Using Performance Assessment to Improve Math Learning

K-12 Testing

Nearly 30 California districts are using a set of common performance tasks to guide professional development and improve teaching and learning in mathematics. The tasks focus on student understanding and the ability to transfer knowledge to new tasks. The districts undertook this effort in part to counter the harmful effects of the state’s standardized tests, which are not good measures of mathematical reasoning. The success of the collaborative shows the value and feasibility of performance assessments.


The Silicon Valley Mathematics Assessment Collaborative (MAC) first mapped out the five core ideas on which it would focus across the grade levels. They then selected the Mathematics Assessment Resource Service (MARS) to develop the tasks for each grade level. The tasks were first implemented in 1999 in grades 3, 5, 7, and 9. Districts score their own exams using their own teachers, with scoring leaders trained by MAC. A sample of five percent of all papers are rescored by MAC, which has concluded that reliability is “extremely high.” Administration, scoring and reporting costs only $7.50 per student, which includes fees paid to MARS as well as teacher time.


Teachers use the scored tests in their classes to help students develop deeper understanding. For example, in the first year (1999), fifth grade students did poorly on the flower bed task (see box). Teachers realized they needed to work more on patterns and functions, so that summer upper elementary teachers engaged in professional development in those areas. The next year, the fifth graders (who had not taken MARS in third grade) performed dramatically better on a task covering similar algebraic thinking.


The scoring sessions provide important learning opportunities for math teachers. The participating districts have become convinced that high-quality professional development is worth the investment. Over the years, strengthening teachers' mathematical knowledge, as well as their ability to uncover student misconceptions and to assess learning progress, has led to major gains on MARS at the elementary levels. The 28 MAC districts have more than 40 math coaches who work with teachers during the school year and in the summer. However, the coaches mostly work with elementary teachers. Perhaps as a result, MARS scores in middle and high school were flat from 1999 through 2002.


Research in other school districts found that students whose scores increased on California’s multiple-choice test often did not do well on the performance assessments. However, success on the MARS tasks has been a strong indicator of success on the state test, with scores on the state test in the MAC districts rising quickly. (Similar findings were reported in Queensland, Australia; see Examiner, Winter 2005.)


With 60,000 students and 1,200 teachers participating in a locally organized assessment that is reliably scored by teachers, the MAC project provides further evidence that performance assessment is educationally beneficial, technically feasible, and economically possible.


• For MAC, see .
• “The Mathematics Assessment Collaborative: Performance Testing to Improve Instruction,” by David Foster and Pendred Noyce, M.D., Phi Delta Kappan, January 2004, 367-374 (available on the MAC site).
• For MARS, see