Exhibit 6.8 presents a profile of the activities most commonly encountered in mathematics classes around the world, as reported by mathematics teachers. As can be seen from the international averages, the two predominant activities, accounting for nearly half of class time on average, were teacher lecture (23 percent of class time) and teacher-guided student practice (22 percent). In general for the United States overall and the Benchmarking entities, teachers’ reports on the frequency of these activities matched the international profile. 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. One noteworthy exception is 26 percent of class time in Naperville spent on homework review, compared with 15 percent for the United States.
Lesson 4 Homework Practice Percent Equation
As shown in Exhibit 6.9, most students internationally (86 percent on average) agreed with teachers’ reports about the prevalence of teacher-guided activities, saying that their teachers frequently showed them how to do mathematics problems. Just as found in the 1995 videotapes, it appears that in the U.S. 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. More than 90 percent of the students in each of the Benchmarking entities reported this also. Compared with their counterparts internationally (59 percent), more U.S. students reported that working independently on worksheets or textbooks occurred almost always or pretty often (86 percent). Working on their own on worksheets or textbooks was also quite pervasive throughout the Benchmarking entities, where more than 80 percent of the students in each jurisdiction reported doing this activity that frequently.
Compared with students internationally, eighth graders in each of the Benchmarking jurisdictions and in the United States overall reported an unusually large amount of classroom time devoted to working on homework. Internationally, 55 percent of the students reported frequently discussing their completed homework. The figure for the United States was 79 percent, and it ranged from 70 to 91 percent for the Benchmarking jurisdictions. An even greater difference was evident for frequently beginning homework in class – 42 percent internationally compared with 74 percent for the United States. In the Benchmarking jurisdictions, from 43 to 90 percent of the students reported beginning their homework in class almost always or pretty often.
Educators, parents, employers, and most of the public support the goal of improving students’ capacity for mathematics problem-solving. To examine the emphasis placed on that goal, TIMSS created an index of teachers’ emphasis on mathematics reasoning and problem-solving (emrps). As shown in Exhibit 6.11, the index is based on teachers’ responses about how often they asked students to explain the reasoning behind an idea, represent and analyze relationships using tables, charts, or graphs, work on problems for which there was no immediate solution, and write equations to represent relationships. Students were placed in the high category if, on average, they were asked to do these activities in most of their lessons. The medium level represents students asked to do these activities in some to most lessons, and students in the low category did them only in some lessons or rarely.
Exhibit R3.7 in the reference section shows the percentages of students asked in most or every lesson to engage in each of the activities included in the problem-solving index. For comparison purposes, the exhibit also shows the percentages of students asked to practice computational skills in most or every lesson. According to their teachers, internationally on average nearly three-fourths of the students (73 percent) were asked to practice their computational skills in most or every mathematics lesson. Nearly as many (70 percent) were asked to explain the reasoning behind an idea this frequently. The other three problem-solving activities occurred much less often. Forty-three percent of students, on average across countries, wrote equations representing relationships in most or every lesson, but only about one-fourth (26 percent) represented and analyzed relationships using tables or graphs, and about one-fifth (21 percent) worked on problems for which there was no immediately obvious method of solution. While the Benchmarking entities did not vary greatly from the international profile, there were differences. For example, twice as many students as internationally reported spending time in most or every lesson working on problems for which there was no immediately obvious method of solution in the First in the World Consortium, the Jersey Public Schools, and the Michigan Invitational Group (44 to 51 percent). More than 90 percent of the students in Jersey City and the Michigan Invitational Group were frequently asked to explain the reasoning behind an idea, and 90 percent of the Naperville students were frequently asked to write equations to represent relationships. 2ff7e9595c
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