Focus on pattern recognition in math shifts emphasis from “what’s the answer?” to “how do you solve this problem?”
As schools struggle to balance conceptual learning and recall of simple facts, a new series of online math education products proposes a different focus: pattern recognition.
Insight Learning Technology, a startup company formed by a pair of academics, has created online math education modules that tap into not only adaptive learning, which uses computer interactivity to individualize students’ lessons, but also the lesser-known field of perceptual learning, which focuses on patterns and relationships.
By focusing on perceptual learning, the software aims to teach students how to learn math—in other words, what pieces of information are most important when tackling a problem.
Three modules, based on the cognitive development research of company co-founders Phil Kellman and Christine Massey, will hit the market in time for the fall semester: MultiRep Insight, Algebra Insight, and Best Basic Math.
Schools would pay about $3 to $5 per student for a year’s worth of each module, with potential discounts based on volume.
Cognitive scientists generally focus on building declarative or procedural knowledge—that is, putting into memory specific facts or steps of a process.
“Most people think that’s all there is, but there’s another [type] of learning for getting good at anything, and that’s pattern recognition,” said Kellman, who chairs cognitive psychology at UCLA.
He cited the example of a young child learning to classify an object as a cat. Through observation of many cats, the child begins to recognize which characteristics are crucial to being a cat—whiskers, pointy ears—and which are not as important.
The concept of perceptual learning applies across all fields: Kellman also has conducted studies in pilot training and medical education. But Insight chose to focus first on math education, a particular pain point in American schools.
Insight’s modules drill students on similar problems until they recognize patterns. The Algebra Insight product, for example, trains students to develop fluency in algebra transformations and operations.
Beginning students generally “know the rules” of algebra, but are very slow in recognizing and applying them, said Massey, director of the Institute of Cognitive Science at the University of Pennsylvania.
Solving algebra problems requires students “to be thinking about a lot of things at once—they have a high cognitive load,” she said.
When students crank through entire problems, they are often distracted by so many other concerns—such as mental math and completing all the steps in the correct order—that they often can’t see the larger patterns, Massey said.
She said Algebra Insight’s perceptual learning approach “takes a lot of the load off” of students by reducing the number of ideas they need to hold in their head at once and instead focusing on recognition of algebraic rules.
Insight’s math education products tap into the thinking processes required not only for learning, but also for developing expertise, Kellman said.
Research shows that when people become experts, there is a “change in the way they pick up information,” he said. “They come to see more patterns” and automatically group information in clusters.
Repeated practice helps people develop higher levels of automaticity—the fluency that allows experts to multitask. Experts can perform lower-level tasks using little thought so that they can devote more attention to higher-level tasks.
“Novice students look at superficial features, while [more experienced] students look at underlying concepts,” said Joe Wise, a physics teacher at New Roads School in California who has piloted the Insight products with his students.
As an example, Wise said a novice would look at a graph and merely see an inclined plane. An expert looking at the same graph would see the bigger picture: The plane actually represents an energy problem, with declining potential energy and increasing kinetic energy.
Wise said the Insight modules help students move away from novice-type thinking.
In the Multiple Representations Insight module, for example, students match up different forms of the same problem to demonstrate recognition that a word problem might convey the same information as a graph, and vice versa.
After spending time on the multiple representation module, students with no previous perceptual learning experience “intuited the ideas of slope and intercept,” Wise said.
In his capacity as director of the Center for Effective Learning at New Roads, Wise has overseen other teachers using the products. Throughout the last several years, he has piloted all three of the new Insight products with his students, involving about 60 students per trial.
Wise said he primarily uses the modules as a supplement for struggling students, who can log onto the online programs from their computers at home rather than losing time in the classroom.
Embedded formative assessments give students immediate feedback and help teachers identify student weaknesses or determine when a student is ready to move on.
Students working through the modules can see their progress on a “mastery indicator,” a bar at the bottom of the screen that shows the students’ advancement to increasingly difficult levels. The concept, borrowed from video games, helps students “feel that they’re closing in on mastering the whole thing,” Massey said.
With today’s emphasis on standardized testing, students today are used to “teach-test” learning, and it can take some time for them to “get used to this kind of learning where they constantly try and get feedback,” she said.
Wise agreed that students have mixed reactions to the modules’ setup, which drops off categories of questions once students demonstrate mastery and instead drills students on question types that they make mistakes in.
Students who prefer being told what to do—often the students who do best in traditional classrooms—tend to find the new format frustrating. In contrast, students who worry less about being right love “constantly being on that edge where you’re being challenged,” he said.
Wise said the Insight modules take education in what he considers a new, better direction: The exercises shift emphasis from “what’s the answer?” to “how do you solve this problem?” so that building thinking and problem-solving skills becomes more important than getting the right answer.
Once students become accustomed to learning this way, the durability is astounding, Massey said.
In research studies asking students to revisit the modules’ material four to five months later, after summer vacation and the change to a new teacher, students “have been just as good on the delayed post-test as on the test right after the module,” she said. “It sticks with them.”