This March 2021 post, Polya – Problem Solving includes many resources for problem solving.
Links to the resources are all provided in the notes below.
Files: pdf: Problem Solving in Mathematics
PowerPoint: Problem Solving in Mathematics
Further Notes (relevant links for each section are also given here)
What is a problem anyway?
GCSE & A Level Reform in particular: GCSE mathematics subject content and assessment objectives where the assessment object AO3 defines what is regarded as Problem Solving at GCSE. It is helpful to look ahead to A Level – see: A level mathematics working group report which is very clear on what may be considered problem solving.
Ask the students
For our students to be good problem solvers who have the confidence to start on a problem without necessarily know where they are going with it they need a classroom environment where they are comfortable to take risks and know that it is OK to make mistakes. They need great teachers who not only understand their subject but the importance of the teacher / student relationship. Here’s what some Year 9 (ages 13-14) students said about Good Maths teachers and this from Year 7 (ages 11-12).
You can see some questions to consider on the slides.
There are several slides here on using diagrams; sometimes we run the risk of getting too formal too quickly – some great diagrams can help with understanding and be very useful in our teaching. Giving students just a diagram and asking them what the question might be can be a very useful exercise too and also be a good way to discuss the vocabulary used in exams.
I always tell students that going backwards can be great for understanding and also making connections – consider expanding brackets and factorising for example.
Links to the resources in this section:
- Nrich – Thinking Mathematically (scroll down the page for Mathematical Habits of Mind)
- Nrich Being determined problems
- Here’s the diagram
- Reference – help students with vocabulary
- Good Mathematicians Can Go Backwards!
- Nrich – Working Backwards at KS2 (also relevant for KS3)
- Using NRich Tasks to Develop Key Problem-Solving Skills
- Rich Tasks (includes link to the outstanding AQA Problems)
Making It Stick
- NRich – Short Problems (UKMT) for Practice and Revision
- NRich – Working Mathematically – Short Problems
- Short Problem example – Almost Constant Digits
- NRich – Thinking Mathematically
- Standards Unit (All resources) S4 Statistics
- GCSE New Content – includes OCR & AQA resources
- Further Maths Support Programme – GCSE Problem Solving Materials
- AMSP Teaching Resources (select Teachers from the menu and resources in each section)
- Desmos Graphing Calculator (all information) and graph page for question