All teachers want their students to succeed in math.
Some teachers view that success as total mastery over the basic arithmetic that seems to be the only math many adults ever use, so to speak. Some teachers view math as no different from art or history or language, in that the best way to learn it is to dive in, explore, and discover through curiosity coupled with trial and error. Teachers’ belief systems about math tend to fall somewhere along that spectrum, and I admit I fall closer to the second camp.
Former NCTM president and Into Math co-author Matt Larson, who wrote Balancing the Equation: A Guide to School Mathematics for Educators and Parents, is quick to point out that since the dawn of math education in the US, there has been a battle between the traditionalists and the pioneers. He points to Nicolas Pike’s 1788 Arithmetic, a textbook devoted to the rules students practice; and then to Warren Colburn’s An Arithmetic on the Plan of Pestalozzi, a textbook in which students answer carefully scaffolded questions in order to discover the rules on their own. Even then, educators were divided: some saw math as rules to master and others saw it as ideas to discover.
1957: The First “New Math” Method
The math pedagogy pendulum that swings back and forth came into special focus in 1957, when the Soviet Union launched Sputnik, motivating the US to amp up math and science education. Elementary students were suddenly encountering “new math” in school and engaging in topics usually reserved for college undergraduates, such as modular arithmetic and Boolean algebra. They were challenged to work in teams to solve novel problems, with little background. Several sets of ambitious math standards along these lines were developed and implemented around the country—but as this approach continued, real problems emerged. While the standards addressed content, they left out context. The psychology of learning wasn’t yet at the forefront for students or their teachers, and a new way of teaching math effectively wasn’t yet clear. Many teachers felt just as lost as their students!
Unsurprisingly, there was a public backlash to the “new math” that will probably sound familiar. Matt Larson often refers to a 1972 article in the Washington Post in which parent James Shackelford complained about his daughter’s elementary school math homework. As a Ph.D. chemist, he claimed, he should be able to understand it, but couldn’t because of how unnecessarily complicated it seemed. Similar thinking led to a back-to-basics movement in the 1970s that was aimed at getting students to just master simple arithmetic.
1989: The Second “New Math”
Throughout the 1980s, between higher expectations of students and an elevated need for math-savvy workers, math education became the focus of a range of research efforts. In many ways, this era became the dawn of today’s learning sciences. In this interesting arena, the National Council of Teachers of Mathematics put forth its first unified set of math standards.
Many math experts praised the standards’ emphasis on mathematics as a process instead of a product. However, as with the first “new math” movement, backlash was swift. Opponents said the standards and “new math” method did not properly emphasize using the standard algorithm and building fluency in the rote arithmetic and algebra necessary for both college-level and real-world math. After all, how many professionals really need to do much math beyond the four basic operations? Moreover, in another case of history repeating itself, critics claimed the standards didn’t help teachers who disliked or didn’t feel capable of teaching math. How, they asked, can you successfully teach something you hate or don’t understand?
2010: What Is the “New Math” Called, Again? The Newest “New Math”
The Common Core State Standards were released in 2010, marking the NCTM’s latest efforts to standardize mathematics for K–12 students across the US. Diane Ravitch, a historian at New York University, wrote an influential New York Times editorial in 2016, not unlike Ph.D. chemist James Shackelford’s 1972 article in the Washington Post about his daughter’s math. Ravitch argued that the “development of the Common Core. . . was a rush job, and the final product ignored the needs of children with disabilities, English-language learners, and those in the early grades.”
Ravitch is not alone in her criticism, with social media abound featuring diatribes and angry photos of poorly written homework and test questions. And it’s worth clarifying that the term “Common Core” is sometimes mistaken for a curriculum, assessment, new way to do math, or list of ways to teach. But judge for yourself; the standards are freely available! They’re brief—but highly specific—guideposts for where students should be in their mathematical development throughout grade school. For example, per the new Common Core math, by the end of first grade, a student should be able to count up to 120. The standards themselves acknowledge the gray area: Of course there are students who will fall behind, and of course there are students who will realize that the next number is 121.
The standards were developed with educators of all stripes weighing in, including committees of experts in child development, learning sciences, early education, graduate-level mathematics, and everything in between. Their perception was that these new standards will not only help students count up to 120 in first grade, but also, they’ll help students learn to reason, instead of memorize, by following a carefully designed sequence. The focus is on expanding students’ understanding of how numbers and formulas work.
Can this approach foster a disposition of curiosity and better prepare students to eventually fill higher-level jobs—jobs that may not even exist as they begin kindergarten? That’s certainly the goal. Also, a more flexible approach that emphasizes reasoning—and a certain type of creative, “let’s try this” mindset toward problem-solving—will ultimately help address and close opportunity gaps. It encourages all learners to expand their thinking and make connections between math and art, philosophy, music, politics, science, and anything that interests them.
Matt Larson says, “We must…attend to how students experience math…because it is their dissatisfying experiences…that cause some students to shy away from math as a subject. Simply put, equitable math instruction must provide access and empower students to see themselves as capable learners, users, and doers of mathematics.”
Fear not—students are still adding, subtracting, multiplying, and dividing. Fractions and decimals aren’t going away, nor are areas of circles, scatter plots, and the Pythagorean Theorem. The method of multiplying you were taught hasn’t stopped working, and I promise teachers aren’t trying to perpetually confuse their students. As you’ve seen, the term “new math” is perennially evolving, and there’s something to be said for where we are now in the evolution of math standards and approaches to teaching.
What Does This Have to Do with Me?
While math history is one thing, how does it affect you, the teacher, parent, or guardian reading this who is perhaps frustrated by not knowing how to teach a particular skill or follow an unfamiliar instructional model? There are a few key things to keep in mind.
Parents and guardians: It’s okay if you stick to the method you were taught and are most comfortable with. The Common Core standards don’t tell anyone how they must do math, only when they should be learning certain math concepts, ideally. Feel free to share with your children how you would solve a math problem or perform a calculation. And whenever possible, switch roles and try to have your child show you how they do it.
Teachers: It’s okay if children show you methods you haven’t taught them or are trying to avoid—in fact, this can be an excellent way for them to learn or clarify what they know. There are many ways to approach problems in math, and all good problems worth solving have more than one way of finding a solution.
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