As Math Skills Slip, U.S. Schools Seek Answers From Asia
TOWNSEND, Mass. -- About five years ago, a statewide test in Massachusetts revealed that students' math skills deteriorated sharply as they went from fourth to sixth grade. Alarmed, the Massachusetts education commissioner suggested an unconventional fix: importing the math curriculum used in Singapore.
Students in Singapore routinely score among the highest in international math tests. The hope was that American kids taught the Singaporean way would improve their math scores.
The approach has been adopted in about 200 schools nationwide, from rural Oklahoma to the inner cities of New Jersey. Early indications suggest that many U.S. students taught with textbooks imported from Singapore do perform better in math. Some children who once found the subject frustrating say they now like it.
Faced with a worrying decline in math proficiency among U.S. kids, a growing number of educators are seeking inspiration from Asian curricula. American children are falling behind their Asian peers in science and math, a shift that could push still more white-collar jobs offshore as the next generation graduates.
"Our kids just don't seem as numerate as they should be, and we decided we needed to try whatever we can to fix that," says David Driscoll, Massachusetts' education commissioner and a former math teacher himself, who had the idea of using Singapore text books in local schools.
Critics assert that math teaching has been dumbed down in the U.S. over the past two decades. They say that too much emphasis is placed on making the subject accessible and fun and not enough on vital, if repetitive, drills such as multiplication tables. Another big criticism: U.S. math curricula tend to cover plenty of subject areas but not in sufficient depth.
Singapore and other southeast Asian countries take a different tack. Singapore's curriculum was developed over the past few decades by math experts hired by the Ministry of Education, who continually interviewed math teachers to find out what works and where kids need help. The elementary textbooks cover only one-third of the topics typically found in U.S. textbooks, but the material is taught far more thoroughly. While rote learning plays a part, kids in Singapore also learn to use visual tools to understand abstract concepts.
Singapore math texts, for example, ask kids to draw bars and other diagrams to visualize problems -- a technique called "bar modeling." When this strategy is applied consistently over a number of years, children tend to be better able to break down complex problems and do rapid calculations in their head.
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Not everyone believes that importing textbooks from Singapore would solve America's math problem. Some states say the approach doesn't meet their standards. American math curriculum varies from state to state, so there is a potential gap between standards set on the material students need to know and what they have covered using the Singapore books. The National Council of Teachers of Mathematics in the U.S. suggests that it might not be possible to copy what Singapore's done simply by importing its books. The success of its math program may have roots in Singapore's highly disciplined culture, where the entire community -- particularly parents -- expects kids to buckle down and work hard, argues the NCTM.
There's little doubt, though, that math teaching in America needs to be overhauled. Tomorrow, Boston College will release a four-year global study that is expected to show the math gap with Asia remains. The college's last study, the 1999 Trends in International Mathematics and Science Study (TIMSS), ranked eighth-graders in Singapore the best in math, while U.S. kids came in 19th, just behind Latvia. American kids also fall further behind the longer they're in school; as fourth-graders, American kids ranked 7th on the 1995 study.
That decline has already had an impact on U.S. universities. Among U.S. freshmen who plan to major in science or engineering, one in five requires remedial math courses, according to the National Science Board, which is part of the government-funded National Science Foundation. Enrollment by U.S. citizens or permanent residents in graduate science and engineering programs, meantime, dropped 10% between 1994 and 2001. Enrollment of foreign students grew 35%.
Because of the skills gap, America risks losing even more jobs overseas. "Many have a gnawing sense that our problems may be more than temporary and that the roots of the problem may extend back through our education system," said Federal Reserve Chairman Alan Greenspan at a Boston finance conference in March.
Reforming the U.S. curriculum is difficult. Unlike Singapore and other Asian countries, the U.S. doesn't have a national curriculum. Each state is responsible for setting standards, while each district retains control over how a subject is taught.
Under the Bush administration's No Child Left Behind policy, funding and jobs depend on how each school rates on standardized state exams. Many district officials are reluctant to try something new for fear of slipping up on those exams.
But a handful are turning to Asia for answers. Georgia plans to adopt Japanese math standards as part of its reform of secondary-school curricula. A teacher-training textbook, based on Singapore's elementary math curriculum and written by a math professor at Michigan State University, is now used at a half-dozen universities in America. Singapore's math textbooks for young kids have the biggest appeal in the U.S. because they're written in English.
