Content
Algebra and geometry are well represented in the 28 TIMSS videos. The main topic of thirteen lessons concerns some aspect of linear expressions, linear functions, or linear equations (see Algebra). Five of the lessons focus on preparing for, learning, or using the Pythagorean theorem. However, statistics, an important topic for prospective teachers, is the main topic of only two lessons (Australian lessons 3 and 4, A3 and A4).
During the TIMSS work session, team members noted that the videos also afforded discussion of other aspects of mathematics important to teachers. For example, a mathematician observed,
N2 would provide an opportunity for teachers to learn a geometric proof of the Pythagorean theorem and then move on to a more general discussion of the importance and meaning of proof in mathematics. Participants thought it would be particularly useful to compare video lessons from different countries to illustrate the variety of ways one could address an issue. HK3 also deals with issues of proof; viewers could examine the similarities and differences in the two lessons’ approach to proof.
Pedagogy
The videos also afford discussion of pedagogical issues. Lessons are indexed by instructional decisions, instructional situations, and instructional strategies. The few lessons that show the use of technology may stimulate thought-provoking conversation, because technology is used very differently in these lessons. For example, computers are used by students for classwork in A1 and by the teacher at the beginning and end of the lesson in J3. The teacher uses an overhead projector to illustrate the proof of the Pythagorean theorem in N2, for class discussion of an investigation in A1, and to assign written work in US2. See Using Technology and Technology.
After the TIMSS work session, a professional developer said,
Our team explored the advantages and disadvantages of the use of manipulatives when teaching the Pythagorean theorem by comparing a Swiss lesson [S3] with a Czech lesson [C1]. Additionally as a team we investigated elements of teaching and learning by comparing and contrasting two examples of teachers’ use of mathematical language in a Hong Kong lesson [HK1] and a United States lesson [US3].
The lessons in English may best illustrate for U.S. teachers issues of precision of language and other language concerns. Lessons are taught in English in three countries: Australia, Hong Kong (with the exception of HK2), and the United States.
Some representations used in the lessons may be new to U.S. viewers. For example, J4 shows the use of a “line graph”—a representation of algebraic relationships. Line graphs and related representations are discussed under Line Models.
J3 has a representation of a word problem that many viewers have found novel and interesting, which involves calculating the amount of money left in two wallets. After reading the problem aloud, the teacher puts the representation of the problem situation on the board and simulates the change from day to day by taking one “coin” from each “wallet” and moving them to the “offertory box.” J3 is also notable for its exceptionally detailed Lesson plan.
Additional resources
The public release lessons often include the related curriculum materials, which viewers can read and think about before viewing the lessons. The public release lessons also include commentaries from researchers and national research coordinators from the various countries, as well as commentaries from the teachers of the lessons. These provide a sense of the different foci of mathematics education in different countries.