Table of contents

You find that you want to erect a building. Presumably you know why - somewhere to live, somewhere to park a car, a kitchen extension, a shop, a gymnasium - a cathedral even. You explain your needs to an expert - an architect, someone who knows how to convert a (more or less) clearly defined aim into a workable plan. The architect consults with a builder, and together they estimate how many bricks, windows, pieces of wood, wires etc, etc they need to make the plan a reality. They should also give you a reasonably accurate estimate of the cost of the building. At least this is what happened when I had to get a new garage and wanted to extend a kitchen. It was all done professionally and both sides were satisfied.

During the summer of 1999 interested parties are looking closely at the government's proposals for the next version of the National Curriculum. New National Curriculums appear much more often than I can afford to alter or extend my kitchen, and there seems to be a major difference in the way an educational system is constructed compared to the way a new building is built. If kitchen extensions were built using the educational method, the user (or customer, as I sometimes like to think of the teacher–pupil symbiosis) would find piles of bricks, window frames, wires and pieces of wood carefully dumped on the front garden. There would also be a rather brief set of instructions, plus some fairly rigid building regulations. We would then be asked to comment on this, and maybe a few extra bricks would be delivered or some taken away.

As a nation of Do-it-Yourselfers we would of course cope. My experience of working with a team trying (with some success) to construct a coherent structure of learning based on the National Curriculum at Key Stage 4 was instructive and character-building. Some vital pieces seemed to be missing (but we couldn't put them in because that would have overloaded the content). Some bits couldn't be fitted in anywhere, so we relied on a large hammer and the natural flexibility of the youthful mind (i.e. they wouldn't remember what they did last week anyway).

But would it not make more sense for the legal definers of the curriculum to take on the responsibility for providing not only clear aims, but also a well-designed structure of learning? Well, it might. But I don't really think so. I'd agree with the aims bit, but would be chary of giving the responsibility for the structural design to a government agency, such as the Qualifications and Curriculum Authority (QCA). Democracy is all very well, but a touch of subsidiarity and localness, not to mention actual expertise, might work much better. The word `authority' has a sinister ring for me. I am currently engaged in a sort of Do-it-Yourself curriculum project with the Institute of Physics: an Advancing Physics A-level and the Post-16 Physics Initiative. It is costing about a million pounds, together with quite a few person-years from some rather talented teachers. The ultimate structure has to be made from the bricks provided by the QCA's Advanced level specifications and conform to their building regulations (i.e. assessment rules). Actually it seems to be turning out quite well - but how much better it would be if we could choose our own bricks!

The community of physics teachers - and interested university teachers - at A-level is fairly small. And it is getting smaller if current trends in teacher enrolment and A-level entries persist. It isn't too hard to get a consensus here, and the expertise required is sufficiently high for the practitioners to make an impact at government level. What is more worrying is the inbuilt inertia at pre-16. I was involved in writing the very first version of the National Curriculum (mea culpa. Mea maxima culpa!) and remember the efforts we all made to ensure that it could be rearranged by users as required. Then some fairly lowly government minister, unbriefed, unthinking and now probably unseated, made a decision to assess everything by `attainment target' - of which there were twenty-odd in Science. It took the emollient genius of Lord Dearing to rescue the system from the ultimate ramifications of that decision. Several years down the line a new Curriculum appears which is to be an improvement on the previous versions. In many ways it is. Lots of things have been tidied up, but it is still organized as slightly neater piles of bricks. There must come a time when the powers that be will realize that what they are doing is getting better and better at doing the wrong thing, and begin the agonizing reappraisal required to start doing the right thing (however badly).

The bottom line, of course, is whether the National Curriculum works. I am depressed to hear so many teachers complaining about how difficult it has become to interest children in Science - especially Physics - at secondary level. League tables and exam results do not reveal this kind of deep-seated failure. The impulse for a national curriculum came from a justified desire and need to give all children an appropriate, effective and balanced education. Politicians felt that this was not happening, and spoke of the `secret garden of the curriculum', the preserve of entrenched `experts' who never had need to justify or explain their doings. But we will not have improved upon this if the garden, however secret, changes to a dry and lifeless desert.

A new Learning and Skills Council for post-16 learning is the latest proposal from the UK Government in its attempt to ensure a highly skilled workforce for the next century. Other aims will be to reduce the variability in standards of the existing post-16 system, coordination and coherence between further education and training, and a reduction in the duplication and layers in contracting and funding.

The proposals include: a national Learning and Skills Council, with 40–50 local Learning and Skills Councils to develop local plans; a strengthened strategic role for business in education and training, influencing a budget of £5bn; a radical new youth programme entitled `Connexions', with dedicated personal advisors for young people; greater cooperation between sixth forms and colleges; and the establishment of an independent inspectorate covering all work-related learning and training, to include a new role for Ofsted in inspecting the provision for 16–19 year-olds in schools and colleges. It is hoped that this programme will build on the successes of the previous systems and that savings of at least £50m can be achieved through streamlining and the reduction in bureaucracy. The intentions are set out in a White Paper, Learning to Succeed, which is available from the Stationery Office and bookshops, as well as on the website www.dfee.gov.uk/post16. Published in addition to the White Paper was `School Sixth form funding: a consultation paper' (available from DfEE publications, Prolog, PO Box 5050, Sherwood Park, Annesley, Nottingham NG15 0DJ) and `Transition plan for the post-16 education and training and for local delivery of support for small firms' (available from Trevor Tucknutt, TECSOP Division, Level 3, Department for Education and Employment, Moorfoot, Sheffield S1 4PQ). The deadline for comments on both the sixth form consultation document and the White Paper is 15 October 1999.

Almost simultaneously with the announcement of the above proposals came the launch of the new Institute for Learning and Teaching in York. This has been established with the aim of raising standards of teaching in higher education and improving learning and teaching methods in universities and colleges. Teaching is felt to be at least as important as research in higher education, and the new Institute will oversee the quality of training programmes for higher education teachers, highlight examples of good practice throughout the UK, as well as recognize and reward good teaching. It will also help to administer teaching and learning support schemes on behalf of the Higher Education Funding Council for England, including a new £1m a year fund for national teaching fellowships.

