Dr. Sherry Mantyka has spent years testing and monitoring math learners, identifying why they struggle, and formulating strategies to help overcome mathematical roadblocks. Now the director of Memorial University’s Mathematics Learning Centre believes she has formulated effective – though not always popular – strategies that could benefit math students of all ages.
Dr. Mantyka’s work in this arena dates back to 1988, when the province instituted a placement test to confirm or refute the notion that students were graduating high school with inadequate math skills.
“The results were unambiguous,” she recalls. “There was a huge pre-requisite skill deficit.”
In 1993, Memorial established the Mathematics Learning Centre (MLC) to give students who did poorly on that test a chance to gain foundational skills through individualized diagnosis and study.
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 in areas they had previously mastered. “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 cognitive psychologist Dr. Michael Rabinowitz, who explained that the human brain has large capacity to store information, but minimal capacity for active processing. Therefore, students did better if they learned the skill so well that it came automatically, instead of requiring conscious thought. The two professors set about finding ways to apply the concept of automaticity 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,” Dr. Mantyka explained. “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.”
School curriculums in Newfoundland and Labrador, as in most of North America, have moved away from repetition and toward a much greater emphasis on problem solving, she said. Dr. Mantyka’s research indicates that students would be better 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, she reports. However, Dr. Mantyka believes Memorial’s foundational math programs 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. The book is primarily intended for teachers, parents and students who want to find remedies for math problems long before they reach university.