Hey there, time traveller!
This article was published 13/9/2016 (2113 days ago), so information in it may no longer be current.
Another school year begins, and fuzzy-math proponents are out in force across the nation.
Neil Dempsey (Make math a joyful learning experience, Sept. 6) writes in glowing tones about the "new way" of teaching math. Never mind the ideas of fuzzy math, including what some call discovery (or inquiry) learning — date back at least 100 years to the early progressive education movement.
In this leftover idea from the romantic era, classical education dehumanizes the child. Learning should be organic, autonomous, as for a wild animal. Practising to master skills and committing facts to heart are discarded or diminished as of lesser importance than "deep insight." Teachers are encouraged not to teach directly, but to arrange for students to teach themselves and each other by solving problems, discovering things and constructing their own knowledge.
Dempsey opens by caricaturing conventional instruction. He says teachers in past years turned students off math by stressing only speed and computation, likening this to learning to read by only practising the alphabet. But a moment’s reflection shows the entire point of mastering basic skills is to give students the tools to move beyond computation. Not having these skills turns students off math, as they find themselves bogged down in more and more mental clutter as complexity of problems increase. Further, knowing the alphabet and recognizing the basic words and rules of grammar are fundamental to reading.
These puff pieces are usually sprinkled with a generous helping of "research shows" without specifics, or generic "researchers" cited as having such and such opinions.
We ask to see this research and, most often, the only reply is dismissal tactics.
Dempsey cites Fields Medal winner Laurent Schwartz about the importance of "deep understanding" versus the drudgery of memorizing facts and mastering mechanics, based on his own exceptional arc of learning. But not the famous 20th-century mathematician Alfred North Whitehead, who wrote: "Civilization advances by extending the number of important operations which we can perform without thinking about them."
The role of mathematics is to extend the human capability beyond our ability to "muddle through" every problem by dwelling on trivial details such as figuring out times-table facts. These facts must be automatic, freeing us to concentrate on higher structure and providing tools for abstract reason. This epitomizes that which distinguishes us from the beasts. Far from holding us back, it is this fluidity with abstract tools that lifts modern man out of the Stone Age in which our ancestors lived.
We can play the game of "cite your favourite authority" and claim "research shows" all day. Such exchanges do not go well for fuzzy math. But, more importantly, what is happening in our schools? What real-world effect does it have?
The fuzzy approach has held sway among the province’s educators since the first implementation of the revised Manitoba curriculum in 1995. But it only really took hold at the classroom level with the rollout of the second version of the curriculum about 10 years ago.
In lockstep with other provinces using the Western and Northern Canadian Protocol curriculum, Manitoba declined in mathematical performance relative to others in the Pan-Canadian Assessment Program. The same pattern shows in the international Organization for Economic Co-operation and Development’s Program for International Student Assessment, which tests comprehensive, life-relevant mathematical skills among 15-year-olds.
Just how bad was our decline? Manitoba’s performance on the most recent national tests are the worst in Canada, and on PISA, below the world average — a very low standard.
But it is not merely that Manitoba went from ranking fifth to dead last in Canada. For broader context, consider the case of Sweden.
Among nations worldwide from 2003 to 2012, Sweden’s raw PISA math performance dropped furthest. The OECD was so concerned about Sweden’s decline, it published a 180-page report on the country’s problems, recommending dramatic policy changes.
The OECD said 41 points is the equivalent of about a year of classroom instruction. Sweden dropped by 30 points. Manitoba’s decline during the same period was 36 points.
The percentage of students attaining a PISA score indicating readiness to study science, technology, engineering and math declined by almost half in Manitoba over that decade. At the same time, the number failing to achieve the baseline level for participation fully in modern society almost doubled — the most severe change in Canada.
For all their sophistry, demagoguery and platitudes, fuzzy-math defenders cannot repair schools’ problems with math education by using a louder megaphone and a more polished sales pitch. This experiment has been tried before; it fails every time.
Robert Craigen is an associate professor of mathematics at the University of Manitoba and director of the Manitoba Mathematical Contest for Grade 12. In 2011, he co-founded WISE Math with Anna Stokke of the University of Winnipeg.