科学美国人60秒：刷应用题能提高数学能力吗?

This is Scientific American’s 60-Second Science, I’m Adam Hinterthuer.

这里是《科学美国人》的 60 秒科学，我是亚当·辛特修尔。

If a train heading east leaves Chicago at noon and a train heading west leaves New York an hour later, will that make you any better at math? New evidence says "No."

“正午时分，一列火车由芝加哥站出发向东行驶，另一列火车于1小时后离开纽约站向西行驶……”刷这种应用题能提高我们的数学能力吗?科学研究给出了否定的答案。

In a report in the April 25th issue of the journal Science, researchers from Ohio State University say the preferred method of teaching math just doesn't make the grade. The researchers taught undergraduates mathematical principles they would need to solve future problems. Some were taught using concrete visual examples, like cups filled with water or a pizza cut into slices. Other students learned abstract formulas in terms like "n=x."

发表在《科学》(Science)上的一篇论文中，美国俄亥俄州立大学(Ohio State University)的研究人员称：老师们偏爱的这种教学方式并不能提高学生的数学成绩。研究人员采用两种方法教给本科生他们后续要用到的数学原理：一部分学生通过具体实例来学习，比如装有水的杯子和切成几份的披萨等;另一部分学生则直接学习抽象的公式，例如“n=x”。

When asked to solve new problems using these teachings, major discrepancies appeared. In one case, abstract-learning students scored an average of 80 percent on a test. Their "real-world" counterparts, however, seemed unable to transfer their knowledge to a new situation, posting only a 44 percent average.

让两组学生用这些知识来解决新问题时，差距就凸显出来了。在一次100分为满分的测试中，通过抽象方式学习的学生平均得分为80分，而他们在“现实世界”中学习的同学却似乎不太会将学到的知识应用到新问题上，平均只获得了44分。

The researchers say using concrete examples is alluring, because students seem to learn lessons faster. However, students who take the time to get abstract concepts down are able to get on the train before it leaves the station.

研究人员说，实例教学具有一定迷惑性：学生们表面上看学得的确更快。但是，花时间消化抽象概念的学生，反而更容易“上车”：遇到实际中的新问题时也能以不变应万变。

Thanks for the minute for Scientific American’s 60-Second Science, I’m Adam Hinterthuer.

感谢收听《科学美国人》的60秒科学，亚当·辛特修尔报道。