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Carly Rabie, Ainsley Sos, Jessie Du and Lily Graff learn math from Harriet Simand while measuring ingredients for ginger cookies at Bishop Strachan School in Toronto on December 6, 2013.JENNIFER ROBERTS

Canada's fall from the top 10 in its international math standing, revealed this week by the OECD's Programme for International Student Assessment (PISA), has been partly attributed to insufficient instruction in the fundamentals of math, such as multiplication tables. Across the country, some of the people most concerned about declining math scores are math teachers, who understand that effective instruction in numbers, algebra and geometry can spark lifelong curiosity and set up children for rewarding careers.

Harriet Simand

Grade 5, The Bishop Strachan School, Toronto. A lawyer-turned-teacher, she earned a Prime Minister's Award for Teaching Excellence in 2012

How would you describe the difference between how you were taught math and how math is being taught now?
I learned math in the 1960s. I remember I always loved math. There was a lot of emphasis on knowing your basic facts early in elementary school. I remember my teachers taught us a lot about deriving equations. A lot of math [now] is more children discover math on their own, so more inquiry. A lot of textbooks are actually quite wordy.

What are the key skills students should master?
Times tables, addition and subtraction to 10 and division should be known off by heart. For example, if you are adding fractions and finding a common denominator, if they don't know their times tables, they will spend most of the time figuring out, for example, what is a common denominator for 6 and 9. I believe that mastery of and confidence in both automaticity of basic skills and conceptual understanding are key.

My analogy: It is really important that students reading a book comprehend the words and the deeper meaning of what they are reading. But they need to be able to read the alphabet first, so they are not stumbling over words.

Do we have a "national emergency" in math, or should we all calm down? Canada is still far ahead of most of the world.
I see the math scores as an issue. When I go out to restaurants with friends, many can't figure out the tax or tip. Everyone should be able to understand concepts that they will need forever, such as mortgages and credit cards. My husband works in the engineering department [of a] university, and he is always telling me that in many classes, kids need calculators to do everything.

Elisha Bonnis

Grade 4, General Wolfe Elementary School, Vancouver. She struggled with math while teaching, turned to the JUMP Math program nine years ago and got her master's in math education from the University of British Columbia two years ago.

What are the problems you see in how students are learning math?

There has been a strong emphasis on discovery and exploration but with minimal practice, along with viewing the teacher as a facilitator rather than teaching concepts explicitly. Many of the math programs today have students beginning the lesson with exploration, often in front of their peers, which will shut down students who do not have the necessary skills or confidence. … This seems to me the reverse order of how learning happens.

Do you stick with the curriculum?

I make every effort to stick to the curriculum, but I do not sacrifice student learning by rushing through concepts if I can see that they are not being understood. I believe that the curriculum is too dense, and that this creates an immense pressure on teachers to force through more quickly than they would, for fear of not covering everything.

Lee Van Cauwenberghe

Grade 8 math and science, Stanley Knowles School, Winnipeg. He was a recipient of a Prime Minister's Awards for Teaching Excellence certificate of achievement this year.

What are the problems you see in how students are learning math?
I am not sure if kids are getting enough practice with math concepts. I do remember sitting at a desk and doing 50 problems of the same type until the concept was burnt in your mind.

Kids are very concerned with being seen as wrong. They are not as willing to share openly with the possibility of not having the correct answer in front of their peers, and we have to work to change their perception. Edison tried many times to get the right argon gas in the electric light bulb before he got it right, and if he had a fear of failure, we would still be in the dark.

What are the math concepts or techniques that all students must know?
I really do feel that kids learning their multiplication tables is a must. When they have to stop and think about what the answer to 6 times 7 is and it takes too long, they have likely forgotten what the focus of the question they were trying to figure out is.

A strong work ethic and a positive attitude are also essential skills that they need to become successful. When my kids show frustration, I have to make sure to tell them that number sense is not learned in one year, it is developed over a long period of time.

These interviews have been condensed and edited.

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