Where the old way of testing math skills just didn’t add up
SAN DIEGO — The traditional methods of teaching math have not been working, San Diego Unified officials say.
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, low-income students, and 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 over the last few years to fix such problems as part of a larger project to rethink 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 by the process of elimination, rather than by knowing how to calculate the correct answer, experts say.
San Diego Unified officials say multiple-choice questions also can confine students’ thought processes to ways of thinking that teachers or test-makers want them to use, and they 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 that 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.
Statewide and across San Diego Unified, there are notable disparities among student demographic groups in math scores on the state’s standardized tests.
About 49% of San Diego Unified students overall met or exceeded state standards in math in 2019, the last year state tests were administered.
But 15% of students with disabilities and students learning English and 34% of low-income students met or exceeded the standards. Meanwhile, about 73% of students from higher-income families met or exceeded the standards.
The gaps also were large between student racial groups. About 73% of Asian students and 70% of white students met or exceeded the standards, while 28% of Black students and 32% of Hispanic or Latino students did.
These 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 these extra chances to practice have an advantage over their peers, he said.
“It wasn’t really a difference in what students were capable of doing. It was a difference in who had access to different support systems,” Callahan 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, said Alexandra Martinez, math instructional coordinator for San Diego Unified.
“This narrow focus really resulted in an over-emphasis 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 pandemic. San Diego Unified rolled out a 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.
Because the test only accepts written, free-response answers from students, the tests revealed students’ life experiences, Martinez said.
On the new math test, Martinez saw students give a variety of answers that showed their cultural background. For a test question with the answer $12, she said, some students wrote “12 dollars” in Spanish or the number 12 with the dollar sign after it.
For another question that asked how long it would take to bike to school, Martinez remembers a student gave the correct answer, 20 minutes, and voluntarily added, “depending on traffic.” That told Martinez that the student regularly bikes to school.
“It made me think about the three-dimensional aspect of students that’s often not acknowledged in assessments,” she said. “Assessments can be really dehumanizing because they bind you into that true-false, multiple-choice box binary.”
The new math 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 last month, 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% of students scored proficient in demonstrating knowledge of math, but 54% were proficient in explaining why and how they solved the problems. About 73% of students were proficient in applying math knowledge.
As with the state math test scores, there were disparities among some student groups. About 26% of students with disabilities, 27% of English learners and 36% of Black students scored proficient in communication. For math knowledge, 58% of English learners, 61% of students with disabilities and 70% of Black students showed proficiency.
Wendy Ranck-Buhr, an instructional support officer for San Diego Unified, said simply changing the way the district tests students won’t bring about better math results. 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.”