1. Metacognitive Strategies to help Year 11 Students to Solve Problem Solving Questions in the new GCSE.

2. Why Problem Solving? New GCSE – Greater problem solving focus.
Source of anxiety and restricting grades.
Context: I was looking for ways to help my top set Year 11 class succeed with the new GCSE papers which have a greater problem solving focus. Many students were frustrated because, despite knowing the majority of the course content well, they were struggling to apply their knowledge to problem solving questions and were performing badly in specimen papers.
The EEF Toolkit suggests that students can make up to 8 months progress by introducing metacognitive strategies. This seemed like a strategy which could directly be applied to help students overcome the barriers to problem solving. It also brought to mind a key reading from my PGCE Year – Polya’s “How To Solve It”.

3. “How to Solve It” – Polya
Separates problems solving into four stages:
Understand the problem.
Devise a plan.
Implement the plan.
Reflect.
Polya’s book is over 50years old but is still one of a few recommended texts on the Oxford PGCE course. It is not written about students specifically but focuses on strategies to help mathematicians get better at problem solving and surely our aim, as maths teachers, is to get all of our students to be better mathematicians!
Polya goes into a lot of detail in his book, but I particularly like the way he splits problem solving into four distinct stages. It became immediately apparent to me that half of the problem was that too many of my students were starting at stage 3, when really they had not yet understood the problem at hand and thought about how they were going to tackle them.

4. Making thinking explicit
For that reason, I decided to initially focus on the first two stages of problem solving – understanding the problem and devising a plan. Polya has a set of prompts that go with each stage and I selected the best of these to use with my students. I printed out two maths problems on the left and next to these I put the prompts.
Students were then asked to explicitly think about the prompts and answer them – they were not allowed to start the problem (other than to add information to the diagram as one of the prompts suggests). Having explicitly answered these prompts, students could then go on to attempt the problem solving questions.

5. Reviewing and adapting
What prompts are the most/least useful? Why?
Ordering the prompts in a natural way.
Allowing student ownership.
After using the prompts with the class for the first time, I then got all the students to give feedback on which prompts they found most/least useful and why. The most interesting findings from this were that all students had different ideas of which was most/least useful. In fact, some prompts were favoured by certain students despite being designated as the least useful to others. It became clear from this that I had to let students take ownership of which prompts they use regularly. The next time I used the prompts with the class, I highlighted the benefits of different prompts but also emphasized the fact that the ultimate aim was not to work through every single prompt whenever they were faced with a problem solving question. Instead, they were asked to focus on the 1/2 prompts which were most useful for them.
I also amended a few of the prompts and reordered them so that they progressed in a more helpful and natural way when used to solve problems.

6. Embedding prompts Prompts in exercise books and on classroom wall.
Referring to them regularly when students are stuck.
Modelling usage of prompts when answering problem solving questions.
I then began embedding the prompts by regularly using them when solving any problems with the class. I referred to them whenever students were stuck and modelled how I would use them when faced with tricky exam questions. I introduced steps 3 and 4 on implementing the plan and reflecting on the problem after they had solved it and stressed the importance of doing this so that they can learn from each problem they solve and become better equipped for the next problem. I produced a prompt sheet which went in the back of students’ exercise books and a large A3 version which was stuck on the wall next to the whiteboard for regular referral.

7. Effectiveness Students referring to prompt sheets in exercise books.
Students explicitly using prompts in mock exams.
Positive feedback in conversations with students.
There was evidence that students were finding these prompts effective. Students could be seen in lessons regularly referring to the prompts in their books and on the wall. Some students explicitly used the prompts in their next mock exam; they listed out the key areas of maths involved as well as useful formulae and used this to solve problems. Students also responded positively to the prompts and communicated that they found them useful and that they were now more confident in answering problem solving questions.

8. Moving forward Introducing prompts to younger year groups.
Avoiding simplification – different students find different prompts useful.
Adapting where necessary.
Looking forward, we are going to introduce these prompts across Year 11 and to younger year groups in order to consistently support problem solving. Some members of the department were keen to simplify the prompts into the four most useful and then create a memorable acronym that could easily be remembered by low attaining students. However, I was quite keen to fight against this and to keep the list of prompts as they are, especially in light of the fact that different students were finding different prompts useful. I think it is important to introduce these prompts to students in their entirety and let them have ownership of the prompts, allowing them to decide which are the most useful.