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Topic: Multiplicative reasoning research discussion - where?
Replies: 51   Last Post: Mar 2, 2009 3:56 PM

 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

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.

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,
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
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 Maria Droujkova
2/21/09 Bishop, Wayne
2/22/09 Maria Droujkova
2/22/09 Michael Paul Goldenberg
2/22/09 Bishop, Wayne
2/22/09 Haim
2/22/09 Paul A. Tanner III
2/23/09 Maria Droujkova
2/23/09 Maria Droujkova
2/23/09 Joe Niederberger
2/23/09 Richard Strausz
2/23/09 Haim
2/24/09 Maria Droujkova
2/24/09 Maria Droujkova
2/24/09 Haim
2/24/09 Bill Marsh
2/24/09 Joe Niederberger
2/24/09 Joe Niederberger
2/24/09 Joshua Fisher
2/24/09 Kirby Urner
2/24/09 Maria Droujkova
2/24/09 Maria Droujkova
2/24/09 Domenico Rosa
2/24/09 Maria Droujkova
2/24/09 Haim
2/24/09 Haim
2/25/09 Maria Droujkova
2/25/09 Maria Droujkova
2/25/09 Maria Droujkova
2/25/09 Louis Talman
2/25/09 Michael Paul Goldenberg
2/25/09 Louis Talman
2/25/09 Michael Paul Goldenberg
2/25/09 Dave L. Renfro
2/25/09 Gary Tupper
2/26/09 Joe Niederberger
2/26/09 Gary Tupper
2/27/09 Joe Niederberger
2/28/09 Bishop, Wayne
2/25/09 Bishop, Wayne
2/25/09 Maria Droujkova
2/25/09 Gary Tupper
2/25/09 Maria Droujkova
2/25/09 Maria Droujkova
2/26/09 Haim
2/26/09 Richard Strausz
2/26/09 Maria Droujkova
2/26/09 Haim
2/28/09 Maria Droujkova
3/1/09 Joe Niederberger
3/2/09 Joe Niederberger
2/28/09 Haim