New Math versus Old Math

A friend is a teacher in the school system and his biggest problem with the profession is the constant scrutiny it gets from the public, whether it is media publicity or constant critique from over zealous “helicopter parents”. But occasionally there is an issue where he has no choice but to side with the public. The recent uproar over how math is being taught is one of them.

Here is how I understand the difference between the new and old methods of teaching math. The old method involved learning or memorizing the multiplication table and formulas to arrive at an answer. The new method places less focus on memorization, and replaces it with text laden, descriptive problems designed to encourage students to discover the answer.

In short, the problem with old math is students had to accept that 2 x 2 = 4. The strength of the new math is that it encourages students to ask why is the answer 4. Proponents of new math argue that the old method is flawed as it is based on memorization and rote, and that the new method is better as it encourages critical thinking and allows the learner to determine the answer in a variety of ways.

Critics of new math argue that students cannot even begin the critical thinking process if they do not have a grasp of simple math concepts. Vocal parents complain that they cannot help their children with homework because the new math might as well be a new language.

Some parents have enrolled their children into specialized math courses like Kumon. Others have decided to teach their children the multiplication tables in spite of the school’s new methodology. In both cases, parents contend that their child’s marks improve dramatically once exposed to the old method.

So which method is better? Here is my take. I am a product of the old and I take exception to the characterization of the multiplication table as memorization. Years ago I was a literacy tutor and the orientation included a numerical literacy module which re-visited the multiplication table.

It was through this module that I discovered the multiplication table from 1 to 10 was not strict memorization. Rather it was a grid of patterns which were not difficult to learn (not memorize). An obvious pattern is the “5” times table, where all the answers end with the numbers 0 or 5.

There may be merit with the new math methodology, but the implementation by school boards has failed to gain acceptance by its primary audience – the students and the parents. I see parallels between this implementation and the Canadian government’s switch to the metric system in the 1970s, which I think was a good move.

While officially a metric nation, what has evolved over 40 years of conversion is Canada adopting a hybrid metric-imperial standard. We measure our distances in kilometres, yet all Canadian vehicles are still sold with speed gauges in miles and kilometres.  Temperature is measured in Celsius, but we still think of our weight in pounds and our height in feet.

So while officially metric, the Canadian government has never really discouraged or eliminated the imperial standard. This, I believe, is the path school boards should take.  New math is the official standard, yes. But do not throw away the old methods. Both can, and should, co-exist.