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Too much math education is based on pet theories

As students go back to school this fall, parents in some provinces will notice changes in math classrooms.

In response to a petition signed by over 17,000 parents, the Alberta government included times table memorization in its curriculum this September. Manitoba added the same requirement one year ago but went a step further to include standard methods like long division and declared JUMP Math, developed by a Canadian charity, a recommended resource. The forward-thinking Winnipeg School Division, which is the largest division in Manitoba, will be adopting JUMP Math in many classrooms this fall. Last spring, Ontario Minister of Education Liz Sandals announced that children in Ontario should be required to memorize times tables, but the Ontario government has not taken formal action to ensure this.

Ontario's recent EQAO results showed that the percentage of Grade 6 students who meet provincial standards fell from 61 to 54 per cent over the past five years. Education Minister Liz Sandals claimed that, contrary to public opinion, the EQAO test results revealed that students did not have difficulties with basic arithmetic but that problem solving stumped students. Sandals neglected to mention that Grade 6 students were permitted the use of calculators and manipulatives like blocks throughout the entire test. It is not surprising that students struggled with problem solving but the ability to push buttons on a calculator does not reflect fluency with basic arithmetic.

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The Ontario government should look closely at the two textbook series used in most Ontario elementary schools – Pearson's Math Makes Sense and Nelson Mathematics. Authors of these texts claim to nurture creative thinking, problem solving and understanding of math concepts. If this is true, why has student performance in math declined over the period in which these texts have been used? It is time to adopt alternatives that include less fuzzy instructional techniques like JUMP Math, Singapore Math or Saxon Math.

Solid education research that conclusively demonstrates the effectiveness of particular instructional techniques is hard to find. Nonetheless, over the last 10 years, teaching methods have tended towards discovery-based instruction, also referred to as inquiry-based learning, 21st century learning or constructivism. In this environment, explicit or direct instruction from teachers is minimized, rigorous practice and memorization of facts is discouraged, group work is the norm and novice learners are encouraged to invent their own strategies for solving open-ended math problems with little direction from adults.

Project Follow Through, which involved 72,000 students over a period of 10 years, starting in 1968 was the largest education study ever conducted. The study concluded that Direct Instruction, characterized by explicit instruction followed by practice, feedback and assessment, resulted in students who had better basic skills, better understanding of math concepts and better problem-solving skills and confidence than those taught using discovery techniques. Ironically, students educated using discovery techniques are less likely to be strong problem solvers than those educated using conventional techniques. Students need toolboxes stocked with knowledge, facts and well-practised skills in order to solve challenging problems and to understand math deeply.

Yet most in the education research community shunned Project Follow Through, choosing instead to conduct more of their own studies, hoping to demonstrate that their pet theories were correct.

Recent research in cognitive science confirms what Project Follow Through found forty years earlier. A 2011 meta analysis of 164 studies led by psychologist Louis Alfieri concluded that explicit instruction, worked examples and feedback benefit learners while unassisted discovery does not. A 2014 study published in Educational Evaluation and Policy Analysis found that only direct instruction, routine practice and drill significantly improved math achievement in struggling math students. Repetition and practice give students the vehicle for storing important knowledge and techniques into long-term memory so that they can be quickly accessed later. Another article, which appeared in Nature Neuroscience in August, found that failure to memorize math facts early results in impaired math learning later on. On the other hand, I have not found one rigorous study showing that discovery-based instruction is more effective than conventional instruction.

Despite the evidence in favour of explicit instruction and rigorous practice, discovery or inquiry-based techniques dominate teacher education sessions, teacher professional development and math textbooks. In other words, teachers are frequently advised to use teaching techniques that do not result in successful math learners, often against their own better judgment.

Proponents of inquiry-based instruction often claim that many adults struggle with math, citing this as proof that their unsubstantiated techniques should be adopted in math classrooms. While it is true that some adults struggle with math, this is not an argument for adopting inquiry-based learning any more than it's an argument for using jumping jacks to teach kids math since inquiry-based learning has not been shown effective. Furthermore, the innovative developments on which society is so dependent today came from individuals educated under the conventional system. (Look at the screen you're reading from.) It is incorrect and insulting to great teachers of past years to argue that instructional techniques used with previous generations did not produce creative problem solvers.

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Provincial governments have wasted time, money and resources on unproven and expensive fads that hinder math achievement instead of nurturing strong, confident, math students who are fluent with computational skills, understanding and problem solving. It's time to start adopting math programs and instructional techniques that work.

Anna Stokke is an Associate Professor of Mathematics at the University of Winnipeg, a co-founder of the non-profit organization Archimedes Math Schools and a co-founder of WISE Math.

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