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  3. In December the Program for International Student Assessment (PISA) will announce the latest results from the tests it administe

In December the Program for International Student Assessment (PISA) will announce the latest results from the tests it administe

admin2019-08-08  52
问题    In December the Program for International Student Assessment (PISA) will announce the latest results from the tests it administers every three years to hundreds of thousands of 15-year-olds around the world. 【F1】In the last round, the U.S. posted average scores in reading and science but performed well below other developed nations in math, ranking 36 out of 65 countries.
   We do not expect this year’s results to be much different. Our nation’s scores have been consistently lackluster. Fortunately, though, the 2012 exam collected a unique set of data on how the world’s students think about math. The PISA 2012 assessment questioned not only students’ knowledge of mathematics but also their approach to the subject, and their responses reflected three distinct learning styles. Some students relied predominantly on memorization. They indicated that they grasp new topics in math by repeating problems over and over and trying to learn methods "by heart." Other students tackled new concepts more thoughtfully, saying they tried to relate them to those they already had mastered. 【F2】A third group followed a so-called self-monitoring approach: they routinely evaluated their own understanding and focused their attention on concepts they had not yet learned.
   In every country, the memorizers turned out to be the lowest achievers, and countries with high numbers of them—the U.S. was in the top third—also had the highest proportion of teens doing poorly on the PISA math assessment. Further analysis showed that memorizers were approximately half a year behind students who used relational and self-monitoring strategies. 【F3】In no country were memorizers in the highest-achieving group, and in some high-achieving economies, the differences between memorizers and other students were substantial. In France and Japan, for example, pupils who combined self-monitoring and relational strategies outscored students using memorization by more than a year’s worth of schooling.
   【F4】The foundation all math students need is number sense—essentially a feel for numbers, with the agility to use them flexibly and creatively. A child with number sense might tackle 19x9 by first working with "friendlier numbers"—say, 20×9—and then subtracting 9. Students without number sense could arrive at the answer only by using an algorithm. 【F5】To build number sense, students need the opportunity to approach numbers in different ways, to see and use numbers visually, and to play around with different strategies for combining them. Unfortunately, most elementary classrooms ask students to memorize times tables and other number facts, often under time pressure, which research shows can seed math anxiety. It can actually hinder the development of number sense.
【F5】
选项
答案为培养学生的数字感，他们需要以不同的方式接触数字，用生动形象的方式运用数字，以及通过不同的技巧组合数字，以使其变得更有趣。
解析 ①本句虽较长，但实为简单句。②宾语the opportunity后接了三个并列的不定式短语作宾语补足语，分别是to approach numbers、to see and use numbers和to play around with different strategies。这三个宾语补足语补充说明opportunity，表示有怎样的机会培养学生的数学感。句末的for combining them作方式状语，修饰谓语动词词组play around with，说明如何使用不同技巧“玩数字”。
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