Third International Mathematics and Science Study What does the study show? What does analysis of the data show later (NCES study 2003)? Watch video clips of classrooms - what types of teaching and learning are in effect? Stephen Hegedus, Department of Mathematics MTH310 - Spring 2006

From Attaining Exellence: A TIMSS Resource Kit, US DoE TIMSS ANSWERS THESE QUESTIONS: Are U.S. curricula and expectations as demanding as those of other nations? How does U.S. classroom instruction compare with that of other countries? Do U.S. teachers receive as much support in their efforts to teach students as their colleagues in other nations? Are U.S. students as focused on their studies as their international counterparts?

From Attaining Exellence: A TIMSS Resource Kit, US DoE How do our BEST 8th graders stack up? % in world’s top 10%

From Attaining Exellence: A TIMSS Resource Kit, US DoE EIGHTH-GRADE CURRICULA The eighth-grade mathematics curricula in Japan and Germany focus on algebra and geometry, while U.S. curricula still include considerable arithmetic. Topic coverage in U.S. eighth-grade mathematics classes is not as focused as in Germany and Japan (although in science, topic coverage may be similar to other countries in degree of focus). U.S. curricula are defined locally, whereas the curricula of most other nations are established nationally.

From Attaining Exellence: A TIMSS Resource Kit, US DoE EIGHTH-GRADE MATHEMATICS TEACHING What we teach in eighth-grade mathematics, most other countries teach in the seventh. The content of U.S. Eighth-grade mathematics lessons require less high-level thought than classes in Germany and Japan. The typical goal of a U.S. eighth-grade mathematics teacher is to teach students how to do something. The typical goal of a Japanese teacher is to help students understand mathematical concepts.

From Attaining Exellence: A TIMSS Resource Kit, US DoE Teachers’ Lives Unlike U.S. teachers, new Japanese and German teachers receive long-term structured apprenticeships in their profession. Japanese teachers have more opportunities to discuss teaching-related issues than so U.S. teachers. U.S. teachers have more college education than those in all but few TIMSS countries. Students diversity and poor discipline are challenges not only for U.S. teachers, but for their German colleagues as well.

From Attaining Exellence: A TIMSS Resource Kit, US DoE Students’ Lives Eighth-grade students of different abilities are typically divided into different classrooms in the United States and different schools in Germany. In Japan, no ability grouping is practiced. In the United States, students in higher level mathematics classes study different material than do students in lower level classes. In Germany and Japan, all students study the same material, although in Germany, lower level classes study it with less depth and rigor. Japanese eighth graders are preparing for a high- stakes examination to enter high school.

From Attaining Exellence: A TIMSS Resource Kit, US DoE Rethinking Common Beliefs- We Know the Problem Is NOT: TIME -- U.S. eighth-graders have more hours of instruction in mathematics and science that students in Japan or Germany, HOMEWORK -- U.S. students do as much or more. TV -- Japanese students watch as much TV, yet do better in school.

From Attaining Exellence: A TIMSS Resource Kit, US DoE Investment In TIMSS Provides objective assessment of where we stand in comparison to other countries. Shows aspects of U.S. education that deserve attention. Helps states and localities reflect on :world- class” education.

Procedural Complexity In NCES 2003 report on Seven countries in TIMSS1999: The complexity of the mathematics presented in the lessons is an important feature of the mathematics but it is difficult to define and code reliably. The complexity of a problem depends on a number of factors, including the experience and capability of the student. One kind of complexity that can be defined independent of the student is procedural complexity—the number of steps it takes to solve a problem using a common solution method. The mathematics problem analysis group developed a scheme for coding procedural complexity and analyzed every problem worked on or assigned during each eighth-grade mathematics lesson (independent and concurrent problems). Problems were sorted into low, moderate, or high complexity according to the following definitions:

Low complexity: Solving the problem, using conventional procedures, requires four or fewer decisions by the students (decisions could be considered small steps) The problem contains no sub-problems, or tasks embedded in larger problems that could themselves be coded as problems. ° Example: Solve the equation: 2x + 7 = 2. Moderate complexity: Solving the problem, using conventional procedures, requires more than four decisions by the students and can contain one sub-problem ° Example: Solve the set of equations for x and y: 2y = 3x - 4; 2x + y = 5. High complexity: Solving the problem, using conventional procedures, requires more than four decisions by the students and contains two or more sub-problems

Role of Mathematical Reasoning

How is Mathematical Reasoning developed? Focus on many or similarly related problems Broader problem-solving situations Unrelated problems lead to fragmented lessons

Broader Pedagogical Traits All countries introduced topics through problem solving. Japan and the Netherlands provided two comparatively distinct learning environments for students as defined by a few basic organizational features: Japanese eighth-grade mathematics lessons focused on presenting new content through solving a few problems, mostly as a whole class, with each problem requiring a considerable length of time In Dutch lessons, private work played a more central role, with eighth- grade students spending a larger percentage of time working on a set of problems, either reviewing old homework or starting on newly assigned homework. In these different structures, the teacher, the written curriculum materials, and the students would seem to play quite different roles.

Conclusion So if TIMSS is assessing complex problem- procedures which are procedurally defined then we have excellent benchmarks, If we are after the development of deep, conceptual problem-solving then we need to look further as the studies do show very different classroom cultures and pedagogies that have a direct impact on student performance.