AAMERICA A a math problem. Its students have been poorly ranked on international mathematics exams for decades. In 2018, 15-year-old Americans ranked 25th in the OECD, a club of predominantly rich countries. American adults ranked fourth behind in numeracy compared to other wealthy countries. Up to 30% of American adults are only comfortable with simple math: basic arithmetic, counting, sorting, and similar tasks. American employers are desperate for science, technology, engineering and math skills: nuclear engineers, software developers and machinists are scarce. And while students’ math scores are bad enough now, they could get worse. On the National Assessment of Educational Progress (NAEP), a national exam, the scores of 13-year-old students have fallen by five points in 2020 compared to their peers in 2012. The status quo does not hold. But teachers and academics cannot agree on the next step.
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The American math problem is over a century old, says Alan Schoenfeld of the University of California at Berkeley. In 1890, high school was an elite enterprise: less than 7% of 14-year-olds were enrolled and they were educated in rigorous math. At the start of World War II, when army recruits were to be trained in the math needed for basic bookkeeping and marksmanship, nearly three-quarters of children between the ages of 14 and 17 were attending high school. The Cold War sparked a second strategic mathematical panic in the 1950s. A new mathematics curriculum, focused on conceptual understanding rather than memorization, was developed after the launch of the Sputnik satellite by the Soviet Union. Then this new program was rejected in a return to fundamentals in the 1970s.
Mathematics education became a concern again when America began to fear being overtaken by Japan. In 1981, the secretary of education appointed a commission to evaluate the program. He produced a report called “A Nation in Peril”. “If a hostile foreign power had attempted to impose on America the mediocre educational performance that exists today,” the report says, “we might very well have viewed it as an act of war.
Since the 1990s, however, mathematics has become more political. Curators typically campaign for classical mathematics: an emphasis on algorithms (a set of rules to follow), memorization (multiplication tables and algorithmic processes), and teacher-directed instruction. Students in these classes focus on the basics, exploring concepts after learning traditional skills, says Bill Evers of the Independent Institute, an Oakland think tank. These methods are familiar to many. For two-digit addition, students would learn a paper-and-pencil method. Add 27 + 45 by stacking 27 over 45. Add the right column (7 + 5 = 12). Write down the 2 and wear the 1 in the left column. Add the left column (1 + 2 + 4 = 7). Write 7. The answer is 72.
Progressives generally favor a conceptual approach to mathematics based on problem solving and number sense acquisition, with less emphasis on algorithms and memorization. Unlike the conservative strategy, students would learn several ways to solve a problem, using objects and other means, before learning algorithms. To solve 27 + 45, students could add the digits instead of the ones (7 + 5 = 12), then instead of the tens (20 + 40 = 60), then add them to get 72. Or they could realize that 27 is 3 digits of 30. They would add 3 to get to 30. Then add 45 and subtract 3 to get 72. Conceptual mathematical strategies encourage students to find many potential solutions for the same problem to develop meaning. numbers, rather than relying on an algorithm.
Although most teachers agree that math education in America is below average, they have not been able to agree on how to improve it. Copying the methods used in highly ranked mathematical countries such as Singapore would be one way. But that would require agreement on what is actually taught in other countries. Successful Asian studies programs reflect the classic position, Mr. Evers said. “Which country do you think has fully embraced progressive education and has been very successful? China is very teacher-led. Singapore’s math is the best in the world. It’s not progressive, ”says Evers. But Schoenfeld believes countries like Japan and Singapore are implementing conceptual study programs.
Part of the confusion stems from the haphazard implementation of the most recent math curriculum, the core curriculum. Implemented in 2010 under the administration of President Barack Obama, 41 states and the District of Columbia have adopted the Principles. Texas, Florida and several others have pulled out. Although it was initially a bipartisan effort (Jeb Bush and other conservatives supported the Obama administration’s effort), it was ultimately criticized by both sides. Some see it as an example of progressive education, while others think it was not progressive enough. Now that the test results are in, many conservatives say the falling scores show the failure of core teachers and progressive teachers. But supporters of the current program are not ready to give up. While NAEP the scores decreased among the 13-year-olds, they remained stable among the nine-year-olds, who would have studied the core throughout their school life.
To further complicate the mess, far-left activists have paired conceptual mathematical methods with more radical concepts. Many opponents of conceptual mathematics believe that the common core, and conceptual mathematics in general, prohibits rote teaching, such as in the multiplication tables. A prominent math education scholar at Stanford University, Jo Boaler, says memorizing multiplication tables is not necessary. The Conservatives have taken this idea as an example of liberal activism gone wild. But Mr Schoenfeld claims that this does not correspond to progressive mathematical values.
Some activists have also linked conceptual mathematics to “social justice mathematics,” the concept that mathematics should be used to help students solve real-world problems and assess the world around them. Nicknamed “mathematics awakened”[s]And tagged with titles such as “In California 2 + 2 = 4 May Be Thought Racist” (as a letter to the the Wall Street newspaper harrumpé), he did little favor to conceptual mathematics by association.
The debate over mathematics in America is polarized and confused. As other countries implement math programs with a balance between rote learning and conceptual learning, America continues to shift from pole to pole decade after decade. Just like the politics of the country, in other words.■
This article appeared in the United States section of the print edition under the title “The maths wars”