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In the battle of old versus new ways of teaching math, our kids are suffering

Matthew Oldridge is a mathematics teacher and father based in Mississauga, Ont.

Another school year approaches, the EQAO mathematics results are released, and we teachers have to ask ourselves: Where is the system going wrong? The same gruesome number again: 50 per cent of Ontario's Grade 6 students are failing to meet the provincial standard, and every parent and teacher across the province is trying to figure out why.

As a mathematics educator who has been teaching Grades 3 to 10 for 15 years – and as a veteran of the debates over how best to teach mathematics (the so-called "math wars") – I am no stranger to these conversations. Going back to the National Council of Teachers of Mathematics (NCTM) reforms of 1989, we have hotly debated how best to teach mathematics for decades. Do kids need to master the so-called basics before they work with interesting problems? Are calculators and smartphones to blame? Are kids doing enough problem-solving? For that matter, what are the basics?

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It is tempting to lay the blame at the feet of either traditional or discovery mathematics, based on what you believe. It's time to get past that argument, too. Pure traditional teaching with endless homework and worked examples may produce kids who are more parrots than thinkers. Pure discovery learning is a disaster – kids need guidance to learn and use powerful mathematical tools and structures. Most educators are somewhere between these two poles with their teaching methods.

Quiz: Can you pass the Grade 6 math test?

Ontario students are caught in the middle due to changing teaching methods and a curriculum that needs adjusting to be more developmentally appropriate. A generation after the NCTM reform and Ontario curriculum revisions in 1997 and 2005, we are still stuck between "old ways" and "new ways." Textbooks have essentially disappeared, and there are no new ones on the horizon. Teachers are encouraged to find and create their own math problems, and they should – but we should also acknowledge the high degree of skill and discernment it takes to select or create interesting problems.

Recent Ministry of Education developments such as the Renewed Mathematics Strategy focus on mathematics content knowledge for teaching hold promise. The biggest revelation in my career has been how much I didn't know about mathematics. Teaching is also learning – may it always be so. Researching how kids learn to count and add and subtract, for example, has changed my thinking about the complexity of early mathematics. Teachers need much more training in mathematical content knowledge – and how to teach it.

Compounding the problem is a 12-year-old curriculum that has good front matter, and a great philosophy, but needs revision to reflect current research in how students learn math. For example, Ontario has a new fractions learning pathway based on research about how kids learn fractions concepts, as well as a document on spatial reasoning that ties spatial thinking to future mathematics success. Each grade has a gigantic list of expectations that teachers are tempted to see as a "shopping list" – to check off.

In reality, the overall expectations that must be graded are more manageable, but it's easy to get lost in the forest of expectations and not see the trees. I would prefer we go the way of British Columbia and foreground the big ideas of mathematics that are to be covered, rather than the minutiae.

If you look at the EQAO data for Grade 6, you see trends such as students struggling with questions about the surface area and volume of a triangular prism. My suspicion is this topic is better left to Grade 7 or left out totally – when was the last time you calculated the surface area of a triangular prism?

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Students also struggle with multistep problem-solving. The questions labelled "thinking" by the EQAO are usually the worst category by score. This is troubling because, after all, humans were born to think. We are thinking beings. Perhaps kids also aren't being given enough chances to engage with interesting and meaningful math problems.

But what exactly is meaningful? One year the EQAO included a question about the mean of the height of the players on the starting lineup of a basketball team but neglected to say that a "starting lineup" is five people. Guess what? Students bombed that question. Lack of knowledge of the context sabotaged them before they even started.

Is it any wonder that students are struggling? They are the ones caught in the middle.

We need meaningful curriculum reform in Ontario and must continue to work on providing teachers with the powerful mathematical content knowledge they need to help their students. Let's allow kids to engage with interesting mathematics problems and give them enough time to practise their skills.

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