Angry Birds and Isosceles Triangles

Iangry birdsn the Times today were a couple of articles about the new Maths GCSE, both of which add more wariness (is that a word?) about the changes that we are facing as maths teachers.

The first had the headline “Rival’s GCSE practice papers too easy, claim exam boards” and I’ll leave it to your imagination as to which two boards were making claims about the papers from the third exam board. The second article had the headline “Tough Questions” and it is this that really touched a nerve for me – the final paragraph states: “It is deeply troubling that the credibility of such an important exam is already being called into question. The case for multiple exam boards rests on the idea that they will compete in the search for excellence in syllabus content and in speed and fairness of marking. Any sign that they are diluting standards in pursuit of clients will strengthen the case for scrapping them in favour of a single national board. That was Mr Gove’s preference. If his successor, Nicky Morgan wants to keep the current system, she will have to show that it is in the best interests of Britain and Britain’s children.”

The idea that the exam boards are competing on syllabus content is laughable. The content has been prescribed by the DFE including sodding Frequency Trees, which will have no use in life for 99.999% of those students that go through the new GCSE. Ask yourself when did you ever need to use one? I’ve managed to get to 42 and never (ever!) needed to use one. The ironic thing about these is that I’ve spent the weekend before last putting together a load of resources to help support a getting ready to teach training thing, and I still don’t see the relevance to real life. There is a legitimate use out there, as has been pointed out to me, but Nope! Still don’t get it! Maybe it’s just me.

What seriously worries me is that our current year 9s (the UKs, I mean) have not been subject to the new content/methodology/mastery approach (call it what you will) at KS3, or during the previous key stages and yet we are expecting them to be fully fluent with the new problem solving style at KS4. This also applies to years 7 and 8 to some extent (but I am less worried about them as we have more time to teach them) but it’s still a worry that these 2 or 3 year groups could end up as a generation that “falls through the gaps”. It’s a little like the new A level is dependent upon the students having been subjected to the new GCSE to some extent and so postponement of the changes at post 16 made sense.

Don’t get me wrong. When I say I’m worried, that doesn’t mean that I doubt my ability to teach the new GCSE but I do think that they are at a disadvantage from the outset. For me, it is this, that brings into question the credibility of the new GCSEs. The resilience required to excel in Maths and “thirst for knowledge” is not something that can be taught as a discrete skill .. it takes time. It also requires access to lots of examples of similar problems (we can’t just make them up on the hoof!) and to develop these properly also takes time.

As an exercise and just for fun I did the 3 questions that were included in the article and I do think that the level of detail that I went into, is something that we, as teachers should be doing, as and when, more practice materials are released. I’d like to think that my awareness of the new content is pretty good and now I need to develop my awareness of how that could be assessed, but more importantly how I could bring different topics together simultaneously. What follows is my thought process as I approached each of the three questions:

AQAThe AQA question was nice. It brings together knowledge of perimeter, isosceles triangle properties, prime numbers and also geometric properties of triangles (how that is taught got me thinking!). As you can see from the below I took very much a listing approach and my one concern is that most students once they find two “solutions” will stop looking and won’t realise that one of them actually doesn’t work. It is this ability to continue to search that I mean by resilience. Genuinely though I liked the fact that my students could be challenged by this type of question through getting them to prove why one of  the solutions isn’t really a “proper” solution. You will note that I have made my isosceles triangle look like an angry bird .. it helps cement which angles are the same (or so I thought .. in a recent observation one of my year 7s said it looked like a flaming teepee… not quite what I was aiming for!).

AQA2edexcel questionThe Edexcel question at first glance is quite nice but has that thing about “real-life” problems that cause students so many issues. There is some conversions between metric units with the prime topic being area. However I had to prove to myself initially that yes 10 tiles would cover the area as it wasn’t initially clear to me, how this could be done. Not because I’m stupid but because you just wouldn’t lay floor tiles like that. Seriously! Most students just wouldn’t think that you could cut them in half to get a “prettier” solution (the question didn’t suggest this and may not be allowed!? I will hunt out the markscheme and check) and it may not occur to them that anyone would want to lay them the way I’ve shown them in the first picture.

It so reminded me of the listing combinations questions a few years ago, where “orange juice” was added as a starter and most students got it wrong as they couldn’t imagine having juice as a starter. They had no “frame of reference” to refer to and that’s the point. We need examples and lots of them to support us to teach this style of problem solving.

Edexcel solution

ocr questionAnd to the OCR question. I like these kind of number based puzzles, but I was left wondering if I could use the operations more than once or if I could have more than 1 set of brackets and I know that would be the kind of questions my students would ask.

Personally I would have liked this better if it had said “The biggest number he can make is X … show how this can be done”

I’ve digressed and so back to the original point: I’m not sure where I stand with a single exam board. It’s not something I can influence so I haven’t wasted my time thinking about it … if only I could be as pragmatic about everything else, because if I’m honest I can’t influence a great deal through this little ol’ blog.

2017-09-03T18:45:39+00:00 December 22nd, 2014|Blog|

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