The Institute has been set up in response to recommendations in the Dearing Report on higher education, and will be an independent body supported by the teaching organisations, universities and colleges of higher education and the funding councils. Besides accrediting programmes of training and development, it will provide a range of services for members. Membership will be open to those engaged in teaching or learning support who have completed accredited training programmes or provided other evidence of eligibility. It is expected that membership of the institute will become a normal requirement for new teachers in higher education. Further information about the Institute may be obtained from the Institute for Learning and Teaching, Genesis 3, York Science Park, York YO10 5DQ (tel: 01904 434222, e-mail: enquiries@ilt.ac.uk).

The 25th Annual Stirling Physics meeting took place on Thursday 20 May on a warm sunny day when the country setting of Stirling Campus could be seen at its best. A total of 225 participants from all sectors of physics education attended. There was an opportunity to view and discuss with exhibitors a wide range of state-of-the-art equipment and teaching materials both before and after the meeting.

The theme of the meeting was `Maintaining Standards'. Gemmel Millar, Scottish Branch Secretary acting as Chairperson for the morning session and in anticipation of the first speaker, wondered if a new unit qualification, the `Planck' might be introduced. Half units would then be `Short Plancks' and how many Short Plancks must there be in a unit? Great stuff.

Scottish Qualifications Authority

Hugh McGill began with a brief history and description of the Scottish Qualifications Authority. Born on 1 April 1997 (a light frisson of amusement swept through the audience) it was a unification between SEB and SCOTVEC and has a range of responsibilities covering schools, further and higher education. It oversees Standard and Higher grades, HNC and HND and SVQs, and it has 500 full-time employees as well as some 13500 appointees who act as examiners, assessors and verifiers etc, without whom its remit could not be carried out.

The committee structure of the Board was outlined, one each for national and higher national qualifications and a third for Scottish vocational qualifications. These will be served by a proposed 19 Advisory Groups. The Science Advisory Group will be the key body for advising SQA on strategic developments to ensure that qualifications meet the needs of both client groups and end users. A consultation paper `Added Value To Learning' was referred to, in which all qualifications available in Scotland are given parity of esteem on a rising 11-point scale.

Mr McGill stated that standards would be best maintained by ensuring continuity in procedures developed over many years. The Physics Sub-panel would still exist. Nominees from this would serve on the Science Advisory Group. An Assessment Panel for physics would be created and a Principal Assessor would be appointed for three years to oversee both Higher and Advanced Higher. There would be continuity in retaining Arrangements Documents.

National Physical Laboratory

Metrology, the science of measurement, was the subject of a fascinating and wide-ranging talk by Dr Keith Berry. He described the origins of NPL, established in 1900 in Bushy House, a Royal property donated by Queen Victoria and not far from Hampton Court. Added to over the years, it now covers 60 acres and employs 700 staff, of whom 500 have professional qualifications in Metrology. NPL holds over 100 standards.

Dr Berry, in addressing the fundamental units of mass, length and time, described the evolution of the standard metre, defined originally 200 years ago as one ten-millionth of the polar quadrant running through Paris but in reality referenced to a standard platinum bar. The bar and its variants survived until 1960 when the metre was referenced to the wavelength of light from ⁸⁶Kr. It is currently defined in relation to the speed of 633 nm light emitted through a vacuum from a stabilized HeNeI laser (1983).

Research was under way to redefine the standard kilogram with something more reliable than the current platinum–iridium standard kg, accurate to only 1 part in 10⁷, possibly by counting the number of Si atoms in a standard macroscopic sample. Refinements in the standard second led to the development of the atomic clock with an accuracy of 1 part in 10¹³. This will vary by no more than 1 second in 300000 years. It is now widely used in GPS satellite technology.

All measurements have to be traceable back to a national standard but each step in the calibration chain results in a loss of accuracy.

Towards the middle of the 19th century, anomalies in national standards (the UK for example had a different length standard for imports and exports!) resulted in the establishment of the Convention Du Mètre, an agreement on the definition of a standard metre to which all signatories would adhere. This now has 48 signatories and has given rise to the International Bureau of Weights and Measures located near Paris but technically not in France (merely surrounded by it). The French Government has accorded its couple of acres international status. The Bureau is the Secretariat to the International Committee on Weights and Measures and it is this committee which has overall responsibility for international standards.

Dr Berry described a proposed international agreement which all national standards institutions will be required to sign. This will result in the production of a database listing the standards being used in all the participating countries and will be totally transparent.

Uncertainties were touched on. A draft NPL document entitled `A Beginner's Guide to The Uncertainty of Measurement' already exists and will be made available to the profession in due course. The Scottish Branch was invited to have an input to this publication.

Dr Berry concluded by describing a number of interesting everyday examples in which measurement was critically important. These ranged from calibration of aircraft altimeters by pressure measurement to the equalisation of National Lottery balls to a paltry 1/1000 inch (more non-SI units!). The audience was left with much to take back to the classroom from a valuable and entertaining presentation.

Advancing Physics

Philip Britton set the scene in a light-hearted and often hilarious introduction, e.g. `when you're in a room full of physicists you don't feel so awkward because everybody else is weird'. The Advancing Physics initiative, he explained, was an Institute of Physics response to a deteriorating situation within physics education in England and Wales, particularly in the following areas:

• too few young people south of the border are choosing to study physics;

• the ratio of boys to girls taking physics is too high;

• a restricted framework of A-level qualifications currently exists;

• there is a crisis in recruitment of physics teachers with only 60 signed up to train for next year.

Some features of the website were described: as a forum for teacher discussions it permits considerable input via an e-mail list to which teachers can subscribe and list messages. A series of resource discussion booklets: `Making Physics connect', `Shaping the future', `Maths in Physics', `Physics in the study of matter' were also highlighted.

The jewel in the crown of Advancing Physics was a brand new A-level physics course (not merely a syllabus) supported by `serious' IT in the form of a CD-ROM, together with comprehensive teacher's notes and course book.

The new CD-ROM was skilfully previewed by Ian Lawrence, who guided the audience through a small selection of the many layers of its fascinating and enticing menu. Philip concluded by assuring us that the Advancing Physics initiative was for everyone and he expected a significant spin-off for the Scottish curriculum and the physics profession north of the border. The audience was greatly impressed with the prospect of an exciting new resource and by a truly memorable presentation.

Higher and SYS Physics prizes

Lunch was followed by the presentation of prizes to the highest scoring candidates at Higher and SYS (sixth year studies) physics in 1998. It was noteworthy that there were six equally placed candidates for the Higher prize, each scoring 100%:

Higher Alistair Gilmour, Mackie Academy, Stonehaven Andrew J Hood, Boroughmuir High School, Edinburgh David Borthwick, Gracemount High School, Edinburgh Iain D Drummond, Denny High School Lynsey Granger, Kilmarnock Academy Andrew J R Allen, Greenock Academy

SYS Andrew D Wilson, Queen Anne High School, Dunfermline

The prizewinners clearly enjoyed the presentation and were accompanied by members of their families and physics teachers from their own schools.

