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“When students have to drill multiplication facts, it’s frustrating, unproductive and it makes them hate math. A better way to master the multiplication table is work on the skills that allow students to multiply quickly and efficiently.”
The most effective and powerful way I’ve found to commit math facts to memory is to try to understand why they’re true in as many ways as possible. It’s a very slow process, but the fact becomes permanently lodged, and I usually learn a lot of surrounding information as well that helps me use it more effectively.
Actually, a close friend of mine describes this same experience: he couldn’t learn his times tables in elementary school and used to think he was dumb. Meanwhile, he was forced to rely on actually thinking about number relationships and properties of operations in order to do his schoolwork. (E.g. I can’t remember 9×5, but I know 8×5 is half of 8×10, which is 80, so 8×5 must be 40, and 9×5 is one more 5, so 45. This is how he got through school.) Later, he figured out that all this hard work had actually given him a leg up because he understood numbers better than other folks. He majored in math in college and is now a cancer researcher who deals with a lot of statistics.
During off-times, at a long stoplight or in grocery store line, when the kids are restless and ready to argue for the sake of argument, I invite them to play the numbers game.
“Can you tell me how to get to twelve?”
My five year old begins, “You could take two fives and add a two.”
“Take sixty and divide it into five parts,” my nearly-seven year old says.
“You could do two tens and then take away a five and a three,” my younger son adds.
Eventually we run out of options and they begin naming numbers. It’s a simple game that builds up computational fluency, flexible thinking and number sense. I never say, “Can you tell me the transitive properties of numbers?” However, they are understanding that they can play with numbers.
I didn’t learn the rules of baseball by filling out a packet on baseball facts. Nobody held out a flash card where, in isolation, I recited someone else’s definition of the Infield Fly Rule. I didn’t memorize the rules of balls, strikes, and how to get someone out through a catechism of recitation.
We are finishing up an experiment in mental math, using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.
Take your time to fix each of these patterns in mind. Ask questions of your student, and let her quiz you, too. Discuss a variety of ways to find each answer. Use the card game Once Through the Deck (explained in part 3)as a quick method to test your memory. When you feel comfortable with each number pattern, when you are able to apply it to most of the numbers you and your child can think of, then mark off that row and column on your times table chart.
If you remember, we are in the middle of an experiment in mental math. We are using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible. Talk through these patterns with your student. Work many, many, many oral math problems together. Discuss the different ways you can find each answer, and notice how the number patterns connect to each other.
My daughter is in 4th grade. She has been studying multiplication in school for nearly a year, but she still stumbles over the facts and counts on her fingers. How can I help her?
Many people resort to flashcards and worksheets in such situations, and computer games that flash the math facts are quite popular with parents. I recommend a different approach: Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together?
We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.
Perhaps the biggest challenge for any middle-elementary math student is to master the multiplication facts. It can seem like an unending task to memorize so many facts and be able to pull them out of mental storage in any order on demand. Too often, the rote aspect of such memory work overwhelms students, eclipsing their view of the principles behind the math. Yet rote memory is not enough: A student may be able to recite the times tables perfectly and still be reduced to counting on fingers in the middle of a long division problem.
We will use the world’s oldest interactive game — conversation — to learn the multiplication facts one bite at a time. But first, let’s take some time to think about what multiplication really means.
Important note: times tables are not math. Math doesn’t need to be made fun; it already is fun. Memorizing your times tables is a rote activity, it requires a fair bit of repetition for most, and it may need to be made fun. Just saying.