In rural Bethel, Okla., school-district superintendent Marty Lewis thought his kids were slipping in math. After his curiosity about Singapore was piqued by the 1999 TIMSS results, he did an Internet search about the Singapore method. That led him to the private Rosenbaum Foundation of Pennsylvania, which funds Singapore math programs in the U.S. and Israel.
The foundation, in turn, put him in touch with Yoram Sagher, a Florida mathematician who trains teachers to teach Singapore math. Mr. Lewis hired Mr. Sagher to give a one-week seminar to all his teachers in July. Bethel kindergartners and first-graders began using the Singaporean books in September.
"I came to a point where I thought: I don't care how crazy people think I am; I'm going to go out and find something that works," says Mr. Lewis.
While Bethel's kids are just getting started, other school districts have adopted the Singapore method wholesale. One is North Middlesex, a farming and commuter district that's an hour's drive from Boston.
North Middlesex's program got rolling soon after the education commissioner, Mr. Driscoll, noticed the decline in math ability among his state's sixth-graders. In 2000, he got a $50,000 federal grant to test whether a Singapore curriculum would improve math scores for kids in his district.
North Middlesex dispatched three teachers with math degrees to work with a math professor at the Worcester State College in Massachusetts. They came up with a seven-day summer seminar for North Middlesex district teachers, based on textbooks from Singapore.
The Singapore-inspired program was started in grades five through eight, which needed the greatest help. As more teachers volunteered, the program was extended to other grades.
On a recent morning in Ashby, a tiny town in North Middlesex, fifth-grade math teacher Bob Hogan asked for volunteers to work out how many women there are in a hypothetical university class of 250 if there are 50 more men than women.
Mr. Hogan, an energetic 30-year-old teacher, asked for volunteers to tell him how to solve the problem using a bar model. Sarah Carter, a 9-year-old with freckles and bright red hair, leaned forward in her seat, arm in air.
First, she instructed Mr. Hogan to draw two bars of equal length, and label the top one "women" and the bottom one "men." She then he told him to add a small square extension to the "men's" bar, and write "50" inside of it. To the right of both bars, she asked him to write "250," indicating the full value of both, together. Looking at this pictorial, she started to solve the problem without pen or paper: She verbally subtracted 50 from 250, and asked him to write the "200" on the board, to the left of the two empty bars, indicating their combined value. Then, she divided 200 by two, and announced there are 100 women in the class, and 150 men.
"I don't know where Singapore is," she said, "but I like the way they do math."
Some teachers were initially skeptical. Steve Keating, a veteran math teacher who teaches seventh grade, says he has lived through a host of new math approaches, including the "new math" craze in the 1970s. "My first thought was, here we go again," he says, referring to the Singapore method.
He was especially taken aback by the textbook. By grades seven and eight, kids in the Singapore program are doing high-school-level algebra. "I thought, wow, that's complicated -- even for me," says Mr. Keating. He was eventually won over when he saw how enthusiastic his own students became about math.
The approach expects a lot of its teachers. Singapore's math program doesn't come with guides that walk teachers through every step of the class, and every problem, as many U.S. courses do. Teachers can't flip to the back of the book for answers. During the first year, Mr. Keating spent two hours every night preparing the next day's lesson. On his summer vacation he took math books to the beach. The effort paid off; his students' math scores improved.
Some parents also had doubts. Suzanne Carter recalls that her daughter Sarah, who'd always struggled at math, came home and drew bars and rectangles instead of working on the sums she grew up with.
"I was frustrated. I had no idea what she was doing," says Mrs. Carter, a sign-language instructor.
Her daughter's school, however, doesn't need more convincing. Students at North Middlesex are already doing better on state exams. Eighth-graders, for example, scored 75.4 points on this year's state "math proficiency index," up from 63.2 points in 2000. That jump was twice that of the state average -- which also improved. Other grades improved, but in line with the state average.
Eager for something more conclusive, North Middlesex recently hired Stanford University's Hoover Institution to analyze a slew of state and district exams to see whether a group of 300 students who'd taken one to three years of the Singapore program were better at math than other students. The study, which is continuing, found the Singapore math students had "significantly" better computation skills.
