Horses for courses…

At Learning with ‘e’s, Steve Wheeler muses that it is:

“…interesting after all these years that people still want to come together face to face to do workshops, seminars, participate in lectures and demonstrations, and generally network in a co-present manner. This despite all the issues of travel pollution, rising fuel prices, travel delays, terrorist threats, stress and anxiety, and so on.”

It happens that I have just been asked to attend and contribute to a conference in Spain. All expenses paid, which raises the additional issue of how money is spent and how it might (or might not) be better directed. It also happens that prior commitments prevent me from accepting … but, putting that aside, what would I feel about attending?

Truth to tell, despite my passionate belief in the importance of synthetic simulations as replacement for “co-present experience”, there are some things that can’t be done through them. Some things need physical, not virtual interaction. And which things those are is not a constant: they vary for each individual and, especially, for each learner.

The interaction around (rather than in) many conferences, workshops, whatever, can in the words of my invitation “create important and helpful synergies“. I value the (physical) research group meetings which I attend roughly every other month, and some professional development activities which involve actually being in the same room as other people; but there are those who do not, who regard them as a waste of time. I am generally less than fully energised by physical attendance at conferences, but I know colleagues whose professional passion depends upon it.

I do about ninety percent, perhaps a little more, of my educational work using electronic means of delivery, but there are subjects, groups and individuals for which this is not suitable. I have a very rewarding voluntary involvement with mathematics and science learning by groups of disaffected teenagers, for example, who need their courage validated and confidence boosted by every interpersonal cue available: they just wouldn’t get what they need from computer mediated communications. And seeing one of those groups wander in shared wonder around the Natural History Museum or across a wetland habitat I cannot imagine an adequate computer mediated substitute … supplement, yes, very certainly: but not substitute. On the other hand, there are a couple of similarly disaffected teenagers for whom social contact is difficult and painful, but for whom CMC provides a way forward.

Horses for courses; most (not all) of us need some sort of professional interaction in physical person, but there’s no “one size fits all” way to provide it for everyone.

The culture of conference as jolly junket, a sort of paid holiday perk of the job, certainly needs attention. So does knee jerk rejection of the new (still sadly all too common). But technology is a glorious enrichment of the available communication options, not a wholesale replacement of them.

For the past ten years or so, I have been running an introduction to ICT in Teaching and Learning for trainee teachers, lecturers and instructors. I have seen the attendees go on into practice. Those who make the richest contribution to their students’ learning are not those who embrace ICT as a new paradigm, nor those who view it as an interesting add on extra; they are the ones who eagerly seek to integrate its advantages into the broadest possible spectrum of educational experience.

[contributed by Felix Grant]

Netbooks on the road

My part of this “netbooks” trial involved much hair loss. Since the base for my work with disconnected teenagers is a cybercafé, there is no obvious rôle for a small, pocketable computer in the normal context of what I do. To make good use of the opportunity, I had to let these machines go out of my control, into an environment where small high value objects are regarded as currency. The sponsors said they were willing to take the risk of loss, provided that I took what I considered reasonable care to minimise it … what, exactly, constitutes reasonable care when handing expensive stuff over to teenagers who may not come back, have class A drug habits, and are due in court on Wednesday for handling stolen goods?

The other question was what exactly to do with these machines, to justify taking the risk. These two issues were linked; my clients had to feel that something worthwhile was going on, if they were to respect the tools involved.

One subject which interests all of them, regardless of gender, is cars. A month before the netbooks arrived, I started discussing with them the relationships between weight, power, speed and acceleration in a car. They have rather more practical understanding of these matters than can be easily explained by legal experience at their age so I concentrated on trying to relate this to theoretical engineering models, first visual and then symbolic.

With the netbooks on hand, I brought the talk around to how we might investigate the actual (rather than maximum or advertised) speed and acceleration values for real cars in daily use. They were very interested in this idea, and were keen to try their hand at using spreadsheets for the purpose. Then they realised that they would have to write down a lot of information and bring it back to the centre, then key it in, before they could do anything with it; at that point, disappointment and loss of interest threatened. Like a good conjuror, I then produced the netbooks.

Gathering data

The scheme they devised involved teams of six, each team stationed downstream from a Pedestrian Light Controlled crossing (this allowed two teams per crossing, getting double data for each red light, at three different crossings). The team leader (let’s call her or him “A”) would stand by the lights themselves, and would have the computer with an open spreadsheet. “B” through to “F” would be at measured distances downstream from the lights.

