My friend Catherine at Tom Snyder Productions showed me this video lecture of Ted Hasselbring talking about the research behind FASTT Math.
His basic points are: (1) one needs to memorize basic math facts (addition and multiplication tables) in order to do higher order math. The reason is to free up working memory for the higher order concepts. If you need to calculate the multiplication, you don’t have any working memory left over to do more complicated things. (2) Practice such as flash cards are good to increase memory recall speed and strengthen the memorization, but they don’t work unless the student has already memorized the fact. He mentions an astounding experiment—a group of kids played a math game for 10 minutes a day for a semester, all about multiplication facts. They loved this game, you couldn’t tear the kids away. At the end of the semester, their math fact memorization had not improved at all. They were just much faster at counting on their fingers. The problems was trying to develop speed before establishing the fact into working memory. (3) To get facts into working memory, you need to repeat a small set of facts–two or three. (4) You can assess fluency by measuring the time to answer a math problem. They use 0.8 seconds. Don’t forget to subtract out overhead such as keyboarding time. (5) It’s important to measure each math fact rather than the average because kids have an easy time with facts involving 0, 1, 2, 3, and doubling. If you measure the average, a student who is very fast at the easy facts can mask that they are slow with the other facts. (6) So FASTTMath will work on just two math facts, measuring response time until they are memorized, and the let the student proceed to a flash-card type game to speed up their recall time.
The overall process for learning fluency is: (1) Understand the concept. (2) Move a few facts into working memory — memorize two or three pieces of info. (3) Move the fact into long term memory—practice known facts with a longer and longer gap between recalls, i.e. 1 sec, 2, 4, 8 sec, etc. FASTTMath fills the gaps with practice on older, established facts to do two things at once. This is okay because the older established facts to not put a load on working memory. (4) Repeat with more bits of info.
I remember when I was learning math—I hated memorization and indeed to this day I do poorly on the math portions of Brain Age. At the time I felt memorization was not a useful skill and my time would be better spent on learning general concepts. This talk has convinced me otherwise. Although I have to say, I’m still reluctant to take the time to memorize my math facts even today. Old habits die hard.