Boston Public Schools tried the Singapore math books in a few classes at one school last year, but decided to drop them. The district had adopted another math program, called the Workshop Model, which promoted group and independent work activities designed to get kids to think about concepts behind math. They didn't want to detract from that by experimenting more broadly with something new, said Ed Joyce, curriculum director for math for Boston Public Schools.
"I wouldn't say anything bad about Singapore math, but I would say there's a lot of programs that would have the same result," he said.
Another hurdle that could limit the appeal of the Singapore method is the U.S. obsession with standardized testing. Kids taking Singapore math might be better at a core set of subjects such as multiplication, fractions, word problems and algebra, but they may struggle with topics that appear on state tests.
So North Middlesex supplements the Singapore books with a few extra lessons in subjects like probability, which are taught in grades four and five in the U.S. but not until later grades in Singapore.
The Singapore method continues to attract fans. Inspired by North Middlesex, 20 schools in 12 different districts across Massachusetts are now running Singapore pilot programs.
William Carey, principal of Beachmont Elementary school in Revere, a blue-collar suburb of Boston, last year began offering "Singapore math" in grades one through four. He reports some early signs of success. Beachmont's grade four class lagged behind the state average by just 3% on this year's state exam, up from the 8% gap between the state and last year's fourth-grade class.
Beachmont's success, in turn, has inspired others. Across town, teachers at Garfield Elementary began to teach math the Singapore way this year. "When something makes a difference, people notice," says Mr. Carey, the principal at Beachmont. "Word is starting to spread."
亚洲数学教材风靡美国学校
大约在5年前，美国麻萨诸塞州举行的一次全州统考显示：该州四至六年级学生的数学水平出现大幅下降。震惊之余，麻萨诸塞州教育局长提出了一个不同寻常的解决办法：引进新加坡的数学教材。
新加坡的学生在国际数学竞赛中一贯表现出众。因此，麻萨诸塞州教育局长希望接受新加坡式教育的美国儿童能提高数学成绩。
全美已有200所左右的学校采用了上述方法，它们有的位于克拉荷马州的偏远乡村，有的则位于新泽西州的繁华都市。初步结果表明，许多接受新加坡教材的美国学生的数学成绩优于其他学生。有些原先讨厌数学的孩子表示他们现在很喜欢这一学科。
