Refreshingly, we have answers to those questions above—and a correction, I might add, to the perception that the USA continues to fail at math on the world scene.
Getting to the answers can start with Peg Tyre’s terrific article on “The Math Revolution” (Atlantic Monthly, March 2016), which spotlights a sub-culture of math wiz teenagers who are bucking the many-years American trend of math failure on the world scene by zooming to the top of international math competitions. Indeed, for the first time in 21 years, the U.S.A. team won first place last year at the International Mathematical Olympiad.
This culture of math wizzes is quite an expanding phenomenon across the country, as is quite apparent in Ms. Tyre’s article. She enumerates many of the prominent math enrichment camps that are highly sought after—like MathPath, AwesomeMath, MathILy, Idea Math, SPARC, Math Zoom, and Epsilon Camp.
Many of the parents out there who are already in the know about these math camps and sending their children to them regularly, see the utter failure that pervades our elementary and middle school math programs in the public schools. Tyre reports that the source of this poor achievement is found in the second and third grade. Inessa Rifkin, co-founder of the Russian School of Mathematics, says that in these two grades, “instruction…is provided by poorly trained teachers who are themselves uncomfortable with math.” Basically, the issue with poor instruction is about misguided emphasis on memorizing rules and then following the procedures. Math, when poorly taught, is mostly about computation and rote repetition. Ms. Rifkin likes to urge her students to “forget the rules! Just think!”
In fact, thinking is precisely what separates the weak math programs from the truly exceptional. Real math thinking is found in story problems, in open-ended math problems that have a variety of solutions, and interpreting complex word problems. Young children, we must all remember and embrace, are creative and surprising thinkers, when given a chance to express themselves and ask questions. Young children will bound back and forth between simple questions and mind-boggling complex questions. The tragedy that is occurring within the poorly taught math classroom is that, according to Inessa Rifkin, “if the teacher doesn’t know enough mathematics, she will answer the simple question and shut down the other, more difficult one.”
I see this all too often in the classroom, where the well-meaning teacher will brush over and dismiss the complex and seemingly absurd question, not seeing the depth that is really being revealed in the question, and will move on to another student who asks a straightforward and simple one. The controversy about teaching math, as Peg Tyre points out in her article, is a controversy that we educators and school heads have heard from parents for many years now. Basically, it goes like this: most parents have been screaming for more rote memorization—knowing and reciting math facts. These are the “drill and kill” parents who can’t get themselves unstuck from the brutal and boring way that they themselves learned math when they grew up thirty years ago. The right side of the argument is that conceptual knowledge should be uppermost in the math classroom. All the professional (and high earning, I might add) STEM-field parents out there, the ones who know what they’re talking about academically, understand the exploratory, problem-solving center of the world of mathematics.
The best practitioners of this problem-solving approach to mathematics is, unfortunately, mostly found in these high-priced, after school programs. Their pedagogies all follow a similar pattern: the teachers task a small number of students, grouped by ability, with open-ended questions that can be solved in any number of ways. Students are not being asked to apply a previously taught algorithm or sequenced procedure; instead, they need to dive first into what the problem is really asking us to solve. The students are then given utter freedom to tackle the problem and then defend their strategies to the class. What is great about this approach? Let me offer a political campaigner’s take on the answer: It’s the thinking, stupid!
The best math classroom—in fact the best learning to be had—happens when students engage in reasoning, investigating, conjecturing, analyzing, and predicting. When students have to think problems through, when they have to apply creative approaches, when they have to puzzle out different solutions—that’s real math, and even more it is real learning.