Just like that…

Responsiveness in a software publisher or supplier is always welcome, and more common than is often realised, but I’ve just experienced a particularly impressive case.On Thursday, I downloaded a 30 day trial copy of FX Draw 3 - part of FX MathPack, a suite of mathematics resources for the secondary education market by Australian publisherEfofex and available in the UK from Chartwell-Yorke).I had in mind buying a copy for use on a laptop with all the neighbourhood teenagers who drop in hopefully for assistance with homework, and in the café based outreach work with which I’m involved. Since the next topic likely to come up is bearings, I skipped to the angle measure resources and specifically to the onscreen protractors.There are two protractors: 180° and 360°. Both are very flexible and intuitive to use: they can be drawn on the fly, during an explanation, in less than a second, with one flick of the mouse. For bearings work, the 360° is by far the preferable one … but bearings are measured clockwise from north, and this protractor showed the full three hundred and sixty degrees only in the counterclockwise direction. After fiddling and exploring on my own for a bit, I emailed a query to Chartwell-Yorke.On Friday I received a reply from Efofex: no, there was no clockwise scale, but they had looked at the issue and would add one.Today, Sunday, another Efofex email dropped into my inbox: a clockwise scale on 360 degree protractors has been added to FX Draw and will appear in the next release (no date as yet for that release, which has to include other developments, but it’s expected “in a few weeks”.)You really can’t fault that.[contributed by Felix Grant]

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]

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]

InspireDaisies

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

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

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

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

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

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

[contributed by Sayid]

Mathemagica - Mathematica Player completes the magic square

I have, in the past, seen the effective use by contributor AbsentCat of magic squares in a remarkable spread of contexts. From the moment they learn to add three single digit numbers together for a two digit answer (the row/column/diagonal sum of a 3×3 magic square is 15), children are fascinated. The intellectual appeal can still be triggered at any age above that - I have seen it enthuse a mixed truancy group with ages from 10-16, a hospital education group containing a very sick 18 year old cancer patient, and a pensioners’ Third Age study group. Only the management and presentation needs to change.

And the magic square is not just an entry point to mathematics: it has ramifications for almost every other curriculum (and wider) context.

Having seen this success I have, naturally, copied it in my own teaching and staff development work. But always on paper. For very small children, a paper sheet is the only approach that works (mark each correctly entered number with a brightly coloured counter or, if appropriate in the context, a sweet or piece of dried fruit). For older pupils, however, hands on ICT approaches offer tremendous potential - and Allmath.com’s interactive “sheet of paper equivalent” (see below) is wonderful. The missing element has, until now, been an instant, hands on generator and explorer of any n×n magic square or squares on demand.

For the teacher, Matlab and many compatible systems (including the free version of Sysquake and its Palm implementation Lyme) offer a very useful command to generate magic squares: “magic(n)” where n is the size of the square. (My thanks to AbsentCat, who pointed me to these resources.) For some older pupils, these are also useful.

There are a lot of useful materials on the web for building an ICT based “magic square portal” in the classroom. All that is needed is an interactive square calculator. For older secondary ages (Y8 for some pupils, Y13 or beyond for others), Sysquake Remote web implementation is a possibility, but not for the primary years. The Wolfram Demonstrations Project and free player, however, offer just the thing: a magic square generator with “dragable” column/row/locus cursor.

This Mathematica demonstration allows a magic square of any (odd number) size from 1 to 13 to be generated instantly using a slider at the top of the frame. A cursor can then be dragged around the square, highlighting the row and column containing a particular selected cell. Computation is left to the pupil, which is valuable arithmetic practice, but the cells involved are clearly isolated which minimises mistakes. A perfect fit for the missing piece in the ICT magic squares session.

Starting points for other material which has served me well are:

• Allan Adler’s Mathforum pages on magic squares
• Allmath.com’s interactive equivalent of a paper magic square sheet

[contributed by Chandra]

Beanbag Thrower still mid-flight

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

[contributed by Chandra]

Learning to start small in Cabri3D

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

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

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

[contributed by BobTheBumbler]

Mathematica 6 opens primary possibilities

Over the last two weeks, I’ve been working with fellow contributor AbsentCat to trial in primary education the use of artefacts from Wolfram Research Inc’s new release six of Mathematica.

I have investigated computer mathematics packages in the past but they never really seemed to be a viable option in real primary schools where the teacher is a generalist with level two mathematics (I am only formally qualified to level two myself), while both the cost and complexity of the software are high.

The availability of a free player, easily packaged graphic entities, and the demonstrations project changes all that - or, at least, I believe that it does, based on this first taste.

I will be back, with concrete tested examples, in a few days.

[contributed by Chandra]

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]

Tackling the fear of algebra

The move from arithmetic to symbolic algebra is the biggest terror of secondary school mathematics, and many of our future scientists are lost over the edge at this fracture plane. Graphical work is popular but must support symbolic work, not pleasurably obscure it.

In an experimental programme, we encouraged a group of 13-14 year old students to record and express what they were doing in standard symbolic short-hand, and to share summaries of the results on an intranet web site. They were introduced to MathType, which was used not only for preparation of handouts but also for real time classroom explanations of simple, common sense events happening in Autograph.

MathType appealed to these teenagers. Its quality of output built their pride in their work; it was used to prepare their worksheets, and they had the experience of feeding back work of equivalent production values. Its ability to produce high quality web material gave them a high-status platform for displaying their achievements.

[Contributed by AbsentCat]