The new GCSE is causing a lot of teachers I know some sleepless nights! The thing which worries me is not so much the new content but the style of the exam papers. The specimen and practice papers published so far are much less routine and less accessible than the current specification. Again, this isn’t really an issue in itself, it’s that we haven’t been given adequate time, information or resources to prepare ourselves and our students for this change.
The main challenge I’m facing with my students is developing their resilience as well as the tools in their problem solving arsenal. I’m a great believer in the simplest solution being the best one and so to tackle my concerns I’m simply trying to expose my pupils to as many different problems as frequently as possible.
Here are some of the things I’m using;
These short problems from nrich make great starters across ages and abilities. They can also be used by tutors during form time if you don’t already have a numeracy programme. There’s a good deal of variety in terms of style of problem and difficulty.
This free problem solving booklet from La Salle comes with teacher notes, I’m using problems from it as homework tasks for years 7 and 8 but it could easily be linked into your SOW for use in lessons.
The premium bundles from numberloving.co.uk were developed specifically with the new GCSE in mind. I frequently use the always, sometimes, never resources and the mysteries, these are both great ways to develop resilience and independent thinking.
The always, sometimes, never resources provide students with 12 statements which they have to explore to decide whether they are always true, sometimes true or never true. They are designed to expose misconceptions which students have so these can be tackled head on. They also require pupils to explain their reasoning – something they will be required to do in the new GCSE. Have a closer look at this bundle here, there are 10 different resources and they all include instructions, solutions and ideas for support and extension.
The mysteries provide pupils with 12 clues which they have to analyse in order to solve the mystery! These are really popular with students and are very good way to develop resilience and different problem solving approaches (like drawing a diagram, making a table etc.). Lots of questions on the new GCSE provide pupils with a lot of information which they have to assimilate – very similar to the mystery tasks. Have a better look at the mysteries bundle here.
When students are working on problem solving tasks I have a rule that they can’t ask questions for 5 minutes (you can get some good timers here). I’ve found this really helps them to start thinking for themselves and exploring different options. I also have a list of strategies on the wall in my room which can sometimes help them get started (see below).
Problem solving strategies
- Draw a diagram or picture
- Make a model
- Try to spot any patterns
- Can you solve an easier problem (make the numbers easier)
- Write what you know on the diagram
- Can you form a right angled triangle
- Try a number and see if it works (trial and improvement)
- Make a list or a table
- Don’t obsess over what you’ve been asked for, focus on what you know and what you can work out
- Can you express anything using algebra
- What topic is this assessing, think about what you know on this topic
Hopefully if I keep at it my students will become more confident and independent mathematicians with a good chance of succeeding at the new GCSE. I’d really like to hear other ideas and resources people are using, tweet me @laurareeshughes.