From kindergarten through fourth grade, addition through division, various levels of “math facts” can be found in just about every elementary classroom. You probably remember them from your own school days—you know, those pages of equations combining all the digits between one and ten or even twelve, the ones you were supposed to memorize backward, forward and upside down…or else!
Well, math instruction may have advanced since then, but if you’ve got an elementary school kid, you’ve probably noticed that math facts are as crucial as ever. If this sounds like pressure, it often is—not just for kids but for teachers, too.That’s why, as the school year ends, packs of flashcards have come to join summer reading lists around the country as common tools for learning at home.Practice, practice, practice, so the line goes, and your child can achieve “automaticity”—perfect, instant recall.
Parents, if you’re wondering what it really adds up to for your kids on summer days, you’re not alone. Are daily summer flashcard drills the “new math” for American kids?
Not at all, say experts in the field. Sure, you can find store shelves packed with workbooks, and you can download math fact sets at dozens of sites online. And yes, says Michael Shaughnessy, Ph.D., President of the National Council of Teachers of Mathematics, elementary math can be “almost like learning to play the piano—even doing a little bit each day can help.” But, he cautions, true math learning goes way beyond rote flashcards and instead challenges the mind to new and exciting levels of reasoning.
In fact, explains Aki Murata, Ph.D., Assistant Professor of Elementary Mathematics Education at Stanford University, straight math memorization can even endanger real math learning. “Drilling is deceptively effective sometimes,” she says. “Kids can learn to spit back what you say, and then you think, ‘Oh, my kid is understanding,’ but if they haven’t had the chance to learn the concepts deeply, it’s like building a huge building without a foundation at the bottom.” Problems may not show up immediately, she says, but later, when the student attempts more advanced work like algebra, the ideas simply won’t make sense.
So what does help? Here is some practical advice from these experts and others:
Use everyday life, every day. Steven Sheldon, Ph.D., Director of Research at the National Network of Partnership Schools at Johns Hopkins University, works with schools to strengthen family involvement that can boost student learning. Instead of worrying about fancy or expensive curricula, he says, families can provide crucial assistance by demonstrating "mathematics in the normal course of life." Small children, for example, can make huge gains in number sense just by rolling dice, counting, and adding. An older child planning a birthday party can practice division concepts by arranging guests into groups of four, or by figuring out how many cookies will go around. To be sure, adds Sheldon, "maybe you don't want your child figuring out the interest on your unpaid credit card balance" but "you do want to see him do things like practice addition and subtraction by creating an allowance budget, going to market and comparing prices, or helping to make change." In short, he urges, everyday life can be as effective as any flashcard when it comes to building math skills that will last.
- Question, question, and explore. "It's not that procedures and facts aren't important in math," says Shaughnessy, but don't be lulled by a kid who just says, "Well, I just knew it." Even with very small kids, ask questions like "Okay, so how did you get that?" or "Well, I thought of it a different way. What about this?" Encourage young mathematicians to talk, talk, talk about their "math reasoning." And as they get older, don't hesitate to invite them to deepen and expand the problems themselves. "Let's say," says Shaughnessy, "that a kid correctly recites a math fact like 8+7=15. That's great, but now there's even more fun. Add some digits, for example, and ask 'What is 18+7? How about 18+17?" With approaches like this, mathematics comes alive as a process, not just a body of fact.
- Take advantage of online resources. Education.com has assembled grade-by-grade hands-on learning activities in all K-12 subjects, including math. If you haven't done so already, explore and enjoy! Shaughnessy's highly regarded organization, the National Council of Teachers of Mathematics, also offers an array of free, online math materials designed by Council professionals.
- Use flashcards. But use them to build understanding. True fluency with math facts, Murata suggests, happens when students truly understand the concepts underlying each one. That's why, she explains, it's great to let kids explore math by counting objects, making drawings, or just counting with their fingers and toes. "Do plenty of that," she says, "and then when the kids start working equations, the learning goes much faster." So the next time you pull out a set of flashcards, she suggests, plan to select at least one card a day and invite your child to make a "math story" about it. For a first grader, you might talk about how "Roger and his brother had three kids over to play. How many kids were there altogether now?" For an older elementary student, you can explore more complicated operations like division: "We are making 20 popsicles," you might ask, "and five people are coming over. How many popsicles can each one have?" Write down one of these a day for an entire summer, she suggests, and perhaps even create a "math facts story book" by the end!
Above all, say all of these experts, make sure you work to build a positive attitude toward math. Pay close attention to your child's saturation point. If your child is frustrated or overwhelmed don't force compliance. Instead, try to understand what's not making sense, and keep exploring different ways to explain it concretely. Everyone, says Shaughnessy, can get confused sometimes, and we need to model ways to get help and to demonstrate that problems with understanding math can be overcome. If we proceed with confidence and patience, he believes, our children's long term gains may be nothing short of a "national cultural shift in our country's view of math"—from cryptic and frustrating to clear and exciting. "I am dedicated," he explains, "to not having yet another generation of people going to parties and saying, 'I was just never any good at math.' I just don't want to hear that anymore."