By Lisa Hummel
My 5th grade son was working on his math homework the other day, and I noted that his knowledge of basic multiplication facts was a little rusty after a long summer vacation. It was really slowing him down. I said that if I give him a problem like 8 x 7, he should instantly know the answer. I suggested that maybe we needed to work on flashcards at home for a while again. He naturally said this would be a waste of time, because he’d rather go play, so I found myself explaining to him what I thought was obvious, but maybe it isn’t. Here’s what I told him:
As a high school science teacher for 15 years now, I have seen the sad and frustrating results of people who never really memorized their basic arithmetic facts when they’re young. In physical science, chemistry, or physics, we often find ourselves setting up multi-step problems to solve for a velocity, density, acceleration, or any number of physical quantities. I have seen many students who can set up the problems expertly using the formulas I taught them, but they are agonizingly slow when it comes to getting the right answer. Now one could argue, as my son did, that you could just use a calculator. But the truth is you don’t always have one with you, or it may not work. These situations should not handicap you. And whether you’re trying to find a calculator, or struggling to work a basic arithmetic problem by hand, it is easy to lose sight of the original problem you were trying to solve.
I used an analogy to reading. What if every time you came across an unfamiliar word, your decoding skills were so inadequate that it took you a really long time to figure out what that single word was, or you had to rely on a machine to decode it for you? Pretty soon you’d lose the meaning of the original sentence or paragraph you were trying to decipher. It’s the same with mathematical and scientific problem solving. If you’re struggling with the multiplication and division, it’s really hard to understand the larger implications of the multi-step calculation.
Maybe the lack of emphasis on memorization grew out of the 60’s counterculture, where anything that smacked of uncritical, unthinking, blind knowledge was rejected. An overemphasis on memorization at the expense of critical thinking is certainly not desirable. But I’ve seen the pendulum swing too far the other way, to where memorizing the most basic facts is seen as unworthy of the time of elementary students and teachers. The consequences of this rejection are crippling when students reach middle and high school.
But it doesn’t have to be an either/or situation. A good teacher or math tutor will help a student understand what it means to multiply or add, and s/he will also insist that students master their math facts with instant recall, just as a good reading teacher or tutor will make sure that students instantly know the sounds letters make. Fortunately, this is not hard. A young child’s mind is like a sponge. It was made for memorization. That’s why it’s so much easier to learn a new language when we’re young. And while an adult might find memorization dull and tedious (maybe because we were raised in or after that 60’s counterculture, and because our brains are different), a young child can find it gratifying and even fun. It can be made into a game or a song, and the child knows concretely how much s/he is learning, which builds true pride and self-esteem. Think about the ABC’s, counting songs and games, rhymes to learn the months of the year, etc. Children eat that stuff up. Even much-disdained flashcards can lead to friendly competition with oneself or a classmate.
Children should and can successfully memorize important facts. Parents and teachers must insist that they do. And we shouldn’t let them reach for the calculator when it is a problem that they should know the answer to faster than it takes them to punch it into the keypad. Even if a child never studies math and science beyond high school, s/he will need basic math skills to be an informed shopper and educated citizen. And now I need to stop typing and go get out the flashcards.
September 18, 2011 at 9:45 pm
Well said! I agree that committing basic math facts to memory is important. It’s also important that both teachers and parents present children with many different ways to learn these facts. For some children, flash cards will be a fun challenge; for others, writing (what we used to call “times tables”) will be more effective. I continue to be amazed at how different individual children are, and how different learning styles work for each. Thank you for your suggestions.