越来越多的教育工作者对美国青少年数学水平的下降 心忡忡，于是转而从亚洲数学课程中汲取灵感。美国儿童的理科和数学成绩落后于亚洲同龄人，因此当他们大学毕业时，更多的白领工作岗位可能会转移到海外。
“我们的孩子似乎不具备应有的数学头脑，所以我们决定应尽一切可能来解决这个问题，”麻萨诸塞州的教育局长戴维?德里斯科尔(David Driscoll)说。他本人曾担任过数学教师，正是他提出了采用新加坡数学教材的想法。
评论家们声称，在过去20年里，美国的数学教育一直停滞不前。他们指出，教学的重点放在如何使数学这门课程浅显易懂、生动有趣上面，但对乘法口诀表等重要的需要反复操练的技能不够重视。另一大问题是：美国的数学课程通常覆盖面广，但缺乏深度。
新加坡和其他东南亚国家则采取不同的策略。在过去几十年里，新加坡教育部(Ministry of Education)聘请数学专家对数学课程不断修订完善。这些专家与数学教师保持密切联系，以了解哪些教学方法效果好，以及哪里是学生的薄弱环节等。新加坡小学教材涉及的主题只有美国小学教材的三分之一，但内容十分详细。虽然也得死记硬背，但新加坡的小学生们还学习利用形像化的工具来理解抽象的概念。
例如，新加坡的数学教材让孩子们画条形图等图表使问题形像化，这一技巧被称为”条形图模型”。当地学校在过去几年里一直采用这一技巧，结果学生们现在能更好地把复杂的问题简单化，很快地进行心算。
并非所有人都认为引进新加坡的教材是解决美国数学教学问题的灵丹妙药。一些州表示，这一方法不符合本州制定的标准。美国各州的数学教材不尽相同，因此各州规定的教学内容与引进的新加坡教材之间可能会出现差异。全美数学教师委员会(The National Council of Teachers of Mathmatics)认为，通过单纯引进教材来借鉴新加坡的教学经验也许是行不通的。新加坡数学教育的成功或许归功于具有高度约束性的本国文化─全社会，特别是学生家长，都要求孩子们认真学习、努力工作。
然而，毫无疑问的是美国的数学教育需要彻底改革。波士顿学院(Boston College)曾于1999年进行了一项名为国际数学科学趋势研究(Trends in International Mathematics and Science Study，简称TIMSS)的调查，结果表明新加坡8年级学生的数学成绩最好，而美国同年级学生的数学成绩名列第19，位于拉脱维亚之后。调查还显示，年级越高，美国学生的数学成绩就越差。在1995年的有关调查中，美国4年级学生的数学成绩排名第7。
上述下滑趋势早已对美国大学产生了影响。隶属于由政府资助的美国国家自然科学基金会(National Science Foundation)的美国国家自然科学理事会(National Science Board)称，在一年级理工科大学生中，每五个人就有一个需要补习数学课程。此外，在1994至2001年间，美国公民或永久居民的理工科研究生入学率下跌了10%，而外国学生的同期入学率上升了35%。
由于数学水平较差，今后流向海外的工作岗位可能会越来越多。今年3月，美国联邦储备委员会(Federal Reserve)主席艾伦?格林斯潘(Alan Greespan)在波士顿举行的一个金融会议上表示；“令许多人感到心痛的是我们存在的问题也许不是暂时性的，而问题的根源也许在于我们的教育体系。”
要对美国的教学课程进行改革是很困难的。与新加坡和其他亚洲国家不同，美国没有全国统一的课程。各州负责制定自己的课程设置标准，而州内的每个学区对课程的教学方法拥有决定权。
根据布什(Bush)政府的“决不让一个孩子落后法案”(No Child Left Behind)，每所学校所能获得的资助取决于在它在标准化的全州统考中的表现。因此许多学区的教育官员不愿尝试新鲜事物，惟恐在统考中失利。
但是，有些州开始借鉴亚洲的教育方法。根据乔治亚州的初中课程改革方案，该州将采用日本的数学教学标准。密歇根州州立大学(Michigan State University)的一位数学教授参考新加坡的小学数学课程编写了一本教师用书，目前已被5、6所美国大学采用。新加坡的数学课本对美国人特别具有吸引力是因为这些课本是全英文的。
在俄克拉荷马州偏僻的伯特利(Bethel, Okla.)，学区负责人马蒂?刘易斯(Marty Lewis)感到区内孩子们的数学水平有所下降。1999年的TIMSS调查使刘易斯对新加坡的教学方法产生了兴趣，于是他在互联网上展开了进一步研究。接著他又来到了宾夕法尼亚州私立的Rosenbaum基金会，该组织为美国和以色列境内的新加坡数学教育项目提供资助。
Rosenbaum基金会又让刘易斯结识了佛罗里达州的数学家约拉姆?赛格(Yoram Sagher)，后者为教授新加坡数学课程的教师进行培训。刘易斯聘请赛格在今年7月为伯特利学区内的全体教师举行了为期一周的研讨会。伯特利的幼儿园和小学一年级从9月份开始采用了新加坡的数学课本。
“严峻现实使我感到不管别人怎么看，哪怕说我是疯子，我都要竭尽全力找到行之有效的办法，”刘易斯说。
伯特利学区的孩子们刚开始接纳新加坡的数学课本，而有的学区早已完全采用了新加坡的教学方法，距离波士顿有一小时车程的农村学区North Middlesex就是其中之一。
