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]

Testing equation editor responses

Following Lakshmi’s post on use of three equation editors, and a conversation with AbsentCat about discussion with the author of Equations, I was curious about how differences in formatting assumptions are perceived by users.

Equations implicitly assumes that the host application (word processor, web editor, or whatever) will see to arrangement of completed equations in relation to its own design priorities. MathType, on the other hand, assumes that a given equation system will be arranged according to a chosen set of mathematical conventions, indepenent of the context within which it is to be placed.Both assumptions have arguments in their favour; but they are nevertheless distinct. I wonder whether there is a possible link between them and Lakshmi’s observation that MathType appealed to her verbal side, Equations to her visual sense.

Yesterday I started a small experiment. I am trying out both programs on a class of fifteen year olds typing up a short physics investigation. None of them has used an equation editor before, so they were all given a training session on both products. They have now been told to use one of two otherwise identical laptops, always available in the lab, to type up their work in booked sessions over the next two weeks. One machine has Equations and the other MathType, but neither reveals which until after log in, and I shall randomly switch their positions. I hope that subsequent questionnaires will show what (if any) differences emerge in their responses.

[contributed by Ross]

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.

Polaris and me

I was going to review Polaris, a science fiction novel by Jack McDevitt. I’ve also been asked to write about what has happened to me since I reviewed Sunstorm as well. They have a lot to do with each other and I don’t think I can do them separately. So am doing them both together, and I hope it makes sense.

Before my English teacher recommended Sunstorm I was not interested in maths or science at all. In this essay I am going to save a lot of explanation by just using bold type to show things and ideas which are new to me since I started reading Sunstorm. I am glad that I was told to use a pen name, because if my friends knew I was writing this I would be socially dead forever.

After I reviewed Sunstorm, I read Donna’s review of Seeker. The thing that I liked most about Sunstorm was the idea of a planet being fired across space to hit a sun, like a stone being fired at a target with a catapult. Then my maths teacher showed me how to model this on a computer, and I realised that it’s actually more like firing the stone from a catapult in London and hitting a melon in Australia or somewhere. Anyway, Donna’s review mentioned that something similar happened in Seeker, so I read that as well.

I found that Seeker is the last book in a set of three about the same characters (the first is A Talent for War and Polaris is in the middle). So then I read the other two as well. All of the books have the same pattern: there is a mystery, the main characters discover it through something to do with the antiques trade, historical research gets them close to solving the mystery, and the mathematics of moving bodies finally gives them the answer. The mysteries are all different, and make you want to read to the end, but I won’t spoil them by describing them here - and anyway, it’s the maths bits that interest me (I never thought that I would hear myself say that). The historical research interests me too.

In Seeker the maths was about how a stellar system is affected by a brown dwarf star passing close by. In A Talent for War, it’s where a spaceship would be after two hundred years. And in Polaris it’s sort of like a cross between Sunstorm and Seeker because a small but super dense star called a white dwarf hits an ordinary G class star like our sun (not deliberately, it just happens) and goes straight through it and out the other side and destroys it.

I have got totally into this moving bodies stuff. I find the ideas exciting. My maths teacher has shown me how to find information about it and I have done a lot of reading. He has also shown me how to use a spreadsheet and a program called Autograph to set up and investigate my own models. I have learnt a learnt a lot but the the biggest thing I’ve learnt is that I have gone as far as I can without learning some pretty scary maths.

I have started studying some AS maths modules on my own. Well not really on my own because my maths teacher is helping me before school and my uncle is helping me at home but I mean not in a class or anything. I have completed module M1, which is the first mechanics module, and started on M2. Mechanics is what they call the sort of maths that will eventually let me cover orbits and trajectories and stuff (M1 and M2 don’t get that far, but I need to understand the basics). To understand some of the mechanics I need other maths, called pure maths, which doesn’t have anything necessarily to do with mechanics but you use it as a sort of way to describe things - my English teacher pointed out that it’s like I can only enjoy poetry if I can already read. So I’ve done quite a bit of P1 as well (that’s the first pure maths module).

I am using some software called Derive to help me with understanding the maths I am doing. There’s a lot of other software as well and none of it would be so exciting without the models which they let you build to try things out.

