In 1995, the Third International Mathematics and Science Study (TIMSS) included a Videotape Classroom Study. This video study was an international videotape survey of eighth-grade mathematics lessons in Germany, Japan, and the United States. Funded by the National Center for Education Statistics (NCES) and the National Science Foundation, the 1995 video study was the first attempt to collect videotaped records of classroom instruction from nationally representative samples of teachers. The study was conducted in a total of 231 classrooms in Germany, Japan, and the United States and used multimedia database technology to manage and analyze the videos.
The Videotape Classroom Study had four goals:
For the report on the methods and findings of the Videotape Classroom Study, click here.
Example lessons from the TIMSS 1995 Video Study were made available in the form of video vignettes of six eighth-grade lessons, two each from Germany, Japan, and the United States. These example lessons were taught by teachers who volunteered to be videotaped for the project. The video vignettes were originally made available on a CD-ROM: Video Examples from the TIMSS Videotape Classroom Study: Eighth Grade Mathematics in Germany, Japan, and the United States (NCES 98092). Now they are all available for viewing through the links below.
In this lesson students practice using what they know about vertical, complementary, and supplementary angles to calculate the sizes of various angles. The teacher concludes by presenting the formula for finding the sum of the interior angles of any polygon.
Presenting and Checking Warm-Up Problems
|The teacher begins by presenting four situations, all drawn on the chalkboard. Each contains intersecting lines and rays that create vertical and supplementary angles. Students are asked to find the measures for ten angles. The teacher helps find four of the angles by asking questions and providing information. Then he asks students to find the rest. After about 40 seconds, the teacher works through the remaining problems in a similar way, by eliciting responses from students using questions such as "If this angle is a right angle and this is thirty degrees, what does F have to be?... And what’s left for angle E?... They all have to add up to...?" The warm-up activity lasts for about five minutes.|
|The teacher asks students to take out the worksheet that was assigned earlier in the week for homework. The worksheet is titled "Types of Angles" and includes definitions of terms (such as "supplementary"), sample problems with solutions, and about 40 problems to work. Answers are checked by the teacher in a question and answer format: "The complement of an angle of eighty-four, Lindsay would be... (Sixteen) You sure about your arithmetic on that one? (Six?) Six. Six degrees. Albert, number four." Moving through the homework in this way continues for about ten minutes.|
|The teacher hands out a worksheet titled "Types of Angles (Continued)" that contains two sample problems with solutions and 15 problems which ask for measures of angles shown in drawings. The teacher introduces the worksheet by working through the first several problems with the students, asking questions such as, "If angle 3 is one hundred twenty degrees and angle 3 and angle 1 are vertical, what must angle 1 be equal to?" While the students work individually on the rest of the problems, the teacher circulates around the room, assisting individual students.|
Providing Extra Help on Challenging Problems
|While assisting students on the worksheet problems, the teacher receives an increasing number of questions on problem 37 (Find the measure of two angles that are equal and supplementary) and problem 38 (Write an equation that represents the sentence: the product of 12 and a number is 192). He decides to work these problems with the class. For problem 37, he says "Two angles are supplementary. Therefore they must add up to one hundred eighty degrees. But they are equal so let’s call one QRS and the other SRT (draws a figure on the chalkboard). Each one of them has to be...?" After both problems have been answered and discussed, the students return to their worksheets.|
Checking More Homework and Introducing a New Formula
|After the students finish the worksheet, the teacher asks them to get out "The worksheet we did on Friday after the quiz." This worksheet has two problems. The first contains a map of two streets intersecting in a 45 degree angle with a triangular shaped piece of land between the streets. A boundary line divides the piece into two parking lots. The task includes finding the measure of the angle formed by the property line and First Street, and suggesting a more equal way to divide the lots. The teacher elicits the answers to these questions from the students, helping out when the students are stuck. The second problem involves finding the sum of the interior angles for a six-sided figure. The teacher asks students for the answers they found using their protractors. The teacher then presents a formula and asks students to try it out.|
Previewing the Upcoming Schedule
|The teacher concludes the lesson by announcing the topic for the next day and informing students of the dates for the next quiz and the next exam.|