In a message dated 95-06-30 18:45:34 EDT, you write:
What, IMHO, are some of the "basic" facts of multiplication?
Multiplication is commutative. Multiplication is associative. 1 is the multiplicative identity. 0 is the multiplicative "annihilator." Multiplying x by -1 yields -x. Given x > 0: if n > 1, then n * x > x if 0 < n < 1, then n * x < x (an example where multiplication "makes things smaller") Additionally, students should be able to represent multiplication through various models (area, arrays, etc.)
>Yet, it *seems* (I have no evidence other than my observations) >that many teachers are far more concerned that students memorize the "times >tables" than they are about students understanding the above concepts. > >Norm Krumpe >Indiana University of Pennsylvania >Indiana University at Bloomington > >
How can students understand the above concepts if they don't know their times tables? By pushing buttons on a calculator so that the magic black box can give them some numbers?