Yes, the “if any” is implicit. Unlike our recent Who Should People Read post, this one is not intended to produce a list of “useful resources”. Rather, akin to this post, it is a challenge to come up with anything. But first, a story.
Some years back, a maths ed person I know was organising a maths day for secondary teachers. The organiser approached me and also a proponent of maths technostuff, asking if we would be interested in taking sides in a debate on the use of technostuff in the maths classroom. After some haggling over the limits of the topic for the purposes of the debate, and some clarification of the ground rules, we both agreed. Then, soon after, the organiser informed me that there had been “a change of plans”, and that there would be no debate. C’est la vie. But then the program for the maths day appeared: the pro-tech person had been paired with another pro-tech person, and these two pro-tech people were allotted a debate’s worth of time to demonstrate the pro-ness of their tech. This decision to change the program was, of course, both stupid and astonishingly rude, and I was, of course, furious.
I later learned that a more senior organiser had overruled the idea for a debate, and I eventually let both organisers know exactly how I felt. The less senior organiser eventually apologised, genuinely, and that is settled, genuinely. I do not know exactly why the senior organiser didn’t want the debate, since they wouldn’t give me a straight answer, but some conjectures come to mind. As to why the senior organiser and my would-be debating opponent regarded my dis-invitation as even remotely acceptable, I don’t know. Perhaps they simply considered insularity and censoriousness and rudeness as business as usual in modern maths ed. They may well be correct.
Anyway, that’s the story, and back to the question: What are the proper uses of “technology” in the school mathematics classroom? And, yes, referring to it as “technology” is perverse, but the theft of a very useful word by maths ed ideologues is probably irreversible. In any case, I’m using “technology” here to refer to anything from basic calculators on through CAS and GeoGebra and Desmos and Mathematica, and spreadsheets and whatever other Software Saviour people wish to propose. (Of course, for example, suggesting CAS is properly used in VCE because CAS is mandated in VCE is funny but is off the point.)
I imagine I’ll be arguing this one without much support, maybe even from myself. Do I really think there is no such proper use? No, not quite, but close. I have a few applications to which I might agree. The more I think about these applications, however, the more I’m sceptical of their value, and am definitely sceptical that more than very little class time should be devoted to them.
So, have it. Prove to me that I’m the Luddite that I am.
Tony Gardiner has commented at length, below. He notes the key question:
How do young human beings construct our shared mental universe of mathematics in their heads?
It is in the answer to this question that I, and it seems Tony, can see little or no role for digital things.
Tony also linked to a debate he had with Conrad Wolfram on this very topic, here. I haven’t listened to it yet, but look forward to doing so.
Here is a link to video of the entire event in which the Gardiner-Wolfram debate occurred, but the debate is incredibly well hidden.
Scroll down until you see the video window:
Below that (but above the PDFs) there is an “image” which can actually be scrolled. Scroll down until you see Smiling Conrad.
Click on Smiling Conrad, and the debate will appear in the video window above.
Simon the Likeable has pointed out to me a relevant post that has just gone up, by Dan “Novices are Kinda Like Experts” Meyer. Dan provides a fine example of, well, whatever the hell the tripe is that he is selling. As I said, …