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

Learning to start small in Cabri3D

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

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

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

[contributed by BobTheBumbler]

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]

Active geometry

Formalised geometry can seem a meaningless set of hurdles. “To do geom” observes Geoffrey Willans’ schoolboy antihero, Nigel Molesworth (Down With Skool, 1958), “you hav to make a lot of things equal to each other when you can see perfectly well that they don’t”. Dynamic geometry software such as Cabrie-Géomètre II (CG2), a program developed in France and powered by the backing of calculator manufacturer Texas Instruments, offers the solution. It is an excellent platform for investigating detailed aspects of the Autograph models — as preliminary learning in advance, as subsequent consideration of observed phenomena, or as both in a refinement loop.

CG2 is a geometry processor adding to axiomatic Euclidean geometry the active, participatory element of transformational or analytic geometry. Here is an opportunity to discover for oneself, in a hands-on way, where the axioms came from. It allows fundamental components (points, lines, shapes) to be combined and moved in ways which obey geometric definitions. If a line is defined as a tangent to a circle at a particular point, for example, then the circle, line and point can all be freely moved around, the circle resized, and so on, but the line will remain tangential to the circle at that point. Additional constraints can be used for particular purposes, as can slider controls. A number of ready-made examples are provided, ready for instant classroom use. During our trial a physics teacher borrowed it and used two lines, a circle and an ellipse to demonstrate both the inverse square law and the cause of eclipses in a single pass.

At every stage, the software encouraged rapid explorative investigation whilst also pegging the mathematical representation back to a concrete reality comprehensible to the pupils.

[Contributed by AbsentCat]