Countries reporting data: Australia, the Czech Republic, Japan, the Netherlands, the Special Administrative Region (SAR) of Hong Kong, Switzerland, and the United States
The 1999 Third International Mathematics and Science Study (TIMSS) included a Videotape Classroom Study of 8th-grade mathematics classes in Australia, the Czech Republic, Japan, the Netherlands, the Special Administrative Region (SAR) of Hong Kong, Switzerland, and the United States. The study used nationally representative class samples from these countries to examine the differences and similarities in mathematics lessons.
The study looked at the percentage of lesson time 8th-grade mathematics teachers devoted on average to reviewing previously studied content compared with studying (both introducing and practicing) new content. In the United States, no difference was found between the average percentage of lesson time devoted to studying new content and the percentage devoted to reviewing. By contrast, classes in Australia, Hong Kong, Japan, the Netherlands, and Switzerland spent more time, on average, studying new content than reviewing. The opposite was true in the Czech Republic, where more time was spent reviewing studied content than in all other countries except the United States (table 1a).
This study also examined how mathematics problems were solved in each lesson. The in-class explanation and discussion of each problem’s solution was classified into one of four types, ranging from "making connections" (or explaining the mathematical relationships and/or reasoning involved in solving the problem) to "giving results only" (without an explanation of any mathematical processes) (see Definitions and Methodology).
On average, in the United States, 1 percent of problems per lesson were solved by making connections; 8 percent were solved with a discussion of mathematical concepts (but not mathematical relationships or reasoning); 55 percent involved an explanation of the steps and rules or the algorithmic procedures for solving the problem (but no explanation of the underlying mathematical concepts); and 36 percent were solved by giving results only. The Czech Republic, Hong Kong, Japan, and the Netherlands had a higher percentage of problems per lesson that were solved by making connections (10, 12, 37, and 22 percent, respectively). Compared with the United States, every other country1 had a higher percentage of problems per lesson that were solved with a discussion of concepts (from 19 to 33 percent) (table 1b).
Figure 1. Average percentage of 8th-grade mathematics lessons spent studying new content and reviewing previously studied content, by country: 1999
Table 1a. Average percentage of 8th-grade mathematics lesson time devoted to various purposes, by country: 1999
Table 1b. Average percentage of problems per 8th-grade mathematics lesson solved by explicitly using processes of each type, by country: 1999
Definitions and Methodology
Under the auspices of the International Association for the Evaluation of Educational Achievement (IEA), the Trends in International Mathematics and Science Study (TIMSS) of 1999 assessed and collected data in 38 countries.TIMSS 1999 included a video study, which examined instructional practices. The 1999 Video Study incuded six countries (Australia, the Czech Republic, Japan, the Netherlands, Switzerland, and the United States) and one region (the Special Administrative Region [SAR] of Hong Kong) in the mathematics portion. These countries were selected because their 8th-grade students had average achievement scores that were higher than those of U.S. 8th-grade students on the TIMSS 1995 mathematics assessment.
During the survey, each of the videotaped lessons was examined to assess various elements of the lesson—such as the lesson’s coherence, the type of reasoning required of students, the level of complexity of the lesson’s content, the connections between parts of the lesson, the kinds of tasks students were asked to engage in as part of the lesson, and the methods students used to solve mathematical problems. For this in-depth analysis of the videotaped lessons, an international team of bilingual representatives from each country assembled to develop and apply codes to the video data.
This indicator presents findings based on the study’s coding of the lesson content and of the problem-solving phase of each lesson. For the latter analysis, four mutually exclusive categories were created to classify the type of mathematical processes that were explicitly explained or discussed during the lesson. In order from the simplest to the most complex, these categories are as follows:
Giving results only in which no processes were explained. Public work consisted solely of stating an answer to the problem without any discussion of how or why it was attained.
Using procedures in which the steps and rules or the algorithmic procedures for solving the problem were explained but underlying mathematical concepts were not.
Stating concepts in which mathematical concepts, such as mathematical properties or definitions, were explained but mathematical relationships or reasoning were not.
Making connections in which the mathematical relationships and/or mathematical reasoning involved in solving the problem were explained.
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