I’ve done a little bit of calculus with my maths teacher and my uncle. Calculus is when you imagine very small bits of a problem so you can get your head round it, then imagine that small bit happening over and over again, forever, to make it back into the big problem again but now you understand it. I haven’t explained that very well, but it’s important and it works. Its how you can start with the velocity of something, and the gravity of a star pulling it, and see where it will go, or the other way round.

By September I think I will have finished all three AS modules. My uncle says I could take the AS exam, even though I won’t have done my GCSE yet. But that would totally blow my cover and everyone would think I was a geek. My teacher says he’ll see if I can take it somewhere else that nobody knows me. I don’t know. I’ll see.

Doing all this other stuff has made me better in ordinary school maths and science too. I used to be rubbish at algebra, but now it seems easy. I know now that when you do experiments you do them lots of times and then look at all the results, not just one, and now the handling data part of maths makes sense too (but I don’t want to do the S1 statistics module cos that looks really scary).

My maths teacher has set up some experiments for me, like rolling a marble across a rubber sheet on a frame. You can poke your finger into the rubber, or put a lead weight on it, and pretend the dent is a gravity well and see what happens when the marble (which is supposed to be a lump of rock in space) passes near it at different speeds. And we tried firing an air gun through an egg in front of a video camera to see what might happen when the white dwarf goes through the G type star in Polaris, which is a physical model instead of the mathematical models which you do with pen and paper or with software.

I’ve started to think about what I want to do in my life. I am still most interested in literature and drama but I’m interested in other things too. I’ve been doing paintings and models from the shapes that all the trajectory models make, and imagined using them for stage sets - weird or what? I just tell my friends they’re abstracts. Because of these novels by Jack McDevitt I’ve got really into history as well, and I’ve seen the same sort of graph shapes in history books as in mechanics, like the way population grows looks like the way a rocket’s height changes as it takes off.

It would be nice to do everything, but I’m not sure you can. People seem to do one thing or the other. Mr Grant who organises this site and asked me to write about this stuff says he did literature as well as maths and sciences when he did his A levels but he’s quite old and I think things have changed since his day. He says that people who write books like Sunstorm and Seeker need to understand the maths and science as well as being able to write, and Jack McDevitt must understand history too, and I suppose that’s true. But A levels are a long way yet. I don’t even start my GCSE subjects until September.

Well, that’s a little bit about Polaris and quite a lot about what’s happened to me since I read Sunstorm. I hope it wasn’t too boring. And I hope nobody I know ever realises who I am.

[contributed by Lakshmi]

McDevitt, J., A talent for war. 1989, Sphere. 0747403333.
McDevitt, J., Polaris. 2004, New York, Ace Books. 0441012027.
McDevitt, J., Seeker. 2005, New York, Ace Books. 0441013295.
Clarke, A.C. and Baxter, S. Sunstorm: A time odyssey. 2006, London, Gollancz. 0575078014

Beanbag Thrower still mid-flight

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

[contributed by Chandra]

Throwing beanbags in Mathematica 6

This is the first in a series, illustrating how Mathematica 6 makes it possible to package complex ideas in a way which is suitable for primary education use. You do not need any mathematical knowledge to use the ideas and materials here. Nor do you need any knowledge of the Mathematica 6 program, although you will need a copy of the software.The equation for motion of a projectile on the horizontal plane is not normally encountered until level three in either mathematics or physics. The intuitive idea of parabolic motion dependent on velocity and angle of launch, however, is easily grasped much earlier. In this case. we experimented with class of 8/9 year olds in a British school, as part of an integrated sports theme.

We started by having one pupil toss a beanbag to another, from one side of a classroom whiteboard to the other, while the rest of the class watched and commented. The shape of the path followed was sketched by each child.

This was then repeated several times, the teacher marking one point on the trajectory each time until the shape emerged. The class discussed the similarities and difference between the shape on the board and their own sketches.

Next we moved outside to the playground, where sheets of flipchart paper had been taped to the side of a school building, from ground level to a height of 2 metres, over a distance of five metres. The beanbag throwing was repeated, but this time the children did the marking in of trajectory sample points themselves. In groups of five or six, they spaced themselves between thrower and catcher and each marked the point at which the beanbag passed in front of her or him; after each throw, a new group replaced the last until each pupil had made one mark. Once again, we discussed the shape of the curve.

The throwers were now asked to throw the beanbag higher, but still to try and drop it into the catcher’s hands. The changing shape of the parabola was watched, and discussed, by teacher and class.

