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Teens from Asian nations dominate a global education test given to 15-year-olds. (AP Video)
Teens from Asian nations dominate a global education test given to 15-year-olds. (AP Video)

PISA

Why does ‘fuzzy math’ persist? It’s a bonanza for consultants, publishers Add to ...

You’ve heard by now that the 2012 PISA assessment shows Canada has fallen from the top 10 in math, out of 65 nations. In four consecutive assessments: 2000, 2003, 2006, 2009, we slid from 6th to 10th and, as of 2012, to 13th.

PISA’s purpose is to inform participants’ educational policy. Three things to keep in mind in considering these data:

First, keep an eye on the trend. More than absolute rank or score, this reveals the effect of policy changes.

Second, focus on changes in educational policy that may account for the results.

Third, understand that PISA ranking represents an objectively low standard.

Let’s dig in. Canada’s scores from 2000 to 2012: 533, 532, 527, 527, 518. For perspective, 500 is the overall average (including low-performers like Indonesia, Mexico, Trinidad, Tunisia and Brazil). Most participants fall in a band from 400 to 600; Canada is in “the pack” near an average that marks functional but decidedly mediocre performance.

Since 2003, every province has dropped: Quebec, insignificantly, by 1 point. Manitoba, dramatically, by 36 and Alberta by 31. Ontario dropped by 12; B.C. and Saskatchewan by 10. Maritimes’ declines have varied from 10 to 27 – every province except Quebec declined significantly.

Quebec (536) stands among the top eight nations. BC (522), Alberta, Ontario and Saskatchewan score above 500, New Brunswick and Nova Scotia right at that mark. The other 3 provinces are below even the OECD average, 494.

Consider (sidebar) two questions from a similar assessment, TIMSS, and how our three participating provinces (our top 3 performers) fared versus the global average and top performers. Question 1 is an easy test of a basic task for handling fractions. Recent studies identify fluency in fractional arithmetic and division as the best known predictor, at this level, of later success. Question 2 zeros in on understanding of a pivotal point in the concept of multiplication beyond the integers; being conceptual, it is the harder question, as seen in the top nations’ scores.

These questions are canaries in the educational coal mine.

Both are multiple choice: Random guessing would lead to a 25 per cent success rate. Any score under 30 is disastrous; you could hardly do worse by guesswork. There’s no “down” to go from there.

Observe, first, that the “world average” is a very low standard. Second, strong education can yield far better results than seen today in Canada. Third, even our top provinces perform badly on some critical skills, both procedural and cognitive.

How has Canadian education changed in recent years? Parents report that kids’ math homework is unrecognizable. A revolution of sorts has taken place – proponents call it “reform” math education; others call it “fuzzy math:” weakened or delayed content, methods and materials that defy conventional wisdom. Standard methods (e.g., long division) gone, replaced by redundant, cluttered “personal strategies;” “indirect instruction” – project-based, open-question “discovery learning;” a motivating philosophy inimical to practice, memory or skill and regarding mechanical fluency as the enemy of the “understanding” – heralded as this system’s strength (but recall what Q. 2 revealed).

Fuzzy math gained a head of steam in Canada after 2000 as the Western provinces’ common curriculum framework, WNCP, underwent revision. In tandem with this, the math “consultant class” executed a full-court press of workshops and inservice training, supported by schools of education, to convince teachers to “get with the program”, transforming the math educational culture.

Maritime provinces adopted or adapted WNCP Math. Insiders there report this selling point: WNCP is “Alberta’s curriculum” and – previously – Alberta has led the nation. But perhaps WNCP Math shares blame for Alberta’s tumbling score.

Changes requiring new resources are greeted eagerly by textbook publishers, who profit when old editions are obsolete. For them the fuzzy math revolution is a bonanza, and they have responded with numerous titles now in use across the country.

How will provinces respond? B.C. has quit the WNCP agreement. Quebec’s “Progression of Learning” is a unique and decidedly un-fuzzy curriculum. This fall, Manitoba returned to the algorithms, worksheets, and memorization of math facts, and is the first to give a provincial recommendation to JUMP Math, a balanced resource showing much promise as a “third way,” that has yielded impressive results for many adopters.

But I fear that some may gravitate to the default: throwing more money at “solutions” that are part of the problem.

Dr. Robert Craigen is professor of mathematics at the University of Manitoba. He is one of the founders of Wise Math.

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