In a school year when in-person instruction is already limited, California math teachers are making up for lost time on the fly.
Since school campuses closed in March due to the pandemic, education experts have sounded the alarm that certain groups, such as low-income and special education students, could fall further behind academically than their peers. And now test scores show that students are struggling in math more during the pandemic than in previous years.
But exactly how school districts have planned to mitigate learning gaps looks different depending on the district and even classrooms within a school.
One of California’s largest school districts, San Diego Unified, is pushing ahead with grade-level math content and addressing questions and gaps in learning as they come up during lessons. That contrasts with past approaches to so-called learning loss — when students lose academic skills and knowledge over a period of time — that have involved testing students at the beginning of the year to determine where they need extra help and offer remediation based on the results.
“Over the summer, we kept hearing ‘Shouldn’t we have a diagnostic exam because they missed so much?’” said Aly Martinez, the instructional coordinator of mathematics for San Diego Unified.
While there was no question that students missed critical class time, she and others had major qualms with the diagnostic approach. One of the biggest concerns was putting students in a position where they feel inept at the start of an already chaotic school year.
“The diagnostic test is an emotional task. It’s designed to find where students don’t know the answer,” Martinez said. “My third-grade son had to take a test at the end of the school year in distance learning, and it took nearly five days, and he cried every day. For me, it was a culminating moment about how we are influencing and shaping their math identity when we start by saying, ‘Look at all the things you don’t know and you missed.’”
This fall, the district is encouraging teachers to keep on pace with grade-level content in math and address questions from students as they come up in a method referred to as “just-in-time teaching.” For example, while teaching multiplying and dividing fractions in sixth grade, some students might need a refresher on fractions from fourth grade. Instead of reviewing fourth-grade fraction lessons for a few weeks at the start of the term, the idea is to incorporate a quick lesson or activity that offered some review of the material needed to master the grade-level standard.
San Diego Unified’s approach stems from guidance shared by education groups, such as the National Council of Teachers of Mathematics, which this summer released a toolkit with guidance on how schools should treat math education as the pandemic continues. Among the top suggestions was that schools should avoid front-loading the fall term with testing and review, and instead move straight into grade-level content and regularly check for gaps that need to be addressed.
“We acknowledge that students have unfinished learning. That’s always been the case,” said Patrick Callahan, a mathematician and consultant who has been working with San Diego Unified on its plan for distance learning. “And, yes, it might have been amplified by school closures. But the answer was not to hold kids back and delay access.”
To develop the plan for this fall, Callahan and Martinez looked to research that found diagnostic testing and individual remediation didn’t lead to significant student growth for New Orleans schools following Hurricane Katrina. They also pointed to studies that have shown holding students back in courses such as Algebra 1 rarely leaded to improve outcomes the second time they took the course.
“We wanted to ensure students had more opportunities to work together and with each other. If you give a diagnostic, you identify different gaps for different kids,” he said. “Diagnostics delay access to grade-level math and discourage students working together collaboratively.”
Over the summer, the district-level math leadership team at San Diego Unified created a set of academic priorities for each grade level to adapt to distance learning. That included a suite of review activities based on common problem areas that teachers can easily turn to if students show signs of struggle or are missing a skill necessary for the lesson.
“We created just-in-time resources for every single unit so teachers don’t have to go searching for it at that moment,” Martinez said. “We did the work to anticipate popular unfinished learning opportunities.”
Diagnostic exams can be useful measures to gauge what students know. Many districts require these kinds of assessments at the beginning of and throughout the year to track progress. Plus, some regression or unfinished learning is typical of any school year, especially after students return to school from an extended break.
But in the era of distance learning, when students have limited and unequal amounts of time with teachers, even larger gaps in learning have been anticipated since schools closed last spring.
Early data is showing that those fears were valid — in math at least. Compared with 2019, about twice the number of students nationwide had a significant decline in math scores, falling at least 20 percentile points from last spring to this fall, test results from the Portland-based nonprofit NWEA showed. The exam tested 4.4 million students in grades 3 through 8 nationwide. Reading scores on the test have remained about the same since last year, however.
Molly Keimach, a ninth-grade math teacher at Kearny High School in San Diego Unified, said she “definitely felt like this year started off with more of a struggle than in past years content-wise.” But she isn’t sure whether that’s been because students fell behind last spring, or simply because of the difficulties of keeping students engaged in an online environment this fall
“At the beginning of the school year, almost a third of my ninth-graders were failing. It’s not uncommon to have a high failure rate for that class, but this was higher than I had ever experienced,” Keimach said, referring to the Integrated 1 math course she teaches.
The model San Diego Unified is pushing is familiar to Keimach. In any given year, many of her students come to high school from middle school with learning gaps. She previously had students take pre-tests and other assessments, but after a few years began detecting patterns in the areas that students needed review on, like the distributive property, an algebra concept that many students struggle with, she said.
Now, she incorporates review activities into her lessons based on what students have needed help with before, plus what she finds they need help with from their current work, and skips the diagnostic.
“Just-in-time teaching and learning is essential during distance learning,” Keimach said. “We have half of the time normally and even in normal years there isn’t enough. My bigger concern is not if they learned this before, but are they engaging in online learning now? That’s the biggest struggle.”
Experts like National Council of Teachers of Mathematics President Trena Wilkerson fear that testing and remediation could lead to segregating students into different groups based on their perceived abilities. Some studies and reports have shown that tracking in mathematics can lead to segregation among students along racial and economic lines.
While students can also be separated by skill level in English and science, math is one of the few subjects where students may be assigned a course track as early as fifth grade that continues through middle high school, which in turn can affect their eligibility for college.
“You don’t want to fall into separating students and get into tracking,” Wilkerson said. “If we start separating them, we are facilitating inequities when really students just didn’t have the same opportunity.”
Sara Feiteria, a sixth-grade math and science teacher at Farb Middle School in San Diego Unified, didn’t notice an increase in learning gaps this fall compared with any previous year. But the added challenges of online learning — like not being able to see students who have their cameras off, for example — has made it difficult to maintain her usual teaching strategies.
The district’s pre-made resources have helped her manage class time, she said. And more importantly, they have freed up time for her to focus on building trust with her students in a strange new learning environment.
“The priority is the emotional wellbeing of these kids right now,” she said. “Before even thinking about problem-solving or critical thinking, you need to think about these human beings who need relationships. No priority is going to be met before that.”
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