When the lights turned red (probably because “A” had pressed the button, but I didn’t enquire too closely), “A” would take up a position beside the frontmost car and enter details (make, model including engine size if possible, number of occupants) into the spreadsheet. When the lights went amber, “A” would raise his or her arm and the others would prepare to start stopwatches (mostly on mobile phones, though a few used the function on their wristwatches). When the lights turned green “A” would drop the raised arm and start walking up the line; the rest of the team would start the stopwatches running.

As the lead car passed each team member, the stopwatch at that position would be stopped. As “A” reached each, the time on their stop watch would be entered into the spreadsheet. In this way, a database of timings at fixed distances for different vehicles was built up. The results were also visible in a predefined scatter plot at the right of the same screen, with an interpolated trend line, so the model could be seen developing as they worked. When complete, the sets of data were merged into a single sheet on the desk top and then filtered to compare different data for similar subsets.

As for the risk, I handed over the complete trial set to the two alpha primes in the group (one male, one female) and left them to arrange distribution; and all came back.

Taking it further

This probably seems an underutilisation of the equipment. The same data collection could, after all, have been done with a pocket PC or similar (in fact, the idea was partly suggested by Chandra’s Big Freeze which used Psion clamshells. But the experience of taking “proper computers” out, and being trusted to do so, was worth its weight in gold and stimulated desire to learn. There were, in any case, two follow ups which would not have been possible with handhelds.

First, there was use of a pure mathematics package to compare the experimental data with a theoretical model. Chandra and AbsentCat had described their use of SysQuake LE for projectile modelling. SysQuake is available for both Windows (in the cybercafé) and Linux (on the netbooks) so I installed both. Having set up a basic acceleration equation (d=½at²) on the PC, we set the value of a by trial and error to give a line which matched the spreadsheet data. The young people found this very empowering, and probably learnt more algebraic confidence in half an hour of SysQuake than in all of their time with me to date. They also learned, to their surprise, that most acceleration is over within a very short time (with speed surprisingly low and surprisingly constant) on urban roads.

Second, AbsentCat scrounged us the loan of a set of plug in USB interfaces allowing various types of switch to start or stop timers on the netbooks. The students had a lot of fun with trying out various switching devices. We were loaned some pressure mats which could be placed on the road, though too often the passing vehicles avoided them. We experimented with home made trembler switches, but they were too sensitive, and hard to position usefully. Lengths of rubber tube, filled with water, were laid across the road with light pressure sensitive microswitches plugged into the ends – these were the most successful, and supplied 95% of our usable data.

Broader benefits

The tremblers were a complete failure in data collection terms but worth their weight in gold for the interest which they provoked. A drop of mercury is placed in the bottom of a glass tube; one electrode is immersed in it, and another arranged as a circular collar around the inside of the tube, fractionally above the meniscus; any motion which shakes the tube causes the mercury to make contact between the two electrodes, completing a circuit. Most of my clients have, at some time, been involved in vehicle theft, and immediately realised the relevance of tremblers to car alarms. We got a lot of chemistry, physics and engineering time out of the resulting investigations – even starting a new set of data collection exercises to investigate the link between tube size, collar spacing, and the trade off between sensitivity and discrimination.

This second (more accurate) phase gave us enough data to further investigate the mathematical model, and to extend it into areas such as mechanical work or power/weight ratios. It also allowed us to compare vehicles by type (small car, four wheel drive, bus, lorry, motorcycle, etc). Most valuably, in some ways, it led on naturally to discussing the range of road behaviours exhibited by different users of the same vehicle.

[Contributed by BobTheBumbler]

Portable constructivism

One of my enthusiasms about ICT in education is the potential of connected systems for building genuinely constructivist activities within which learners can invent their own ad hoc subcommunities in mutual support of organised work. Which sounds very fine and impressive, and is in many ways real, but sometimes runs aground on the fact that those learners often have to leave their learning context to access the facilities for doing the constructivist thing. (I’m talking science here, but change the specific examples and everything applies just as much to arts and humanities.)

Real science.

The advantage of portable computing devices is that they encourage “real science” activities out in the world – look at Sayid’s “Pushing up daisies” quadrat activity, for example. To have a spreadsheet available at the same time as fishing around in a ditch for tadpoles, or recording estimated speeds and accelerations of aircraft lifting from a runway, or exploring a lemonade bottling plant, brings the analysis of data vividly to life as part and parcel of the phenomena being observed. When it comes to sharing the excitement with others, though, these devices have their shortcomings.

Generally speaking, a pupil with hand held computer has to store field data in a spreadsheet or database, write notes in a word processor; return to school or home; upload both to a PC or Mac; and only then start to merge them or share them with peers.

