New study by Everett instructor shows value of real-world context in teaching algebra

In what some math experts are calling “the latest evidence that teaching algebra differently works,” a new study co-authored by an instructor at Everett Community College underscores the importance of helping students understand how intermediate algebra is used in the real world.

Christopher Quarles, who teaches math at the Everett school, worked with Mickey Davis, a former researcher and lecturer at the University of California Berkeley, to study how well students retain knowledge of intermediate algebra after a few months have gone by. Their study was published in Community College Review.

In high schools, intermediate algebra is often part of courses called “algebra 2.” It’s also taught in community colleges because students often arrive without having mastered it, and it’s a prerequisite for college math.

The researchers looked at how well students did on a test of their math knowledge. It showed that students who hadn’t taken a math class for four months or longer did equally well on “conceptual” math problems as students who’d just finished a math class. Conceptual problems involve verbal reasoning, graphs, algebraic manipulation and familiar non-mathematical contexts.

In other words, those problems provided a context that made sense to the students, and allowed them to use problem-solving skills to figure out the answer, even after several months had passed, Quarles said.

But students who hadn’t taken a math class in four months, or more, did 42 percent worse on “procedural” problems than those students who’d recently finished a math class. Procedural problems require students to memorize an abstract formula to solve an equation.

Math texts often require students to repeat the same procedure over and over, using different numbers in the formula, to try to hammer procedural lessons into their memories, Quarles said. But “solving a bunch of equations doesn’t teach you how to use those equations, or solve problems in the real world,” he said.

Math course experts at the University of Texas Dana Center agreed. “To see improved degree completion rates, colleges need to support their students in developing flexible thinking and making connections, rather than rigid, rote procedure,” UT’s Frank Savina and Connie Richardson, said in an email. Both are specialists in higher-education mathematics courses.

As a math instructor — he’s been teaching for 17 years — Quarles said he had a hunch that students would do better on conceptual problems.

Davis, the other researcher who worked on the Everett study, said intermediate algebra is designed to prepare students for calculus, which many students will never need for their careers. Intermediate algebra is often taught at a fast pace, and students are focused on learning enough to pass the class. “I think we saw pretty strong evidence that those kinds of skills deteriorate rapidly,” he said.

Quarles said he hopes the study helps reinforce state and national efforts to change the way algebra is taught in community colleges.

The Dana Center experts said math instructors have been emboldened by evidence like the Everett study, and that they’re working to modernize the way math is taught in 15 states, including Washington — with help from a model known as the Dana Center Mathematics Pathways.

In 2015, they said, five leading professional associations of U.S. mathematicians came together to collectively develop a modern vision for math education. The report, A Common Vision for Undergraduate Mathematical Sciences Programs in 2025, calls the status quo unacceptable, Savina and Richardson said. The report focuses on areas that need improvement, including “the need to modernize the curriculum, emphasize conceptual understanding, and teach mathematics that is relevant to students’ future careers,” they said.

But because most instructors have a lot of flexibility in how they teach math, they said, “widespread change can be slow to take hold.”