Time to check in on college algebra homework
Dan White’s experience with mathematics homework has improved markedly since a 2003 paper in which he and colleagues conducted rigorous tests on the difficulty of preparing and doing homework for college algebra. “People use a calculator differently when they are worried about procrastination,” explains White, a software consultant in Austin, Texas. He would spend five hours a week on a wide variety of mathematical problems but gradually prioritized, reducing effort for problem sets that his mother had predicted would be more difficult. After incorporating such increased expectations into his practice, White says, he saw what turned out to be minimal increases in performance, compared with previous years. White also noticed an immediate improvement in his own math scores. “I liked it,” he says.
White decided to conduct more rigorous tests on how math homework is composed and assigned, so he worked with colleague Julian Raybarger and their colleagues at the University of Texas at Austin to conduct extensive study-targets-means experiments on a variety of math problems: doing two things at once, extracting large quantities of data with less error, and estimating ranges and variables that use one type of input while providing a different output. “Instead of looking at whole chunks of time, where you can’t predict how they’re going to evolve over time, you can construct them and expose them to various conditionalities, such as how many times a mistake appears in the results or the likelihood of the number being as high as the first error,” says White. “We’re measuring the expectation aspects rather than the amount of time you spend,” he says.
When the time for students to study a required math exam arrived, White and his team found that not only did they want to spend less time on their math homework, but they liked it less, too. “I found what I was initially concerned about true for the researchers,” he says. “They like the problem more when they have more expectations, but they are less likely to do well on it when they have lower expectations.”
The authors were surprised to find such a connection between exam expectations and exam performance. “How do you know it’s a problem that won’t help them succeed in college if it can’t help them succeed in high school?” White asks. It’s likely, he hypothesizes, that the variation in exam performance across students reflects differences in the way they learn the problem. Students might have been expecting to study for it long enough to be ready in a format they could use in other tasks. Or they might have been surprised that certain problem sets required several back-to-back actions, rather than one or two. The latter approach is less effective. “I see this in people who play games, too,” says White. “They like that, but they are less likely to do well with a game.”
Finally, White explains, the prospect of failure can nudge college students to push themselves harder. The only exception, he notes, is when young students “think about it as a practice run for the real test,” which wasn’t much of a problem in the Bush administration, since work-study jobs, enrollment in STEM courses, and financial aid usually covered college tuition.
Chad Carroll, an associate professor at Emory University’s Goizueta Business School who studies assessment and assessment programs, recently polled college students and found that 97 percent were satisfied with how well their homework was preparing them for college courses, compared with 91 percent who agreed with the statement they were overworked and stressed. The survey also found that 67 percent did homework as an end-of-term assignment that differed from what they were told to expect during their unit.
Carroll cautions that testing is just one way to manage homework. Teachers can help students with homework challenges by bringing in experts and by looking at how problems are constructed. He also says that adding real-world experience to homework helps reduce the pressure to do well. When professors offer students a chance to work in groups on problems that require collaboration, for example, they find students often enjoy the challenge, with positive effects on their ability to learn. “Teachers could offer enough options for students to pick from without providing the overall expectation that they will get a passing grade,” Carroll says. “And then they can have an end-of-term exam that’s really the last chance to meet the grade, to prove that they do well on this grade.”