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Topic: CT Academy Launches Another Five-Year Plan
Replies: 40   Last Post: Sep 25, 2010 8:37 PM

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Jonathan Groves

Posts: 2,068
From: Kaplan University, Argosy University, Florida Institute of Technology
Registered: 8/18/05
Re: CT Academy Launches Another Five-Year Plan
Posted: Sep 19, 2010 9:48 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 9/17/2010 at 5:06 pm, I wrote (in part):

> Alain Schremmer notices that one problem with the
> book's organization
> is that it makes him wonder what the "story behind
> the mathematics"
> is, that is what the point of the development of this
> math is, where
> it leads, what it allows us to do. He has noted that
> I still appear
> trapped in the usual mode of presenting math as a
> series of disconnected
> topics rather than as a unified whole but that he can
> also tell that
> I'm trying to escape that mindset. That is, I
> believe he is thinking that,
> if I continue the book with this organization, I may
> make much further
> progress in escaping this mindset than most do but
> that I still won't
> escape that entirely.
>
> I wonder where he gets that idea when he hasn't seen
> the text of the book.
> But maybe he can see something in that organization
> that tells him this
> fact whereas I don't see it.
>
> Here are two of his responses:
>
> http://mathforum.org/kb/message.jspa?messageID=7208094
> &tstart=0
>
> and
>
> http://mathforum.org/kb/message.jspa?messageID=7208113
> &tstart=0



Bill,

When I had thought more about Alain's remarks yesterday morning, I had
realized what he means when he says that a mathematics course tells
a story: The course develops ideas along the way that lead to a final
big idea in the end, something like a "punch line." Another way to say
it is that the course in one continuous stream of ideas that lead to
some ulimate goal rather than multiple little streams of ideas that are
not connected and do not really lead anywhere. Many math courses, especially
general education math courses or survey math courses, do not lead anywhere
but instead have students meandering aimlessly throughout different parts
of Math Land. That is, such courses are really just a hodge-podge of
different mini-courses all thrown together into one course.

Based on Alain's comments, I really do question if my arithmetic book
as it stands would really lead anywhere--that is, if the book really does
lead to an ultimate goal at the end that makes it clear to the students what
the point of arithmetic really is. That is, I will need to make it clear
in the book what big reason arithmetic was developed for and not just simply
what various smaller questions arithmetic was developed for.

Of course, we know that arithmetic leads to algebra and other higher
mathematics, but how meaningful is that goal to students? Even if that
happens to be meaningful to students (I really question that), can an
arithmetic book really prove that this goal is accomplished? Another goal
is number sense, but how meaningful is that goal to students? Even if we
use this as a goal, we still need to motivate the need for number sense.
In fact, there are two problems with this goal: (1). Can we really prove
to students that such a course leads to this goal? (2). What exactly does
this goal mean? What is number sense? I have a good intuitive idea of
what that means, but I cannot articulate a clear, precise definition
of what number sense is. No wonder many students end up thinking that
mathematics is just a formal requirement in schools, that math is just
"one of those courses you have to take to get a diploma."


Jonathan Groves


Date Subject Author
9/16/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/16/10
Read Re: CT Academy Launches Another Five-Year Plan
Dave L. Renfro
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
GS Chandy
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Pam
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Bill Marsh
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Pam
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Bishop, Wayne
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Bishop, Wayne
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Pam
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Louis Talman
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Bishop, Wayne
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Pam
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Richard Strausz
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/17/10
Read Re: CT Academy Launches Another Five-Year Plan
Robert Hansen
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Bishop, Wayne
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Pam
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/18/10
Read Re: CT Academy Launches Another Five-Year Plan
Bill Marsh
9/19/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/20/10
Read Theory of arithmetic
Clyde Greeno @ MALEI
9/20/10
Read Re: Theory of arithmetic
Jonathan Groves
9/21/10
Read Re: Theory of arithmetic
Clyde Greeno @ MALEI
9/21/10
Read Re: Theory of arithmetic
Robert Hansen
9/21/10
Read Re: Theory of arithmetic
Dave L. Renfro
9/19/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/19/10
Read Re: CT Academy Launches Another Five-Year Plan
Robert Hansen
9/20/10
Read Re: CT Academy Launches Another Five-Year Plan
Jonathan Groves
9/20/10
Read Re: CT Academy Launches Another Five-Year Plan
Robert Hansen
9/25/10
Read Re: CT Academy Launches Another Five-Year Plan
Haim
9/25/10
Read Re: CT Academy Launches Another Five-Year Plan
Louis Talman
9/25/10
Read Re: CT Academy Launches Another Five-Year Plan
Joe Niederberger
9/25/10
Read Re: CT Academy Launches Another Five-Year Plan
Haim

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