The catcher was then removed, and each child took a turn at throwing. They were encourage to vary the strength of their throw, but to aim always just above head height. The effect of throw strength on range was one they already understood, but the changing yet conserved shape of the trajectory as new to them.

Having established the idea of curved trajectory, affected by both angle and strength of throw, the action moved back indoors where the pupils worked in threes and fours. In the centre of the room was laptop with a copy of Mathematica 6, showing a graphic demonstrator (prepared beforehand) which was projected onto an electronic whiteboard.

The demonstrator, which we had called The Beanbag Thrower, allowed the pupils to experiment very rapidly with different combinations of strength and angle of throw, by adjusting “slider” controls. (Double click the illustration on the right to see it full size.)

We decided not to issue specific prompt material at first (though we had them ready, just in case), preferring to see what would spontaneously emerge from free experimentation. WE gave each child a sheet with two columns labeled “what did you do?” and “what happened”, then left them to devise their own strategies. This optimistic but risky approach was vindicated when, after less than minute, the first group announced that “setting the angle half way always sends the beanbag furthest, whatever strength you throw at”. The rest of the class immediately switched to testing this hypothesis, and quickly confirmed it.

The next surprise was when another group correctly interpreted the meaning of negative y values, where the curve drops below the start point. “That’s where nobody catches the beanbag” said one girl, “and so it falls lower than your hand was when you threw it”. Her friend extended this to “And then it goes on falling, lower than your feet, like if the ground wasn’t there”, to which a boy added “Like if you were on top of a building, and your throw took it over the edge”.

Clicking a “+” symbol at the end of a slider opens an input box and a small set of CD player type controls. The box lets you type in an exact number for height or angle, so the pupils were able to check that maximum throw distance really did occur at exactly half way along the angle range, not just approximately.

The CD type controls bar lets you run variable through its full range automatically in various ways. When they discovered this. the pupils’ reaction was to set both height and angle running simultaneously, as fast as possible, in opposite directions - which, while fun, didn’t reveal very much. After a while, though, they realised the value of setting one variable to a fixed value and letting the other roam repeatedly up and down its range in slow motion. Watching the height, the range, and the value of the changing variable, they came to several useful insights. When they realised that you don’t have to maximise the range but can find an infinite number of ways to deliver the beanbag to a particular point, they became very excited: this related directly to football, netball, cricket, tennis, badminton, and darts.

They were also intrigued by the realisation that, for any given distance and strength of throw, there are two possible trajectories. There was much animated discussion over the relative advantages and drawbacks of high versus flat trajectories, eventually leading to understanding that the flat option usually give a competitive advantage.

We, too, were excited by the outcomes of the experiment. The class teacher felt that her pupils had learned lessons in sports, ICT and applicability of mathematics, not to mention transferable skills in group work, co-operation and the efficient conduct of a scientific enquiry. I felt that I had a new range of useful possibilities to explore in wedding maths and science to wider curriculum through IT.

You can download our Mathematica demonstrator model here (see bottom of this post), to experiment with it yourself in a copy of Mathematica. Unfortunately it will not run in the free Mathematica Player, as such graphics are only usable in a special file format can only be produced by the publishers, Wolfram Research . As soon as I have time (during the Spring break in a couple of weeks, perhaps) I hope to work through the process of submitting it for publication as a demonstration for the player.

There are, if you want to try them out, already some projectile models on the Wolfram Demonstrations Project site, but they are more complicated and not (in my view) suitable for primary school use. The exception is “Dart Practice”, which I plan to try with older (age 10/12) pupils.

• The free Mathematica Player can be downloaded from http://www.wolfram.com/products/player/
• The Dart Practice model (usable in the free player) is at http://demonstrations.wolfram.com/DartPractice/
• The Wolfram Demonstrations Project site is at http://demonstrations.wolfram.com/
• You can look at all of the available projectile models here.

You may also like to look at the Kinetic Books Virtual Experiments which were reviewed by AbsentCat last month.

The record sheet and Mathmatica notebook which we used are in a zip file which you can find here. If you are interested in the works behind the demonstrator, and brave enough to tackle the level three mathematics involved, there is also full explanation sheet in the same zip file. If you are unable to use the zip file, send an email to the editorial address for these education pages (you can find in on the “contributors” tab) with “Beanbag materials request” in the subject line.

