Tuesday, 29 September 2015



Geography – GCSE level.

The concept of a spherical earth dates back as least as far as the 6th century BCE, and is commonly attributed to Pythagoras. Ptolemy’s world map of 150CE, despite a mistaken measure of the earth’s circumference, is clearly based on a sphere with lines of longitude and latitude to record its coordinates, and contrary to popular belief, even in the dark ages hardly anyone thought that the earth was flat.

However, maps are often more useful than globes – they fold for convenient transport, they can be laid out flat for simple perusal, and they can be easily made at a vast range of different scales. Take a large scale globe with you on your travels and instead of a conquistador, the natives might think you were a pilates instructor.

But the problem of map projection – portraying a sphere’s surface on a plane – has existed for as long as the knowledge that one can’t sail off the edge of the world, and in the early 19th Century, Gauss’s Theorema Egregium proved once and for all that a sphere’s surface couldn’t be represented on a plane without distortion. Which brings us to this attempt to fit an oblate spheroid peg into a two-dimensional hole...

The teacher has made a good choice of map projection by avoiding the infamously distorting Mercator projection, which was deprecated with all other cylindrical projections in a 1989 resolution by seven North American geographical groups. The Mercator projection maps the sphere on to a rectangle, and the teacher here is clearly using a pseudocylindrical projection, using only the central meridian as a straight line. From the shape of the oval that she has drawn around her continents it looks like she is using a Mollweide or Tobler hyperelliptical projection – a good compromise between not distorting shapes and preserving area measure.

The Mercator projection, albeit useful for mariners with its ability to represent lines of constant course as straight segments that conserve the angles with the meridians, infamously makes Greenland larger than Australia. At least the teacher has avoided that error, albeit by not putting either Greenland or Australia on her map. Any map larger in scale than 1:1 must omit some detail, and the best maps are masterpieces of simplicity and clarity (consider Harry Beck's iconic London Underground diagram to realise that what is left out is as important as what is put in), but leaving out entire continents really cannot be excused. Although this photograph is undated, Australia was definitely discovered before the whiteboard was invented. Or indeed photography.

The Mercator projection is also criticised for being Euro-centric, for example showing Finland as extending further from north to south than the vast Indian subcontinent. Again, the teacher has avoided that politically incorrect error, but by not putting either Finland or India on her map. In fact, it would be easier to list what is on her map: the Americas (although Ferdinand de Lesseps would have a hard time building the Panama Canal across this Central American isthmus that is barely narrower than Brazil), Africa, and a blob that by a process of elimination must represent all the intricate islands and peninsulas of Europe. Russia extends east into Asia, but the age of discovery ends here, without so much as a “Here be kangaroos”.

Even with a globe in front of her to copy from Ptolemy’s map looks better than this, and he didn’t have the advantage of having a whiteboard to rub out any mistakes.

3/10 A good start, but over-simplified and incomplete to the point of being useless.

Wednesday, 6 May 2015






RM 343
W 2-3
TH 1-3

English – primary school level.

It is a truth universally acknowledged that any criticism of another’s spelling will itself contain a spelling mistake. One is not just putting one’s head above the parapet, but doing so whilst wearing an oversized, illuminated ‘Shoot Me Quick’ hat. The phenomenon is indeed so well-known that it has become known as Muphry’s Law. Nevertheless, it must be pointed out that an English teacher, particularly of an introductory course such as this, should be able to spell the word ‘grammar’. There are no excuses, not even one about Kelsey Grammer.

George Bernard Shaw, Mark Twain et al might have had a point about reforming English spelling, but German-style changes are unlikely to happen here and we will all just have to learn to work with our historically idiosyncratic system, including English teachers. In fact, especially English teachers.

Dyslexia is of course a serious issue, but if your spelling is this poor you probably shouldn’t become an English teacher, in the same way that if you are colour-blind you shouldn’t become a train driver, if you can’t swim you shouldn’t become a lifeguard and if you have a peanut allergy you shouldn’t get a job taste-testing Snickers bars.

In fact, there probably hasn’t been a spelling mistake this embarrassing since a spelling game DVD hosted by Eamonn Holmes spelled his name on the front cover as Eamon, leading to the first 10,000 units being scrapped. Thankfully, Eamonn's career was unaffected and he can still be seen regularly on ITV.

