So the draft specifications have been published for the new GCSE, which meant that whilst the footie was on last night I was working through the sample assessment materials (I know! I am soooo rock n’ roll!!). It did however turn out to be an interesting and hysterical evening, with too many people to mention to thank for their involvement (but they know who they are!)  … Such fun!

I first sat my GCSEs in 1988 (to save you time the answer is 42 … my age that is, as I am sure some of you are trying to work it out!) and I have no recollection of stem and leaf diagrams, box plots or frequency polygons, yet they are examined today. I have never questioned their inclusion as I know maths is constantly evolving and there are academics across the world, working on, and developing new ideas and I just trusted the fact that they must have been developed/invented by someone and have bona fide origins. Last night my thoughts were all over the place, as it would appear to be extremely easy to just invent “stuff” by including it in an exam as one of AQA’s sample questions shows. Foundation paper 2 question 24 mentions a “frequency tree”:

AQA Paper 2 Q24

Having never heard of such a “thing” I’ve done some investigating and can find no reference anywhere about the existence of such a thing and am gobsmacked that an exam board appears to be inventing “new maths”. It also got me thinking about the other topics I’ve mentioned that were new to me but it turns out that their origins have solid roots in academia: stem & leaf diagrams and box and whisker plots are both accredited to John Tukey who played a massive role in developing and studying statistics (look him up … fascinating!). Frequency polygons however are a misnomer in that they were originally used to plot midpoints of histograms that have frequency density on the vertical axis, and have “morphed” into a new way of displaying frequency and I don’t have an issue with that … their background is good and having histograms “as a mate” gives it good credentials.

Returning then to our “frequency tree” I think it is only right for me to give the benefit of the doubt to AQA, as it may be that they can point me in the direction of the relevant research about “frequency trees” and if that’s the case I will walk away red-faced and humbled. Apart from the obvious issues (of which there are many!) I have with the concept of “frequency trees” as a maths teacher, I know some of you may think that its no “biggie” that the term has been used in a sample exam and how wrong you are. It is not down to the exam boards to invent new maths, its not down to Gove either. New things are developed from a “need” to do things differently, to do things better or even to do something new. Just popping in a new term in an exam paper (even if draft!) may seem minor but given the fact that the stakes are so high with exam results (jobs rely on them and students future too!) teachers will assume its a “thing” and teach it. That’s what we do … we teach what we need to in order to get results and if that means I had to teach “frequency trees” I would. (no really … I won’t!)

Now here’s the “science bit” … Mr Gove are you listening? I can save you a fortune! You don’t need exam boards to invent “new maths” just send every maths teacher on twitter a bottle of wine and set the date … I can assure you we’ll be there! In fact don’t even bother with the wine, we’ll do it for free (the wine might oil the cogs and get the creative juices flowing)  as it turns out its really easy to invent “stuff” and all we need now is an exam body to publish it and voila you’ve got “new maths”.  Last night we came up with some corkers but my favourite has to be from Dawn Denyer: 

Drum roll please ….

Let me present …

Guinea pig1

Guinea pig2

**Disclaimer: I am not just focusing on one exam board. Someone had to be the first! Sorry AQA!**

***PPS: AQA if you are reading this you might want to take off the £ on the answer line of question 14 on paper 2 (foundation) **

AQA Paper 2 Q14 £

EDIT: I have now done a follow up on this blog post here