Halting the slide in math

International and national assessments are continually showing Manitoba students' math skills are in steep decline — the percentage of 15-year-olds performing at the lowest levels on international tests doubled from 2003 to 2012, while the percentage of students in the highest-performing level was cut in half. Manitoba recently stood out as the lowest-performing province in Canada on a national math assessment.

The results of the tests are reliable, contrary to some claims. Both assessments involved randomly selected schools, except First Nations schools, which were excluded in the sample. Students at an obvious disadvantage, such as a cognitive or developmental disability or with limited language skills, were also excluded.

The province recently made some good moves to arrest the slide. But there's work to be done to ensure our kids get a good foundation in math — a key to academic success and prosperity in a knowledge- and technology-based economy.

First, some helpful changes: Jump Math, an effective classroom resource written by a Canadian charity, is now provincially recommended. Beginning in September, future K-8 teachers will be required to complete two math courses in university, making Manitoba the first province outside of Quebec to require more than one math course prior to certification.

The government recently reinstated standard methods such as column addition to the curriculum, a tried and true skill for young children. Times tables, a basic multiplication skill for many of us, were also reintroduced, but in Grade 5.

While these are positive steps, the curriculum remains weak in comparison to past curricula. Children used to memorize times tables in grades 3 and 4. Fraction arithmetic, which is extremely important for later math success and requires time and practice to master, was once taught in grades 4 and 5 and is now introduced in grades 7 and 8. These are just two of many examples that illustrate the deterioration of the provincial math curriculum.

But there is another element to the way pupils are taught math today that must be addressed.

A harmful ideology persists among consultancy groups that direct teacher professional development, advise teachers and design provincial curricula and teachers' guides. Trendy techniques in Canadian math classrooms overemphasize hands-on materials, multiple strategies, open-ended problems and project-based instruction, often pushing aside direct instructional techniques such as explicit instruction and pencil-and-paper practice.

These methods are rooted in a learning theory called discovery-based learning, a chameleon that goes by a number of titles: inquiry, student-centred, experiential, project-based, problem-based and 21st-century learning.

These techniques are woven into curricula, prominent textbooks and teacher professional development sessions. But they are not backed up by solid research.

As I detail in a newly released C.D. Howe report, research in cognitive psychology consistently shows direct instruction, where students are explicitly taught procedures that are practised to mastery before attempting complex problems, results in better learning, better understanding and better problem-solvers.

This makes sense, because effective instruction caters to the limitations of working memory, which can accommodate about seven pieces of information at a time, such as a phone number. Following sufficient practice, facts and techniques are moved from working memory to long-term memory to be recalled later to solve new problems. When novice learners are presented with multiple strategies, unclear instruction or open-ended problems, working memory is overloaded, which hampers learning. Discovery techniques can do their most harm to struggling students, who need a great deal of structure, practice and guidance.

While many argue for balance between discovery and traditional techniques, the balance should favour proven, effective methods. A good rule of thumb is the 80/20 rule — at least 80 per cent of instructional time should favour conventional techniques while at most 20 per cent should favour discovery methods.

Given that other provinces have also experienced declines in math, why has Manitoba seen the greatest decline? The answer may be related to a lack of rigorous data collection and transparency surrounding student performance.

Other than the Grade 12 provincial exam, the province does not administer uniform provincial tests. Most Canadian provinces administer standardized tests yearly at various grades and publicly post school-level performance results. Manitoba abandoned standardized provincial tests in earlier grades by the year 2000. The way was paved for the discovery movement to take over Manitoba classrooms because provincial data were not available to reveal its failure.

We can be encouraged by the government's responses to an obvious problem with student math skills. More needs to be done. More transparent measurement of subject- and school-level performance, the adoption of instructional techniques that are proven to be effective and a more rigorous math curriculum are obvious next steps.

Parents need to keep the pressure on their schools and their MLAs to improve math education in Manitoba.

 

Anna Stokke is a math professor at the University of Winnipeg who co-founded the advocacy group WISE Math (Western Initiative for Strengthening Education in Math) and the non-profit organization Archimedes Math Schools.