Long service award

Dr Norman Fancey paid a warm tribute to Alan Duncan, one of the original organizers of the Stirling Meeting in 1973 and who continued this work for many years afterwards. Dr Fancey thanked Alan for the considerable thought, energy and effort which he had expended on our behalf. Alan was presented with a handsome decanter; in reply he thanked the Branch Committee, his wife for her many hours of unpaid secretarial help and his colleague and friend, Jim Jardine, for his many years of support.

Missing from the official programme simply to guarantee the presence of its self-effacing recipient was a surprise presentation by Heather Reid to Jack Woolsey for his many years of organizing the Stirling meeting. Jack, suitably abashed, received his gift to roars of approval from the audience.

Chaos

In a witty, well-rehearsed and entertaining set piece, the audience was presented with an introduction to chaos by Sarah Thompson and Jim Matthew of the University of York. Jim played the part of a convergently thinking prechaotic mathematician who contended that everything could be circumscribed by existing (non-chaotic) mathematics, and Sarah was a laterally thinking chaos junkie and practitioner of this new mathematics, which is embedded in the behaviour of simple physical systems.

Some simple chaotic systems were examined: an insect breeding system, a pendulum with magnet under the base, an electrical circuit with a diode (plus other unspecified components), a weather-chart. Each in turn was examined in great detail. The insect system was a computer model and illustrated perfectly how a small change in input conditions could produce massively different outputs. We could see the characteristic period doubling and period trebling. Fractals were clearly visible. Jim of course dismissed all this as a property of the computer software. A real diode circuit was then produced and examined. Initially, for small input amplitudes, a sinusoidal input voltage produced a rectified sinusoidal output with the same period. The amplitude of the voltage input was then increased and the output voltage/time graph examined. The output period had now doubled. Further increases produced period trebling. Jim conceded there might be something in it but insisted on returning to the simple pendulum, which he thoroughly understood. Sarah agreed but wanted to examine a simple pendulum with forced oscillations using a computer model. Again, changing the size of the input force produced the characteristic period doubling seen in earlier examples. Basically he had to concede the argument. Sarah explained that chaotic systems exist in familiar contexts such as astronomy, meteorology, molecular vibrations, plasma physics, fluid dynamics and the stock market! Chaos limits scientists' ability to predict the future but has applications in, for example, detecting arrhythmic beating of the heart (period doubling again) and is the subject of much research. Chaotic systems are ones in which changes in initial conditions produce massively different outcomes. This chaotic effect may not be detectable until some time has elapsed from the input change. The final example was a meteorological one in which two slightly different weather charts were computer modelled over a period of several days and ended up predicting entirely different results. Jim Matthew concluded by thanking the technician who had assembled the demonstration apparatus. The audience had been treated to an entertaining, informative and thought-provoking presentation.

London representative

Catherine Wilson was delighted to be up at Stirling yet again. It was good, she said, to meet Alan Duncan for the first time and all the participants were to be congratulated on such a successful day and engaging programme. She was particularly pleased to see the presentation of prizes taking place at the meeting and felt that these young people encapsulated what the event was all about. Catherine expressed her wish to be with us again next year.

Drawing the meeting to a close, Heather Reid thanked all those who had attended.

Postscript

We were shocked and saddened to learn of the untimely death of Alan Duncan in July. A full appreciation of Professor Duncan's contribution to physics will appear elsewhere in the physics press.

Physics research projects undertaken by secondary or high school students are once again being sought for consideration in the annual international competition entitled `First step to the Nobel Prize in physics'. This, the eighth in the series, is being organized by the Institute of Physics of the Polish Academy of Sciences for the academic year 1999/2000, and as in previous years the competition is open to all secondary (high) school students regardless of country, type of school, sex, nationality etc. The only conditions are that the school must not be a university college and the participant's age should not exceed 20 years on 31 March 2000 (the deadline for competition entries).

There are no restrictions on the subject matter of papers, their level, methods applied etc but they must have a research character and deal with physics topics or topics directly related to physics. Participation in the competition does not need any agreement from the candidate's school or educational authorities: the students must conduct their research in the most appropriate way for them. More than one paper can be submitted by a participant but each paper must have only one author; papers must not exceed 25 typed pages in length.

The winners do not receive financial prizes or gifts but instead are invited to undertake a month's research work at the Polish Institute of Physics, with their expenses (except travel) paid for by the competition organizers. Entries should be sent by the competition deadline to Mrs M E Gorzkowska, Secretary of the First Step, Institute of Physics, Polish Academy of Sciences, al. Lotnikow 32/46, PL 02-668 Warszawa, Poland. All those who receive an award will have their papers published in the competition proceedings. Information on the competition can be found in the pub/competitions subdirectory of the anonymous section of the server ftp.ifpan.edu.pl (see also nobelprizes.com/firstep/).

Applicants are invited for the Hertfordshire Science Teaching Scholarship which is sponsored jointly by publishers John Murray and biology author Don Mackean. Although the award is administered by Hertfordshire County Council, it is open to candidates from all over the UK. The award itself is worth up to £7500, most of which must be used to fund a teacher's replacement whilst he or she is seconded to work on a project. This project should have the aim of making the teaching of science more effective through the production and testing of new ideas, rather than by academic research into a science subject or educational theory. The project should be of benefit to the school, the region or even science teaching in general.

The scholarship is available to science teachers with at least three years' experience who work in secondary schools, middle schools or colleges of further education, or to teachers in primary or special schools who have an interest in science teaching. It will enable a teacher to apply for a secondment for one term or an equivalent period of time (such as one or two days per week over a longer period). Besides the teacher's replacement being paid for over this period, a grant of up to £500 can cover expenses for travel, photocopying and the purchase of materials and equipment.

Full details and application forms are obtainable from the Science Adviser, Wheathampstead Education Centre, Butterfield Road, Wheathampstead, St Albans, Herts AL4 8PY. The closing date is 1 February 2000.

A physics textbook for the new A-level and AS-level syllabuses has been the aim of the 1999 award holder, Brian Arnold of Roade School, Northampton.

