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Creative Ways to Assess Math Understanding

Traditional math assessments tend to provide a narrow gauge of student learning—here’s how some teachers are going deeper. 

January 15, 2021
High school student writing in class
Jacob Lund / Alamy Stock Photo

Math teachers are rethinking student assessments in creative ways that allow them to get a broader picture of kids’ conceptual math understanding, writes Madeline Will for Education Week. And while this creative approach to assessing student knowledge is, at least in part, due to remote learning, the strategies are powerful and make sense during a normal school year.

“I think this is good for a lot of us math teachers because it’s forced us to rethink what assessments are supposed to accomplish,” math teacher Matthew Rector told Will. “In the past, most of us have thought about assessments as ranking tools—give a kid a grade and move on. Assessments should be about moving mathematical knowledge forward.”

While teachers have been rethinking assessments for some time, the shift to remote learning “has helped continue the momentum,” Trena Wilkerson, the president of the National Council of Teachers of Mathematics told Will. “Teachers are thinking creatively and out-of-the-box in how to assess student understanding and student thinking, and then how to use that to support instructional decisions.”

Use Familiar Tech Tools to Get at the Thinking Behind the Math

Rather than routinely asking students to solve a series of equations, Will spoke with teachers who are now asking students to explain a math concept, or “break down a problem and explain how they reach its solution.” Students can choose how to record their work: in a Google doc, via video, or by snapping a photo of their work on paper. “It allows them to express their thoughts better,” high school math teacher Bobson Wong told Will, and “it’s very hard to plagiarize."

High school math teacher Emma Chiappetta likes to ask her advanced linear algebra students to create videos teaching their classmates applications and concepts. To check how effective her students are at explaining algebraic concepts, they each attempt to solve a few problems associated with a peer’s video lesson.

Theresa Williams, a middle school math teacher at the University of Wyoming Lab School in Laramie, Wyoming, does five-minute interview assessments to gauge her students’ progress and inform her teaching. It’s helpful to create a checklist of what you expect a proficient student to be able to say, notes Williams. “It works great for kids who know a lot more than they showed on a [traditional] assessment,” and gives students “multiple opportunities to show that they are proficient.”

Try Math Magazines or Reflective Journaling

Writing can be a powerful mode of learning “because it engages both hemispheres of the brain,” writes middle school math coordinator Alessandra King. “Effective writing also clarifies and organizes a student’s thoughts.” Some teachers are asking students to do “reflective journaling about math concepts” to assess students’ grasp of the material, writes Will, providing a rich snapshot of where kids are at in a math unit.

King likes to get her math students reflecting and writing about math by asking them to create a math magazine where they focus on how math concepts are applied in the real world. “This has been one of my most popular projects—students are amazed to discover some of the myriad applications of math.”

She starts by curating a list of math-related articles from newspapers, journals, podcasts, and videos for students to choose from and then summarize for an online magazine. “For assessment, I’ve created a simple rubric that looks at content understanding, clarity of communication, editing, critical thinking, initiative, and creativity,” King says. Especially for students who enjoy reading and writing more than the “computational side of math,” the project gives them an opportunity to showcase  their understanding of math concepts—while gaining a “stronger appreciation of the usefulness and effectiveness of math.”

Assign Projects With Real World Implications

Using the Massachusetts census, secondary math teacher Joey Grabowski’s Algebra 1 students select categorical groups like gender or race, and quantitative variables like income or age, then “compare the distributions of two or more groups of people.” Then they write a report about their statistical analysis. Using projects rather than unit tests to assess his students gives Grabowski a unique lens into their thinking, writes Will. “[With a statistical report], they are analyzing and critiquing things,” he says. “Computers can do a lot of these calculations for us, but they can’t interpret data.”

When the pandemic hit, high school math teacher Chiappetta moved her statistics students’ project proposals online. She traded gallery walks for virtual ones on Flipgrid and asked students to leave feedback for classmates’ projects there. “After a certain point, it's not meaningful for me to quiz my students on their execution of calculations,” said Chiappetta. “The projects that my students do allow me to assess their ability to apply those calculations in context.”

Actively Embrace Mistakes

Creating a mistake-friendly classroom is valuable for all students across academic subjects—but especially in math class, which can be an anxiety provoking environment for students. Carol Dweck, a professor of psychology at Stanford University and author of Mindset: The New Psychology of Success, famously said: “Every time a student makes a mistake … they grow a synapse.”

Will notes that teachers are tapping into this idea in assessments too, normalizing errors and asking students to grapple with problems that are purposely solved incorrectly, requiring students to identify the mistakes and then figure out how to solve them.

Algebra 1 teacher Robert McAusland told Will he likes to give students opportunities for redos, giving students time to work through problems they struggled with in prior assessments. With students learning from home, he found that “initial assessment scores were unnaturally high, possibly because students were looking up answers at home.” But as his students became more confident in their abilities to tackle tough problems, “scores are normalizing” and he’s been able to convey to students that “learning to understand mathematics is not about right or wrong. … There are no bad mistakes.”

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