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Get the 'fuzzy' out of Manitoba math

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A curtain was drawn back on math education on Dec. 3 with the worldwide release of data from the 2012 PISA, a test given by the OECD to 15-year-olds in some 65 countries.

Much hand-wringing ensued as Canada's score continued its slide, dropping from sixth in 2000 to 13th in 2012.

Manitoba's picture is bleak. At the Canadian average in 2003, Manitoba now ranks in the bottom three provinces, below the falling Canadian average and even below the world average.

Manitoba's score dropped farther (36 points) than that of any other province.

Particularly worrisome is that since 2003, the number of Manitoba students performing below Level 2, which OECD calls the baseline level "to participate fully in society," has nearly doubled, to 21.2 per cent from 11 per cent.

At the same time, the fraction of Manitoba students with "high level skills" (Levels 5 and 6) fell by half to 10.2 per cent from 19 per cent.

We are failing our strongest and weakest cohorts. What went wrong?

Manitoba's performance fits a larger pattern: Provinces showing the worst decline have also, between 2003 and 2012, adopted a collection of teaching approaches sometimes called by advocates "reform math" or by critics as "fuzzy math," which predominate among the "consultant class" -- not teachers per se, but professionals who advise them: trainers and clinicians, popular textbook authors and curriculum and resource specialists.

Advocates often maintain a false dichotomy between skill and understanding. All math educators agree understanding is the ultimate goal, but one fuzzy doctrine prescribes delaying systematic skills development, holding that skills impede understanding.

Repetition and practice, the very foundation for mastery, are discouraged, with pejorative slogans like "drill and kill." Instead, one sees the "spiral curriculum," which revisits topics year after year without closure -- children, apparently, will master topics in their own good time.

Thus conventional arithmetic (adding and subtracting in columns, "vertical" multiplication and long division) is delayed or eliminated in favour of strategies: tricks for calculation that work for small numbers or in special cases (for example, to multiply by eight, double three times).

Another fuzzy favourite is "rich tasks" -- variants on elementary problems with missing information or no specified goal (etc.); apparently lack of structure and unclear expectations are a feature, not a bug.

Individual work and paper-and-pencil skills are de-emphasized; social and verbal skills predominate. Students are to generate knowledge spontaneously through group work and discovery instead of receiving explicit instruction. Another common mantra: "The teacher is not a sage on the stage, but a guide by the side."

But research in cognitive science supports the common sense view such "minimal guidance instruction" is a poor way to teach novices.

The 2010 PCAP, a Canadian assessment administered by education ministers, found "direct instruction," teacher delivering content knowledge to students, strongly correlates with positive learning outcomes; conversely, "indirect instruction" is strongly associated with negative outcomes.

Yet fuzzy math advocates, undaunted by such evidence and falling math scores, continue to favour the "guide by the side" approach.

Over this period, the western provinces adopted a fuzzy curriculum under the Western and Northern Protocol.

The Maritimes followed suit, citing WNCP is "Alberta's curriculum." Indeed, Alberta once led the country on assessments -- before this curriculum.

But Alberta's decline is second-steepest (32 points) next to Manitoba's. The top province is Quebec, the only Canadian system that remained distinctly "unfuzzy" during this period.

Manitoba's education department seems to have seen the writing on the wall, and this September we became the first WNCP province to return the algorithms and memorizing of math facts to the curriculum. Though many problems remain, this was a positive, courageous first step.

Even more recently, the Canadian-designed JUMP Math was added to Manitoba's recommended resource list. Several schools are trying JUMP; perhaps more will follow suit.

Some in the consultant class continue to vocally resist these changes. I worry at each announcement of more numeracy funding: Will more resources be diverted to the very sources of our current ills? Historically, Manitoba has done well in math; a return to established wisdom is needed, not doubling down on the fuzzy experiment that turned millions of North American children into guinea pigs.


Robert Craigen is an associate professor of mathematics at the University of Manitoba and co-founder, with Anna Stokke of the University of Winnipeg, of the Western Initiative for Strengthening Education in Math (

Republished from the Winnipeg Free Press print edition December 19, 2013 A15


Updated on Thursday, December 19, 2013 at 8:14 AM CST: adds image

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