The Third International Mathematics Study

Ironically, the findings of international tests that included the Third International Mathematics and Science Study (TIMSS) showed that, while Japanese teachers taught according to the NCTM Standards documents, the Standards were not widely applied by teachers in the United States. In 1995, TIMSS gathered data on half a million students from 41 countries, focusing on student achievement, curricula, and teaching. The fact that Japan’s students scored highest while U.S. students scored below the international average sparked a huge call to look carefully at the U.S. education system to determine where improvements could be implemented. In the report A Splintered Vision (Schmidt, McKnight, and Raizen, 1996), an examination of the curriculum and teacher data of TIMSS revealed that the U.S. curriculum was redundant and less challenging than those of many other countries. This report was a major catalyst for generating interest in developing a coherent and national vision on curriculum, such as the Common Core Standards.

Soon after the TIMSS report, the National Research Council published the book Adding It Up: Helping Children Learn Mathematics (2001) which included recommendations supporting NCTM’s recommendations for improving teaching, curriculum, and teacher education in grades PreK-8. The council identified five interdependent components of mathematical proficiency:

1. Conceptual understanding refers to the “integrated and functional grasp of mathematical ideas,” which “enables them [students] to learn new ideas by connecting those ideas to what they already know”

• 2. Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• 3. Strategic competence is the ability to formulate, represent, and solve mathematical problems.
• 4. Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification.
• 5. Productive disposition is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’ own efficacy
• (116)

Although much has been written about TIMSS content results, it is important to note that TIMSS 1999 also videotaped classrooms of seventh- and eighth-grade math and science lessons in Australia, the Czech Republic, Hong Kong SAR, Japan, the Netherlands, Switzerland, and the United States (http://wwwtimssvideo.com). Each lesson includes transcripts, comments, and reflection by the teacher. The analysis of the videotapes of eighth-grade mathematics teaching in typical classrooms of the six countries show that while 54% of the mathematics lessons in Japanese classrooms challenged students to work on nonroutine problems, 0-52% in the U.S. eighth-grade mathematics lessons did so (Hiebert et al., 2003).