Thursday, September 10, 2015

What Things In Our Math Curricula Do You Think Have Become Outdated (...Or Even Obsolete?)

The always interesting Keith Devlin writes here about the future of math. As a mathematician, he has a good perspective on the ways in which math education has changed. For Devlin, our education systems are lagging behind the world of math. Math has changed, but has how we teach it?

I will quote a whole paragraph here:

"To most people, mathematics means applying standard techniques to solve well defined problems with unique right answers. They have good reason to think that. Until the end of the 19th Century, that’s exactly what it did mean! But with the rise of the modern science and technology era, the need for mathematics started to change. By and large, most people outside mathematics did not experience the change until the rapid growth of the digital age in the last twenty years. With cheap, ubiquitous computing devices that can do all of the procedural mathematics faster and more accurate than any human, no one who wants – or wants to keep – a good job can now ignore that shift from the old “application of known procedures” to new emphasis on creative problem solving."

Jordan Ellenberg is also quite persuasive on this topic, and if you haven't read his book, How Not To Be Wrong, you must. Machines can do the laborious work of long calculations, so our brains are freed up to do what we do best-think.  Conrad Wolfram is another who sees computing as a large part of the future of math.

We may not need to do long laborious calculations by hand, but we do, of course, need basic number sense, combined with our intuitions and our operational skills. One example from my own schooling is calculating approximations of square roots by hand- I remember doing it in school, but I am not aware of anyone who teaches it now. Of course, if you are a certain age, you remember having to use slide rules and log tables. Probably nobody is nostalgic for that!

I got to thinking today, after an interesting conversation with @MathiesUnite. We talked about how, with the dawn of Desmos, drawing graphs by hand is a less useful skill than ever. Have you ever planned a lesson that involved drawing a graph, and looked around 20 minutes later, and some kids hadn't even put the scales on the axes yet?  I have. I have seen terrible hand drawn graphs. The worst. I have seen graphs so scary bad they  didn't even look like any more than a bunch of squiggles on a page. Why  should we not use the tools at hand to draw graphs more effectively?

But Desmos (and others) are so much more than that-you can compare two data sets, at a glance, within minutes, freeing up time for discussion, interpretation, and analysis. Nobody would argue that we don't need good data interpretation skills these days.  

@BrianPenfound offers some pushback on the idea of digital tools replacing graphing by hand completely:

The discussion got me thinking, and I posed this question, later:
That's not to say our students will do FiveThirtyEight level data visualizations, nor that they don't need to know how to use conventional graphs. I just wondered, in the age of pictographs, incredible fan-made baseball data visualizations, and so on, if that might be another "new" area of math we should explore with our students.

The definition of data visualization offered by Wikipedia makes me wonder if it might not be its own literacy, on its own.

So graphing by hand might be one, do you have any other ideas for items from math curricula that you suspect could be obsolete, or, at the least, outdated in their conception?

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