“Let’s not do math today”

Kids learn by example

A classroom of kids cheer with joy. Later that day a boy runs in the front door of his house and says: “Mom, teacher said we didn’t have to do math today!”

Math class is cancelled.

Sound like fiction?

It’s not. A mathematician colleague of mine told me that her son experienced this in his elementary school.

Some kids don’t enjoy math. That’s not the surprising part. The shocking thing is that our schools can reinforce the message that math is punishment. If the messaging comes from teachers themselves that math is not important or worse, then we should expect impressionable young students to absorb that message.

Numeracy matters

Children learn key life lessons in school, and take those into their adulthood. Numeracy matters, just like literacy matters.

Mathematics comes up everywhere: in the sciences, engineering, and increasingly in the social sciences, medicine, and business. We need more people with strong math skills to progress the discipline. A generation with weak training in mathematics should be cause for concern.

A caveat: as a mathematician, I am aware of how our discipline is misunderstood by the public. Part of that is our fault: we don’t do a great job helping people understand what we do or why it is important. This is why I write blogs.  Our community needs to better communicate the beauty and majesty of mathematics.

What the data says

Canada does OK but is not at the top in math scores worldwide.

In 2015, the think tank Organization for Economic Cooperation and Development (OECD) published a ranking of math education in 76 countries. Canada came in a semi-respectable 10th.

The USA was well below average, ranking a distant 28th. The top countries for math education were all in Asia.

Screen Shot 2013 12 03 at 5.29.16 AM
Numerical data from the OCED study, showing mathematics, reading, and science scores by country. The top five countries for math scores were all in Asia.

OCED education director, Andreas Schleicher offered his two cents as to why Asia dominates test scores:

If you go to an Asian classroom, you’ll find teachers who expect every student to succeed. There’s a lot of rigor, a lot of focus and coherence. These countries are also very good at attracting the most talented teachers in the most challenging classrooms, so that every student has access to excellent teachers.

I doubt very much math class is ever cancelled in Singapore.

My home province of Ontario is below the national average for math scores. Based on OCED and Conference Board of Canada data, Ontario ranked behind the provinces of Quebec, Alberta, and British Columbia, but ahead of Manitoba, Saskatchewan, and the Atlantic provinces.

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Too little too late in Ontario?

I read on CBC recently that several teachers colleges in Ontario will now require all their teachers-in-training to review elementary school mathematics. Laurentian, Lakehead, and Trent all require their students in teacher’s college to learn basic proficiency in math, regardless of whether their goal is to teach Mathematics, English, or Physical Education. By basic math we are talking about topics like fractions and percentages.

This is a good start. We expect our teachers to be literate, so they should also be numerate.

In April 2016, Ontario Education Minister Liz Sandals announced the Renewed Math Strategy for elementary schools in Ontario. This includes a number of strategies, such as a mandatory one hour of math instruction for all students in grades one through eight, and a dedicated math Professional Development Day for teachers. Ontario is making improving numeracy in our schools a priority, investing $60 million in the Renewed Math Strategy.

Way to go, Ontario. Maybe someday we will rival Quebec’s scores, which is second ranked after Japan.

The Honourable MPP Liz Sanders works on a math problem with a student. She has a Master’s degree in Mathematics from the University of Waterloo, and has taught computer science at the University of Guelph.

We can only hope these developments make an impact in my province. Is it too little too late, or are these measures enough to foster student success?

We will have to wait for the next OCED-type study to find out.

The distributive law

Applications of mathematics and discovery are both wonderful tools to foster learning. I love to include those with my students when I lecture on mathematics.

However, our students also need competency in basic math skills. If you don’t have the tools to do math, it will turn into an exercise of frustration. Our students need to learn the fundamentals of mathematics before they can progress to the more advanced topics so prevalent in STEM disciplines.

One example of this surrounds the distributive law for multiplication:

a(b + c) = ab +ac.

I was surprised to hear from my colleague that kids in Grade 7 math class don’t learn this fundamental arithmetic property. That might be an anomaly with that teacher or school, but that something so basic is missing in early math education is a cause for concern. Without knowing the distributive law, students will not learn how to manipulate polynomials, which will slow their progress learning Calculus or Algebra.

Having taught introductory Calculus many times and at several universities, I’ve witnessed the frustration of students when they realize their basic math skills need to improve. Motivated students rise to the challenge, but some just don’t make it. We provide more and more review of high school math in the first weeks of university Calculus, but it never feels like enough.

In a few years those same Grade 7 students who have never heard of the distributive law will be faced with a problem like this one in integral Calculus:

My fellow lecturers would call this an easy example of an indefinite integral in a first-year Calculus course, one that relies on a routine trigonometric substitution.

Will your kids be ready?

Anthony Bonato

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