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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  41
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.
【F4】
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答案数字感是所有学数学的学生都需具备的基础——本质上来说就是对数字非常敏感，能灵活地、富有创造力地运用数字。
解析 ①本句为主从复合句，包含一个定语从句。②句子的主干为The foundation is number sense。主语The foundation后跟有一个省略引导词的定语从句，说明这是所有学数学的学生需具有的基础。③破折号引出的内容可视为插入语，补充说明number sense。句末with引导的独立主格结构，与前面a feel for numbers具有逻辑主谓关系。them指代的是numbers。
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