With the trial set of Asus netbooks, I was able to take groups of students out and make the computing a seamless part of the fieldwork. There are several levels to this.

Most basic level: sneakernet.

This applies in most field contexts. Here, the pupil enters his or her own data and makes his or her own notes, as in the usual handheld setup. However, a single USB flash drive is circulated continually around the group, each pupil backing up their work to it as it reaches them and then copying a complete set of files back to their own machine. It’s necessary to name the files logically (Jesh_Kaur.doc, Jesh_Kaur.xls; John_Smith.doc, John_Smith.xls; and so on) and to avoid overwriting and keep individual work distinct, but once that habit is established it means that every member of the group has both multiple recent backups her or his own work (on both the USB drive and the computers of other members of the group) and also reference access to near current copies of everyone else’s.

The next level: WAN to go.

This was amazingly easy to set up and use, though not suitable for all settings. All that is required is a wireless router, a power supply, and a relatively small study area. When in a museum, that lemonade bottling plant, or many other visit sites, a temporary wifi zone can (with site permission) be set up in an area such as the café or visitor centre. No internet access is available, but work sharing becomes immediate. If a wifi hard disk is attached to the router, so much the better – all shared work is then available to anyone within the coverage area, regardless of whether its author is within reach. If an adaptor is carried for running the router and disk from a vehicle’s cigarette lighter, good use can also be made of time on the minibus home afterwards.

Continuity at school and at home.

If each pupil is made an author on a shared blog, with restricted readership (to avoid predation risks, but also to provide the group with privacy from nonparticipant peers) and the teacher as administrator, subsequent write ups and analysis can be pooled. By copying and pasting material from the word processor or spreadsheet such blog entries are quickly and easily generated, then can be edited and developed in place. The blog takes care of permissions – each member of a group can red everyone’s material but only change his/her own. A small portable computer continually in the same pupil’s hands, allowing work to be done when that pupil feels like it (at home or at school), able to access the blog whenever and wherever wifi access is accessible, a great incentive to participate.

Team science

All in all, my trial period with these “netbooks” has been the best opportunity yet to develop in pupils a genuine constructivist experience of working in a real community of team science. The pupils working on this pilot responded magnificently, simultaneously nourishing and feeding from each other, exchanging ideas and critiques, competing to be the best contributors to shared success.

All I have to do now is get funding to buy a full class set for long term use!

[contributed by KateQ]

Testing equation editor responses - results

Having marked the physics assignments submitted during my mini experiment (see Testing equation editor responses), after some delay caused by the flu which is doing the rounds, I sat down to look at what they revealed. Questionnaires were given to the students after hand in, disguised to appear as enquiry into attitudes and responses to aspects of school itself rather than the equation editors, supplied some valuable information about students viewpoints and inclinations. Information form other staff, including assessments and reports, provided a third reference point.

Taking all of that together, the results broadly corresponded with Lakshmi’s perception.

Students whose favourite subjects include the visual and dramatic arts, and whose best marks are in those subjects, tended to handle Equations! with more confidence than MathType, and to produce better designed physics assignment pages when working on the machine on which it was installed. Interestingly, this was also true of those whose focus is physical activity (games, sports, physical education).

Students with a preference and bias towards English Language, literature, history, geography, and sociology showed the reverse inclination: they performed best, and felt greatest confidence, when using MathType.

Surprisingly, the split was also visible within the subgroup of students who prefer and perform best in the sciences. Students whose chemistry is stronger than their biology had a MathType leaning, while their peers who lean towards biology but have a weakness in chemistry preferred Equations!. Those whose strength is in physics and/or maths, however, were indifferent to which package they used, were equally competent and confident in either, but showed irritation at having to switch from one to another, in either direction, when resuming an assignment on a different machine.

One final split emerged. Formulator Express is freely available to all students on all other school computers apart from the two laptops which they were required to use for this assignment. In roughly equal numbers, some students preferred either of the trial packages to that established option while others reacted against the need to shift away from it. None of them placed preference for their usual tool above one of the trial packages but below the other - either they preferred it to both, or they didn’t.

[contributed by Ross]

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]

The joy of equations

Part of my summer holiday was spent in trying to learn something about stuff outside the textbook areas of maths I’ve been looking at. They are fascinating, but because I’m still an arts and humanities girl at heart I needed something more romantic to lighten them up a bit.

