Lesson Study for Problem Solving

“A problem is a task that the individual wants to achieve, and for which he or she does not have access to a straightforward means of solution”. (Schoenfeld 1985)

Problem solving is the process of tackling unstructured problems that require students to model situations with mathematics, make reasoned assumptions, construct chains of reasoning and interpret solutions in context. Problems may be approached in many different ways and will have many possible solutions. These solutions matter and must be evaluated as to their suitability.

The diagram describes the processes involved in Problem Solving.
We usually begin with a situation. This is usually, but not always, in a real-life context.
Problem solving flowchart.png
  1. In the first step you try to formulate the problem mathematically. This usually involves making assumptions and simplifications so that the problem becomes more manageable.
  2. In the second step you begin to analyse and solve the problem using a variety of mathematical tools, such as drawings, graphs, tables, algebra and so on.
  3. When you have made some progress, you step back and interpret what you have done in terms of the original situation. Are your calculations meaningful?
  4. Then you evaluate the reasonableness of the solution you have achieved. Is it good enough? Maybe you need to modify your assumptions and go round the cycle again.
  5. When you think you have a solution, you communicate it to others.

Students must thus make many reasoned decisions when problem solving. The skills of problem solving will be ever more important for people of the future who are seeking to make sense of – and change – the world around them.
Of course, this neat cycle of processes is not what actually happens in practice! There will be many times when we move back and forth between the processes. It is however a very useful conceptual tool to refer to when discussing problem solving.