Nowadays, the use of spell-checkers is widespread, but even these won’t catch every error and students should learn that a CV containing a spelling mistake will often be consigned straight to the bin. It is worrying that Professor Gunn has made it this far in education and one can only be more concerned about the literacy levels of his superiors. Professor Gunn has no excuse for not brushing up on such basics as he only appears to work for three hours a week. Hopefully the test on Friday will involve actually using punctuation, and sentence structures that are more complex than

3/10 Could do bettar.

Thursday, 30 April 2015

Wednesday, 29 April 2015


(32F)U/2N = LU.4S(4/T)
4F(U/2n) = LU3S(4/T)
F(U/2n) = LUS(4/T)

Mathematics – GCSE level.

To begin with, the presentation is non-standard and quite sloppy. Firstly, numbers should go before letters, so for example the right hand side of the second line should read 3LUS(4/T). Secondly, all the parentheses are unnecessary as multiplication is associative – careful positioning of symbols next to fractions should obviate any confusion as to whether to multiply by the numerator or denominator. Thirdly, the 'N' on the left hand side changes to an 'n' and back again. Finally, it is more usual to use all lower case letters for unknowns. 

Algebra may mean ‘reunion of broken parts, but there's no happy reconciliation for this equation. It is quite impossible to make FUN=LUST as there is an error in each step of the calculation. The basic rule of manipulating equations in this way is that whatever is done to one side of the equation must also be done to the other side.  This rule has not been followed: 

At the second step, the left hand side has been divided by 8, but the right hand side by 4/3. 

At the third step, the left hand side has been divided by 4, but the right hand side by 3. 

At the final step, the left hand side has been multiplied by 2NUN-1, but the right hand side by T2/4.

Taking the first line as the starting point, the closest to FUN equalling LUST that can actually be achieved is FU/2N-1 = LUS/T.

The teacher could have instead started with 2nu/ts = (2/f)lu, which can be rearranged to show that fun=lust. (Although nuts flu does sound rather like something that may be a result of too much fun lust.)

If the teacher is looking for a way to show how fun algebra can be by making words out of the symbols, she might instead try asking her students what the volume of a circular pizza of radius z and height a is.

2/10 A nice try in engaging students, but riddled with errors. 

(Answer: pi.z.z.a – now that is fun!)

Friday, 24 April 2015



U-turns over
double yellow lines

10 2
Keep Hands
on wheel


LeFT   B

Driver’s Education

It is a promising start that the first thing on this blackboard is SEAT BELT as putting one on is the first thing one should do when getting into a car. Seatbelts have been a major contribution to road safety – they reduce the risk of fatal or serious injury in a collision by as much as 50%. Risk compensation theory, where drivers who feel safer in one way instead take risks in other ways, does muddy the statistics somewhat, but there is no doubt that it is better to wear one. Volvo’s decision to make the patent for their three-point system open and let other car manufacturers copy it for free should be applauded. (Drug companies, please take note.)

Anecdotes about car users who died terrible deaths because they were trapped by their seatbelts, or who miraculously survived a collision specifically by not wearing one abound, but whilst it is true that seatbelts may cause serious injury or death (or their non-use save lives) in particular accidents, these incidents are much rarer than those in which the use of seatbelts saves lives. The occurrence of these rare incidents is also usually much overstated, like referring to a 100-year-old who smokes 20 a day, but not mentioning the thousands who die young of lung cancer.

Cries of civil liberties regarding the mandatory use of seat belts should also be ignored – not wearing a seatbelt is not a victimless crime when an unrestrained body becomes a lethal missile for other car occupants. Even for accidents involving just a single driver the cost to society of more serious injury or death cannot be discounted. Clunk click every trip.

As a side note, another safety issue to note before even getting into a car is that bare or stockinged feet are not recommended behind the wheel. They are also unacceptable in a classroom situation and the teacher should enforce this for both theory and practical driving lessons.