The 1999 Education Group Conference attracted some 60 teachers and educationalists to the salubrious outskirts of the city of Leicester on 2–3 July. The title of the conference was The ICT revolution: just how will ICT change my physics teaching? For those not au courant with current jargon ICT stands for Information and Communications Technology, or, in short, computers.

ICT was certainly to the fore from the presenters, who practised what they preached. Every talk was delivered using Microsoft PowerPoint, obsolescent overhead projectors serving only as laptop stands. Animated slides, computer generated and controlled, were projected on to a screen and supplemented as required by (fairly) instant live excerpts from relevant computer programs.

The theme of the conference was set by the opening discussion led by the trio PowerPoint, Ian Lawrence (chairman of the Institute of Physics Education Group) and Philip Britton (vice-chair). They gave us the slogan Physics first! with technology, however brilliant or politically correct, only significant and valuable insofar as it helped students learn physics. And learning is a social activity: any system that places one child in front of a computer screen for hours on end should be suspect. Much the same could be said of a voltmeter, of course, and the minimal situation must include a pair of students and a teacher as well as the apparatus. Another message: think of the computer system as just another piece of equipment whose use is determined by the learning task, not as an item that determines the task.

Figure 1. Jason Wye, Secretary of the Education Group, opening the Conference.

It may not be surprising that the level-headed delegates agreed whole-heartedly with these sentiments, but they were also supported and reinforced by all the speakers as the conference went on. The first speaker was Jerry Wellington, ex-physics teacher, now at the University of Sheffield. In his presentation `Multimedia in science teaching: friend or foe?', he gave us a useful overview (with `live' excerpts) of a number of multimedia CD-ROMs - the good, the bad and the ugly. The organizers arranged the programme so that each presentation was followed by group discussion about the points raised (or skated over) by the presenter, and Jerry, with customary efficiency, had listed these. In brief:

• Multimedia can be misleading, making science too clean and `easy' compared with messy experiments that don't always work.

• Many good CD-ROMs are American, with different spelling etc. Is this a problem?

• The best-selling CD-ROMs are revision aids: knowledge-rich, skill-poor, packaged as a commodity. They are used at home, with little or no teacher involvement. Good or bad?

• How `authentic' is learning via multimedia? A subtle point too deep to be considered here.

• Multimedia can be motivating: almost as good as TV - compared with the poor old teacher with a piece of chalk.

The discussion groups took these points head-on: choose appropriate activities to back up or precede the multimedia; Americanization is inevitable; teachers can enrich - and know their students (who appreciate being known); the novelty of multimedia wears off with time, teachers go on for ever.

Laurence Rogers (University of Leicester) has produced a number of computer programs that help students use and make sense of graphs. He spoke about the latest version of his Insight program. Essentially, this allows students and teachers to delve into the meaning of graphs, attacking concepts which we physicists tend to take for granted but are serious stumbling blocks for students. This fact may go unrecognized, as it seemed to with the audience, who thought in general that the cure was more complex than the disease. Maybe the ideas were too new: one teacher was a user of the program and found it extremely useful. In view of the increasing use we make of graphs and the ease with which spreadsheet programs generate them, this topic merits a closer look.

The first day finished with a `Show and tell' session. Half a dozen delegates showed items of ICT that they had developed themselves or downloaded from the Internet. All of interest - too varied and complex to describe here, but look out for Leicester University's Challenger Learning Centre (space and astronomy) which gets on (limited) stream in October, and a really useful sample of excellent computerized astronomy activities from Gettysburg University.

Day 2 of the conference maintained the high standard of Day 1. It began with a presentation by Steve Dickens of Dixon's City Technology College. Technology colleges were `invented' by the last government to provide well-funded schools with a technological bias, the funding coming from a combination of industry and central government. The Dixon College provides computers at a rate of one per four students; all students have e-mail addresses and see computer use integrated into all subjects. Many have computers at home. So computer literacy is not a problem for either staff or students. Steve gave us examples of how the College makes use of its comparatively rich resources, but again emphasized that the prime objective of any activity or lesson was learning - and only if computer systems and programs could help in this were they used. All this fitted into the key messages that the conference was developing. Discussion centred this time around provision of equipment, time for `free' access, and the attitudes of teachers to ICT. A quick survey showed that about one-third of the delegates were confident that their schools or colleges would be as well-equipped as Dixon's in the very near future. There was a tantalizing glimpse of a change in methods of learning from a strongly teacher-directed experience to a form of `supported self- study'. We saw the danger of a development in which some students (perhaps most) had computers at home whilst a more impoverished group did not - yet another feature of a divided society. There seems to be an equally deep divide between ICT enthusiasts (and those of us willing to give it a go) and the entrenched opponents who from `fear of flying' or a deep conservatism are almost rabidly opposed to ICT. It will need more than merely technical training to overcome such a negative attitude to ICT.

The next session brought us into contact with a possibly less high-flown but to me a more exciting application of ICT - enthusing real children with basic common-or-garden physics. John Scaife of Sheffield University showed us a way of using ICT that, like a well-known beverage, reaches the parts that others do not reach. Instant nostalgia hit the more elderly participants as they saw that he was using the old and much loved BBC computer - but it will also work (with more fuss and bother) on a PC. It was simple enough: a motion sensor connected to a piece of neat software (Laurence Rogers again). You stand in front of it and it draws a horizontal line on the screen. Move about and the line slopes or wiggles. You are challenged to move in such a way that your `graph' matches a preset line. Add metre rules to introduce some measuring and we have the kind of maths-based but concrete activity that lies at the heart of physics. Students were quoted (from a Doncaster comprehensive school):

`I enjoyed using the motion sensor - it looked boring but it was OK. (higher praise hath no man)'

`It is fun but you also have to think to work out how you should move to copy the pattern on the screen. I learnt that to copy steeper slopes you have to move faster ... this is because you have to move further in the same amount of time.'

`Whoever said `A picture tells a thousand words' must have been a physics teacher.'

All this was backed up with appropriate research linked to the algorithm PEOR - Predict (what should happen), Explain (your prediction), Observe, React (comment, discuss ...). This is all very Vygotskian (we learned) - and it is constructivism in action. Brilliant, I thought.

In a parallel session Ian Lawrence demonstrated the use of ICT (via CD-ROM) in the IOP's new Advancing Physics A-level course. It gives an extremely flexible and user-friendly set of resources for teaching physics that all A-level students and teachers should find useful and indeed stimulating. It has working simulations, details of lab activities, extension readings, questions and an A-to-Z Wordlist that is a revision tool on its own. At an anticipated price of £10 it is a sure-fire buy.

