When symbols from one system enter another system they can often cause confusion. Here are five of my favourite examples from exam papers. Interestingly they often catch out the more able students who might read the symbols logically, rather than looking for a lapse in the exam question itself. 

  1. Gas meters. The old fashioned sort with spinning dials and rotating numbers were featured commonly in maths exams a few years ago. Essentially the student was asked to look at two pictures and work out the difference between the two displayed numbers. But many students hadn’t seen a gas meter before and very sensibly thought the meter numbers would be reset to zero after a bill was payed, meaning they didn’t know whether to subtract the numbers or not.
  2. Indirect Speech. Many maths questions these days use two speakers in dialogue. The information is contained in indirect speech. For example in a maths disagreement between Peter and Tina, the exam candidate is the arbiter of who is right and who is wrong. Although, it is meant to be simple, whole philosophical theses have been written on the logic of belief statements, which is what Peter and Tina are presenting. There can sometimes be two entirely contradictory yet logically correct answers when questions are set out this way.
  3. Poor diagrams. In physics exams, usually printed in black and white, arrows to describe motion can often be confused with physical parts of the machinery object being described. A different weight of line and shading is what we might expect when arrows are layered upon machinery illustrations. But if the candidate has never seen the machine before either and the arrows lie on top of it with the same weight of line, the diagram can be impossible to work out.  
  4. Strange punctuation. One pupil was baffled by a maths question laid out in the following way. There was a semicolon after a maths expression at the top of the page, then there were two further expressions down the page with gaps in between for answers. The first of these expressions also had a semicolon whilst the last had a full stop. To my eyes it looked like a strange vertical sentence almost a sort of hieroglyphic, but to the pupil she believed quite reasonably that the semicolon was being presented as a mathematical symbol. She new about factorials which are maths calculations symbolised by the exclamation mark (!) and assumed the semicolon (;) was an alternative calculation.
  5. The identity sign (a three-lined equals sign) is often written incorrectly as an equals (=) sign in maths questions. It is hard to explain why this is a lapse but the closest analogy I can think of is that identities are always true, a bit like saying all cats are mammals, whereas equals are only sometimes true, a bit like saying some cats are mammals. So the candidate is being expected to infer that when an examiner writes equals (=), they should actually read that symbol to be an “identity”. Ironically I have a similar problem here because my website doesn’t actually allow me to write the identity sign even though I know it’s the one I want to write!