魅影直播

Average mathematics performance for the 13 Benchmarking states was clustered in the middle of the international distribution of results for the 38 countries. All of the Benchmarking states performed either significantly above or similar to the international average, yet significantly below the high-performing Asian countries.

The Benchmarking Study underscores the extreme importance of looking beyond the averages to the range of performance found across the nation. Performance across the participating school districts and consortia re遝cted nearly the full range of achievement internationally. Although achievement was not as high as Singapore, Korea, and Chinese Taipei, the top-performing Benchmarking jurisdictions of the Naperville School District and the First in the World Consortium (both in Illinois) performed similarly to Hong Kong, Japan, Belgium (Flemish), and the Netherlands. At the other end of the continuum, urban districts with high percentages of students from low-income families, such as the Chicago Public Schools, the Rochester City School District, and the Miami-Dade County Public Schools, performed more similarly to lower-performing countries such as Thailand, Macedonia, and Iran, respectively, but significantly higher than the lowest-scoring countries.

The 魅影直播 1999 Benchmarking Study provides evidence that some schools in the U.S. are among the best in the world, but that a world-class education is not available to all children across the nation. The 魅影直播 index of home educational resources (based on books in the home, availability of study aids, and parents’ education level) shows that students with more home resources have higher mathematics achievement. Furthermore, the Benchmarking jurisdictions with the greatest percentages of students with high levels of home resources were among the top-performing jurisdictions, and those with the lowest achievement were four urban districts that also had the lowest percentages of students with high levels of home resources. These and other 魅影直播 1999 Benchmarking results support research indicating that students in urban districts with a high proportion of low-income families and minorities often attend schools with fewer resources than in non-urban districts, including less experienced teachers, fewer appropriate instructional materials, more emphasis on lower-level content, less access to gifted and talented programs, higher absenteeism, more inadequate buildings, and more discipline problems.

It is good news that in mathematics at the eighth grade, the 魅影直播 1999 Benchmarking Study shows relatively equivalent average achievement for girls and boys in each of the Benchmarking jurisdictions. This follows the national and international pattern where the United States was one of 34 countries in 1999 with girls and boys performing similarly.

Of the five mathematics content areas assessed by 魅影直播, U.S. eighth graders performed higher than the international average in fractions and number sense; data representation, analysis, and probability; and algebra; but only at the international average in measurement and geometry. Despite the major differences among the Benchmarking participants geographically, economically, and culturally, most to some extent followed the national pattern. It will be important, however, for each participant to determine its specific relative strengths and weaknesses in mathematics achievement.

The Benchmarking results indicate that students’ relatively lower achievement in geometry is most likely related to less coverage of geometry topics in mathematics classrooms. Teachers also expressed the least confidence in their preparation to teach geometry.

The content area emphasis differed dramatically from jurisdiction to jurisdiction, however. For example, teachers in Naperville reported emphasizing algebra for nearly all their students (91 percent), and those in the Academy School District, the Michigan Invitational Group, and Montgomery County for about half. In contrast, about 70 percent of the students in Jersey City and Rochester received a combined emphasis on algebra, geometry, number, etc., and nearly half the students in Chicago had an emphasis mainly on number.

Research shows that higher achievement in mathematics is associated with teachers having a bachelor’s and/or master’s degree in mathematics.(10) According to their teachers, however, U.S. eighth-grade students were less likely than those in other countries to be taught mathematics by teachers with a major area of study in mathematics (41 percent in the U.S. compared with 71 percent internationally, on average). Among the Benchmarking jurisdictions, the percentages of students taught by teachers with mathematics as a major area of study varied dramatically from 70 to 73 percent in the First in the World Consortium, Naperville, and Rochester, to less than one-quarter in the Delaware Science Coalition and Jersey City.

In general, teachers in many Benchmarking entities and in the United States overall may be overconfident about their preparation to teach eighth-grade mathematics. More teachers in the Benchmarking jurisdictions and in the U.S. nationally reported feeling very well prepared to teach mathematics compared with their counterparts in other countries. In half the Benchmarking jurisdictions, 90 percent of the students had teachers who felt “very well prepared” to teach across a range of 12 general mathematics topics covered by 魅影直播. Across the Benchmarking entities, the smallest percentage of students with teachers highly confident in their preparation to teach mathematics was 75 percent, which was higher than the international average of 63 percent. The comparable figure for the U.S. was 87 percent.

