Math Isn't Easy Without First Learning the Basics
(Telegram Forum article as it appeared in The Telegram, September 17, 2000)
by Dr. Sherry May, Director,
Mathematics Learning Centre, Memorial University
In two recent articles, the head of the mathematics department at Memorial University, Herb Gaskill, discussed "the math problem" and outlined why the department considers it a serious problem ("Math problems, solutions" and "Math problems can't be ignored" - The Telegram, Sept. 2-3).
In fact, this concern led the department in 1988 to create the nucleus of what is now the Mathematics Learning Centre. Since its inception, the Centre has grown to encompass instruction in mathematics skills and research in the teaching and learning of mathematics.
The primary research mandate has been to discover how it is that high school students can get decent grades in their mathematics courses and yet get less than 50 per cent on the Mathematics Skills Inventory (MSI).
This is a concern not only of parents, post-secondary instructors and government officials, but also of dedicated teachers in the K-12 school system. I do not include the students themselves. This is not merely a stylistic exclusion.
Our research suggests that this is, in fact, at the root of the problem. Students measure their attainments, not by the depth of understanding they have achieved, nor by the stock of useful skills that they have acquired as a result of the learning process, but merely by virtue of having been a participant.
Someone who decides they want to learn to play the piano but only attends one lesson per week and does not practice, does not learn to play the piano well; similarly, someone who decides they want to learn to play soccer, but only attends a game once a week and does not practice the component skills in between games does not learn to play soccer well. These individuals, who have participated in these activities at a recreational level, have developed a "familiarity" with them, and that is well and good.
But post-secondary programs are not about
recreational involvements with mathematics. They are about being
able to do mathematics which is useful, and that entails an
involvement with the subject that goes far beyond familiarity. It
entails, as it would with learning to play the piano or soccer;
hours of rigorous, repetitious practice.
Given the multitude of objectives a high school program is trying to address, it is easy to see how capable students forego establishing a strong, enduring, working knowledge of mathematics. There are too many competing priorities - extracurricular activities, jobs, athletic pursuits, student council, friends. Is it any wonder that many graduating students find they have made some poor choices along the way?
In an attempt to address the motivational issue, there has been a deliberate shift in emphasis towards higher-order reasoning and problem solving and away from basic skills. It was thought that these were two important process skills that were not being given enough attention in the traditional curriculum, and that these areas were more appealing to a broader range of students than a drill of basic skills. It was assumed that, although the requirement for specific basic skills would be reduced, the learner would be more motivated and able to pick them up on his/her own when the need arose.
Unfortunately, this does not happen. Instead, the sacrifice made of basic skills has an unanticipated double effect. Learning processes themselves need to be learned, and this is most often achieved through duplication of previous experiential patterns of behaviour. But our students are no longer given extensive learning experiences of basic skills and so they have nothing to duplicate.
They can do Internet searches for information and produce PowerPoint presentations of this material, but they do not know how to teach themselves to rearrange simple linear equations. This means they cannot properly input data into statistical software packages or spreadsheets so they are unable to use the software widely used in today's world.
At the Mathematics Learning Centre, we do not teach students how to engage in mathematical processes, per se. We teach them how to engage in independent learning.
This learning must be focussed and
well-organized, and it cannot be selective. It cannot skip over the
hard parts and settle only on popular topics. It must stick with a
topic until understanding and skill have been achieved. The new
knowledge must be connected to all other knowledge which the
student holds, in order to both increase understanding and to make
the new knowledge useful.
Given the multitude of
Most of us are not born with an innate sense of what it takes to learn independently. We have to be guided through the process. Historically, the complexity of mathematical content and reasoning provided an excellent vehicle for training in this learning process. It still does, but the process has been compromised by competing demands.
In order to graduate and be a productive member of a technological society, students must be able to do at least one or the other: students must either have been given sufficient repetitious practice at solving linear equations so that they can solve them with reasonable competency, or they must have been given enough experiences in mastering some basic skills that they know to duplicate this process whenever their study or work demands it. Students who get less than 50 per cent on the MSI can do neither.
Today's world is rich in opportunities; it is also complex. It is not sufficient to merely expose our youth to what they might do.
We must adequately prepare them for making their
choices. We must teach them how to work hard. We must teach them to
reason and give them some basic skills to reason with. We must
teach them how to learn. We must teach them how to make choices,
and we must teach them to accept responsibility for the choices
they make. Nothing less will do.
We, too, must make some choices. We must learn humbly from our mistakes. We must accept responsibility for what we demand of our educational system. We must work together to find a better balance in our educational curriculum, and we must demand more from our youth.