The Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » Education » math-teach

Topic: Multiplicative reasoning research discussion - where?
Replies: 51   Last Post: Mar 2, 2009 3:56 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: 4,713
Registered: 12/6/04
Re: Multiplicative reasoning research discussion - where?
Posted: Feb 24, 2009 6:31 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Wayne:

> If you are interested in the concept, and not a lot
> of Beautiful Sunshine about the subject, just take
> any good elementary mathematics sequence (Singapore
> Math and Saxon Math come to mind), read the
> appropriate sections and, if necessary, do some of
> the related exercises in the problem sets.


I wasn't clear what age range we were talking about here,
but if we're talking an older brand of teen, then just
sticking with Saxon or Singapore would be considered
inappropriate where I teach.

What's important is to ask about "types of object" and
whether objects of this type are able to multiply with
one another, and, if so, how does that look.

Typical of well-designed multiplication regimes is you'll
have a multiplicative identity, associativity, and some
concept of a multiplicative inverse. There are many
similarities with addition so far. You'll likely be
looking for multiplication *in contrast* to another
operation....

What makes our algebra more like the "abstract algebra"
of the college courses, is we know to single out the
operation (multiplication) while changing the types, i.e.
hold the operation in view while flipping through several
"types that multiply". This is standard in the text
books on that subject, but in avoiding all use of a
machine logic, they deprive themselves of the constructive
experience of actually looking under the hood, defining
the operator itself in some language capable of doing so
(Ruby, Python...).

I agree that not everyone gets to go to some private
sector company school managed by Silicon Forest execs,
so what I'm saying just falls by the wayside in most
alien contexts. We do have a marketing edge however,
which is we don't have the overhead costs of purchasing
either Saxon or Singapore. More intelligent curriculum
writing is easy to come by, with more interesting work
at the end of the tunnel.

Also, in any city with reasonably good town-gown
relations, you'll have your private sector company
trainers willing to lend a hand in getting the public
teachers up to speed, not even on school budget
necessarily, as it's considered an investment in our
future to help kids stay in this century, not fall back
to 1900s or 1800s, which is where most curriculum writers
will put you (not heaping blame -- many of them had no
access to the 21st century when writing their materials,
e.g. Dom Rosa's teachers, or Paul Tanner III's -- not
true from this point forward though, so don't accept
carbon copies with minor changes (those just won't fly
anymore, just not suitable if you're really thinking
about the future job market and what skills it makes
the most sense to cultivate)).

Kirby


Date Subject Author
2/21/09
Read Multiplicative reasoning research discussion - where?
Maria Droujkova
2/21/09
Read Re: Multiplicative reasoning research discussion - where?
Bishop, Wayne
2/22/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/22/09
Read Re: Multiplicative reasoning research discussion - where?
Michael Paul Goldenberg
2/22/09
Read Re: Multiplicative reasoning research discussion - where?
Bishop, Wayne
2/22/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/22/09
Read Re: Multiplicative reasoning research discussion - where?
Paul A. Tanner III
2/23/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/23/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/23/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/23/09
Read Re: Multiplicative reasoning research discussion - where?
Richard Strausz
2/23/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Bill Marsh
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Joshua Fisher
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Kirby Urner
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Domenico Rosa
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/24/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Louis Talman
2/25/09
Read Creativity and Originality in mathematics (Was: Multiplicative reasoning research discussion - where?)
Michael Paul Goldenberg
2/25/09
Read Re: Creativity and Originality in mathematics (Was: Multiplicative
reasoning research discussion - where?)
Louis Talman
2/25/09
Read Re: Creativity and Originality in mathematics (Was: Multiplicative reasoning research discussion - where?)
Michael Paul Goldenberg
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Dave L. Renfro
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Gary Tupper
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Gary Tupper
2/27/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/28/09
Read Re: Multiplicative reasoning research discussion - where?
Bishop, Wayne
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Bishop, Wayne
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Gary Tupper
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/25/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Richard Strausz
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
2/26/09
Read Re: Multiplicative reasoning research discussion - where?
Haim
2/28/09
Read Re: Multiplicative reasoning research discussion - where?
Maria Droujkova
3/1/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
3/2/09
Read Re: Multiplicative reasoning research discussion - where?
Joe Niederberger
2/28/09
Read Re: Multiplicative reasoning research discussion - where?
Haim

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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.