在麻萨诸塞州教育局长德里斯科尔发现本州6年级学生的数学水平下降之后，North Middlesex随即启动了教学改革计划。在2000年，德里斯科尔获得了联邦政府的5万美元资助，以检测新加坡数学课程能否提高其所在学区的数学成绩。
North Middlesex派出了3名拥有数学硕士学位的教师与麻萨诸塞州Worcester State College的一位数学教授共同合作。他们根据新加坡的数学课本，为North Middlesex学区内的教师举行了为期一周的夏季研讨会。
新加坡式的教学计划首先在5至8年级的学生中实施，因为这些年级的学生最需要帮助。后来，随著自愿进行尝试的教师越来越多，该计划扩展到其他年级。
不久前在North Middlesex的小镇Ashby上，5年级数学教师鲍勃?霍根(Bob Hogan)出了一道题，假设在某大学班级中共有250名学生，其中男生比女生多50名，问一共有多少女生？
现年30岁的霍根充满活力，他问哪位学生能自告奋勇，通过条形图模型来回答这个问题。脸上长有雀斑、头发红红的9岁女孩莎拉?卡特(Sarah Carter)在座位上举起了手。
卡特首先让霍根画了两根长度相等的长条，并在上面一条上写上”女生”，下面一条上写上“男生”。然后她告诉老师在“男生”这一条上加长一点，标上数字“50”；另外在两根长条的右端写上“250”，表示男女生的总数。看著这些图形，卡特开始口头解决这个数学题：她从250中减去50，然后让霍根在两根长条的左侧写上“200”，表示总数。接著，她把200除以2，宣布这个班上有100名女生，150名男生。
“我不知道新加坡在哪里，”卡特说，“但我喜欢他们做数学题的方式。”
有些教师起初抱著怀疑的态度。资深数学教师史蒂夫?基廷(Steve Keating)教授7年级学生，他表示自己接触过许多新的教学方法，包括上世纪70年代的“新数学”浪潮。“开始我想，这次又来了，”他说。
新加坡的教学课本尤其让基廷感到吃惊。接受新加坡式教育的学生们到了7、8年级已经开始做高中难度的代数题目了。“我想，天啊，这是很复杂的─即使对我来说，”他表示。当基廷看到自己的学生对数学充满了热情时，他终于信服了。
这种教学方式对教师的要求很高。与美国的教材不同，新加坡的教材没有给教师提供如何上课的详细指导。教师们不能翻到教科书的后面寻找答案。在开始采用新加坡教材的第一年里，基廷每天晚上要花两小时备课；夏天度假时还带著数学书籍。他的努力获得了回报：学生的数学成绩提高了。
一些家长也怀有疑虑。苏珊娜?卡特(Suzanne Carter)回忆说她的女儿莎拉以前总是为数学头痛，现在回到家后开始画条形和长方形，而不是像过去那样开始计算。
“我起初很灰心。我不知道她在做些什么，”身为手语指导老师的卡特太太说。
但莎拉所在的学校无须多费口舌。North Middlesex学区的学生在全州统考中成绩出色。例如，8年级学生在今年的全州“数学能力测试”(math proficiency index)中获得75.4分，高于2000年的63.2分，是全州平均水平的两倍，当然，麻萨诸塞州的整体水平也有所提高。该校其他年级的水平也上升了，但与全州的平均水平一致。
急于得到结论的North Middlesex学区最近聘请了斯坦福大学(Stanford University)的胡佛学院(Hoover Institution)对大量全州统考和学区考试进行分析，以了解300名接受了一至三年新加坡数学教学的学生成绩是否优于其他学生。这项调查目前还在进行之中，不过调查发现这些学生的计算能力“远远”好于其余学生。
去年，Boston Public Schools的一所公立学校在一些班级中试用了新加坡的数学教材，但后来决定放弃。该学区采用了另一套被称为Workshop Model的教学方法，这种方法通过集体和个人活动让孩子们思考数学背后的概念。Boston Public Schools的数学课程主管埃德?乔伊斯(Ed Joyce)说，他们不想因为尝试新的东西而背离了这一宗旨。
“我不想诋毁新加坡的数学教育方法，但我想指出有许多教育方法能达到同样的效果，”乔伊斯说。
另一个可能会削弱新加坡教学方式的魅力的障碍是美国人对于标准化测试的迷恋。接受新加坡教材的学生们也许会在诸如乘法、分数、文字题和代数等核心课程上取得好成绩，但全州统考中的题目也许会让他们感到吃力。
因此，North Middlesex学区除了采用新加坡的数学教材之外，还补充了概率等课程。这些科目在美国是4、5年级的课程，而在新加坡是高年级的课程。
新加坡的教学方法依然很吸引人。受到North Middlesex学区的影响，马萨诸塞州其他12个学区的20所学校如今都采用了引进新加坡教学的试行方案。
威廉?凯利(William Carey)是位于波士顿郊区Revere的Beachmount小学的校长，那里居住著大量的蓝领。凯利去年在1至4年级中推行新加坡式教学，并显示了初步的成功。在今年的全州统考中，Beachmount4年级学生的数学成绩仅落比全州平均水平低3%，而去年的差距是8%。
Beachmount的成功感染了其他学校。Garfield小学的教师们今年开始采用新加坡数学教育方式。“不同的效果引起了人们的注意，”凯利说。“一传十，十传百，大家都知道了。”
