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Press Release · October 11, 2011

Diagnostic Tests Result in Big Math Gains

Evidence from San Diego Shows Timely Feedback Helps Teachers Help Students

SAN FRANCISCO, October 11, 2011—Participation in a math testing program that gives teachers timely, detailed feedback on individual students can result in strong achievement gains, according to a study released today by the Public Policy Institute of California (PPIC).

A mandatory testing program recently used in the San Diego Unified School District—the state’s second largest—made use of tests that are freely available to middle and high school math teachers in California through the Mathematics Diagnostic Testing Project, a joint program of the California State University and University of California. Using data from fall 2001 to spring 2007, the PPIC study found that gains for students were large—enough to move a student originally at the 50th percentile in math to the 57th percentile a year later.

The Mathematics Diagnostic Testing Project offers course-specific tests and sends teachers feedback on individual students and the entire class—often within a week after testing in the spring. The tests are graded locally in 10 regional offices, where coordinators work with local schools to interpret and use the results.

The San Diego district’s goal in requiring this testing was to help math teachers place students in classes of appropriate difficulty the following year. Schools also used the tests to identify students who should attend summer school. The PPIC report concludes that San Diego was successful in both areas. Students were more accurately placed in math classes suited to their skill levels, and low-achieving students were more likely to attend summer school.

“The timely information from diagnostic testing allows teachers to act quickly on what they learn about a student’s math skills,” says Julian Betts, PPIC Bren policy fellow, who co-authored the report with Youjin Hahn, assistant professor at Monash University, Australia, and Andrew Zau, senior statistician for the San Diego Education Research Alliance, hosted by the economics department at the University of California, San Diego. “More districts could use this type of testing to direct help to struggling students and place them in classes that will help them succeed.”

The PPIC study found that if a student took a diagnostic test a second consecutive year, the benefits persisted and increased slightly. But if the test was not repeated, the benefits begin to dissipate, suggesting that repeated diagnostic monitoring across grades is important to reap tangible benefits over the course of a student’s career.

The diagnostic tests were used a second way in San Diego. Many teachers used the program to test individual classes. (Teachers statewide have used the test this way for several decades.) This voluntary testing was not used to recommend summer school placement or to channel students into appropriate math classes. The PPIC authors found that voluntary testing failed to achieve the same benefits as systematic use. A possible reason is that widespread testing encouraged the whole math department at a school to work together on diagnosing and overcoming students’ difficulties.

The timely feedback offered in the diagnostic testing program is a contrast to the main state test, the California Standards Test (CST), used in the state’s school accountability system. The CST has many goals, but its primary one is to measure student proficiency and determine which schools receive interventions and sanctions set out in the federal No Child Left Behind law. Students also take the CST in the spring, but results arrive late in the summer. This is too late to help students in the year they take the test and often too late to help steer students into summer school or help teachers make appropriate math class placements.

The PPIC report has implications for the CST. Although the CST provides some information on students’ skills, it could do more to pinpoint for teachers the areas in which students need more help. Computerizing the CST could also yield faster feedback and allow a teacher to address students’ weaknesses before they move on to a new grade. The authors note that California’s membership in the SMARTER Balanced Assessment Consortium may offer an opportunity to address these issues. This national consortium is planning computerized testing and is interested in providing teachers with tests designed to diagnose how well students have mastered material they have just been taught.

Does Diagnostic Math Testing Improve Student Learning? is funded by the Donald Bren Foundation. The California Academic Partnership Program also provided support to the authors for related research.


PPIC is dedicated to informing and improving public policy in California through independent, objective, nonpartisan research on major economic, social, and political issues. The institute was established in 1994 with an endowment from William R. Hewlett. As a private operating foundation, PPIC does not take or support positions on any ballot measure or on any local, state, or federal legislation, nor does it endorse, support, or oppose any political parties or candidates for public office.