Roger Frost is a well-known author and expert on making use of ICT. He is also a very funny `presenter', with a firm grasp of reality and a keen eye for the incidental absurdities often associated with the higher technology. He took us through a wide range of ideas and programs that were seriously enriching, finishing with a demonstration of a yet to be released piece of datalogging software and associated sensors (from Pasco Scientific) that seem likely to revolutionize this aspect of ICT.

In the final session Ian Lawrence and Philip Britton reprised their opening talk with the aim of getting some `action points' that the Education Group could use in forming opinions and/or lobbying authority. For interactive ICT you need a set of laptops (otherwise no bench-space) and an electronic projector or white-board. Start saving now.

This conference is not the end of discussion: you can join in the online conference by e-mailing PTNC_request@iop.org, saying `subscribe PTNC your.e-mail address'

Useful follow-ups

Jerry Wellington: report on evaluation of ICT use available at www.chemistryschool.com

Useful astronomy programs downloadable (unzip needed) from www.gettysburg.edu/academics/~physics/clea/CLEAhome.html

Physics education based in IT - sorry ICT!

Which, of course, makes for a nifty headline, but as is so often the case with neat slogans, little else.

Two formative questions:

What, in another decade, will the government of the day call `What you lot should be doing with computers'? and What, of the many things that currently exercise our intellects, will there be anything special to say about in a decade, concerning the use of computers in the teaching of physics?

Advancing Physics represents some attempts to come to grips with the second of the two questions above. The first is left to a higher wisdom. In thinking about learning, what can we do with the huge processing power, increasingly available in smaller and less obtrusive packages? What will we do that helps people learn physics, both tomorrow and in 2009? Here are a few suggestions based on development work so far.

• Wide, reliable and shared access to well ordered learning resources. We have created a CD-ROM, with versions for both student and teacher, that provides a wide range of resources. These do not teach, but do provide.

• A commitment to allowing a course to evolve and adapt. Electronic publication puts the costs into origination, and not into publication and distribution. A website allows for the community of users to contribute. E-mail networks support individuals and propagate good practice.

• You can create and explore your own microworlds. The interactive nature of models, and the crafted relationships between the models and the natural world give an insight into the creative imaginary worlds of the physicist. The unreasonable, but pleasurable, success of mathematics in describing the natural world can come to the fore.

• Measurements that were not possible before are now possible. What was previously indirect, and inaccessible, now becomes a direct measurement, making relationships transparent in new and fruitful ways. The dichotomy between measured and fundamental variables can be resolved along a number of different axes.

• Shaping data to create understanding is also possible. Plotting, re-expressing and re-plotting can all happen within a time-span that retains the connections to the original physical situation. Making sense of the data can become a more active and integral part of doing physics.

Two advantages for physics teachers:

Firstly, the computer is another piece of equipment - one amongst the many that we already deploy based on our considerable experience. It may be a better intellectual prosthetic than some, but it is just one amongst many: good for some things, not to be let near others. Secondly, physics necessarily describes nature. Thus the chance of losing contact with our roots in a virtual canopy is slim; nurture and insight will always come from interaction with the physical.

A summative question:

Which, of the information and communication technologies available to students, is the most effective in stimulating, promoting and nurturing learning?

(The more astute reader will notice the discontinuity between the implications of the embracing title, ICT, and the rather narrower, what we do with computers, somewhat closer to the current obsessions, rather meekly followed by the author in this piece. This final question has only one correct answer, several ramifications, and seeks to redress the balance lacking in the rest of this brief survey.)

Ian Lawrence

Maps and vectors

Where would we be without vectors? Vectors are vital to a proper description of a variety of phenomena in physics. They are also notoriously difficult for students to come to terms with.

Many students meet vectors for the first time in their A-level physics course when they learn mechanics. And this topic is often taught first. The vectors they meet - velocity, acceleration, force - can seem rather abstract, and acceleration in particular, being a rate of change of a rate of change, is fraught with conceptual difficulties. When students meet vectors, they are taught to add them, to subtract them to find components in various directions. This means they have to come to grips with Pythagoras's theorem and with trigonometry at the same time as learning the rules about how vectors behave: the magnitude of the sum is not the same as the sum of the magnitudes, for example.

Rather than developing ideas about vectors at the same time as the difficult ideas encapsulated in Newton's laws, perhaps it might be better to develop a physical understanding of what vectors are and of how they combine first. One way of doing this is by considering maps: these represent, on a two-dimensional sheet of paper, the topology of a landscape. A road map represents a layout of towns, and by considering (straight line) journeys from town to town, ideas about vector addition can be developed: going from town A to town C via town B can be represented by the addition of two displacement vectors. And if these three towns are not in a straight line, then the magnitude of the sum is not the same as the sum of the magnitudes (the magnitude here is the straight line distance, of course). What's more, knowing the straight line distances between a small collection of towns - similar tables of distances can be found in many road atlases - allows the map to be reconstructed. But unless you know which way is north, the distances themselves give only the relative positions of the towns. Notice that these relative positions do not depend on the coordinate system (determined by our choice of north) so that vector sums are coordinate independent.

Introducing a coordinate system - defined by compass directions - and thinking about how far north or east a particular journey takes you leads to ideas about components. And considering a map of mountainous country means that you can think about how three components can be represented on a flat piece of paper. This leads to generalizations of Pythagoras's theorem in three dimensions.

Perhaps these ideas might help students to develop an intuitive understanding of what vectors are about. When they meet more complex and abstract ideas they might, then, see their way through the mathematical representations to the underlying physics. We might have to spend more time teaching the basics, but the pay-off could be a much better understanding later.

Simon Carson

At the end of June a new website was launched to enable young people to get involved with the UK's national Foresight programme and to help shape the future. `School of the Future - Young people with Foresight' will provide young people with the means to contribute to the national programme which develops scenarios of the future, looking at possible needs, opportunities or threats and deciding what should be done now to make sure these challenges can be met. The site can be found at www.asset.org.uk and it will be run by the Association for Schools' Science, Engineering and Technology (ASSET).

The latest round of Foresight began in April and panels are taking a look at the aging population, crime prevention, built environment and transport, aerospace and systems, energy and the natural environment, information, communications and media, materials and sustainable development, amongst other topics. Information about Foresight activities and events can be obtained from the Office of Science and Technology or the Foresight Knowledge pool at www.foresight.gov.uk. The pool will act as a unique and freely accessible electronic library of views and information about the future that young people will be able to draw on for assistance and reference material.

