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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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快手刘

冯骥才

    ①人人在童年,都是时间的富翁。我有时待在家里闷得慌,就不免要到离家很近的那个街口,去看快手刘变戏法。

    ②快手刘是个摆摊卖糖的大胖汉子。随身背着的绿色小木箱,上面插着一排排廉价的棒糖。他变戏法是为吸引孩子们来买糖。戏法很简单,俗称“小碗扣球”。一块绢子似的黄布铺在地上,两只白瓷小茶碗,四个滴溜溜的大红玻璃球儿。他两手各拿一只茶碗,你明明看见每只碗下边扣着两个红球儿,你连眼皮都没眨一下,只见他一边叫天喊地,东指一下手,西吹一口气,嘿!四个球儿竟然全都跑到一只茶碗下边去了。

    ③有一次,我亲见他手指敏捷灵活地一动,把一个球儿塞在碗下边扣住,便想揭他老底,禁不住大叫:“在右边那个碗底下,我看见了!”“你看见了?”快手刘明亮的大眼珠子朝我惊奇地一闪:“不会吧!你可得说准了,猜错就得买我的糖。”“行!我说准了!”谁知快手刘突然把右边的茶碗翻过来:“瞧吧,在哪儿呢?”咦?怎么碗下边什么都没有呢?快手刘又把左边的茶碗掀开,同样也没有。球儿都飞了?只见他将两只空碗对口合在一起,举在头顶上,口呼一声:“来!”双手一摇茶碗,里面竟然哗哗响。打开碗一看,四个球儿居然又都出现在碗里面。怪,怪,怪!围看的人发出一阵惊讶不已的唏嘘声。“怎么样?你输了吧!不罚你钱,买块糖吃就行了。”我臊得脸皮发烫,在众人的笑声里买了块棒糖,站在围了几圈的人后边去。从此我只站在后边看了,再不敢挤到前边去多嘴多舌。他的戏法,在我眼里真是神奇无比,那时他是我最佩服的人。我童年和少年的许多时光,就是在他令人痴想不已的表演中慢慢消磨掉的。

    ④我上高中是在外地,人一走,留在家乡的童年和少年就像合上的书。快手刘带给我的美好故事,就像鲜活的花瓣夹在书页里,再翻开都变成了干枯的回忆。

    ⑤高二暑假回家,一天在离家不远的街口看见十多个孩子围着什么又喊又叫,走近一看,竟然是快手刘!他依旧卖糖葫芦和变戏法,但那只木箱,已经破损不堪,再也看不出先前那悦目的绿色。再看他,饱满的曲线没了,尖尖的骨形突露,眸子没了光彩。这双手尤其使我吃惊,手背上青筋缕缕,污黑的手指头上绕着一圈圈皱纹,好像吐尽了丝而皱缩下去的老蚕……他抓住两只碰得破破烂烂的茶碗口,缓慢迟钝地翻来翻去,四个小球一会儿没头没脑地撞在碗边上,一会儿从手里掉下来。

    ⑥孩子们叫起来:“球在那儿呢!”“在手里哪!”“指头中间夹着呢!”叫声让他慌张不已,手抖抖索索,连他自己都不知道球在哪儿了,无怪乎周围的看客只是寥寥无几的孩子。

    ⑦“在他手心里!绝对没错!”孩子们吵着闹着叫他张开手,他却攥得紧紧的,几乎用请求的口气说:“是在碗里呢!我手里什么也没有……”可这些稚气的小孩儿偏偏不依不饶,非叫他张开不可!他哪能张开?一张开,就会漏洞百出。我真不愿意看见他这幅窘相,走到孩子们中间,用手指那木箱说:“球在这箱子上呢!”

    ⑧孩子们被我这突如其来的话,弄得莫名其妙,都瞅那木箱。就在这时,我瞥见快手刘用一种尽可能快的速度把手里的小球儿塞在碗下边。“球在哪儿呢?”孩子们问我。

    ⑨快手刘笑呵呵地翻开地上的碗说:“瞧,就在这儿哪!怎么样?你们说错了吧?买块糖吧!”孩子们给骗住了,再不喊闹。一两个孩子掏钱买糖,其余的一哄而散。只剩下我和快手刘呆立在那儿,他灰蒙蒙的眸子里充满疑问,显然他不明白,我这个陌生的青年何以要帮他解困。

    ⑩在饱经风霜的岁月里,艺人的高超技艺,却没有人来传承,他晚年竟变得如此凄凉,为什么呢?我陷入了沉思之中。