Date: Jul 3, 1995 10:03 AM
Subject: Learn the multiplication facts?
I have been enjoying the discussion about learning facts and have to jump in
now with some personal observations.
1) I work with students who are "having trouble" in math class at the 4th and
5th grade level. I have noticed that unless they are given STRONG motivation,
they do not generally learn the traditional basic facts. A good many of these
students will rely on whatever tool they have--fingers, calculators, touch
points, whatever--to do even simple addition and subtraction problems. Now, I
don't really mind this, and even teach them how to use various "tools of the
trade" to complete arithmetic problems. But, those who don't have those
"facts" in their heads don't have the knowledge to see patterns in numbers!!
This I find challenging to work with. For a student who doesn't see patterns,
it seems, no number of samples will guide him to construct any personal
algorithms. Balance is critical, but learning facts seems to support
understanding of other concepts.
2) Through all of this I am reminded of one of those "eye opening" experiences
I had with my own son a couple of years ago. He had just finished 4th grade
and had a teacher who DEMANDED that all of her students learn ALL of the "basic
facts", including multiplication through the 12s. He had been successful.
That summer we were traveling in Mexico when he saw a road sign indicating that
we were 120 kilometers from our destination. He wanted to know how far that
was in miles. (Wow, I thought, a chance for an authentic application of some
math during the summer!!) So, I told him that if you divide by eight and
multiply by five you can get pretty close. In my mind I am seeing the division
problem and saying "12 divided by 8 is 1 remainder 4, 40 divided by eight is 5,
multiply by 15 by 5, 75 miles". He is still thinking (no paper or calc
around). I asked him to talk to me about his thinking and he says: Well, I
know there are 3 40s in 120 and that 40 divided by 8 is 5, so 5 times 3 is 15
and then 15 times 5 is 75. That must be the answer. That is mentally much
easier than my method. But, it seems to me that only a child with a facility
with the "basic facts" would look for ones he knows (3x4, 40/5) to accomplish
this problem. I see him do this all the time (now going into 7th grade), but I
rarely see my "factless" students even try. I am sure there are other factors
involved with my students, but without knowing the facts, how do they have a
Just some thoughts.
Resource Math Teacher/Technology Coordinator
Holaway Elementary School