Q: Last year in third grade, we thought our son, Jared, learned his times tables. Now in fourth grade, he's struggling in math. His teacher says he hasn't developed "automaticity" and suggests drilling him on multiplication facts. What does that mean? And what might make "drilling" fun?
A: The teacher means that Jared can't retrieve his times tables automatically. So when solving problems, he has to stop and figure out, "Now, what is 3 times 6 again?" And that slows him down.
This is common, says elementary teacher Nancy Bourne of Jupiter, Fla., who was given a 2014 Presidential Award for Excellence in Science and Math Teaching.
"First, check to make sure that he understands the conceptual model that underlies multiplication," she says.
This is important, says Bourne, because rote memorization can cover up lack of understanding. "Math educator Marilyn Burns often cites a time she was helping a struggling fourth-grader," she says. "She asked him to explain what he knew about multiplication. He said, 'Well, 6 times 8 is 48.' She asked about 6 times 9. He said he hadn't learned that one. Asked how he knew the answer to 6 times 8, he said, 'That's easy. Goin' fishin', got no bait, 6 times 8 is 48.' He'd memorized a fact, but multiplication was still a mystery to him."
If Jared's concept mastery is weak, ask his teacher for activities to develop it. Bourne loves working with number arrays (a set of numbers or objects that follow a specific pattern, often in rows, columns or a matrix) to develop understanding.
"A number array representing a box of chocolates with 5 rows of 6 pieces makes some pretty tempting multiplication connections!" she says.
Once Jared "gets" multiplication, work on automaticity -- the ability to retrieve facts immediately without using working memory. In other words, knowing them by heart.
First, suggests Bourne, "Clue him into helpful patterns and rules, such as 'When multiplying by 5, the product will always end in a 5 or 0.' Or the commutative property rule states that it doesn't matter the order; you still get the same answer. When kids learn that 6 times 4 and 4 times 6 yield the same answer, it's a eureka moment."
Second, have some fun. Bourne likes the book "Times Tables The Fun Way," by Judy Liautaud and Dave Rodriguez (City Creek Press; 1999), for its kid connections, such as "You have to be 16 to drive a 4-by-4." Teach mnemonic devices such as "1, 2, 3, 4. I like math, let's do some more!" (12 equals 3 times 4.) Or "5, 6, 7, 8, I think math is really great!" (56 equals 7 times 8.) Play fast games with two dice; have players alternate between adding and multiplying the two numbers. The first to get a total score of 100 wins.
Third, work for fast retrieval. "Bottom line, even with all the tricks, most kids still have to practice, practice, practice to be speedy," says Bourne. "Flashcards get great results. Websites such as multiplication.com, sumdog.com and apps such as Brownie Points and That's a Fact help, too.
"Just five minutes a night goes a long way to enshrining these in the brain forever!"
(Do you have a question about your child's education? Email it to Leanna@aplusadvice.com. Leanna Landsmann is an education writer who began her career as a classroom teacher. She has served on education commissions, visited classrooms in 49 states to observe best practices, and founded Principal for a Day in New York City.)