Discovery-based methods just not making the grade

C.D. Howe report calls for return to basics in Canada for math teaching

Canadian students’ math skills have been on a decade-long decline because rote learning was replaced by discovery-based methods that promoted multiple strategies and estimations, according to a new report that calls for a return to tradition.

“You know what’s the worst kind of instruction? The kind of instruction that makes kids feel stupid. And that’s what a lot of that discovery stuff does; their working memory gets overloaded, they’re confused. That’s bad instruction,” said Anna Stokke, an associate professor in the University of Winnipeg’s department of mathematics and statistics, who wrote the C.D. Howe Institute report.

The report draws on results from national and provincial tests as well as an OECD assessment performed every three years in more than 60 countries that measures how well 15-year-olds can apply skills in reading, math and science to real life situations.

Canada fell out of the top 10 countries for math in 2012. The report notes that all but two Canadian provinces also saw “statistically significant” declines in their math scores, compared with their 2003 performances. Alberta, once a math leader, and Manitoba saw the steepest drops, while only Quebec held its ground. Saskatchewan declined slightly but not enough to be considered significant. Beyond that, the pool of students at the lowest achievement levels grew while those at the very top shrank.

“You can look at it in terms of where do we rank et cetera, et cetera, but when we see that our students are doing worse, relative to 10 years ago, there’s no excuse for that,” said Stokke.

The report found students’ working memories get overwhelmed if they don’t know their times tables and can’t quickly put a standard algorithm to work to solve a more complex problem, both features of what’s known as “direct instruction.” Key operations, such as addition and subtraction of fractions, are overly delayed until the middle school years, just as students need that facility to tackle algebra.

Such concepts should be introduced earlier, says the report. And while it stops short of throwing discovery learning out completely, it says the curriculum balance should be tilted in favour of direct instructional methods, recommending an 80/20 split as a rule of thumb.

Ann Kajander, an associate professor in math education at Lakehead University in Thunder Bay, criticized the research basis for recommendations against discoverybased learning techniques.

“How can we have a report that makes significant recommendations in mathematics education when absolutely none of the major mathematics education journals … are included in the reference list?” she said. “As a researcher, that’s absurd.”

The report, however, does cite published research in science, psychology and neuroscience.