Polya - How to Solve It

George Polya's book provides clear guidelines on how to solve problems. I came across Polya's book last year whilst completing a MOOC, "How to Learn Math", by Prof. Jo Boaler, Stanford University. Polya's work is useful for students by providing them with a framework and helping them to scaffold problems themselves.

Basic Outline of Polya:
1. Understanding the Problem
2. Devising a Plan
3. Carrying out the Plan
4. Checking and Looking Back

Summary here University of Utah

I've used the diagram below to help students when working on investigational problems (diagram is stuck in the back of each students book). It gives a structure and hopefully it helps develop resilience. When a student gets stuck, I ask them to look at the diagram. If they continue to be stuck, I prompt them, using the diagram, by asking questions such as, "Have you done this?" or "What about..?" etc. and point out various parts.

source: math-mom.com

This has worked well with Bowland Assessment Tasks, Nuffield's Applying Mathematical Processes, cre8ate Maths Resources and NRICH activities.