The level of procedural complexity of problems in Japanese eighth-grade mathematics lessons was different from that in the other countries (figure 2).

	Figure 2 Average percentage of eighth-grade mathematics problems per lesson at each level of procedural complexity, by country: 1999 1Japanese mathematics data were collected in 1995. 2AU=Australia; CZ=Czech Republic; HK=Hong Kong SAR; JP=Japan; NL=Netherlands; SW=Switzerland; and US=United States. 3High complexity: JP>AU, CZ, HK, NL, SW, US. 4Moderate complexity: HK>AU; JP>AU, SW. 5Low complexity: AU, CZ, HK, NL, SW, US>JP. NOTE: Percentages may not sum to 100 because of rounding. For each country, average percentage was calculated as the sum of the percentage within each lesson, divided by the number of lessons. SOURCE: U.S. Department of Education, National Center for Education Statistics. Third International Mathematics and Science Study (TIMSS) 1999 Video Study. (Originally published as figure 4.1 of the report from which this highlights summary is drawn, Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study [NCES 2003-013]).

The overall complexity of the mathematics presented in the lessons is an important feature of the mathematics but is difficult to define and code reliably. This is due, in part, to the fact that the complexity of a problem needs to take into account the experience and capability of the student encountering the problem. What is complex to one student may be less complex to his or her classmate. One type of complexity that can be defined and examined independent of a student is procedural complexity: the number of steps it takes to solve a problem using a common solution method. Three levels of complexity were defined: low, moderate, and high. Low complexity was defined as a problem that required four or fewer decisions by a student to solve it, using conventional procedures. Moderate complexity was defined as a problem that, using conventional procedures, required more than four decisions by the student to solve it and could contain one sub-problem. High complexity was defined as a problem that required more than four decisions by a student, and at least two sub-problems, to solve it, using conventional procedures. Across the three levels of complexity, each of the countries, with the exception of Japan, included, on average, at least 63 percent of problems per lesson of low procedural complexity. At the other end of the scale, up to 12 percent of problems per lesson, on average, were of high procedural complexity, again with the exception of Japan. In Japan, 39 percent of problems per lesson were of high procedural complexity, a greater percentage than in any of the other six countries.