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The familiar high school math sequence – Algebra I, geometry, Algebra II, trigonometry – is so ingrained that it’s easy to forget there are other ways to learn mathematics. In fact, if we look at countries that outperform the United States on international math assessments like the Trends in International Mathematics and Science Study (TIMSS), we might discover superior routes to mathematical mastery. On the 2007 TIMSS, U.S. fourth-graders finished behind students in eight Asian and European countries, while U.S. eighth-graders were behind students in five Asian countries.
Among the top-performing countries, no pattern in pedagogy emerges. There is, in fact, wide variety in mathematics teaching practices worldwide, as documented in the 2006 article, “What Does Teaching Look Like Around the World?”
But if the key to high math achievement isn’t a particular pedagogical approach, what is the answer? William Schmidt, an expert on math education at Michigan State University, has identified three issues: the coherence and depth of the curriculum, the quality of assessments and the content knowledge of teachers.
Math curricula in the U.S. tend to be “a mile wide and an inch deep,” Schmidt said in a 2003 speech at the “Summit on Mathematics” called for by U.S. Education Secretary Rod Paige. U.S. curricula tend to introduce too many topics in the early grades, and they do so arbitrarily. While students in top-performing countries transition to algebra, geometry and even basic trigonometry in middle school, U.S. curricula emphasize basic computational skills through eighth grade and even beyond.
“Particularly in the early years, the expectations expressed in U.S. state standards far exceeded those in the countries that performed best on the TIMSS 8th grade assessment,” Schmidt and Leland S. Cogan wrote in a November 2009 article in Educational Leadership.
U.S. textbooks are similarly wide-ranging.
“Not surprisingly, in the face of documents that embody incoherent and unrealistic intentions, [teachers] teach substantially different content – often even within the same state, district, or school.”
American math assessments rely heavily on multiple-choice questions – which are particularly poor at signaling where a student’s thinking went wrong. Did a student get a question right simply by guessing correctly? Did an error result from a sloppy miscalculation, or from a fundamental misunderstanding?
A 2009 study by the American Institutes for Research analyzed math assessments given to third-graders in Massachusetts and Hong Kong. The study’s authors found that 71 percent of questions on the Massachusetts exam were multiple-choice, while in Hong Kong only 14 percent were. Furthermore, the Hong Kong test was much more difficult: 97 percent of the Massachusetts questions were classified as being of low computational difficulty, compared to 61 percent of the Hong Kong questions.
It’s no secret that American elementary and middle school teachers often have weak math skills. “This is to be expected because most teachers – like most other adults in this country – are graduates of the very system that we seek to improve,” Deborah Loewenberg Ball, dean of the University of Michigan School of Education, and colleagues wrote in a 2005 American Educator article.
In 2009, Massachusetts became the first state to require elementary teachers to pass a mathematics subtest before earning certification. Just 27 percent of those taking the test at its first administration achieved passing scores.
Contrast this with Singapore, where students score at or near the very top of the TIMSS rankings. Future teachers graduate in the top third of their high school class and receive a free, four-year education courtesy of the government. They are also very well-compensated when they enter the profession: Stanford University professor Linda Darling-Hammond, an expert on teacher quality, reports that beginning teachers in Singapore earn more than beginning doctors.
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