Experiments with a one-per-student computer

Asus’ EEE PC, though useful in many other areas (see more extensive review here), is a computer designed specifically for education. A wireless platform cheap enough, light enough, robust enough, small enough and powerful enough to be seriously proposed as a go anywhere, work anywhere, one per child point of wireless entry into a networked school system. We don’t know whether this vision is about to become reality at this moment, but we don’t doubt that it will come about in time – and the EEE PC is certainly closer than anything else we have seen to the keystone which would make it possible.

Over the past few months we have been sharing a set of these machines, moving them around different groups for a week or two at time and comparing notes on the results.

The machine is small enough to just about go into a handbag, as some of our young female teenage students demonstrated, is big enough for adapted touch typing after some practice, has on board wireless or wired network connectivity, is provided with three USB ports plus microphone/headphone jacks and is remarkable resilient.

Prices start at £167 (about $300 or €230 at time of writing), although the the ones we used were those with two or four megabytes of storage at £220 or £250 respectively ($400/€300 or $450/€340). Each machine in our set was also provided with a one gigabyte SD/MMC card, on which the default documents folder was configured to reside.

Despite some remarkably rough treatment, the complete set survived and were returned to the supplier in full working order.

That’s it for now. We will follow up with individual posts on our separate experiences over the trial period.

[Contributed by Chandra on behalf of the whole trial group]

Muzak to math by

We are in the throes of initial planning for a series of “Music and Maths” sessions aimed at 16-19 year old students, to culminate in a public performance. Using a mix of computing technologies and Blue Peter style building from scratch, the idea is to start from rediscovery of the twelve note scale and build up through construction of instruments.

The first problem we have encountered is an apparent dearth of devices or software which will listen to a note and read out its frequency. There are plenty of them (aimed at instrument tuning) which will do it the other way round, reading out a note name (C, F#, G, etc), but not a frequency. And although we did work out an alternative approach based on these guitar tuners, the interference from a building full of computing equipment, hearing aid loop generators, WiFi networks, several hundred cellphones etc, swamped them and made them useless.

A microphone attached to an oscilloscope is too unwieldy for our purpose: first introduce the oscilloscope, then explain the setting of time bases, learn to disregard noise … a one hour session would be over before anything useful had even stared. It will be useful and interesting further in, but not at the beginning.

Plan C involves auditory comparison of a tone generator signal to played keyboard and guitar string notes, by tweaking the frequency specified in the generator and deciding by consensus when a played note has been matched. This looks initially promising. We have started with NCH’s tone generator, which works well; the synthesiser at National Taiwan Normal University’s physics department also looks promising:

An alternative, offering sequential playing of different frequencies will be needed for subsequent work; a purpose made interface for preference, though it could be done using a mathematics package or even BASIC at a pinch. Ivor has written one as a Java Applet, but security measures in the browser environment where it will be used are raising barriers which have still to be resolved.

More as the idea progresses…

[contributed by Ivor McGillivray and Felix Grant]

Global warming and the Prisoner’s Dilemma

Yesterday’s early morning email included a message from Pauline Laybourn of Minnesota, pointing me to the following video:http://www.glumbert.com/media/global

I recommend watching it through, viewing it as an educational resource. Thank you, Pauline.

Having watched the clip, I followed Mike Willcox’s ‘YouTube’ example and used it as the departure point for a discussion session with some thirteen year old students within a “Public Understanding of Science” strand.

Which side you happen to sit on the global warming debate doesn’t matter; nor does whether or not you are persuaded by the argument in this presentation. The important point is the number of themes which are here.

There is, of course, the straightforward global warming issue which the presenter is addressing. In my group of young teenagers, there was a lot of very intelligent and perceptive discussion around the examples, choices and language involved in completing the four cells of the decision grid shown on the whiteboard in the video. Are the “worst case” squares really the worst cases? Are they exaggerated? Are they understated? Are they off the track altogether? Are they both so unacceptable that the whole exercise breaks down?

There is also a very accessible entry point to game theory (game theory is a branch of mathematics, but you can go a long way in general educational terms without any explicit mathematical work). The result is an introduction to What he’s sketching out is what game theorists call a saddle point - more specifically, the type of saddle point known as a “minimax”. A minimax is a decision which minimises the maximum harmful outcomes in a given situation. A well known example of a situation where minimax may apply is the Prisoner’s Dilemma thought experiment: a good Prisoner’s Dilemma link, with an very accessible introduction leading to deeper material, can be found here at the Stanford Encyclopedia of Philosophy; other links include a Wikipedia entry, an online game at Princeton University, and a page of links connecting the dilemma to public ethics issues at the Constitution Society site.

Looking away from science to the wider context, the decision consideration process involved here is a valuable tool for thought in general. The video would be a valuable trigger for an AS level Critical Thinking session with sixteen year olds, but the critical thinking which it involves is an equally valuable component for any study, of any subject, at any school level. I plan to try it with eight year olds later in the week.

[contributed by Felix Grant]

Mathemagica - Mathematica Player completes the magic square

I have, in the past, seen the effective use by contributor AbsentCat of magic squares in a remarkable spread of contexts. From the moment they learn to add three single digit numbers together for a two digit answer (the row/column/diagonal sum of a 3×3 magic square is 15), children are fascinated. The intellectual appeal can still be triggered at any age above that - I have seen it enthuse a mixed truancy group with ages from 10-16, a hospital education group containing a very sick 18 year old cancer patient, and a pensioners’ Third Age study group. Only the management and presentation needs to change.

And the magic square is not just an entry point to mathematics: it has ramifications for almost every other curriculum (and wider) context.

Having seen this success I have, naturally, copied it in my own teaching and staff development work. But always on paper. For very small children, a paper sheet is the only approach that works (mark each correctly entered number with a brightly coloured counter or, if appropriate in the context, a sweet or piece of dried fruit). For older pupils, however, hands on ICT approaches offer tremendous potential - and Allmath.com’s interactive “sheet of paper equivalent” (see below) is wonderful. The missing element has, until now, been an instant, hands on generator and explorer of any n×n magic square or squares on demand.

For the teacher, Matlab and many compatible systems (including the free version of Sysquake and its Palm implementation Lyme) offer a very useful command to generate magic squares: “magic(n)” where n is the size of the square. (My thanks to AbsentCat, who pointed me to these resources.) For some older pupils, these are also useful.

There are a lot of useful materials on the web for building an ICT based “magic square portal” in the classroom. All that is needed is an interactive square calculator. For older secondary ages (Y8 for some pupils, Y13 or beyond for others), Sysquake Remote web implementation is a possibility, but not for the primary years. The Wolfram Demonstrations Project and free player, however, offer just the thing: a magic square generator with “dragable” column/row/locus cursor.

This Mathematica demonstration allows a magic square of any (odd number) size from 1 to 13 to be generated instantly using a slider at the top of the frame. A cursor can then be dragged around the square, highlighting the row and column containing a particular selected cell. Computation is left to the pupil, which is valuable arithmetic practice, but the cells involved are clearly isolated which minimises mistakes. A perfect fit for the missing piece in the ICT magic squares session.

Starting points for other material which has served me well are:

• Allan Adler’s Mathforum pages on magic squares
• Allmath.com’s interactive equivalent of a paper magic square sheet

[contributed by Chandra]