Futher assistance for students will also be on offer from museums and art galleries from now on, thanks to additional funding which has been made available over the next three years. Forty museums and galleries will share up to £2.5m for projects intended to improve students' literacy, numeracy and science skills as well as their understanding of history and art. Examples of the imaginative projects which have been put forward include use of the large collection of steam engines at the Museum of Science and Industry in Manchester to assist boys' science and literacy skills. The Museum of London will be working with over 2000 schools in the South East to provide materials for the schools' own mini-museums on the Romans, Anglo-Saxons and Vikings in Britain; and the Football museum in Preston plans to help local pupils with their literacy and numeracy skills by preparing newspaper reports and football results tables. In this role of supporting education the various bodies will be both helping teachers to deliver the curriculum and also bringing their own cultural resources to life for the students.

On a related theme, the Royal Observatory at Greenwich has just introduced its own Open Museum course to prepare adults with an interest in astronomy to study for a GCSE in the subject. The course begins in October and lasts for nine months, covering topics such as the Earth and Moon, solar system, stars, galaxies and observing techniques. Those undertaking the course will be able to use the Observatory's 28 inch refractor and a Meade LX10 Schmidt–Cassegrain telescope. Further information on the course and the Open Museum is available from Joy Affection (tel: 0181 312 6747) or from the NMM website at www.nmm.ac.uk.

Physics teacher Andrew Morrison from High Pavement College in Nottingham has recently been appointed as Schools' officer for particle physics by the Particle Physics and Astronomy Research Council, as part of the Council's Public Understanding of Science programme.

As well as his role as an experienced physics teacher, Andrew has acted as marketing manager for his college and chair of the Nottinghamshire section of the Association for Science Education. He will now be working two days each week in his new role with PPARC, acting as a link between the science education and research communities, helping researchers develop ideas for promoting particle physics and leading some specific new projects for the production of schools materials.

Andrew can be contacted at High Pavement Sixth Form College, Gainsford Crescent, Nottingham NG5 5HT (tel: 0115 916 6165 or e-mail: morrison@innotts.co.uk).

On the other side of the Atlantic, an 18 year-old student at Atlee High School in Mechanicsville, Virginia, USA was the recipient of the `1999 Young Scientist of the Year' award. Jakob Harmon submitted a project on magnetic levitation (maglev) in this extracurricular competition organized by PhysLINK.com, a leading Internet authority on physics and engineering education. The prize was a summer placement at Virginia Polytechnic Institute, Blacksburg, where Jakob continued his education in one of the most active maglev research and development groups in the USA. He also received science books and software as part of the award.

The PhysLINK.com award was established to recognize, encourage and foster talented high school students in physics and engineering, with the prize being designed to fit the specific needs and aspirations of each individual winner. Details of next year's competition, along with Jakob's project and more about magnetic levitation can be viewed at www.physlink.com or by contacting Anton Skorucak of PhysLINK.com at 11271 Ventura Blvd #299, Studio City, CA 91606, USA (fax: (1) 818 985 2466, e-mail: info@physlink.com).

Physics Education Research (PERS) is a new supplement to the American Journal of Physics which was published in hard copy along with the July 1999 issue (volume 67 no 7) of the journal and distributed to all member subscribers. It was also made available electronically from the end of June but payment and a license agreement are required for electronic access. Nonsubscribers to AJP can obtain the July issue together with PERS for the sum of $22 by contacting the American Association of Physics Teachers' members and subscriber services at aapt-memb@aapt.org.

`Heroes of British Science' is the title of a unique live event to be staged at the Royal Institution in London on Thursday 28 October 1999. Television science presenter Adam Hart-Davis and his team will be giving three shows during the day, the first for younger science enthusiasts (age 7 upwards) and their families, the other two for those aged 12 and above. All three shows will be packed with live experiments and there will be the chance to meet Adam and ply him with questions afterwards.

The first show `Smoke rings, bubbles and steam' commences at 11.30 am; `Adam's heroes of British science', illustrating the ingenuity of Britain's great scientific minds, takes place at 3 pm and 7 pm. Seats can be reserved by e-mail and will be held for 10 days, but bookings can only be accepted by post, with accompanying cheque. Seats in the main auditorium are £12 for adults, £8 for children under 14 and seats in the gallery are £9 for adults, £6 for children under 14. The address for bookings is: Screenhouse Productions Ltd, The Old Baptist School, 378 Meanwood Road, Leeds LS7 2JF.

All the Letters to the Editor in this issue are in the same PostScript or PDF file.

Contents

The imaginary Sun? Harold Aspden Energy Science Ltd, PO Box 35, Southampton SO16 7RB, UK

Difficult physics?Tim Akrill Chief Examiner, A-level Physics, Edexcel Foundation

Was it a dream?Bill Jarvis 6 Peggy's Mill Road, Edinburgh EH4 6JY

A technique using linguistic references in the communication of a physics class to characterize class integration is introduced. Measurement of a traditional physics class shows only marginal integration. Measurement of a modified physics class shows that integration can be dramatically improved. A measurement of a best-selling textbook shows very good integration of the section text, but poor integration of discretionary blocks, such as examples, problems, tables and illustrations. Various graphical techniques are presented to visualize the reference data.

In this resource article, an exceptional bubble chamber picture - showing the annihilation of a positron (antielectron e⁺ ) in flight - is discussed in detail. Several other esoteric phenomena (some not easy to show on their own!) also manifest themselves in this picture - pair creationor the materializationof a high energy photon into an electron-positron pair; the `head-on' collision of a positron with an electron, from which the mass of the positron can be estimated; the Compton Effect ; an example of the emission of electromagnetic radiation (photons) by accelerating charges (bremsstrahlung ).

An educational project primarily aimed at teachers and 15 to 18 year-old students describing the essential features of a modern high energy physics experiment has been created. The whole education package is available on the Internet. It gives a detailed description of the physics processes involved and the Standard Model of Microcosm. Real particle collisions produced with the facilities at the European particle physics laboratory (CERN) are displayed using the platform-independent programming language Java, enabling interaction with the user. The project has been used by several groups of teachers and students, and has increased their knowledge of, and interest in, particle physics. This project complements the traditional physics education and introduces students to contemporary fundamental physics.

