Influenced by a petition signed by over 12,000 parents, Alberta’s Education Minister, Jeff Johnson, announced recently that Alberta students will be required to memorize times tables as of September 2014. Liz Sandals, Ontario’s Education Minister, followed suit with a statement expressing her view that recall of basic math facts is important and should be a central goal in Ontario classrooms.
Committing times tables to memory should certainly be a priority – this frees up space in working memory so that children can concentrate on more difficult problems. While the addition of times table memorization to math curricula is a positive step forward, this alone will not fix the math crisis in Canada.
Parents might wonder how it is that something as central as times table memorization is not currently required in most Canadian provinces. Anti-memorization advocates set up false dichotomies between basic skills and understanding – “we want kids to understand math, not memorize math facts and procedures.” The idea that students can both understand math and memorize math facts and master standard procedures seems not to occur to them. Attaining both of these things should be a goal of math education.
Many other things need to change. Curricula and textbooks insist that students learn several convoluted methods for simple arithmetic problems.
The use of pictures, blocks and number lines are considered appropriate methods for doing actual calculations. (For example, to add 36 and 48, represent 36 by drawing 3 sticks and 6 dots and 48 by drawing 4 sticks and 8 dots. Regroup the 14 dots into 1 stick and 4 dots, for a total of 8 sticks and 4 dots.) Standard methods, such as addition with a carry and long division are eschewed or de-emphasized.
It is often desirable to explain why standard methods work using pictures and blocks but these concrete materials should not be used as actual strategies for working through arithmetic problems – our ancestors moved beyond such primitive techniques centuries ago. These convoluted strategies take up so much time that children are still working on basic arithmetic at the end of their primary school years when they should be moving on to more advanced topics such as fraction arithmetic and algebra, like their counterparts in high-performing jurisdictions like Singapore. Some Canadian children are left hopelessly confused by the multiple, convoluted strategies and do not master basic arithmetic at all.
This leaves them with shattered confidence and unprepared for learning further mathematics.
Further to this, inquiry-based or discovery-based learning has swept North American schools over the last several years. As if multiple strategies weren’t confusing enough, teachers are encouraged to use open-ended problems that have several possible solutions as a primary instructional tool for teaching novice learners. For example, “The answer to my question is 62. What might my question be?” or “Create a sentence that uses the numbers 22 and 73 and the words share and almost.”
While questions like this are an interesting complement to be occasionally used in the elementary classroom, children cannot become proficient at basic arithmetic – the foundation required for higher-level thinking in mathematics – when constantly immersed in this environment.
Parents might also wonder what evidence led ministries to adopt these approaches. I have been asking discovery-learning advocates to provide me with research studies that support its use in classrooms for the past three years. I have not been given a single sound research study so I can only conclude that it is not supported by solid research, contrary to the unsubstantiated claims of its advocates.
Education ministers seem to acknowledge that some basic skills are important to later success in math but they need to go much further. The standard methods for arithmetic – addition with a carry, subtraction with a borrow, long multiplication and long division – need to be central to elementary school math curricula, instead of convoluted, time-consuming methods for straightforward arithmetic problems. Teachers should not be required to bombard new learners with multiple strategies and curricula and textbooks that insist on this confusing approach should be replaced. Students need to move quickly beyond pictorial methods and onto symbolic approaches so that they are prepared to tackle more challenging problems. Until further changes are adopted in addition to times table memorization, we can expect more of the same – confused children and angry parents.
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.