Mastering math ... again and again
by Leslie Vryenhoek
For years, Dr. Sherry Mantyka has worked closely with students struggling in mathematics. By incorporating principles found in cognitive psychology, she has identified ways to overcome the stumbling blocks to math competency. Now she’s put those strategies in a book to aid parents, teachers and students of all ages.
Dr. Sherry Mantyka has spent 18 years helping math learners
solve their problems. She’s put what she’s learned into a guide for parents,
teachers and students.
As the director of Memorial’s Mathematics Learning Centre, Dr. Mantyka has tested and monitored students, identified problems and conducted controlled experiments into why so many students struggle with math, and how they can succeed.
Her work in this arena dates back to 1988, when the provincial government struck a task force after post-secondary institutions identified issues with math. According to Dr. Mantyka, a placement test was designed to collect data that would either confirm or refute the notion that students were graduating high school with inadequate math skills. “The results were unambiguous. There was a huge pre-requisite skill deficit.”
At that time the Department of Mathematics and Statistics, in which Dr. Mantyka is an associate professor, offered some voluntary programming for students who wanted to upgrade. In 1993, the Mathematics Learning Centre was established with support from the federal and provincial goverments. Here, students who do poorly on the math placement test can gain foundational skills through individualized diagnosis and programming.
Over time, Dr. Mantyka discovered a consistent trend: students could understand and perform certain mathematical tasks, but when they moved on to a more complex equation, they began to make mistakes. “They couldn’t incorporate what they knew at a more sophisticated level. There was a breakdown somewhere along the line.”
Perplexed as to why bright, capable learners with strong achievement in other areas had these
problems, she turned to Dr. Michael Rabinowitz, a cognitive psychologist at Memorial. He helped her to understand that the human brain has a massive capacity to store information, but that its capacity for active processing is limited. The two professors began to study how the concept of automaticity learning a skill so well it comes automatically, instead of requiring conscious thought could be applied to math education.
“If students don’t acquire math skills to the level of automaticity, which is measured by accuracy and speed of finding the right answer, then they have trouble,” she explained. “To gain functional automaticity, students first have to gain an understanding of the math. Then they have to do repetitious drills to get fast and accurate before they move on to the next level of sophistication.”
Dr. Mantyka said school curriculums have moved away from repetition and toward a much greater emphasis on problem solving. However, her research indicates that students would be well-served if both sides of the learning equation were emphasized.
But students who enter the MLC don’t always appreciate the approach and, in fact, can be downright hostile. They often find the repetition boring, distasteful, and usually counter to what they were asked to do in school, Dr. Mantyka reported.
Nonetheless, she believes the foundation math programs offered at Memorial are among the most effective in North America.
“At other institutions, foundation math programs tend to be short and intensive.” However, she said, when programs run only a few weeks or even months, students don’t have time to hone their skills so that they become automatic. “Here, the most diligent students can do the program in two semesters, but most need three.”
Dr. Mantyka has set down the methods that she and her colleagues have found most effective in a book called The Math Plague, set to be released this winter. While the book contains references to her research data, it is primarily intended for teachers, parents and students themselves.
“It’s for people who are concerned, who want to know what they can do, as individuals, to remedy learning challenges and motivate students,” she said, adding that many of the learning strategies she puts forth can be applied to other disciplines.
On Sept. 28, Dr. Mantyka will discuss her work as part of the Cognitive Science Lecture Series (For related story, click here).