We describe a simple and novel method for identifying misconceptions. This approach utilizes the Certainty of Response Index (CRI) in conjunction with answers to multiple choice questions.

This paper presents an analysis of an astrophysics institute designed for high school students. The study investigates how students respond cognitively in an active science learning environment in which they serve as apprentices to university astrophysics professors. The manner in which students implemented the behaviours of the experts with whom they were collaboratively engaged in a study of important cosmological questions was monitored and analysed. We found evidence that, by their participation in the program, students enhanced both (a ) their content knowledge of unfamiliar physics and (b ) their authentic practice of science in addressing contemporary cosmological problems. These results suggest that programs of this nature can support the development of expert science behaviours.

This article outlines research that details the mathematical difficulties of physics students and it also discusses various projects to overcome these difficulties. The successes of these projects are very encouraging and show a way forward for A-level physics teaching.

The discovery of quantum mechanics at the beginning of our century led to a revolution of the physical world view. Modern experiments, made possible by new techniques on the border of the classical and the quantum regimes, offer new insights and better understanding of the quantum world and have an impact on new technological development. Therefore it seems important that students at university and in the final years of high school gain an appreciation of the principles of quantum mechanics. A suitable way seems to be through treatment of the EPR gedankenexperiment (thought experiment).

Stereograms are very easy to create. An intriguing way of generating stereograms is presented that uses only simple geometry.

Robert Bunsen did not actually invent the Bunsen burner, but he did make major contributions to physics in areas such as gas analysis and spectroscopy, as described here.

The number of broadly based physics texts written at a level corresponding to second year and above of UK physics degrees is limited. This is such a book thoroughly updated in a third edition, the first edition having been published 20 years ago. The book is unusual in that the reader is referred to the Freeman website www.whfreeman.com/physics for some additional sections. It will be interesting to see whether this proves to be an attractive feature.

The coverage reflects the US emphasis on topics and contains both theoretical and experimental details. It should not be regarded as an introductory text although it is clearly written. Thus the first two chapters take the reader straight into relativity, concentrating mainly on special relativity but going on to general relativity. From here the reader is led to ideas of quantization of charge, light and energy, followed by an exploration of the nuclear atom, wavelike properties of particles and Schrödinger's equation. Solution of this equation for the hydrogen atom introduces a section on spectroscopy. The next chapter on statistical physics includes Fermi-Dirac and Bose-Einstein statistics and brings to a close Part 1, which concentrates on the theoretical groundwork. Consistent with its title, the book does not cover traditional aspects of thermodynamics and electromagnetic theory.

Part 2 is entitled `Applications' and begins with a chapter on molecular structure and spectra. Lasers and masers are included here but geometrical, physical and nonlinear optics get limited or no coverage. Solid state physics follows but, despite the title of the book, there is little on modern devices, although the section on superconductivity mentions high temperature materials. The chapters on nuclear physics, fission, fusion reactors and medical applications and a chapter on particle physics are comprehensive. Finally a chapter on astrophysics and cosmology is referred to, but the reader must find this at the website. As this is an attractive chapter it is a pity that it is not printed within the book. Although viewing the chapter on the Web gives the benefit of full colour, it is not easy to read the textual information off the screen.

Within the printed material, there are good diagrams with the addition of a single colour, burgundy, a colour that is wasted on those of us who are red-green colour-blind! Each chapter is provided with an impressive number of graded problems (it is not easy to provide such a comprehensive range of problems at this level) and numerical answers are given in the back for every third problem. There is a student solution manual available for these problems and a complete instructor's solution manual has also been produced. It is therefore a useful book for both students and lecturers.

When handling , I recalled how one set of sixth-form students that I taught affectionately referred to Jim Breithaupt's large format book Understanding Physics for Advanced Level as `Big Jim'. This package, for GCSE students and teachers, is its younger brother.

Key Science Physicswas reviewed in this journal over four years ago. Now it is in a new edition with an expanded ring file of teacher resources (a Teacher's Guideand Extension File). It has been expanded for a wider range of students to meet the requirements of all GCSE syllabuses with additional topics for IGCSE and IB. The international bit seems to be among materials in the file of resources and does not appear in the title of the students' textbook.

This is not one of those purchases that will only get occasional use and be left in a department library but it is one that contains sufficient excellent material to become central to any GCSE Physics course.

For the students there is a single-volume 396-page textbook in full colour (not a heavyweight book). Marginal comments point out places where an Activity or Assignment from the Extension Filefits in. All the materials in the teacher's Extension Fileare cross referenced to the numbering of this textbook, i.e. its Themes, Topics, Checkpoints, Tests etc, not to page numbers. The margin is used in other attractive ways to highlight a summary, propose a first thought or provide a topic summary. The text is fruitful mix of pure physics, applications and personalities.

To support the students' practical work the Extension Filecontains photocopiable sheets. For the activities and assignments a few contain a harder version to give access to the higher levels of attainment. Four alternatives to practical questions are given; there are also exam questions and multiple choice questions for each topic. These all have helpful mark schemes on the teacher's answers pages.

What else do you get? A Glossary collection of sheets to photocopy with space to enter a definition in a second language. Versions of many key diagrams in the student book are enlarged and reworked in clear black and white to make OHP transparencies. There is a mention of these also being in colour on a CD-ROM.

The organization of the Extension Fileis as clear as is reasonably possible. As a user, I would add coloured page dividers to mark the sections within it. The Teacher's Guideis admirable in its restraint - just 26 sides of topic notes - which includes the answers to the non-numerical checkpoint questions missing in the student book. It is not wordy or full of educational theory but succinct and relevant to the day-to-day business of learning with these materials. Reading it, I was aware of the snags that a novice teacher might be glad to know but were missing. As always, materials like these should come with a health warning - try out all homework sheets, instructions for activities and assignments before your students!

It is well known that magnetism is a relativistic effect. The combination of Coulomb's law of electrostatics and Einstein's special theory of relativity demands the existence of magnetic forces and hence magnetic fields. However, although many books have drawn attention to this fact very few have attempted to use it as the basis of a unified treatment of electricity, relativity and magnetism, and none, as far as I am aware, have extended that treatment to include the quantum theory of magnetism. Derek Craik's new book does all of the things, and does them with considerable thoroughness and a good degree of clarity. For these reasons it will be a valuable addition to many college and university libraries and will be of interest to all those involved in the teaching of electricity and magnetism at tertiary level.

