The availability of transcripts from the June GCSE EdExcel maths papers provides an extraordinarily rich resource to try to make sense of students’ thinking in engaging with the questions. I spent a rewarding couple of hours with a head of maths looking at questions in the ‘crossover’ i.e. where they appear on both the foundation and higher papers. That would imply that these are all targeted at grade 4 or grade 5. One very clear and immediate conclusion to be drawn is that it is easier to get a 4 if you take the foundation level exam. Comparing higher and foundation responses to the harder crossover questions, a 4 could be achieved without success in these but a 5 was not achieved even with success on some of the crossover questions at higher. This will need a more detailed analysis, but anecdotally it seemed very clear. This HoM’s school achieved outstanding results at grade 4 with a strategy of erring on the side of entry at foundation.

It seems clear that despite grade 4 being the critical judgement point this year, it will not be for long. Top Universities and the professions are sure to be looking for grade 5 as soon as they catch on. See this UCAS briefing for Universities as early evidence.

The outcome of this effort is a plan to prepare input sessions for year 11 students in the Spring term to support them in exam preparation strategies. Broadly, there are two critical question types which are of a different character to previous exams; (i) context based questions with problem solving, (ii) ‘show’ (or of course ‘prove’) questions in the sense of mathematical proof. The latter are the re-emergence of a traditional question type and need technical mathematical skills. In this session, we only dealt with the former.

I will share some of our observations that lead to action points for students:

- EAL is an issue which is increasingly ignored as students show high levels of facility in spoken English. Please read Jim Cummins on BICS and CALP to remind yourself that technical English takes so much longer to acquire. So,
**action 1:***read through the question slowly, twice. Underline the key words that give information you will use and that tell you what to do.* - The issue is to unpick the question, recognising it solely as an exam question. Resist the temptation to see this as ‘problem solving’ or ‘real world’ in any way. The best example being the 5 metal strips in a rectangular framework with one diagonal included. The diagram is clearly not five metal strips, it is a geometric diagram even to the extent of including the right angle marks. The maths teacher is well versed in ignoring the relationship between ‘context’ and diagram, so it seems trivial. To learners believing this really is somehow about the ‘real world’ it can be deeply destabilising. So,
**action****2:***highlight the set of words in the question that say exactly what is shown in the diagram.* - We noticed that students who were successful, frequently had worked something out as their first step, before really knowing what they were going to do with it. This seemed to secure their involvement in the question. In the metal strips example, the obvious thing to work out is the length of the diagonal using Pythagoras’ theorem since the diagram (but NOT the context) shouted Pythagoras at you. So,
**action****3:***work something out to get yourself started.* - Then, successful students seemed to organise the information such that they knew things to work out. The best example of this was the two stage trans-Penine journey where the average speed, distance and time for the two phases and the average speed for the whole journey needed to be found . Writing the formula for each stage, then filling in what was known and working out the rest, then for the whole journey, was effective (but done in a very different organisational way by different successful students). So,
**action****4:***write down formulae or organise the information for the things you need to work out. Fill in the things you know, work out the others.* - The question often then asked you to do something with the outcome of the calculations and successful students had identified this clearly. The metal strips asked about the weight in the last line. It would be easy to have assumed it was a Pythagoras question and left it that. So,
**action****5:***go back and check through the question to make sure you have answered the actual question that was asked.* - We also saw evidence where students had done all of the things and still got nothing, because at an early stage they failed to work something out and then gave up. In multi-step questions continuing a well worked out strategy with one wrong value will get most of the marks, but these were missed because it was assumed it had gone wrong. So,
**action 6:***if one calculation has gone wrong or you don’t know what to do, carry on with what you have or make up a sensible value and carry on.*

This is a first stab at setting out principles. It is very important to note that students who followed these principles did it in different ways, so trying to set out anything hard and fast or too prescriptive will be damaging. Also, students who were successful with one question of this type, were sometimes not so with others. We will aim to gather a working group to continue this work as preparation for the student sessions.

Download the presentation: Developing Problem Solving at KS3 (for KS4)