Practice and drills are the keys to math success

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This article was published 2/9/2014 (1757 days ago), so information in it may no longer be current.

Three years ago, math professors in Manitoba began advocating for improved math education. As a result of our work with the deputy minister of education and other key individuals, changes were recently made to the provincial math curriculum. Children must now memorize times tables and learn standard methods for arithmetic such as long division, though these requirements still appear at much later grades than in high-performing jurisdictions. Last fall, Manitoba became the first province in Canada to list JUMP Math — a strong math program developed by a Canadian charity — as a recommended resource. The Winnipeg School Division is working hard to improve math learning through various initiatives and is adopting JUMP Math in many classrooms this September.

These are positive changes but much work remains to improve the provincial curriculum and to ensure teachers receive appropriate training in math and professional development that stresses conventional instruction, which includes understanding and problem-solving.

Very little data about the performance of Manitoba students is publicly available at a provincial level, but Manitoba students take part in PISA, an international test written by a sample of Grade 10 students, every three years, with the most recent assessment having occurred in 2012. Almost all provinces experienced statistically significant declines in math performance since 2003, but Manitoba students came in below the world average and saw a greater decline than in any other province. Particularly alarming is the percentage of Manitoba students performing below the baseline level to participate fully in society nearly doubled between 2003 and 2012, while the percentage of students performing at the highest two levels halved. As a parent, and as a math professor who recognizes the importance of math for a variety of careers, this concerns me.

The predominant instructional method in math classrooms has changed drastically over the last 10 years. Going by such names as discovery or inquiry-based learning, 21st-century learning and constructivism, these teaching techniques are characterized by less explicit instruction by teachers, excessive group work, project-based learning, multiple strategies, limited practice and less emphasis on memorization of facts. It is argued this breeds creativity, flexible thinking and understanding and students are freed from the drills and worksheets of the past.

Contrary to claims, past curricula and textbooks emphasized understanding, but hard work, perseverance and practice were also emphasized. These are essential for success but are often not stressed enough in today's classrooms.

In reality, the discovery approach typically involves fuzzy instructional techniques, often resulting in students without skills and with false self-esteem, which is deflated once they reach higher grades, post-secondary education or the work force. Ironically, students taught in an environment where basic skills are neglected do not have the foundation to solve simple math problems, let alone think creatively or understand math deeply. This approach hinders creativity because students cannot solve complex problems without a toolbox stocked with memorized math facts, knowledge and well-practised skills.

The shift in instructional methods and the eagerness of provincial governments to jump on the discovery bandwagon is perplexing since rigorous research shows conventional instruction is more effective than discovery-based instruction. A large-scale study called Project Follow Through, conducted over 10 years beginning in 1968, showed explicit instruction by a teacher, followed by practice, feedback and assessment, resulted in students who had stronger basic skills, better understanding of math concepts and more confidence than those taught using discovery techniques. Fast forward to 2014, when recent studies by cognitive scientists have shown students who commit basic facts to memory early by practice and drill are in a better position to succeed in later mathematics. Referring to an article that appeared in Nature Neuroscience in August, cognitive psychologist Mann Koepke advised children work through addition and multiplication drills because "experience does matter."

The problem extends beyond times tables and examination of teacher education sessions across Canada reveals teachers are frequently advised to use instructional techniques that do not result in successful math students. Textbooks emphasize confusing, long-winded methods and, instead of stressing important concepts such as fraction arithmetic early, provincial curricula have moved these concepts to later grades, weakening expectations of students. For example, in 1985, Manitoba students were taught to add and subtract fractions in grades 4 and 5. These concepts are now taught in grades 7 and 8. A similar pattern is seen with concepts such as basic arithmetic, ratios and percentages. Students cannot be expected to perform as well as in the past when expectations have been lowered and important skills are not taught early enough for techniques to be consolidated into long-term memory.

Progressive thinkers in the education community are realizing the unsubstantiated methods that have been promoted for the last 10 years are not helping students and a more common-sense approach to teaching math is warranted.

Manitoba Education is on the right path by adding requirements for times-table memorization and standard arithmetic methods to provincial curricula. However, much more needs to be done if we are to see real improvement for Manitoba students.

Anna Stokke is an associate professor of math at the University of Winnipeg and a co-founder of WISE Math.