My history teacher showed me some examples of how models can be used to try out ideas and see whether they fit what really happened in the past - for instance, I’ve played with a set of equations for the expansion of the Mongol empire mentioned in Sunstorm, and the spread of the Black Death in fourteenth century CE Europe. He also introduced me to sociology, where equations describe the behaviour of large numbers of people.Anyway, to get back to scientific computing, I find the way equations are written very beautiful but the way they go into a lot of software programs is ugly (especially spreadsheets). I often need to write them out myself before I can relate to them. Mr Grant lent me a computer with several programs which just write equations, the way you would by hand but typing them on screen. I’ve also been given a school copy of a free one (supplied by the government education ministry) to use on my own computer. I’ve had a lot of fun with these programs, and they have made the final connection between the excitement I feel about physics models and the “aesthetic me” that loves poetry and drama and painting.

The free program is Formulator Express, and is part of a set of programs given to teachers. I am very glad to have it for my own, but I hope to get my own copy of either MathType or Equations! (both of them have to be bought, but my uncle is talking about getting me one for my birthday). They are both very good, and do more than the free program, but I think different people would buy them. MathType appeals to the part of me which likes to write words, and Equations! pleases the bit of me that likes pictures - equations are both descriptions and pictures of something I can’t see with my eyes, only in my head.

All of these programs come down to picking and combining symbols, then letting the computer take care of drawing, spacing, arrangement and so on. The result is wonderfully sensual, with all the curves of a proper font setting off the beauty of the equation itself. They give you all sorts of ways to control and fine tune the way the equation looks, but won’t let you break the rules which control how an equation is supposed to look. They are magic. They have all the best bits of hand writing equations but let you adjust everything until it’s just right.

Equations! and Mathtype both help you to do a techie language called LaTex as well. I don’t think Formulator does, or if it does then I haven’t found it. I’m only just starting to figure this out, but it’s a way to describe equations. I’ve sort of got my head round the basic idea, but I don’t think I’d ever have the patience to get good at it - so it’s a good thing that these equation editors do a lot of it for you. For myself I found Equations! best for this part, it seemed more like the way I think, although MathType does whole pages of stuff at once.

I said before the summer that I had started painting equations. The equation editors have encouraged me to develop that work, and I have several sketchpads filled with arrangements of equations and graphs combined on the same page. (Apart from being beautiful, this is also useful. I tried to make sense of Einstein’s relativity stuff from a book, and got closest to understanding it through my montaged watercolour sketches.)

Now my English teacher (who started me on this stuff in the first place) and the art teacher have suggested that I work up some of my sketches into background scenery for a German play called Die Physiker, about Newton and Einstein. I am worried about this, as I don’t want to get known as a geek, but the idea does make me feel excited. I have done some experiments in the drama studio after school this term, putting Equations! equations and Autograph curves from the computer onto large sheets of calico to see how the forms and dynamics work together on a large scale.

[contributed by Lakshmi]

• Autograph and Equations! were supplied by Chartwell Yorke (who also stock MathType).
• Formulator (from Hermitech Laboratory in the Ukraine) is licensed for educational use as part of a standards pack from the UK Department for Education and Skills. The free version used by Lakshmi, Formulator Express, can be downloaded, or a full version purchased.
• MathType was supplied by Design Science.

Cabri3D: building big models on small beginnings

Over the summer, I spent a lot of time getting to know Cabri3D better, after the success with a simple net demonstration.

Truancy work has to continue through holidays - not at the same level as term time, perhaps, but there must be some continuity or the youngsters disappear you simply lose all that you’ve done. So, there have been drop ins and workshops at intervals over the summer. I used some of this time to get my young clients exploring Cabri on my behalf, letting them teach me - something which engages them in a way that a lesson the other way around can rarely do.

They particularly liked the “models” class of packaged examples, and that led to a lot of impromptu work in which I hastily learned about some of the ideas embraced by Lakshmi in earlier posts. They were fascinated by the basketball example, in which a single bounce through the hoop is repeated and rotated through 360 degrees. They also made the link for themselves between this sort of mathematical modelling and the animation of computer games - in fact they commented, without my prompting, that movement in video games is generally less realistic than the Cabri3D bounce or “Claude on a swing” and “Claude on a Trampoline” which cracked them up. The GPS system model appealed to the boys (though not the girls) as a techie toy.

Several of the girls were fascinated by “Escher’s stairs”, and that was their way into the actual works of Cabri3D - they wanted to know how it was done, and set about finding out. The boys were then challenged by macho pride into exploring how to do it as well. So now all of them are conversant with the Cabri3D innards, and are making progress with teaching me. Models have also, as a result, become a regular talking point, and basic maths is improving visibly in consequence.

