The Problem With Giving Math Tests Online, and How Teachers Are Solving It

In the midst of the coronavirus pandemic, teachers have had to rethink pretty much everything they do with students—and that includes how they give math tests.

With many students working remotely, there’s no point in administering assessments that ask students to come up with a single answer; it’s simply too easy to cheat. Instead, teachers are focusing more on assessing students’ conceptual understanding of the mathematics—and they’ve had to do that without being able to gauge students’ body language or talk in person.

These changes are especially prominent in schools that have remained completely remote, but they hold true even when students come to school a few days a week. Teachers in schools doing hybrid instruction say they don’t want to spend all their limited in-person time administering tests and quizzes, so remote assessments are still a factor. And even when school buildings do reopen for full-time in-person instruction, some teachers say they hope this shift in how they assess students will continue.

“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,” said Matthew Rector, a math teacher and department chair at Grant Union High School in Sacramento. “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.”

Of course, making sure students can explain the math they’re learning isn’t a new concept: The Common Core State Standards, which were created more than a decade ago and are still being used by the majority of states in some form (though often under a different name and with some modifications), encourage math teachers to balance conceptual understanding, procedural skills, and fluency with real-world application. There has long been a debate about the right balance of procedural fluency and conceptual understanding in instruction, but most educators agree that both are necessary.

“I think we’ve been seeing this shift [in assessments] in the last few years,” said Trena Wilkerson, the president of the National Council of Teachers of Mathematics. “[The transition to remote instruction] has helped continue the momentum. … I think 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.”

Instead of having students solve a series of equations, teachers are asking students to break down a problem and explain how they reach its solution, either online, on video, or by sending a picture of their work on paper. They might give students problems solved incorrectly and ask them to find the mistakes. Some teachers are assigning projects rather than tests, asking students to do some reflective journaling about math concepts, or allowing students to redo problems they got wrong.

“We’re in an age where every answer we could possibly imagine is in the palm of our hand,” Rector said. “It makes absolutely no sense to give an answer-getting test, because what’s the point?”

Getting Creative

This year, asking students to record themselves explaining a math concept or telling how they would solve a problem has become a popular grading tool for many teachers.

“It allows them to express their thoughts better,” said Bobson Wong, a high school math teacher in New York City. And there’s another benefit: “It’s very hard to plagiarize.”

Meanwhile, Joey Grabowski, a math teacher at Pioneer Valley Performing Arts Charter Public School in South Hadley, Mass., said he has pivoted to unit projects instead of unit tests. For example, he had his Algebra 1 students use Massachusetts census data to select a categorical group (like gender or race) and a quantitative variable (like income or age). Students then had to compare the distributions of two or more groups of people, and write a report discussing their statistical analysis and their conclusions.
“[With a statistical report], they are analyzing and critiquing things,” Grabowski said. “Computers can do a lot of these calculations for us, but they can’t interpret data.”

Robert McAusland, an Algebra 1 teacher at American Martyrs School, a Catholic private school in Manhattan Beach, Calif., said he tells his students at the beginning of the year: Learning to understand mathematics is “not about right or wrong. … There are no bad mistakes.”

After every assessment, he allows students to attempt similar problems to the ones they got wrong, which will add to their overall grade. At the beginning of this remote semester, he said, initial assessment scores were unnaturally high, possibly because students were looking up answers at home. But as the semester has progressed and students become more assured in their ability to try again, McAusland said he’s finding that “scores are normalizing more toward a traditional expected outcome.”

Image shows a conceptual math question where students are asked to explain, evaluate, or synthesize.

Bobson Wong, New York City high school math teacher

Still, focusing assessments on conceptual understanding can mean a lot more work for teachers than checking to see if a student solved a problem correctly. A nationally representative survey by the EdWeek Research Center, administered Sept. 30 to Oct. 8, found that teachers are working an average of 10 hours a day, an hour more than they said they worked prior to the pandemic.

