美国教育的重大危机

数学和科学学科在美国中学教育到大学教育中的薄弱性早已显示出来。美国中学生对数学的基本训练越来越弱。美国大学生对数学的兴趣越来越低。最近的一份教育调查报告显示，美国百分之五十的八年级学生不能解涉及到分数除法的应用题。学生如果没有掌握分数问题，那么学习代数就遇到巨大的障碍。二零零七年的对十五岁中学生国际数学测验结果显示，在三十个发达国家的比较中，美国学生被排在了第二十五位。美国学生数学的落后在学习代数时就完全显现出来。

面对这一现象，美国的有识之士早就开始发出严重警告。微软总裁比尔盖茨多次发出教育改革的呼吁。他认为只有三分之一的高中毕业生作好了进入大学，参加工作，成为公民的准备。他指出：“当我把我们的高中与我看到的其他国家高中相比的时候，我对我们培养的明天的劳动力感到可怕。”美国教育部的数据也显示，美国生产的科学与工程方面的博士数量的份额正从高于50%的水平下降到2010年的15%。

由布什总统任命的美国国家数学教育顾问委员会的报告建议：强化学生学习代数的关键技能；放弃以学生为中心的自我探索与以老师知道为中心的传统教育方式孰优孰劣的争论，两种方法并用；教学大纲必须把概念理解，解题技巧，与计算技能联合起来；压缩中学数学的覆盖范围以强化深度。

专家建议还利用现代心理学的最新研究强调掌握基础数学知识并把它们置放在长期记忆中，为工作记忆留出更大的空间来解更复杂的数学问题。

Report Urges New Focus On Math, Problem Solving In U.S. Education System

By Tamar Lewin

THE NEW YORK TIMES

March 14, 2008

American students’ math achievement is “at a mediocre level” compared with that of their peers worldwide, according to a new report by a federal panel, which recommended that schools focus on key skills that prepare students to learn algebra.

“The sharp falloff in mathematics achievement in the United States begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation.”

The report, adopted unanimously by the panel on Thursday and presented to Education Secretary Margaret Spellings, said that pre-kindergarten-to-eighth-grade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement. It contains specific goals for students in different grades. For example, it said that by the end of the third grade, students should be proficient in adding and subtracting whole numbers; two years later, they should be proficient in multiplying and dividing them. By the end of sixth grade, the report said, students should have mastered the multiplication and division of fractions and decimals.

The report tries to put to rest the long, heated debate over math teaching methods. Parents and teachers have fought passionately in school districts around the country over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to do problems and then drilled on them, versus reform or child-centered instruction, emphasizing student exploration and conceptual understanding. It said both methods had a role.

“There is no basis in research for favoring teacher-based or student-centered instruction,” said Dr. Larry R. Faulkner, the chairman of the panel, at a briefing on Wednesday. “People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.”

The report found that, “To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills.” Further, it said: “Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive.”

The president convened the panel to advise on how to improve math education. Its members include math and psychology professors from leading universities, a middle-school math teacher and the president of the National Council of Teachers of Mathematics.

Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel recommended that math curriculum should include fewer topics, spending enough time to make sure each is learned in enough depth that it need not be revisited in later grades. That is the approach used in most top-performing nations, and since the 2006 report, many states have been revising their standards to cover fewer topics in greater depth.

The report calls for more research on successful math teaching, and recommends that the secretary of education convene an annual forum of leaders of the national associations concerned with math to develop an agenda for improving math instruction.

Spellings said Thursday that she would convene such a meeting. She emphasized the importance of math education for all children and said the report underlined the need for parents to teach even young children about numbers and measurements.

Spellings said she hoped the report would help persuade Congress to approve the president’s fiscal 2009 budget request for almost $100 million for Math Now, an instructional program proposed last year and not financed.

The report cited a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving.

Fractions are especially troublesome for Americans, the report found. It pointed to the National Assessment of Educational Progress, standardized exams known as the nation’s report card, which found that almost half the eighth graders tested could not solve a word problem that required dividing fractions.

Panel members said the failure to master fractions was for American students the greatest obstacle to learning algebra. Just as “plastics” was the catchword in the 1967 movie “The Graduate,” the catchword for math teachers today should be “fractions,” said Francis Fennell, president of the National Council of Teachers of Mathematics.

After hearing testimony and comments from hundreds of organizations and individuals, and sifting through a broad array of 16,000 research publications, the panelists shaped their report around recent research on how children learn.

For example, the report found it is important for students to master their basic math facts well enough that their recall becomes automatic, stored in their long-term memory, leaving room in their working memory to take in new math processes.

“For all content areas, practice allows students to achieve automaticity of basic skills — the fast, accurate, and effortless processing of content information — which frees up working memory for more complex aspects of problem solving,” the report said.

Faulkner, a former president of the University of Texas at Austin, said the panel “buys the notion from cognitive science that kids have to know the facts.”

The report also cited recent findings that students who depend on their native intelligence learn less than those who believe that success depends on how hard they work.

Faulkner said the current “talent-driven approach to math, that either you can do it or you can’t, like playing the violin” needed to be changed.