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    Students perform better when their instructors use hand gestures—a simple teaching tool that could generate benefits in higher-level math such as algebra(代数).

    A study published in Child Development,the top-ranked educational psychology journal,provides some of the strongest evidence yet that gesturing may have a unique effect on learning.Teachers in the United States tend to use gestures less than teachers in other countries.

     "Gesturing can be a very beneficial tool that is completely free and easily employed in classrooms," said Kimberly Fenn,study co-author and assistant professor of psychology at Michigan State University."And I think it can have long-lasting effects."

    Fenn and Ryan Duffy of MSU and Susan Cook of the University of Iowa conducted an experiment with 184 second-,third- and fourth-graders in Michigan elementary classrooms.

    Half of the students were shown videos of an instructor teaching math problems using only speech.The others were shown videos of the instructor teaching the same problems using both speech and gestures.In the speech-only videos,the instructor simply explains the problem.In the other videos,the instructor uses two hand gestures while speaking,using different hands to refer to the two sides of the equation.Students who learned from the gesture videos performed better on a test given immediately afterward than those who learned from the speech-only video.

    Another test was given 24 hours later,and the gesture students actually showed improvement in their performance while the speech-only students did not.

    While previous research has shown the benefits of gestures in a one-on-one tutoring-style environment,the new study is the first to test the role of gestures in equivalence learning in a regular classroom.

    The study also is the first to show that gestures can help students transfer learning to new contexts—such as transferring the knowledge learned in an addition-based equation to a multiplication-based equation.

    Fenn noted that U.S.students lag behind those in many other Western countries in math and have a particularly hard time mastering equivalence problems in early grades."So if we can help them grasp this foundational knowledge earlier," she said,"it will help them as they learn algebra and higher levels of mathematics."

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阅读下面的文字,完成下列小题。

    ①作为高速发展的新兴国家,中国一脚踏着过去,一脚踏进未来,新老问题同时存在于过去和未来的两个时空中,于是,中国不得不同时操作两种游戏:现代游戏和全球游戏。就是说,中国的现代性到今天仍然在建构过程中,可同时又已经深深加入了全球游戏,参与建构世界的未来。双重游戏制造了今天复杂疑难的中国的问题。

    ②为什么对于今天的问题,思维容易受挫?思维失效的典型表现在经济学、政治学、哲学以及历史学等领域的话语变得非常可疑。比如说,十年前经济学是很受信任的,但是最近几年尤其是金融危机之后声誉大挫,人们发现经济学家并不那么可信。这不是经济学家的错误,而是长期以来一直使用的那些现代思维框架、概念和方法论可能不再适用新游戏,至少不足以反思新游戏。有个反潮流的经济学家纳西姆·塔勒布指出:现代知识论的追求本身就非常可疑,现代试图预知未来,确定一切情况,然后建立坚不可摧的秩序或系统,以便应对一切挑战。可是人算不如天算,一旦遇到未知的挑战,这秩序就变得非常脆弱而崩溃。塔勒布说,真正能够保证有效生存的思维必须是反脆弱的,能够在不断受挫中受益,能够不确定地应对不确定性。塔勒布的反脆弱思维几乎就是老子那种行道如水的方法论的当代回声。在一个充满变数的时代,这种思维应该是更有效的。

    ③为什么人们总是忘记应该像一个灵活多变的生命那样去思考?关键在于一个时代都有其既定利益的受益者,于是时代的主流观念总是拒绝思想,总是希望人们不要去思想,而去遵循既定观念。每个时代的既定收益主体希望人们不要去想新的问题,不用去颠覆秩序,以便维持自己的收益。因此,在一个时代终结的时候,人们总是迅速捍卫某一个对自己有利的立场,回避反思,回避新思想,回避新问题,而直接把立场当成结论。这就是今天在网络和微博或其他言论空间所看到的那种无思想状态。只有立场,缺乏理性论证、分析和灵感,这就是一个时代正在终结的不思症状。

    ④在没有准备好如何思考剧变世界的时候,现代既有的那些观念就是话语的救命稻草,所有想维持现代游戏的人,都拼命抓住和捍卫那些其实已经步履蹒跚的现代观念和价值观,那些观念成为不思考的借口,被毫不犹豫的宣布为不可质疑的。如果只能遵循政治正确的观念,那人们还能思想吗?安迪·沃霍尔可以无节制地复制世俗形象,从而使世俗形象从习以为常的无意识状况变成一种对象化的反思,可是,复述政治正确的观念却没有那样幸运,恐怕不可能变成艺术,而只能把被强加的宣传变成主动接受的专制。

    ⑤现代观念本身并不是错的,它们都是现代的伟大成就,对于现代游戏很有效。然而现代观念未必能够解决全球时代的新问题。所以用现代概念来掩盖、回避或对付新问题是不对口的且无效的。如果坚持用现代性去理解全球性,思维和行动必定自我受挫。

                                                                                                                                                   (节选自赵汀阳《现代性的终结与全球性的未来》)