A GREAT deal has been made of student achievement data in international comparisons. Less information has been gathered about in various countries. We have a few field studies, such as those reported in The Teaching Gap, by James Stigler and James Hiebert, and in Knowing and Teaching Elementary Mathematics, by Liping Ma. Neither depicts a particularly robust portrait of what American know about mathematics or how to teach it. With the new emphasis on highly qualified teachers from the U.S. Department of Education, teacher quality has moved to center stage. Two new studies add a bit to our knowledge of here and abroad. The first is Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 Video Study, in which videotapes of actually teaching eighth-grade mathematics in seven countries were studied. The report (NCES 2003013) was put together by Hiebert and a host of other researchers and is available at www.nces.ed.gov/timss. The second is Preparing Teachers Around the World, from Aubrey Wang, Ashaki Coleman, Richard Coley, and Richard Phelps of the ETS Policy Information Center. It is available at www.ets.org/research/pic/teachprep.pdf. In 1995, as part of the original TIMSS (Third International Mathematics and Science Study), videos of were made in three nations: Germany, Japan, and the United States. In general, U.S. and German focused on teaching procedures, while Japanese emphasized conceptual matters. One accidental finding cropped up when people coding the videos had a What the hell was that? reaction to noises on the tapes. Those noises were mostly interruptions by the intercom, visitors, etc. More than 30% of American classes suffered interruptions. Zero percent of Japanese classes suffered an intrusion. The TIMSS 1999 Video Study extends the original research to seven countries, adding Australia, the Czech Republic, Hong Kong, the Netherlands, and Switzerland and omitting Germany. (A more detailed summary of this study, by the TIMSS Video Mathematics Research Group, can be found in the June 2003 Kappan.) These countries all scored high or relatively high in TIMSS and TIMSS-R (Repeat). In TIMSS-R, only the Czech Republic did not have a score that was significantly higher than that of the U.S., which scored 502 as compared to the Czech Republic's 520. (The international average was 487.) Getting coders to agree on what they were seeing was difficult in the original study, and it was exponentially more difficult to get coders to agree about what they were seeing when viewing videos from seven countries. In addition, they might have missed something important, as overall judgments of quality did not correlate with judgments on the specific indicators of quality. (These results are from a presentation made at the annual meeting of the American Educational Research Association in April, not from the report itself.) Coders first looked at how much time in different countries spent introducing new content, practicing new content, or reviewing earlier content. American spent more time reviewing old material than anyone else except the Czechs. None of the countries spent a great deal of time practicing new material, but Japanese did allot 60% of their time to introducing new content. Only Japan's lessons were considered to be of high or moderate complexity, 39% and 45% respectively. The U.S. had the fewest lessons considered to be of high complexity (6%) and the third-highest number judged to be of low complexity (67%), behind Australia (77%) and the Netherlands (69%). Only Japanese offered many proofs. Twenty- six percent of the problems in any given lesson contained proofs, and 39% of the lessons contained at least one proof. Second-place Switzerland posted just 3% and 11% respectively. The researchers asked whether the lessons consisted of stating concepts, using procedures, or making connections between mathematical facts. …
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