All of which I call a worthwhile result

[contributed by BobTheBumbler]

• Cabr3D was supplied by Chartwell Yorke

Stonehenge - mathematics and environmental education

This is a brief description of the Stonehenge trip mentioned on May 1st this year under the heading Sun, moon and stones.

A much fuller description is provided on the Articles and papers page.

The Field Visit

A-Level and pre-GCSE Mathematics students took part in a Field Visit to Stonehenge in 1^st May 2007, one day before Full Moon. The curriculum comprised practical project-based activities integrating content from mathematics, astronomy, climate science and history¹. The party was permitted full Stone Circle Access in the evening – and an opportunity to observe moonrise and sunset from the centre of the monument. These activities were documented on film, and students were encouraged to take part in its production. The Field Visit had two main aims:

• to improve mathematics motivation;

• to afford learners a powerful affective experience of the natural world.

The latter goal features prominently in certain understandings of environmental education.

Summary of findings

• The Field Visit was highly rated by student participants.

• There is some evidence that the Field Visit improved interest in mathematics within both pre-GCSE and A-Level cohorts. In the case of the pre-GCSE cohort, however, this effect seems to have been temporary, although situational interest was stimulated on the day. This cohort seemed to especially appreciate the opportunity of using mathematical tools. Some amongst the A-Level cohort expressed a preference for contextualising mathematics within integrated project-based curricula.

• Stone Circle Access afforded a majority of student participants a powerfully affective experience. Here are some of the words that students chose to describe their experience: inspiring, fabulous, stunning, intriguing, mystical, awesome, epic, great, fascinating, indescribable.

• The experience of some individuals might be characterised in terms of cosmological based identification. For example, one student reported
  …it was like in Physics when you talk about the Universe. Inside the circle she felt small. The builders of Stonehenge were probably smaller than her. But still managed to put up those big stones. She felt small in comparison to them.
  

[1] The objective of the A-Level mathematics activity was to calculate the azimuth (bearing East of True North) of the Summer Solstice sunrise in 2000 AD, 2000 BC, 3000 BC as seen from the centre of Stonehenge using a theodolite and trigonometry. The sunrise azimuth slowly varies over millennia due to oscillation of the tilt of the earth. This oscillation is one of the three Milankovitch cycles and it is thought to have been a causal factor in the alternation of glacial and inter-glacial periods between one and three million years ago.

InspireDaisies

I have a standard data collection activity, borrowed from AbsentCat, which I call “Pushing up the daisies”. That’s not a very good name, bearing no relation to what actually happens, but it has the virtue of amusing pupils.It’s a quadrat exercise. Each pupil takes a pen, an old sock rolled into a ball, and a sheet of A4 card with a 100mm square hole in the centre of it. We all go to the centre of a convenient expanse of grass, form a circle facing outward, and throw our socks. Where the sock lands, put your sheet of card and count how many daisies are visible through the hole. Write the number down on the sheet of card, throw your sock again. Repeat until the novelty wears off, then return to the centre of the grass area to collate the results.

Sometimes, with a small group, I will replace both card and sock with a frisbee in the centre of which a circular 113mm hole (to match the area of the 100mm square) has been cut.Throwing things around in the open air is always preferable, on a sunny day, to being indoors. We usually take a picnic along, and a set of palmtop computers, so we can conduct the subsequent analysis of our daisy data in relaxation amongst the daisies themselves. This approach pays dividends: I get a lot of good natured work out of children who would get bored and impatient if we did academically equivalent work indoors.

This week, instead of the palmtops, my year fours (age 8-9) took a laptop with InspireData (reviewed here). Instead of writing their results on the card, and collating them later in a spreadsheet, the pupils brought each count back to the laptop and typed it into InspireData’s data entry “questionnaire”. Each observation was identified by the child’s name, and a photograph of a daisy was imported to replace the standard marker, so as the session proceeded we watched a growing histogram of labeled daisies gradually assemble on screen.

The class kept on gathering data much longer than usual, keen to see their name on screen as often as possible. Result: a much larger results database than usual, and more pupil involvement in the analysis phase.

I plan to follow up, at the end of this week, with botany and geography lessons based on the results using the InspireData histogram as a reference point for analogy with quantitative methods in both of those fields.

“Pushing up the daisies” is a good educational activity, offering a number of painless entry points to maths and science topics. InspireData adds immeasurably to it.

[contributed by Sayid]

Polaris and Lakshmi

Re Lakshmi’s Polaris and Me:

Can’t remember when I’ve felt better about my writing career … please tell her I said hello. And that she makes me proud.

I can’t help wondering whether we won’t all be hearing from this young lady again.

[contributed by Jack McDevitt]