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 The video vignettes were originally made available on a CD-ROM: Video Examples from the TIMSS Videotape Classroom Study: Eighth Grade Mathematics in Germany, Japan, and the United States (NCES 98092).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.
After briefly checking the homework for today, the teacher poses a problem that can be solved by setting up and solving an algebraic inequality. Students work on the problem, then share their solutions with the class. The teacher then poses some follow-up problems.
|The lesson begins with the traditional bow. The teacher asks six students to write the solutions for six of the homework problems on the chalkboard. The problems involve solving inequalitites, such as 6x - 4 < 4x + 10. While they are working, the teacher walks around the room to check whether the students completed their homework. About seven minutes are spent going over the problems, explaining methods, and checking correctness of solutions.
Posing the Problem
|The teacher introduces the main problem for the day by saying, "I will have everyone use their heads and think a little, okay? Until now, we’ve just done calculation practice, but today you will have to use your heads a little." The teacher then puts up a poster with the problem: There are two different types of cakes, one costing 230 yen and the other, 200 yen. You want to buy 10 cakes, but you don’t want to pay more than 2100 yen. How many of each type should you buy? The cakes costing 230 yen "look more delicious." The teacher clarifies the problem by restating it in several ways, and then asks the students to work on the problem individually, for about three minutes, using whatever methods they would like.
Students Presenting Solution Methods
|After about six minutes during which the teacher observes and assists students as they work individually, the teacher asks a student to share her solution method. The student reports that she computed the cost for ten 230-yen cakes and that the total was too much. She reduced the number of 230-yen cakes by one and computed again. She said she had planned to continue this process but ran out of time. Other students, who used the same method, build on her explanation and report that the solution is three 230-yen cakes and seven 200-yen cakes.
Teacher and Students Presenting Alternative Solution Methods
|The teacher introduces another method by saying, "I’ve thought about it too, so... what do you think about this way of thinking." He then describes a method of subtracting off the savings of a cheaper cake (30 yen) from the amount needed to buy all delicious cakes (2300 yen). One would need to subtract seven times to get below the 2100 yen, so one could buy only three delicious cakes. Not all students understand his explanation so he asks another student, whom he knows has used an algebraic inequality, to explain. The student verbally describes the inequality 230x + 200(10-x) < 2100. After the student’s presentation, the teacher challenges students to come up with explanations that others can understand.
Teacher Elaborating on a Student’s Method
|The teacher indicates that the last student’s presentation on using algebraic inequalities captured his goal for the lesson. He says he would like to review the method carefully so others will understand: "To tell you the truth, I was going to set up today what Rika set up but I wanted you all to come up with a number of ways to come up with it. So... we are going to try to do the problem using an inequality equation." He then spends about seven minutes leading the students step by step through the method. At the end of this discussion, he points out the advantages of using this method over the trial-and-error methods presented earlier in the lesson: "The answer will come out quickly... you don’t need to figure out each number one by one."
Posing and Solving Follow-Up Problems
|The teacher presents two similar problems and asks the students to use the method just discussed to solve these problems. One problem was: "You want to buy 20 apples and tangerines all together for less than 2000 yen. Apples are 120 yen each and tangerines are 70 yen each. Up to how many apples can you buy?" He reminds the students about the advantages of using this method and then gives the students about 12 minutes to work individually on them. As he walks around to assist students, he asks two students to write their methods on the chalkboard. The teacher completes this part of the lesson by talking through the students’ work displayed on the board.
Summarizing the Lesson Objective
|The teacher summarizes the major point of the lesson: "What we talked about today was the solution using inequality equations. That is, when you work out problems, instead of counting things one by one and finding the number, it’s usually easier if you set up an inequality equation and find the answer." Then the teacher passes out another worksheet for homework and teacher and students bow to end the class.