At the third grade level teachers start emerging the children into the world of multiplication, perhaps spending a short period of time helping them conceptualize what multiplication is before slapping the drill sheets in front of them. The children are asked to memorize the basic facts. Practice them at home. Take the test. Flashcards, wrap-ups and multiplication charts are used along with countless other tools to help children simply see answers. The finger tricks and litty jingles ( I ate and I ate till I threw up on the floor, eight times eight is sixty-four) also are used. What a great way to tie language arts to math, and what teacher doesn't enjoy a little rhyme about puke?
Now, with all of this work to get children to memorize the facts, what do they really come to know about the facts when they are all done, that is if they ever get done? As far as I know, junior high school teachers are always complaining that their sixth and seventh grade students don't know their multiplication facts, but still this hasn't tipped us off in countless years that maybe we should look at how we teach the facts. Maybe if our efforts are grounded more in mathematics children might have more interest and understanding of the facts.
Of course, the same could be said of the addition facts as well, which are taught in a similar fashion in first and second. For the most part, teachers and parents try to beat the facts into the students with rewards and consequences. The real question is how necessary are these ancient tactics?
Multiplication should be introduced as repeated addition, doubling, and skip counting, gradually escalating to more efficient strategies for calculating more efficiently. Along the way commutative and distributive properties will be taught. Children will learn the ideas behind partial products ( 5 x 6 = 5 x 3 + 5 x 3), fact relationships ( 9 x 8 = 8 x 10 - 8) and commutatively ( 7 x 5 = 5 x 7). Imagine if children can remember that 9 x 5 = 45 because they know that it's half of 9 x 10 instead of simply knowing that 9 x 5 = 45 because they memorized it?
Progressive mathematics instruction calls for children to be taught so that they do see these connections as they learn the basic facts. The children will not need to drill on the facts if they are being instructed systematically in such a way that allows them to explore and construct the understanding of what multiplication is and how the facts all connect.
Start your reading and join the club. You wouldn't know from looking at what goes on in schools that this progressive model is what the NCTM has been expecting us to do for some time.
