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Edutopia
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.
By Emelina Minero
January 15, 2021
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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