“It takes a little bit more time to read responses—to not only grade them, but to respond to them in order to give feedback,” NCTM’s Wilkerson said. “It’s not a question of whether a student got a right answer or not, it’s more about their thinking and what they need [in terms of support].”

Math teachers say they have tried to streamline their curriculum to only teach the most relevant content this year, given that instructional time is at a premium. Experts have advised focusing on skills and understandings that are going to be most important to students’ future success, and prioritizing depth over breadth.

“I feel very overwhelmed with grading, as every teacher I know feels,” Wong said. “It’s forced me and other teachers to think about what’s really important—to think about what concepts we really need students to know because we all have limited time. It forces us to think about, ‘What lessons do I really need to do, and how do I test that with as few questions as possible?’”

This summer, math teachers at De Pere Middle School in De Pere, Wis., spent a lot of time looking at the standards within their content area and coming up with a list of the highest priorities, which students must know and be able to do by the end of the school year. Those essential standards, the teachers agreed, would be what they write their common formative assessments around and the areas in which they would provide the most time and support.

In a logistically challenging school year where time is limited, that kind of focus and clarity was critical, said Adrianne Burns, a math coach and interventionist at the school: “If we know exactly what we’re doing, we can do that in a more succinct way.”

The planning quickly came in handy. Teachers started the school year in a hybrid model, with kids coming to campus two days a week. But due to rising COVID-19 case numbers, the De Pere school district went completely virtual before teachers even made it to the end of the first math unit.

Teachers then had to grapple with the question, “When you’re not there fully monitoring what they’re doing, how do we evaluate that work?” Burns said.

Students solve math problems with pencil and paper, then scan their work into Google Classroom for it to be graded. And teachers now more frequently assess students with questions that promote explanation and creation, Burns said.

For example, teachers might ask students to explain why multiplying a positive number and a negative number equals a negative number. Or instead of asking students what 10 + -14 equals, teachers might ask students to create an addition problem with the sum of –4. “We’re giving them the parameters, but they’re creating the problem,” Burns said.

These types of assessment questions—as well as reviewing scanned images—do take longer for teachers to grade, Burns said. But having the essential standards in place has helped them narrow down what they need to focus on in their curriculum and what they need to assess, cutting out any extraneous concepts.

Changes From States?

Experts say much of the assessment change has remained at the classroom level, with individual teachers or schools revamping the tests they give. Most states have not changed their standardized tests to better fit into the new reality of remote instruction and assessment, said Scott Marion, the executive director of the Center for Assessment, which works with states and districts to design and implement more meaningful assessments and accountability practices.

But if states assess some of their students in person and the others online, the results may not be comparable, he said, given the concerns about both student cheating and student motivation. Some states might consider remote proctoring, where the proctor watches the students take their test through a webcam. Still, Marion said there are ways for students to still cheat on the exam, depending on the camera angle.

It remains to be seen if it will be possible to test students in person safely this spring, and states will need federal approval to skip required standardized tests. But some states have already said they won’t administer tests remotely, Marion said, and the federal government can’t force them to do so.

A policy adviser for President-elect Joe Biden said in October that the transition team would have to look into whether states would receive waivers from federal testing mandates this year, and it “depends on how much progress we can make in supporting our schools and getting them up and running.”

Some educators have called for a moratorium on standardized tests altogether this year, including Alan Schoenfeld, a professor of education and mathematics at the University of California, Berkeley, who was one of the lead authors for the mathematics content specifications for the Smarter Balanced Assessment Consortium, which develops common core-aligned tests.

Schoenfeld has long advocated for a “balanced diet” of skills, concepts, and problem-solving in math curricula and assessment, saying that approach helps students apply math concepts long after the class is done. Assessments should reflect that approach, he said.

Remote learning, Schoenfeld said, has opened the door for a meaningful change in assessment: “This should be a, ‘What do you have to lose?’ situation.”

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