
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.
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 welldesigned 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 towngown 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

