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『如今，美国的数学教育引起了国人的广泛担忧。数学源于实际生活应用，但美国现行的数学课程已与生活脱节。』
How to Fix Our Math Education
如何调整美国的数学教育
August 24th 2011∣from The New York Times
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THERE is widespread alarm in the United States about the state of our math education. The anxiety can be traced to the poor performance of American students on various international tests, and it is now embodied in George W. Bush’s No Child Left Behind law, which requires public school students to pass standardized math tests by the year 2014 and punishes their schools or their teachers if they do not.
All this worry, however, is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.
Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.
For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.
A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein’s famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.
Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the woq�ky"http://kaoyan.koolearn.com/zhuanshuo/mt/" target="_blank">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"http://www.nytimes.com/2011/08/25/opinion/how-to-fix-our-math-education.html?_r=1&ref=opinion">http://www.nytimes.com/2011/08/25/opinion/how-to-fix-our-math-education.html?_r=1&ref=opinion |
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发表于 2017-8-6 14:53:41