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math education

If the United States is going to remain economically competitive and a leader in new technologies, the capacity of its high school and college graduates to do math must improve. Two decades of international comparisons show that the longer American students are in school, the further they fall behind their counterparts in other developed nations. William Schmidt, a Michigan State University professor who studies how U.S. students match up against those in other countries,  says most American eighth-graders cannot do relatively simple tasks – such as add fractions – that students in other countries master by fourth grade. Just under half of U.S. eighth graders can correctly place three fractions – 2/7, 1/2, 5/9 – in ascending order. This question, from the 2007 National Assessment of Educational Progress (NAEP), was categorized as “medium” in difficulty, and students could even use calculators to solve it.

“This is not mental Olympics,” Schmidt says. “It’s not about one country doing a little bit better than others. It’s really about our kids being able to function.”

According to the “Nation’s Report Card,” as NAEP is widely known, only 39 percent of fourth-graders, 34 percent of eighth-graders, and 23 percent of twelfth-graders score at or above the “proficient” level in mathematics. In colleges, demand for remedial math education is high. A 2009 report from Jobs for the Future, a policy and advocacy organization focused on education and workforce opportunities, found that 60 percent of community college students must take at least one so-called “developmental” course before enrolling in college-level classes. Many high school graduates arrive at college needing to learn not just basic algebra but also basic arithmetic.

The sum of these statistics is this: math education in the United States “is broken and must be fixed,” according to the National Mathematics Advisory Panel’s 2008 report. “This is not a conclusion about any single element of the system. It is about how the many parts do not now work together to achieve a result worthy of this country’s values and ambitions,” the authors of the report stated.

Skip Fennell

Francis “Skip” Fennell, a member of the advisory panel and former president of the National Council of Teachers of Mathematics, adds: “More and more of our kids are taking algebra than ever in our history, and yet we have high school performance that is either stagnant or declining, and we have too many kids moving into higher education and having to immediately take remedial classes. To me, that suggests a system that is more than a little out of whack.”

Here are six aspects of the problem that math and policy experts say must be addressed:

1.  Standards. All 50 states have content standards that say what students should learn in mathematics. Although the standards vary, experts agree that current content standards are generally too voluminous, scattered and repetitive. They don’t give teachers clear guidance about what is important. They also return to the same topics over and over. Good standards, as with those that guide instruction in higher-achieving countries, focus on a few topics each year that students are expected to learn in greater depth. When students proceed to the next grade, most have mastered the material and the teacher can move on to teach new topics and skills. That’s not the case in the U.S., however.

But change is coming: the National Governors Association and the Council of Chief State School Officers have designed academic standards for math and English to ensure that students who have mastered them are ready to enter college or career-training programs. Those standards will be finalized in late spring 2010.

Although 48 states, Washington, D.C., Puerto Rico and the U.S. Virgin Islands are participating in the Common Core State Standards Initiative, it’s not known how many actually will embrace the new standards or the new tests that will accompany them. States competing for the $4.35-billion “Race to the Top” program earn points for adopting these standards or their equivalents. “Fewer, clearer and higher” was a guiding principle in the development of the new standards. “The idea here is less is more,” Skip Fennell says. “Let’s ensure we’re teaching what’s important and ensure that kids really have it.”

2.  Curriculum. The federal advisory panel’s report argues that curricula should be designed to prepare elementary and middle school students to take a formal algebra class by eighth grade. Students need to understand whole numbers, fractions, measurement and basic geometry if they are to succeed in algebra. Yet, the panel’s survey of algebra teachers found that many of their students do not even know the multiplication table or how to do long-division. The teachers surveyed generally blamed such shortcomings on students’ overuse of calculators.

3. Graduation Requirements. Many states are increasing the number of math courses students must take to graduate. In Arkansas, beginning with the class of 2010, high school students must complete four years of math, including one year beyond Algebra II. The percentage of high school graduates taking Algebra II or even more advanced math rose from 56 to 77 percent between 1990 and 2005, according to NAEP’s High School Transcript Study. Now, 20 states and Washington, D.C. require Algebra II for high school graduation. Prior to 2005, only three states – Arkansas, South Dakota and Texas – had such a requirement in place.

But despite recent increases in graduation requirements, mean scores on the math section of the SAT remain flat, having climbed just six points – from 509 to 515 – since 1972. And when Achieve, Inc. – a nonprofit organization that works with states to raise standards and improve graduation rates – administered an end-of-course assessment for Algebra II in 2009, only 15 percent of students scored at the prepared or well-prepared levels.

4.  Textbooks. U.S. math textbooks are typically 700 to 1,000 pages long. Because they are unable to cover everything, teachers often sample the material without a coherent plan.

“Traditional U.S. textbooks rarely get beyond definitions and formulas,” focusing on the mechanics of mathematics, concludes a 2005 report by the American Institutes for Research on math education in the United States and Singapore. By contrast, in Singapore, textbooks “build deep understanding of mathematical concepts through multistep problems and concrete illustrations that demonstrate how abstract mathematical concepts are used to solve problems from different perspectives.” Singapore’s textbooks cover fewer topics and are more focused.

5. Teaching. Among its most notable findings, the federal advisory panel concluded that researchers have no definitive answers about what constitutes good math teaching. The panel challenged claims about the superiority of “student-centered” teaching or “teacher-directed” lessons. There is no high-quality research supporting the exclusive use of either method. The report also found limited benefits from learning math through “real-world” situations. Many math educators have long argued that math is more relevant if it used to solve problems that arise in daily life, such as how to divide a six-slice pizza evenly among eight people. Numerous elementary math programs also use objects, such as cut-out squares of paper or rods of different lengths, to represent quantities. The idea is that numbers themselves are abstract and hard to understand. But this approach frustrates many parents, who don’t know how to help their children learn the math. Many also worry that calculators undermine students’ knowledge of basic math facts.

The panel concluded that it is essential for teachers to have a deep knowledge of the math they’re trying to teach. The panel called for more math content to be covered in teacher preparation programs, increased mentoring of early-career teachers and more opportunities for professional development.

6. Culture. In most countries, math literacy is expected, but in the United States it seems socially acceptable to say “I hate math.” Many citizens and parents are complacent about math education. For instance, a 2007 poll of Kansas and Missouri parents conducted by Public Agenda found that only 25 percent thought their children should be studying more math and science; 70 percent “think things are fine as they are now.”

In raw numbers, the U.S. actually produces far fewer math majors today than the country did in the 1970s (see graphic), despite large increases in overall college enrollments. Math-averse students are missing out. A 2009 ranking by found that America’s top three jobs – based on income, employment outlook stress, work environment and physical demands – were: 1) mathematician; 2) actuary; and 3) statistician.

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