[contributed by Chandra]

Seeker

McDevitt, Jack. Seeker. 2006, New York, Ace.

Chase Kolpath, the narrator of Jack McDevitt’s novel Seeker, is a grave robber. So is her boss, Alex Benedict. They’re good at it, too, but prefer to think of themselves as antiquities dealers.

Alex and Chase have made some significant finds during their careers, and have collected both friends and enemies along the way. Now they are on the trail of the biggest find of their careers and somebody wants to stop them, badly enough to kill them.

Their introduction to the case arrives with an old plastic cup with ancient lettering, brought to their office for appraisal by Amy Kolmer, a woman obviously ignorant of its true value but hoping for a quick sale. Analysis of the cup reveals it to be approximately 9,000 years old. The lettering is in an ancient language known as English, and their AI (artificial intelligence) gives an initial translation of Searcher or Explorer as the name of the ship it must have come from.

Alex Benedict is a very successful antiquities dealer. If there is one 9,000 year-old cup from a ship, there is a chance of more. All he has to do is find the ship.

Alex makes the decisions, but it seems Chase does all the legwork, and there is plenty of legwork involved. How did the cup come into Amy’s hands? What was the real name of the ship? Where did it sail from? Most important of all, where is it now?

An historian is able to tell them the ship’s name — the Seeker, one of two ships belonging to the ancient Margolians. Nine-thousand years before, the Seeker had left an America mired in religious and political oppression for a world where “not even God will be able to find us.” They were never heard from again. Their disappearance became one of the most enduring myths of human colonization, and one cup from that lost colony was sitting in Alex Benedict’s safe. He now had an even greater prize than just a ship full of treasure. He was on the trail of the Margolians, and he intended to be the one to finally answer the question of what had happened to the lost colony.

Eventually they find the ship, and another set of mysteries, and that’s where the science comes in.

Chase spends several chapters hunting down clues as to where the ship currently is. Searching through old ship logs and questioning owners of the cup over the previous 30 years may not seem like science, but it is. A large part of any scientific investigation is the gathering of evidence.

Among the bits and pieces Chase uncovers is evidence that the actual discoverers of the Seeker were killed in an earthquake and resulting avalanche 30 years previous. They had been with Survey, and had spent the twelve years following their retirement from Survey returning to the same location in space again and again, with no record of where they had gone beyond the incomplete memories of their daughter, a young girl at the time of the accident. Was it someplace they had found during their time with Survey? Finding the answer to that requires learning something about how to set up an efficient flight plan, then comparing that plan to possible variations that might account for a shift to study a G-class star at the end of its hydrogen burning cycle, a type that was of particular interest to them. The deviation tells Chase where to look for the Seeker.

The Seeker is found, full of dead colonists, mostly children. Eric theorizes that it appears they were trying to escape some sort of catastrophe. There are no live Margolians, and the only planet that once might have sustained human life now has an extreme orbit creating long winters where humans could not survive. Investigation of the Seeker reveals that many original parts had been replaced with those from its sister ship, the Bremerhaven. An empty space dock is also found, but the Bremerhaven is not. So a new question—what happened to the Bremerhaven?

What if a comet, or some other object, had hit the planet or passed nearby? Could it have caused the changes in the orbit of their suspected colony world? How big would it have to be? When would it have happened? Would the colonists have had enough notice to plan an escape? Could there have been two escape plans, one for the majority of the colonists, with another, less risky, plan to get their precious children back to Earth? If yes, where did they go with the Bremerhaven, when it no longer had star-flight capability? Where were they now? This time a friend, and her knowledge of astrophysics, provides the answers they need. How she does it, and what they find afterwards, you’ll need to read the book to learn. It’s a good read, and you’ll learn a bit about the movement of planetary bodies, too.

One more mystery they solve before the end — they also find out who’s trying to kill them, and why.

[Reviewed by Donna]

Virtual experiments from Kinetic Books

Supplier: Kinetic Books, http://www.kineticbooks.com.

One of the challenges in tackling the declining popularity of science subjects throughout education, or seeking to increase the scientific literacy of those who will not be scientists, is how to make experimental science concepts accessible, fun and relevant. Tapping into the skills and environments which young people already inhabit is one very good way to tackle that challenge.

