Learning Math Virtually: What’s Essential in Assessment?

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What a difference a pandemic makes. Just last week, the University of California system broke with decades of tradition by deciding to permanently suspend the SAT and ACT tests as admissions requirements for the system’s nine undergraduate campuses.

Evidence of the high-stakes tests’ racially disparate impact has been clear for years, as has research showing that high school grades are the strongest predictor of students’ performance in college. Still, it’s hard to imagine the university moving so swiftly without the forced cancellation of SAT and ACT test administrations this spring. (A civil rights lawsuit claiming that the tests constitute illegal discrimination is currently moving through the courts and may also have played a role.)

That, in turn, forced universities around the country to envision admissions without admissions tests. Just as the COVID-19 pandemic has given rise to the concept of essential work, the urgency of responding is leading educators to re-think what’s essential with respect to learning.

It’s helping illuminate how traditional forms of assessment, especially standardized tests, often fail to address the uneven playing field that results from racial and socioeconomic disparities. They also contribute to the high-stakes nature of math education in particular. When it comes to assessing students, what’s essential is fostering learning and expanding opportunity, rather than ranking and sorting students.

This applies not just to admissions testing, but to classroom testing as well. Particularly in math, traditional tests can provide a limited picture of students’ abilities: Their emphasis on speed, procedural knowledge, and correct answers can trigger anxiety while only measuring superficial learning at best. In fact, typical math tests seem to be designed more for efficiency than for authenticity with respect to the real-world use of mathematics.

“The traditional rules for testing are about reducing time for grading,” notes Hal Huntsman, mathematics professor at Antelope Valley College in Lancaster, Calif. “If all I’m doing is looking to see if you got the right answer, and maybe a little bit of work that shows you didn’t copy from somebody, that takes me almost no time.”

Under distance learning, an emphasis on “answer getting” makes even less sense, since students can easily turn to calculators or online materials. Therefore, despite the challenging conditions for learning, the pandemic may prove to be fertile ground for cultivating more growth-oriented approaches to assessing mathematics that Huntsman and other equity-minded math instructors in schools and colleges are already embracing. These include:

Instead of trying to prevent students from “cheating,” design your test (or homework) knowing that students have access to a range of tools and resources.

Francis Su, Harvey Mudd mathematician and past president of the Mathematical Association of America, notes that standardized exams “drive too much of what we teach.” His recent blog includes new test questions he’s developed during the COVID-19 crisis, such as this one:

Choose one interesting problem from the text of medium difficulty that was not assigned. Describe why you find it interesting. Then either solve it, or find a solution online and work through it, using your own understanding to critique that solution and improve it.

Provide opportunities for students to improve their grade through feedback and revision, just as they might revise a paper in a composition class.

“Learning doesn’t happen in the submission, it happens in the revision” was one of the messages in Tests, Assessments and Learning Math: Equitable Alternatives in Pandemic Times, a recent webinar hosted by TODOS.

“If you see math not as something to complete, but something to connect to and ask questions about, that’s a very healthy place to be when it comes to learning,” said Vanson Nguyen of College of Alameda.

Nguyen’s co-presenter, Amanda Ruiz of the University of San Diego, noted that she no longer gives students a numerical grade when she returns exams the first time. Instead she gives them a C (for correct), P (for partially correct), or NY (for not yet correct). The point is for students to experience mistakes as opportunities to learn rather than to be penalized.

De-emphasize tests, while emphasizing the multiple ways students have to demonstrate learning during class — including discussions and projects.

“Unlike math problems requiring an identical solution from each student, project work puts students in the role of ‘makers’ who manage their work, see the varied and concrete results of their efforts, and learn from each other,” note Phil Daro and Harold Asturias in the Just Equations publication, Branching Out: Designing High School Math Pathways for Equity.

When his classes were still meeting, Huntsman says his PreCalculus students would spend half the time at the board working on problems together. With distance learning, he’s trying to replicate that as much as possible through Zoom breakout rooms as well as Socratic conversations to observe students’ learning processes. But, since some college students participate asynchronously, making this happen with virtual learning is more challenging at the college level than, say, in K-12. Even for those students who attend class, though, it is not easy to view each others’ work. Let’s keep our eyes open for innovations to solve this dilemma.

These examples show how resourceful math educators can respond to the pandemic by adapting their assessment practices in ways that actually foster deeper learning.

As classroom teachers adapt to these changes in real time, the University of California has given itself four years to either come up with a new assessment to replace the SAT and ACT or simply admit students without traditional assessments. (Students have the option of submitting SAT or ACT scores for two years, and the system will be test-blind for admissions after that.)

As UC faculty and administrators ponder their next steps in admissions policy, they, too, should think outside the box. Given the limits of traditional multiple-choice tests, they should give a closer look to next-generation forms of assessment that allow students to more authentically demonstrate what they’ve learned.

These include portfolios, capstone projects, graduation profiles and digital badges — and other forms of performance assessment that provide a range of ways for students to share their work. Using them sounds challenging because they don’t plug neatly into a formula like an SAT score. Just like traditional math tests, traditional bubble tests are easy to use. But they may be equally limited as reflections of students’ capacity.

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