Is there a crisis in math education? Lots of people seem to think so.
From worries about where the United States ranks on international tests to arguments over the Common Core, the way teachers teach and students learn math continues to be debated widely, leading to proposed changes in the ways mathematics is taught. But what really works for students in the math classroom? And when changes to the techniques are necessary, how can they be implemented effectively and appropriately across an entire system? This Text to Text lesson plan confronts those questions and more.
As millions of students return to math classes across the country to face new teachers, new techniques and new standards, we pair Elizabeth Green’s 2014 New York Times Magazine article “Why Do American’s Stink at Math?” with the Edutopia video “How to Make Math Meaningful.”
Elizabeth Green’s “Why Do Americans Stink at Math?” tells the story of Akihiko Takahashi, a teacher who helped change the course of mathematics education in Japan in the 1980s by adopting innovative practices. The sources of those techniques were teachers and organizations in the United States, who at that time were calling for changes in the way math was taught in their own country.
Ms. Green’s piece details Mr. Takahashi’s work encouraging discussion among students using strategically constructed example problems and practicing jugyokenkyu, or lesson study. Ms. Green places Mr. Takahashi’s work in the broader context of the history of math education, touching on the new math of the 1960s and today’s Common Core standards.
We decided to pair Ms. Green’s article with an Edutopia video that shows what teaching conceptual understanding can look like. In the video, Mr. Abrahamson, an associate professor of secondary mathematics education at the University of California, Berkeley, demonstrates teaching the concept of ratio and proportion through experimental approaches, which he says can “help kids see the world mathematically.” He argues that “mathematics is all about making sense of the world,” and that “unless we can ground all this scribbling in something concrete that we really get, we’ll never understand what we’re doing.”
That sounds very similar to one of Ms. Green’s central affirmations: “To cure our innumeracy, we will have to accept that the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work. We will have to come to see math not as a list of rules to be memorized but as a way of looking at the world that really makes sense.”
We invite students to use both of these sources and the questions below, as well as the Going Further resources, to consider the complicated and important question: What are the best ways to teach and learn mathematics?
Key Question: What are the best ways to teach and learn mathematics?
Activity Sheets: As students read and discuss, they might take notes using one or more of the three graphic organizers (PDFs) we have created for our Text to Text feature:
Text 1: Excerpt from “Why Do Americans Stink at Math?” by Elizabeth Green
Takeshi Matsuyama was an elementary-school teacher, but like a small number of instructors in Japan, he taught not just young children but also college students who wanted to become teachers. At the university-affiliated elementary school where Matsuyama taught, he turned his classroom into a kind of laboratory, concocting and trying out new teaching ideas. When Takahashi met him, Matsuyama was in the middle of his boldest experiment yet — revolutionizing the way students learned math by radically changing the way teachers taught it.Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun.Takahashi quickly became a convert. He discovered that these ideas came from reformers in the United States, and he dedicated himself to learning to teach like an American. Over the next 12 years, as the Japanese educational system embraced this more vibrant approach to math, Takahashi taught first through sixth grade. Teaching, and thinking about teaching, was practically all he did. A quiet man with calm, smiling eyes, his passion for a new kind of math instruction could take his colleagues by surprise. “He looks very gentle and kind,” Kazuyuki Shirai, a fellow math teacher, told me through a translator. “But when he starts talking about math, everything changes.”
Text 2: “How To Make Math Meaningful” by Zachary Fink and Dor Abrahamson
For Writing and Discussion
- Do you agree with Ms. Green’s claim in the magazine article that “the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work”? That students aren’t learning how to think mathematically when teachers focus only on procedures, and not on what the procedures mean? Or is this a false definition of “traditional mathematics”?
- Do you believe teaching with a stronger emphasis on conceptual understanding, like the kind that Mr. Abrahamson explains, will improve students’ performance in math?
- According to Ms. Green, Mr. Takahashi’s main inspiration for improving mathematics in Japan came from American teachers. Why might the ideas Mr. Takahashi used have been accepted in Japan while not accepted in America?
- What are some of the potential obstacles one might face in trying to change the way mathematics, or any subject, is taught? Consider why various groups — politicians, teachers, parents, and students — might object to or support changes in the way schools are run and subjects are taught.
- Think back on your own history as a math student. What teaching-and-learning techniques have worked best for you? What do you think math class needs more of? What do you think math class needs less of? Why?
Join the Debate
Elizabeth Green uses the relationship between math education reform movements in the United States and the way math is taught in Japan to make a larger point about why “Americans Stink at Math.” She argues that the traditional way of teaching math and the way we support and train our teachers leads to underperforming students. But Tom Loveless, a former sixth-grade teacher and Harvard public policy professor, doesn’t accept her reasoning.
Read his critique for the Brookings Institution, “Six Myths in The New York Times Math Article by Elizabeth Green.” Then write a response to either Ms. Green or Mr. Loveless weighing in on the debate.
Or, if you would prefer to get beyond the specifics of the article and debate how mathematics should be taught, read this Op-Ed by two mathematicians who call for more real-life problems in math curriculum. And consider this piece by a political science professor that started an uproar by suggesting that algebra was unnecessary, inspiring this related lesson plan from the Learning Network. Finally, you might interview a few math teachers in your own school, and add all these points-of-view to the ones you have considered in the Text-to-Text pairing to take your own position on how math should be taught.
Test your math skills on these sample items from the New York State eighth-grade math test. Do these problems seem easy, hard, or just about right for an eighth grader? According to New York State, only 22 percent of the eighth graders who took the Common Core math test passed.
Or try your hand at these math problems from an international eighth-grade exam that the Times columnist Nicholas Kristof featured in his Op-Ed “Are You Smarter Than an 8th Grader?” Mr. Kristof was making a similar claim as Ms. Green — that American students are underperforming in math — though a science reporter for Slate disagreed.
Do You Have Math Anxiety?
Do you get nervous when solving math problems? What about your parents? Read this article about math anxiety and how it can be unwittingly passed on from generation to generation. And follow up with this piece by Jessica Lahey, who gets some advice from teachers about how best to solve math problems while avoiding math anxiety.
Then, write your own column about how to deal with math anxiety, perhaps interviewing friends, relatives or teachers to find out what suggestions they have.
You can find many more math-related lesson plans on our bloghere.
You can read more about Elizabeth Green’s work in this interview, and read about her book “Building a Better Teacher” in this interview.
And K-12 education isn’t the only schooling under the microscope. People are rethinking the way college courses are taught. For example, this recent opinion piece asks “Are College Lectures Unfair?”