Electricity, Relativity and Magnetism: a unified textis divided into four substantial chapters. The first, and shortest, is devoted to special relativity. In just 35 pages it covers the essentials of the subject, including length contraction, time dilation and the transformation laws of velocity, acceleration and force. The other three chapters deal respectively with electromagnetism, magnetic behaviour and design (including practical field calculations and the energetics of domain structure) and the quantum theory of magnetism. Each of these latter chapters is about a hundred pages long, and therefore in some danger of becoming indigestible, but all of the chapters are subdivided into manageable sections and subsections that are usually just a few pages in length. The sections are well focused, but unusually wordy for such a mathematical text. Indeed, wordiness is one of the hallmarks of this text. The author is seriously concerned to present a specific approach to his subject, not merely a catalogue of results. This is refreshing and worthwhile, but it does mean that even in the second chapter, which deals with such familiar topics as dipoles, polarization, Maxwell's equations and electromagnetic radiation, the reader will have to pay close attention to the text in order to fully appreciate Craik's particular approach.

The author's concern to adopt an individual approach to his subject is evident throughout this book, but his deep familiarity with the material really becomes apparent in the third chapter. It is here, amidst notes on numerical techniques for field calculation, comparisons of SQUIDs and conventional magnetometers, and discussions of magnetic behaviour at high frequency, that one really feels in contact with modern magnetism. It is telling that the list of references at the end of this chapter runs to more than 30 books and papers (including one of the author's own papers), whereas the relativity chapter ended with just two references, one of which was to Einstein's 1905 paper.

Craik's discussion of the quantum aspects of magnetism is not unusual in itself; such standard topics as spin-orbit coupling, exchange integrals, crystal field effects and spin waves are all included, but it is unusually self-contained for such a relatively brief treatment. It starts with a 15 page survey of non-relativistic quantum mechanics, and follows this with a similarly concise survey of Dirac's relativistic electron theory, leading to an approximate wave equation for the electron in an electromagnetic field that includes spin in a natural way. These surveys should have the effect of making the book more than usually accessible, but their density means that those trying to use them for this purpose must be well motivated and perhaps even doggedly determined. It is for this reason that I regard the book as one for the library and for the professional, rather than one for the student.

Since the dawn of history philosophers have sought to explain vision and the behaviour of light. David Park ranges across almost 25 centuries from the Ancient Greeks to quantum optics and lasers. Philosophical ideas dominate the first half of the book, giving way to physics in the later chapters. The oldest and longest lasting theory of vision proposed a `visual ray' emanating from the eye, somehow sensing the object and returning through the pupil to create an image. It was challenged by an alternative idea that every object gave off some sort of ghostly matter that carried information to the eye. Neither theory had any obvious role for light in the process of vision, but a role had to be found, since we cannot see in the dark. The basic ideas of geometrical optics were known, but the metaphysical role of light was more important, especially for the early Christian church. The light shining in the darkness was a metaphor for good overcoming evil, and much intellectual effort was spent on elaborating on the light of creation in the Genesis story.

Greek and Roman knowledge was lost in Europe during the Dark Ages but came back via Islam and the Arab world, so that Aristotelian philosophy was the norm up to the scientific revolution. Despite all attempts by the established authorities, the ferment of new ideas could not be stopped. Newton's Opticksoffered the first comprehensive modern study of light, but it established a new orthodoxy lasting until the 19th century, when the wave theory of light finally ousted the particle theory. Maxwell's theoretical insight linking light to the electromagnetic field seemed to have settled the problem once and for all, but in this century quantization and wave-particle duality have provided a twist in the tail of the story.

Park's approach is intentionally discursive. This helps to clarify the connections between events which are more often described in isolation from one another. It also dispels many of the simplifying myths that have become accepted in conventional accounts. Newton came down in favour of the particle theory of light, but he was not as firmly attached to it as is generally thought. He endowed the particles with bizarre properties more akin to those of waves in order to explain the interference and diffraction phenomena. Newton provoked some strong reactions, notably from Goethe, whose curious Theory of Colourshows that, as late as the 19th century, philosophers still felt they could challenge mathematicians in explaining science.

The difficulty with the discursive approach is the concentration needed to follow the story through all its twists and turns, especially in the early chapters where the concepts are unfamiliar. Major themes become entangled with the many side tracks and with Park's own commentary. In an American book one expects American spellings, but occasional colloquialisms jar badly. Referring to venerable philosophers by their given names is particularly irritating. It is surprising to see an author who is an Emeritus Professor of Physics using the term `focal point' incorrectly, and confusing real and virtual images, even if it shows nothing more than poor proof-reading.

The lengthy bibliography is evidence of the author's extensive research, but it is not a book intended for the scholar. Some effort has been taken to make the book accessible to readers with no scientific training, there are almost no equations, and technical terms and usages are explained, but it is not popular science either. It is too long and complex for that, and in many respects it is a very personal testimony. One would hesitate to recommend it to any but an exceptional student. Science educators would benefit from the breadth of background information it provides, but it is the sort of improving reading that, sadly but inevitably, is neglected in today's pressured world.

I write this review as a PGCE maths tutor, and therefore from the perspective of using parts of this series at A-level. The sample video, `Take-off - moving bodies with constant mass', is a good example of combining real footage with commentary as the viewer is invited to think about modelling the take-off of an aircraft. The style is reminiscent of Open University presentations and here the challenge is to determine the necessary length of the runway.

The video is split into two sections. The first, commentary, section works quite well, although it jars a bit to hear Newton's Third Law put across as `Action and reaction are equal and opposite'; this is a familiar offering but one that still causes mystification in the sixth form. The viewer is invited to think about setting up equations, and reminded that the chain rule will be necessary to solve the differential equation generated from Newton's Second Law. This gives a good indication of the level of mathematics required. Unfortunately the flow is then somewhat disturbed by a strong emphasis on boundary conditions. If the student can cope with the general level of calculus required, this aspect of the challenge would also seem to fit more naturally into the second section of the video.

This second section looks at setting up the equations and `solutions'. It can be used after classroom discussion, and takes the viewer through three, increasingly sophisticated, models involving functions for drag and resistance forces. On the whole this is clear and helpful, but for some reason the solutions each stop with an equation linking the length of the runway to the take-off velocity, failing to make use of the second equation to eliminate this intermediate variable.

All in all, it is a useful addition to resources for A-level, particularly if students are also following the sort of mechanics syllabus (within mathematics) that emphasizes modelling.