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 chance?
Just some thoughts.
Rosemary Beck Resource Math Teacher/Technology Coordinator Holaway Elementary School Tucson AZ email@example.com