It is also good that the dangers of U-turns over double yellow lines (the road marking indicating the division between oncoming lanes in this jurisdiction) are being highlighted. The chalk marks around ‘U-turn’ indicate a thorough demonstration of what a U-turn is with several such manoeuvres clearly shown. This kind of diagram, combined with the repetition of the drawing action can particularly help visual learners who might be struggling with the concept of ‘U’. There might indeed be another such demonstration below the words ‘double yellow lines’ to give extra reinforcement to the point, unless those are meant to be double yellow lines, in which case they are a rather poor effort, being neither yellow nor entirely double.

Whilst at one time ‘10 and 2’ was indeed the preferred position for hands on a steering wheel (although this diagram actually shows something closer to 10:30 and 1:30), the advent of power steering means that the extra leverage gained by beginning a turn with a larger downward movement is no longer necessary. Indeed, the advent of airbags means that ‘10 and 2’ is actually dangerous, with the airbag explosion turning the driver’s hands and forearms into face-seeking projectiles. ‘8 and 4’ or ‘9 and 3’ is now the recommended configuration – it is clearly time to update curriculum materials and send this teacher on a refresher course. Indeed the entire concept of using an analogue clock as a reference is rather outdated – perhaps iPod controls would be more relevant to this cohort, so instead of ‘hands at 9 and 3’ they would be taught ‘hands at skip back and skip forward’.

In the overtaking manoeuvre diagram, the curved arrows showing the overtaking vehicle’s path show that it approaches dangerously close to car B before swerving sharply into the oncoming lane, possibly even clipping the rear bumper. Such manoeuvres should be planned further in advance, executed more smoothly and not bring vehicles into dangerous proximity with each other.

The left signal (or ‘LeFT Signal’) also comes far too late to give other road users warning of the driver’s intentions. Remember: mirror, signal, manoeuvre, not manoeuvre, signal, learn how to use lower case letters.

It is also worth noting that 32% of jurisdictions drive on the left (and rising – the last right-to-left switch was in 2009, whilst the most recent left-to-right change was over 30 years before that), so in those parts of the world this last diagram would show an undertaker rather than an overtaker – something that the learner driver might need if she follows those arrows.

5/10 Good work on buckling up, but the rest of the ideas need bucking up.

Thursday, 5 January 2012






C2H6O Example 1
  H H
  | |
  | |
  H H

Chemistry – A-level standard.

Education cutbacks are clearly hitting hard – this establishment can only afford a periodic table with four elements, and a hand-drawn one at that. Though not displayed in the correct order, all the information about the elements is correct, with the exception of lanthanum’s atomic weight. According to IUPAC, to three decimal places this should be 138.905 instead of 138.906 (actually 138.90547, so the rounding error is not great). Analysing the history of IUPAC’s regular redefinitions of elements’ atomic weight (as scientists become more accurate in their measurements) it can be deduced that not only is this teacher using a hand-drawn periodic table containing only four elements, but that it is at least seven years old (lanthanum's atomic weight was first published as its current value in 2005) and possibly dates back as far as 1969 (when 138.9055 replaced the previous figure of 138.91). Highlighting tiny discrepancies in atomic weight may seem like nitpicking, but it is this kind of fourth decimal place analysis that led to the discovery of deuterium.

What kind of chemistry can be taught using just these four elements is unclear - even the ancient Greeks thought there were at least five elements (according to Aristotle, air, fire, earth, water and aether - none of them actually elements). Fluorine will bond with pretty much anything, so that’s a good start, but not much useful can be made with them together. Lanthanum fluoride can be used as an ion-sensitive electrode, and beryllium fluoride is used in liquid-fluoride nuclear reactors, but you’d have a hard time making the rest of one with just rhodium and lanthanum. Indeed it is ironic that these impoverished students will be devoting a quarter of their time to studying rhodium, the most expensive element that it's actually possible to buy.

What is also ironic is that none of these elements are actually used in Example 1, which uses the much more common (though sadly unknown to this institution) elements of hydrogen, carbon and oxygen to make ethanol. It would be more useful to give the molecular formula of C2H5OH rather than the empirical one, to distinguish it from dimethyl ether, but the structure shown is correct. It’s just a shame that it will mean as much to these students as lanthanum would have done to Aristotle.

6/10 A good effort in trying economic times.

(Many thanks to Vytautas for sending this picture in.)