The problem with problem solving part 3 … Finding the maths

Students sitting the newly reformed maths GCSE from 2017 onwards will be required to do significantly more problem solving in their exams. For many teachers it may seem a daunting task to move away from preparing students by ensuring they have learnt a checklist of procedural skills to engendering some ability to synthesise information and select methods within an unscaffolded question. The key to this process will be embedding the problem solving skills into teaching and learning alongside traditional skills based work.

While educational fads come and go, swinging between chalk and talk, discovery, mastery, and other buzzwords depending on who has most influence at a given time, the key is probably offering students a balanced approach. Students should experience the most appropriate form of learning around a given topic in order to challenge and engage them, rather than being channelled down a single pedagogical route regardless of context. Getting this balance right is easier said than done, but while such wide ranging reform could be seen as an unwelcome imposition, it is also a great opportunity for departments to pick schemes of work apart and share best practice between teachers. With “Progress 8” double weighting Maths and English in performance tables, heads of department have a great opportunity to demand additional departmental time from school leaders in order to ensure they are well prepared for the changes.

So what about these practical approaches that I promised in the last blog on problem solving? It all comes down to training students to “find the maths” in any given situation and students must be given opportunities to do this as a matter of course rather than as an added or optional extra. This begins with the structure of practice tasks; picture a standard text book exercise which may have 20 or 30 short, skills based questions focusing on different aspects of a technique, before eventually moving on to a handful of more word heavy, context based tasks. Many students will spend all their available time on the first batch of questions and will never experience the rest. If they do this every lesson then they may never practise problem solving. Teachers should consider carefully how many “skills based” questions are absolutely necessary and minimise these as much as possible. One approach may be to begin setting these kinds of exercise by presenting students with options such as:

Attempt questions 7,8,9 and 10

For question 7, 1a, 1b and 1e will help

For question 8, 1d, 2b and 2c will help…

By directing students first to the chunky questions, they will have a clear expectation of what work it is essential that they complete, but signposting the earlier questions that use the same mathematical principles will provide not only a first place to look for help, but also a link between the wordy questions and the mathematical techniques needed to answer them, providing a framework to help students “find the maths”. Over time, many students will get more used to the concept that simple skills can be wrapped up in chunky questions and start to search for the links themselves, allowing teachers to give less guidance on where to go within the exercise for help. In the long term, this ought to transfer to “finding the maths” in GCSE questions aimed at examining assessment objectives 2 and 3.

Keep reading my blog for more practical approaches to problem solving, OCR’s sample assessment material for the new GCSE can be found here .

About the author

Darren Macey - Subject Specialist - Mathematics

I joined OCR in April 2014 as a Subject Specialist within OCR’s Maths and Technical team, currently I am involved in the development of reformed A Levels in Maths and Further Maths, and commission the creation of resources and CPD events. I also look after the OCR (MEI) A Level course (3890, 3892, 7890 and 7892), as well as the OCR Maths Twitter account and podcast.

I taught maths in a variety of secondary schools in the East of England and also taught PE after coaching rugby, cricket and football. I spend most of my spare time in training for triathlons and endurance events.