Since entering teachers make up a relatively small percentage of the teaching force, improving teacher quality depends on providing opportunities for professional development. Across the Benchmarking participants, there was considerable variation in the type of professional development that teachers engaged in. For example, only in the First in the World Consortium and Montgomery County did more than half the students have mathematics teachers who reported both observing and being observed by other teachers. In many of the Benchmarking entities, half or more of the students had teachers who reported that their professional development activities emphasized curriculum, but only about one-quarter had teachers who reported that their professional development activities emphasized content knowledge.

The choices teachers make determine, to a large extent, what students learn. In effective teaching, worthwhile mathematical problems are used to introduce important ideas and engage students’ thinking. The Benchmarking results show that higher achievement is related to the emphasis that teachers place on reasoning and problem-solving activities. This finding is consistent with the video study component of 魅影直播 conducted in 1995.(11) Analyses of videotapes of mathematics classes revealed that in the typical mathematics lesson in Japan students worked on developing solution procedures to report to the class that were often expected to be original constructions. In contrast, in the typical U.S. lesson students essentially practiced procedures that had been demonstrated by the teacher.

In 魅影直播 1999, about half the Japanese students had teachers who reported a high degree of emphasis on reasoning activities in their mathematics classes, more than in any other country. The degree of emphasis on reasoning and problem-solving varied dramatically among Benchmarking participants. At the top end, between 41 and 46 percent of the students in Jersey City, the First in the World Consortium, and the Michigan Invitational Group had teachers who reported a high degree of emphasis on mathematics reasoning and problem-solving. Oregon and Chicago had the smallest percentages of students (eight and nine percent, respectively) with teachers reporting this degree of emphasis.

In general, the 魅影直播 1999 data reveal that in most mathematics classes teachers do not focus on mathematics reasoning. Just as was found in the 1995 videotapes, it appears that usually the teacher states the problem, demonstrates the solution, and then asks the students to practice. Ninety-four percent of U.S. eighth graders reported that their teachers showed them how to do mathematics problems almost always or pretty often during mathematics lessons, and 86 percent reported working from worksheets or textbooks on their own this frequently. According to U.S. mathematics teachers, class time is spent as follows: 15 percent on homework review; 20 percent on lecture style teacher presentation; 35 percent on teacher-guided or independent student practice; 12 percent on re-teaching and clarification; 11 percent on tests and quizzes, six percent on administrative tasks; and four percent on other activities.

The 魅影直播 1999 data indicate that the instructional time for learning mathematics, beyond being spent primarily on demonstrations of procedures and repeated practice, becomes further eroded by non-instructional tasks. In Japan and Korea, more than half the students were in classes that never had interruptions for announcements or administrative tasks. Among the Benchmarking participants, the results ranged from 22 percent of the eighth graders in such classes in Naperville to only five percent in Jersey City. Also, 74 percent of the U.S. students reported that they began their mathematics homework during class almost always or pretty often, well above the international average of 42 percent. In most Benchmarking jurisdictions, the results followed the national pattern, although the percentage varied from 43 to 90 percent.

The Benchmarking Study shows that students in schools that are well-resourced have higher mathematics achievement. Among the Benchmarking participants, three-fourths or more of the students in the Academy School District, the First in the World Consortium, and Naperville were in schools where the capacity to provide mathematics instruction was largely unaffected by shortages or inadequacies in instructional materials, supplies, buildings, space, computers and computer software, calculators, library materials and audio-visual resources. These high percentages exceeded those of all the 魅影直播 1999 countries, with the highest percentages (about 50 percent) reported by Belgium (Flemish), Singapore, and the Czech Republic.

Discipline that maintains a safe and orderly atmosphere conducive to learning is very important to school quality, and research indicates that urban schools have conditions less conducive to learning than non-urban schools.12 For example, urban schools report more crime against students and teachers at school and that physical con遡ct among students is a serious or moderate problem. Among the Benchmarking participants there was considerable variation in principals’ reports about the seriousness of a variety of potential discipline problems. In several of the urban districts, however, 10 percent or more of the students were in schools where absenteeism, classroom disturbances, and physical injury to students were felt to be serious problems. Also in several of these districts, 20 percent or more of the students were in schools where intimidation or verbal abuse among students was a serious problem.