With new math approach, San Diego Unified School District moves away from regular standardized testing

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New test eliminates multiple choice and aims to capture more insight about how students are solving math problems.


The traditional ways of teaching math have not been working, according to the San Diego Unified School District.

Years ago, the district surveyed students and found that many of them couldn’t explain what their answers meant or why they were learning the math concepts.

What’s more, some student demographic groups were succeeding in math while students with disabilities, English-learners, and low-income, Black and Latino students all tended to do worse than their peers, according to district math scores.

San Diego Unified says it has been working the past few years to fix those problems as part of a larger project to change the way it teaches math.

One strategy is to change the way schools test students’ math skills.

Standardized testing is the only way to compare the academic performance of students across California and the country. Standardized tests can be graded quickly, and they provide a simple number score to help show how students are doing academically.

But critics say standardized tests present a limited picture of students’ knowledge and capabilities.

For one thing, the tests often rely on multiple-choice questions. Students can get a multiple-choice answer correct by guessing or the process of elimination, rather than by knowing how to calculate the correct answer.

San Diego Unified officials say multiple-choice questions also can confine students’ thought processes to those that teachers or test-makers want them to use and can obscure information about how students are choosing to solve a problem.

“Multiple choice is often called forced choice because you’re forced to think about the problem in the way that they presented the solutions,” said Patrick Callahan, a consultant San Diego Unified hired to reform its math program.

Callahan said traditional standardized testing also favors students whose families have more resources, such as access to tutoring or summer programs, leading to apparent disparities in math performance.

Federal judges panel says the mandate will be paused, pending appeal, as long as the district continues offering vaccination deferrals to pregnant students.

Nov. 29, 2021

Statewide and across San Diego Unified, there are significant disparities among student demographic groups in math scores on the state’s standardized tests.

Overall, about 49 percent of the district’s students met or exceeded state standards in math in 2019, the last year state tests were administered.

But just 15 percent of students with disabilities and students learning English, and 34 percent of low-income students met or exceeded the standards. Meanwhile, about 73 percent of students from higher-income families met or exceeded the standards.

About 73 percent of Asian students and 70 percent of White students met or exceeded the standards, while 28 percent of Black students and 32 percent of Hispanic or Latino students did.

Those disparities exist partly because some students have been given more tutoring, after-school programs and other chances to practice and get feedback on their math work, Callahan said. Because math traditionally focuses on computation, speed and accuracy, students who get extra chances to practice have an advantage, he said.

Alexandra Martinez, math instructional coordinator for San Diego Unified, said the focus on computation also doesn’t help students when they graduate from high school and enroll in college or apply for jobs, because colleges and employers want students who are critical thinkers who can apply their math knowledge, rather than be human calculators.

“This narrow focus really resulted in an overemphasis on procedural skills at the expense of being able to apply creative solutions to solve real-world problems,” Martinez said.

Last spring, schools were allowed to replace the state’s tests with their own internal tests because of the COVID-19 pandemic. San Diego Unified rolled out a new districtwide math test that moves away from multiple choice and a reliance on computational skills.

The district’s new test has no multiple-choice questions and requires students to write out their answers. The test asks students to explain how they are using formulas and math concepts.

“What approaches they use, how they solve the problem is valuable information, in addition to whether they got it correct,” Callahan said.

The new test provides three scores rather than one — for students’ knowledge of math, such as whether they know key math concepts and formulas; their application of math knowledge; and their ability to communicate their reasoning.

Results from the spring test, released in October, revealed that nearly half of students struggled to explain their answers and why they solved a problem the way they did, even though they were generally successful in choosing the right answers.

About 82 percent of students scored proficient in demonstrating knowledge of math, but 54 percent were proficient in explaining why and how they solved the problems. About 73 percent of students were proficient in applying math knowledge.

As with the state math test scores, there were disparities among some student groups. About 26 percent of students with disabilities, 27 percent of English-learners and 36 percent of Black students scored proficient in communication. For math knowledge, 58 percent of English-learners, 61 percent of students with disabilities and 70 percent of Black students showed proficiency.

Wendy Ranck-Buhr, an instructional support officer for San Diego Unified, said simply changing the way the district tests won’t bring better math results for students. Rather, the new test will provide teachers with more details of what students know and how they are thinking so that teachers can give them instruction that is more tailored to their needs, she said.

“An assessment itself is not going to close the gap,” Ranck-Buhr said. “It’s to show opportunities for teaching, where teachers can give more targeted feedback for students.”


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