There’s change coming to Ontario elementary schools, with a return to back-to-basics teaching methods for mathematics. Premier Doug Ford and Education Minister Lisa Thompson have said these changes will be coming down the pipeline in a matter of weeks. Teachers, whose lesson plans for the Fall are already drawn, will no doubt be scrambling to implement the new curriculum.

What exactly are “back-to-basics” teaching methods for methods? In *traditional methods* of mathematics education, there is more emphasis on drills, formulas, and memorization. If you are old enough (like me), then this was how you were taught mathematics in grade school. In contrast, *discovery-based methods* mathematics (or “discovery math”) spends less time on rules and puts more emphasis on problem solving and applications.

The two methods have somewhat opposing approaches. In traditional methods, rules are taught first and then drilled into students via memorization and solving problems. In discovery methods, problems and examples come first and are abstracted to rules and formulas.

For example, in a traditional math lesson, children are told the rule that the order of multiplication of two numbers doesn’t matter, and then they would work on problems related to that topic. In discovery math, children would work out examples such as 2 times 3 and 3 times 2, and then abstract this to the general case. Both approaches teach the same thing but in different ways.

No one should be surprised by these changes after the PC party won a majority in the Ontario provincial election in June. During the election campaign, Doug Ford tweeted the following:

An analogous change was announced regarding Ontario’s sex-ed curriculum, and elementary school teachers are now required to teach a curriculum essentially dating back to 1998.

### Which is better?

*Neither*, in my opinion. Both traditional and discovery methods on their own have their pros and cons.

My issue with the debate about the “correct” way to teach mathematics to children is the way it is phrased as a binary, either-or approach. The choices we are given are:

- drill students endlessly on things like fractions and timetables
- have them discover math rules and formulas from scratch

Neither approach in isolation does justice to math education or reflects how people learn mathematics.

Learning rules and formulas in mathematics is an essential skill, as you need a foundation from which to build. Children need to know what the product of 6 and 8 is without having to rediscover it every time.

At the same time, children gain critical problem-solving skills via discovery. They get to think more deeply about the subject. *No one would teach language skills by only teaching grammar*. You teach children the rudiments of grammar to get them speaking, reading and writing.

In my own university teaching, I employ a mixture of traditional and discovery approaches. For example, in a Calculus course, I may introduce a formula or rule first, but spend most of the class working out examples interactively with the class so they may figure out how things work. In graph theory, I might state a theorem or problem, but then break up the class into smaller groups and have the students discover the proof with hints from me along the way.

### A third path: Math specialists

When I was in elementary school, our classes had the occasional visit from specialist teachers who focused solely on art or music. They didn’t do regular, daily instruction in classes but floated between classes enriching the curriculum. It was always a treat when these specialist teachers came and it was a break from the routine of everyday instruction.

Let’s imagine something like this with mathematics education. Math specialists could be teachers with a mathematics background in their university education, or even math professors or students with the proper training to engage with elementary school classes. I can think of plenty of fun and engaging lessons on graphs and networks for a Grade 6 class, for example. They would float between classes with the sole goal of enriching math education for kids.

There is much more to mathematics education than test scores and math formulas. It is vital that our children be exposed to a rich, engaging mathematics curriculum, even if they don’t become mathematicians or have anything to do with STEM directly in their lives. Numeracy, like literacy, is an essential skill in our modern world. A generation with weak math skills will not be competitive to tackle the next set of challenges in our knowledge-based economy. And a dislike of math tends to pass on from one generation to the next.

While we are rethinking math education in Ontario, let’s use the best of both traditional and discovery methods and add in math specialists. Done properly, this should increase test scores and bolster student engagement.

Let’s also take the time and effort to make math *fun*. Imagine if children were excited to learn mathematics? Isn’t that what we all want?

Anthony Bonato

[…] Which method is better for children to learn math, discovery or traditional? The Intrepid Mathematician suggests a combination of the two and how to implement that teaching in A third path for early math education. […]

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