And while there may still be some adults who say they are nostalgic about the manner in which they learned math, we have to acknowledge it wasn’t very effective for large numbers of individuals.
We are no longer just asking students to memorize formulas and plug in the answers to problems but are making sure they can compute and understand the math they are doing at a deep conceptual level. It’s that kind of learning that will prepare young people for 21st century careers and will ensure they are competent with math for life.
If you learn the subject this way, when you come across an unfamiliar math situation years later, long after you have forgotten the rules used to solve a problem, you should still be able to reconstruct the math using your core knowledge and build to the solution. It’s somewhat like riding a bike. It may take you a while to learn how to balance, push the pedals and take off on your own. However, once you get it, it is a skill you own forever.
And while there may still be some adults who say they are nostalgic about the manner in which they learned math, we have to acknowledge it wasn’t effective for large numbers of individuals. The evidence? The United States is currently near the bottom of developed countries in math performance rankings, and surveys show math anxiety is high among American adults. About one- third say they’re not good at math, according to a study by Change the Equation, which works to promote STEM literacy. More than half of adults say they’ve had trouble doing some type of everyday math, such as estimating distances or weight. Nearly one-third would rather clean a bathroom than solve a math problem.
Further, a recent study also found math-anxious parents who help their children with homework create math anxiety in their children — a multi-generational ripple effect. Parents naturally want to help with homework, and we certainly want to encourage that. But we have to help ease the stress at that kitchen table —and improve student success —by empowering parents with more information about the math their kids are learning.
It took me a while to come around to understanding what we need to do differently as math educators. Early on in my career teaching high school and university math, I was perplexed when students would do well with daily lessons and homework but then do poorly on a test. When we went over the test, students would say “If I had known what you wanted me to do, I could do that,” meaning that if they had known the strategy to be applied, they could do the mechanics. At first I thought it might be a problem with directions, but that wasn’t it. Rather, my students did not really know why they were doing what they were doing. They had merely memorized a particular rule that they could use when I told them very explicitly what to do.
Further, most traditional textbooks are setup to perpetuate memorization of particular rules without developing an understanding of the mathematics. Problems in a particular section or chapter reflect whatever rule is being taught. However, when the problems from different sections are interspersed on a test, students often can’t identify which strategy works for each problem, become frustrated and don’t do well.
For example, one section might focus on multiplying a given number by 10. A student becomes familiar with a pattern of “moving the decimal to the right” or “adding a zero to the end of the number” without understanding the product is 10 times larger than the given number. The student does great in that section and appears to have mastered the concept. Later, when dividing a given number by 10, the student might memorize that the decimal is “moved to the left” or that an ending zero is “dropped” without understanding the original number is one-tenth of the original size. The student still does well while working in that section. However, when multiplication and division problems are intermingled, it is common to hear a student say “Which way do I move the decimal?” Here is where the understanding of what is being done and why it works becomes critical. Students must be able to grab the appropriate knowledge when it is needed.
Today’s approach also emphasizes teaching more than one strategy or model for solving problems. You can think about the need for students to have a deep understanding of math and various ways for solving problems, sort of the way you might think about travelling between two cities. If you are only familiar with the interstate and it becomes blocked, do you just stop and sit on the side of the road until it is cleared? No, you understand the goal is to reach your destination and you try something different.
That’s what we want students to do with math. Understand what defines success, determine what is needed, and have various routes available to them.While parents are starting to see the benefits of teaching math this way, they often don’t know how to help their children. That can be frustrating. Fortunately, though, educators are developing resources that can help.
At the nonprofit where I now work, for example, we make parent tip sheets available. School- and district-sponsored family math nights also have been very successful. In Lafayette, Louisiana, for example, the school district officials packed the CajunDome with hundreds of people for a family math night in which children led adults in math lessons. The district also has put together and sends home parent newsletters for each new math unit students are doing.
In addition, more online resources are available for parents. The New York State Education Department has a large library of resources aimed at informing parents on its EngageNY site. In Rhode Island, the Barrington district created a fun and informative website that helps explain math terms that might be new to today’s parents, such as ten-frames, for example, a graphic organizer used to teach kids addition and subtraction facts for numbers that add up to 10.