>>I would be curious to know how many students (at any level) know that 7 x 8 >>= 56, but also think that multiplication always "makes things bigger." To >>me, this latter "basic fact" is far more important than the former. >> >>Norm Krumpe > >Don't know what grade you teach but this isn't true for numbers between 0 and >1. One of the books I'm using does ask number sense questions like this. > >michael >
I think some are misunderstanding what I said (and, as I re-read it, I realize I worded it poorly). Yes, *I* know that multiplication does not necessarily make things bigger. The point is, I think some teachers are content in knowing that their students know that 7 x 8 = 56 (along with the other "basic facts"), but aren't quite so concerned if the same students think that multiplication must "make things bigger" (which is clearly incorrect). I think we may be spending too much time on those basic facts, and not enough time trying to shatter the misconceptions the students have about multiplication -- misconceptions which, I think, we as educators may be partially responsible for creating.
UCSMP's books seem to support this idea. They make a great effort to reinforce the concepts of multiplication (using area models, size change factor models, etc.), and little or no time on exercises that require knowledge of the traditional "basic facts."
By the way, multiplication by numbers between 0 and 1 does not necessarily "make things smaller" either. For example, .5 x -8 = -4 (which is larger than -8).