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 gigabytes 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]

InspireData (review)

Inspiration, the mind mapping software, is widely used in education. InspireData is a new addition, in this academic year, from the same publisher.The principle behind InspireData is much the same as its established sibling: visual learning by direct manipulation through an intuitive interface. I’ve never seen anything to compare with it: data are entered (or copied and pasted) into a conventional looking worksheet, instantly familiar to an Excel user, but nothing after that resembles what you may be used to in a spreadsheet, graphics program, or other data manipulation package. In trials with pupils and students aged from eight to eighty three, over the past few weeks, I’ve found it uniquely effective.

When you first switch from the worksheet to visualisation, you will find your data points scattered randomly all over the desktop. I found that this works well with introductory sorting exercises with found objects or record cards - especially if you start by applying a Venn diagram.

I say “applying” a Venn diagram, not “drawing” one, deliberately. Everything you (or the student) do here assembles itself before your eyes, each data point moving across the screen from its random initial position to the appropriate place in the graphic. Click the on screen Venn diagram button twice, to create two set loops; click each loop in turn and define them as “male” or “female”. Assuming that you have entered the name and gender of each pupil as your data, the points will travel quickly (but not too quickly) across the screen and cluster in the appropriate loop segments. Now switch on data point labels with another click, choosing “name”, and each point will show which pupil it represents. Now each member of the class can watch her or his own personal avatar move about in subsequent work.

Now click the stack diagram button. The Venn loops disappear, the points move again, and when everything comes to rest your pupils are stacked up in two bars above “male” and “female” markers, graphically showing the gender balance of the class.

Everything works the same way. If you entered the heights of your class members in centimetres, along with their genders, click the variable used for that stack chart and select “height”. More visual rearrangement, as the names shift around to align with the height bands which appear across the x-axis to replace the gender labels, for a schematic histogram. Select colouring, and the point beside each name changes hue to reflect gender - blue for girls, red for boys, perhaps. The way height is distributed by gender is immediately there for discussion. You can, if you wish, take the colouring back into a Venn diagram but this time define the loops as (for example) “height more than 120cm” and “height less than 150cm”, then discuss the way genders divide across the three set segments.

Pie charts work the same way. Leave the gender colouring in place, and define the sectors of the pie to reflect height bands - maybe start with the same three, then add more to increase the resolution as discussion develops. With each change, the names will shuffle about the screen to adopt their correct positions.

This needn’t seem to have anything to do with maths, so it’s a wonderful way to painlessly develop categorisation and quantitative vision alongside science as fun - possibly in an apparently nonscience context. I spent a session with a ten year old soccer team, feeding in their own choice of vital statistics for their personal heroes (club, field position, age, height, weight, number of goals last season…; for Beckham, Gerard, Rooney…).

Though I didn’t use it here, there is the facility to use custom icons (either across a whole variable or case by case), so a small photograph of each player would have been a valuable addition. Discussing the patterns which InspireData threw up, they generated their own questions, hypotheses, lines of enquiry. One of them had read a rule of thumb for ideal relation of height to weight - and InspireData moved the players (colour coded by performance) into a scattergram. Then, two hours in, one lad said: “could we use this for maths?”Getting the information into the worksheet is simplicity itself. There is a simple data entry form, called “Questionnaire”, into which each student can individually type their chosen information without having to navigate the worksheet at all. You can, if you wish, add helpful comments to each field (such as “how many goals did your player score last season?”). The user types into clearly laid out boxes, edits until they are happy, then a click commits the result to a row in the sheet.

For its purpose, and its level, I can’t praise this program highly enough. If you do any kind of data handling, in any subject, at any level where your learners are new to data analysis and would benefit from a visual approach, buy it.

[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]

Beanbag Thrower still mid-flight

Sorry, everyone: I had hoped to have the Mathematica 6 Beanbag Thrower packaged and submitted to the Wolfram Demonstrations Project this week, but time has run out on me. I shall do it as soon as I can. It’s the packaging to Wolfram’s specification that I haven’t yet come to grips with - I have had offers of help, but want to get it done myself. Watch this space…

[contributed by Chandra]

Learning to start small in Cabri3D

I was interested in AbsentCat’s Active Geometry post, talking of a “geometry processor” doing wonderful things, but learning to use it sounded too much to cope with in the endless pressure of a school day. I work with young teenagers who should be in early Key Stage Four, but, because their previous education has been disrupted by events beyond their control or a teacher’s capacity to imagine, are in most cases struggling to master KS2 or even KS1. How could this active geometry business help them or me? But, during a staff development workshop, I was shown the ready made examples accompanying a copy of the three dimensional version, Cabri3D, mentioned by Philip Yorke. One of them addressed a topic which I was due to tackle with my youngsters: the nets of a solid. When I expressed interest in that example, I was offered a short loan of the laptop on which the workshop demonstration had been run.

Very uncertainly, I rigged up the machine and waited for my class. And they loved it. They are very videogame savvy, and related to the direct manipulation of an onscreen object in a way they had never related to paper or cardboard equivalents. The software allows them to pick up a single section of the flattened net, swing it along a guide path, and have the attached panels follow it. The cube assembles itself. Then a face can be swung back, restoring the 3D solid to flat net. As many times as they wish. With the ice broken, they were then amenable to physical exploration in a way that they had never been before.

Since then, I have read Chandra’s account of her Beanbag Thrower - another example of starting small, with a simple and manageable aspect, not being overawed by the greater power available. I have learned a lot from the experience, and learned a lot too from her account. Next time, I shall be bolder - integrating the software into a lesson plan, as she has, rather than just starting with it. I have borrowed the demonstration machine again, and next week I shall be using the 2D version, Cabri II Plus, for a more ambitious project around bicycle wheels. I intend to watch the demonstration videos, have signed up for another workshop on geometric software in CDT, and plan to spend the summer reinventing myself - bring it on.

[contributed by BobTheBumbler]