo the point of teaching.
>

As mentioned earlier, we differ rather profoundly on what 'the point of teaching' may be. I claim there is really no such thing as 'teaching' in isolation. There IS 'teaching + learning' - which is rather a different thing. .

The rest of RH's remark follows my signature.

GSC
The rest of RH's post:
>
>However, I
> am open to two points of teaching. Teaching for
> appreciation and teaching for doing. I focus more on
> the second form because that should (reasonably) be
> the majority of the effort. I mean, a class aimed at
> just appreciating calculus would be easy and short
> (and shouldn't even require a grade) while a class
> aimed at mastering calculus would be much harder and
> much longer.
>
> Bob Hansen



Message was edited by: GS Chandy


Date Subject Author
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Clyde Greeno
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Jonathan Crabtree
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy

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