Back in the day (you know, the ’80s), most of us were taught there was one way to add, one way to subtract, one way to multiply, and one way to divide. You sat at your desk, listened to the teacher, and did worksheet after worksheet till those formulas were drilled into your brain. There was no “creativity.” Usually, there was no context (how many times did you ask “Why do I need to know this?”). Your parents could be relied upon to help you at least until middle school. And there were definitely no calculators. Um, that was what we called cheating.
Oh, how the times have changed. Just check out this snapshot of math in Terri Gratz’s fourth-grade class at Meadowbrook Elementary School, in Golden Valley, MN: After the kids pull out blue calculators and their student reference books, Gratz says, “Raise your hand if you know which country has the biggest land mass.”
“Russia!” one boy announces.
“Which country has the most people?” asks Gratz.
A girl half raises her hand. “Either India or China?”
“China, right,” Gratz says. “So, how do we figure out what percent of the world’s population lives in China? Which two numbers do we need?”
It’s a tough question, but the class is up to the task: They soon figure out that they need to know how many people live in China compared with the rest of the world. Then they turn to their book to find a population chart. The world’s total population at that time, they learn, is 6,378,000,000. Gratz wants to know if the students think that’s the exact number. The kids smile and roll their eyes. As if! Then they look again to find China’s population: 1,298,840,000.
Throughout the lesson, Gratz and the students have been cheerfully lobbing questions and answers, and she’s clearly delighted that her class enjoys the give-and-take. Soon 28 sets of hands furiously punch numbers into the calculators, and then the first kid gets the answer: about 20 percent. Gratz asks her to come to the front of the class to show how she solved it.
Welcome to the world of “reform math” (the experts call it “inquiry-based math”), a catchall phrase for a group of new methodologies that aim to teach students how to reason their way through a problem instead of simply regurgitating a set of facts and formulas to get the answer (which is how most of us learned). If you have a child in elementary school, she’s probably learning under one of these programs. Think of it this way: If traditional math is a paint-by-numbers replica of the Mona Lisa, reform mathematics is more like performance art, where the audience is invited to paint the canvas. The goal is to engage, excite, experiment, and find creative solutions. Because when kids care about math and understand how it works in real life, experts say, they’ll be more likely to stick with it. More important, that ability to think outside the formula, so to speak, will be absolutely critical when they have to compete in the global economy. (And, given that ranking, the U.S. can use all the edge it can get.)
Now you’re probably thinking “Great! Fabulous! We’re raising the next generation of innovators!” That is, until you actually have to help your child with her homework and find yourself questioning whether you really know how to divide. Their new math looks and sounds very different from ours, and after you get over the shock that many actually get to use calculators, you’ll likely be faced with accusations like “You’re doing it wrong! That’s not how we do it in class!” Elaine Replogle, a mom of three in Eugene, OR, is all too familiar with this kind of frustration: “Because my husband and I don’t know the same methods or terms, the kids tell us we know nothing. And we both have Ph.D.’s!” To banish the frustration, we talked to teachers around the country to get a handle on the basic philosophies of the most widely used math programs so you can feel more prepared and, let’s face it, a little less clueless.
New Math Mission #1: Emphasize the process, not the solution.
This is a tenet that programs like Investigations in Number, Data, and Space as well as Everyday Mathematics share. (Don’t know the name of the method your school uses? None of the parents we spoke to for this article did, either! But a call to the teacher can fix that.)
This doesn’t mean the kids don’t have to get the correct answer. Instead, the goal is to teach them to understand how numbers interact, how to recognize patterns, and to experiment with different ways to get there. “Students are more comfortable switching strategies and exploring ways to find the answer,” says Jennifer Scoggin, who used Everyday Mathematics when she taught second grade at a New York City public school.
So take adding: When we learned how to add 349 + 175, we stacked up the numbers, added the ones, carried the tens, added those, and so on in order to get the answer (524). With Investigations, third-graders, for instance, explore different methods for arriving at the answer. They may add the hundreds, tens, and ones separately (300 + 100, 40 + 70, 9 + 5) or break the numbers into rounded chunks (350 + 175 = 525 – 1 = 524).
New Math Mission #2: Help kids “see” math.
This goes right along with the idea of providing different learners with different ways of understanding. In lower grades, students might use objects like cubes or tiles (known as manipulatives) during a subtraction lesson, or they might use the hundreds board, a grid with 100 numbered squares, to figure out the answer to a problem like 41 – 29: The kids put a finger on 41 and then count back to 29. “They can count by tens, by ones, or count forward from twenty-nine to forty-one,” says Scoggin, now a consultant. “It’s fun—like counting spaces on a board game.”
Keith Kinney, a fifth-grade teacher at the Parker Middle School, in Chelmsford, MA, uses the reform program Math Expressions and shares how it uses visuals to teach: When we learned to calculate the area of a rectangle, we memorized the formula: length x width = area. But Kinney’s fifth-graders draw a rectangle on graph paper; they can then simply count the squares to calculate. This process can help students internalize the formula (they’re seeing it and doing it on their own), teach them about geometry and algebra, and reinforce their multiplication skills. They then discuss the various solutions as a group.
New Math Mission #3: Introduce concepts—then introduce them again.
This technique is called spiraling, and it’s used in Everyday Mathematics, as well as in the Saxon method. Whereas we might have had our fractions lessons in one solid block, teachers now often circle back to concepts again and again to reinforce the skills.
Ruth Nettelhorst, a third-grade teacher at the Nancy Cory elementary school, in Lancaster, CA, describes it like this: “Saxon introduces concepts in a way that builds upon the previously learned skills. It moves them from the concrete to the abstract in a very logical, methodical way.” And that makes sense to us.