Kinetic Books offer a system of online or CD based textbooks and virtual labs; I was particularly interested in the Virtual Labs, and concentrated mainly on those. The system is explicitly designed for learning across a range of physics topics, but the way they are presented makes it very easy to incorporate selections from the material into other courses too. Mathematics, of course, is an obvious beneficiary, but scientific thinking components can be introduced or strengthened within other areas from social studies through critical thinking and public understanding of science to art history.

There is a core of instructional material, with good use of hypertext sidebars offering expanded information plus frequent check and stimulus questions. There are also links to material elsewhere, and graphically simulated experiments. It could be used as a self study resource pure and simple; there will be contexts in which that is appropriate, but for me the strength lies in the ease with which bite sized parts can be used to enrich other approaches.

The levels of mathematics involved encourage this second view. Learners do not need calculus, but are expected to be comfortable and fluent in manipulation of inverse quadratics. The interactive simulations, on the other hand, could be used alone to develop intuitive understanding at any level from infant school upward. Selecting portions in this way, I’ve experimented successfully with learners aged from 8 to 34. There is also the question of national differences in curriculum; British teachers would find frequent discontinuities between US and UK content if they tried to work exactly to KB’s structure without adaption.

For me, the simulations are the real centre. Using graphics to good effect they provide the opportunity for hands on experiment with a range of models which are difficult or impossible to set up physically, and hard to observe reliably.

The motion of a simple projectile can be modelled easily enough using a bouncing ball, but monitoring the velocity and position of that ball with any precision requires either video recording or specialised equipment and lots of time. Getting access to a helicopter is usually both difficult and expensive. Orbital mechanics are entirely beyond any realistic classroom or lecture theatre environment. Using Kinetic Books’ virtual physics lab, all three become very quick and trivially easy to explore, with unlimited reruns allowing deep exploration in the time needed just to set up a ball bouncing experiment.

The simple projectile is modelled as a cannon ball (one dimensional motion having already been covered beforehand). First it rolls out of the muzzle and falls vertically to ground. Then, by adjusting the muzzle velocity, the learner attempts to drop it into a pile of sand some distance away - unsuccessful attempts remaining on the ground where they land, as markers, while trial and error brings subsequent shots closer and closer until the sand pile is scattered by a direct hit.

The cannon starts in a fairytale Arthurian style castle, then later appears on a globe as Newton’s Cannon for the first introduction to orbital and escape velocities. After that, it is replaced by the moon - which, in a game style setup, must be restored to orbital velocity before it falls and destroys the Earth. Further simulations involve docking of two spacecraft on different orbits, the twin moons of Mars, and so on. The orbits concerned are not simple geocentric circles, either - Deimos, for instance, changes its elliptical motion in relation to both Mars and Phobos, its velocity visibly changing between perigee and apogee.

I’ve concentrated on projectile motion because it is a key part of the freely available trial material, but there are plenty of other topics - waves, thermodynamics, electricity and magnetism, light and optics - at levels from the concept of measurement to special relativity and quantum or nuclear physics.

Pricing is realistic in comparison to other resources, and can be managed in various ways to suit different usages - even light use will justify the expenditure on perpetual licences, and individual private copies are affordable by any student who already buys course books. The experiments rely on Java, Quicktime and Flash, but those are free downloads. I hit an initial problem with some of them not displaying correctly, but response from Kinetic Books to my call for help was prompt and effective - the solution is a simple tick box in Quicktime’s setup.

Nothing in this world is ever perfect, and a review wouldn’t be complete without mentioning a couple of minor reservations, and the textbook entry on SI units illustrates both.

The importance of “powers of ten” is presented, and 1000 metres in a kilometre is given as an example (though this is an American text, so be prepared for US spellings of “meters” and “kilometers”). The principle of ten to the power three as a standard spacing, however, is not made clear without following further links.

Then there is the embedding within a wider, nonscience cultural context. This is one of the things I really like about Kinetic Books, and a reason why I would recommend them, but it has its tightropes and pitfalls. For instance, while I am very glad to see the origins of the SI set in the larger picture of revolutionary France, I might have preferred students to decide for themselves, rather than be told, that the “revolutionaries were a little extreme (as revolutionaries tend to be)”.

But, I repeat, these are minor details in a well designed and thought out whole which I recommend.

I’m very grateful to Donna (see contributors page) for pointing me towards these resources.

Supplier: Kinetic Books, http://www.kineticbooks.com.

[Contributed by AbsentCat]