Monday, December 26, 2016

Technology

I saw a funny ignite talk "Algebra Inferno" the other day comparing disliked teaching practices to the various circles of hell a la Dante.



Among the sinners list were the survivalists: those who refused to ever allow the use of technology in their classes.  While I chuckled at the clever pun, I don't really totally agree with this point. My contrarian instinct is that there is a huge body of math out there that doesn't need calculators that one need never stray from and quite successfully conduct a lesson. And on the converse most of the math lessons that try to use them often turn out to be more about practice punching buttons than thinking mathematically.

There's some larger existential questions wrapped in this debate. In the era of  ubiquitous cellphones and Wolfram Alpha what parts of elementary school mathematics are relevant and can you skip them without throwing away the ladder to higher level skills?

Leaving that question aside, in practice, as often is the case I'm more pragmatic than my initial instincts. The other day my son was working on a problem and asked if he could use Desmos to plot the graphs of some inequalities. That seemed like a very reasonable usage and I'm happy how much he is excited by desmos having only been recently introduced to it. So feeling like another hand plot wasn't needed, I said "of course."

I don't have that  luxury during Math Club where there are neither calculators or computers around. But were that the case these are just a  few of the uses I  think really are worthwhile:

  • Investigating the patterns of digits in repeating decimal numbers is vastly sped up by just trying them out.
  • In the age of infinite precision calculators its now possible to check all those modular arithmetic stumpers  like which is bigger 63^45 or 33^54  directly in python.
  • I love the use of 2-d and 3-d graphs as long as they are a natural extension of a larger problem.
  • Geogebra makes a nicer version of pen and compass constructions and is very useful in exploring more complex geometry proofs.
  • We were recently doing a comparison problem at home between 2^1/2, 3^1/3 and 5^1/5.  Visualizing the graph of x^1/x in desmos made this much richer. 
  • If you want to practice finding factors for larger numbers like say 2017, calculators help speed things up quite a bit.

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