Wednesday, April 2, 2014

"Old" and "New" math

There's a lot of talk about "new" math and "old" math.

If I had to distill the math wars down to a simple idea, I would probably say that constructivist (new) math calls for an increase emphasis on understanding while simultaneously calling for a decrease emphasis on direct instruction of facts and algorithms.

The math wars get heated when critics come to see these changes to mean an elimination of basic skills and precise answers.

I would like to address three frequently asked questions about constructivist math:

Math hasn't changed and neither have kids, so why are we changing how we teach math?

Maybe math and children haven't changed, but our understanding for how children learn math is more sophisticated than generations ago.

Memorization is important and it is a very real product of learning, but memorization is not the primary purpose. Memorization is something that happens because children learn and understand mathematics first.

In math there is one right answer. Doesn't this new math just confuse kids and convince them to hate it?

Let's not pretend that traditional math instruction didn't confuse and turn a lot of students off of math. When adults think back on their schooling, it's easy to succumb to something called Nostesia which is a hallucinogenic mixture of 50% nostalgia and 50% amnesia which distorts rational thinking.

I remember dividing fractions. I was told to flip the second fraction and then multiply. It was a trick that enabled me to get high scores on tests. To this day, I have absolutely no idea why I flip the second fraction and multiply. This felt like magic when it should have been math.

If we want to confuse and turn students off math, I can think of no better strategy than to make math a ventriloquist act where children are merely told the most efficient ways of getting the right answer. When students are simply told the most efficient way of getting the answer, they get in the habit of looking to the adult or the book instead of thinking things through.

Canada's ranking on international tests like PISA are dropping. Doesn't this mean we should go back to basics and traditional math?

Since 2009, Alberta has dropped from 9th to 10th place in world rankings. A 2 per cent drop in our raw scores on math over two years has led to hysteria. The sky is not falling. It's also important to note that the children who wrote the 2012 PISA test had "old" math for their first seven years of school and only 3 years of "new" math.

My point is not to indict "new" or "old" math. There are many variables that may be responsible for the score changes. One factor is class sizes are growing. Since 2009, Alberta has added 41,000 new students and only 106 teachers.

Too many people confuse causation and correlation in an attempt to draw convenient conclusions that they simply can't prove. No one can prove that the change in PISA scores were because of teacher instruction. For example, we know that the strongest predictor of student performance on achievement tests is socio-economic status.

By idolizing PISA rankings, we risk chasing after Asian countries who achieve high scores with very different priorities and questionable means. PISA envy can lead us to aspire to be more like top-ranking Asian education systems even though those same Asian countries are desperate to reform their schools to look more like ours.

The math wars, like all wars, are ultimately destructive. Let's keep in mind that too many of us merely endured math or flat out hated it. Either way, it's safe to say that not enough of us loved it.

And we aren't going to get more children to love math by pretending that school already doesn't have enough lectures, direct instruction, worksheets, textbooks, tests and memorization.

This is a shorter version of a longer post that I wrote on the math wars here.


  1. Love this, Joe. Thanks for writing.

    I'd also like to consider that what most people call "new" math is REALLY the oldest method of becoming a mathematician or thinking mathematically. Before the invention of the printing press (which eventually led to industrial age math textbooks and worksheets), people learned mathematic concepts by doing, not ciphering incessantly.

  2. Bang on, Michelle! The "new" math is in fact a very old math -- maybe the oldest.

  3. Joe, I really appreciate this simple explanation of the hysteria I'm hearing all around me. I'm passing your blog around.

  4. I was quite worried about the "new" math, until I started reading more about it. The reasons you mention above are why I'm in favour, as a parent. It's true that possibly it may not work well for one of my kids ... but that's an issue with ALL OF SCHOOL for him so not something to really base an opinion on.


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