The report from the C.D. Howe Institute says that Canadian students' math performance in international exams has been declining between 2003 and 2012.
The report says that all but two provinces showed statistically significant declines on the exams administered by the Organization for Economic Co-operation and Development.
Report author Anna Stokke says teachers should base 80 per cent of their math classes on direct learning such as memorizing multiplication tables and practising long division.
She says only 20 per cent should come from discovery-based learning techniques, which see students rely more on independent problem-solving and hands-on materials and less on instructions from the teacher.
Stokke also says most provincial math curricula need to start teaching concepts such as fraction, addition and subtraction at earlier grade levels.
Stokke's report said the preference for direct learning is based on the way the human memory functions.
It said discovery-based learning puts too much burden on a person's working memory, which can only retain information for a few seconds at a time.
Asking students to master division through drawing pictures or other discovery-based techniques makes the learning process more complex than it needs to be, the report said, adding this approach is currently endorsed in six provincially approved math textbooks.
Stokke said tackling math instruction through direct learning may be more repetitive, but ultimately more successful.
When information in our working memory is sufficiently practised, it is then committed to long-term memory, after which it may be recalled later," the report said.
"An expert in mathematics stores a wealth of information in long-term memory, acquired through hours of experience and practice; when a new problem is encountered, knowledge and techniques are recalled from long-term memory to solve it."
The report cited Canada's performance on the OECD's Program of International Student Assessment (PISA) as evidence that a fundamental shift in math instruction may be necessary.
The report said that eight of 10 provinces recorded statistically significant decreases in PISA scores between 2003 and 2012, adding Quebec held steady while Saskatchewan logged a much smaller decline.
The scores dropped particularly sharply in Manitoba and Alberta. By 2012, Manitoba had joined Newfoundland and Labrador and Prince Edward Island as provinces with total scores below the OECD average.
In addition to her other recommendations, Stokke also suggested that future instructors should be required to pass a math content licensure exam before being allowed to teach the subject.
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