and its relevance in ……, and will be able to describe how…. They will appreciate its relevance in an industrial setting and know how to select appropriate…..”There are university departments and even universities where this is the prime mode of teaching.It requires quite different arrangement and use of rooms and staff time.Problem-solving is often used to add variety to the curriculum.
For over 30 years, with NCTM reforms, we have been talking about “teaching through problem-solving”, rather than teaching *about* problem-solving. I am not sure “teaching through problem-solving” is all that well-defined.We who are, broadly speaking, constructivist teachers need to answer for how kids will do enough math, to be good at math, in problem-solving classrooms, but that’s a topic for another post. Somewhere, on a dusty shelf, you might have an old binder full of problems.That binder might be organized by problem-solving strategies, like: working backwards; solve a simpler problem; or make a table or chart.Solving problems is not really something that can be taught like that.That approach could be characterized as “teaching about problems”, or “teaching how to solve problems”.Problem – a state of desire for reaching a definite goal from a present condition  Solution – the management of a problem in a way that successfully meets the goals set for treating it   Problem solving on Wikipedia  Introduction to Problem Solving by Robert Harris One important call-out is the importance of having a goal.As defined above, the solution may not completely solve problem, but it does meet the goals you establish for treating it–you may not be able to completely resolve the problem (end world hunger), but you can have a goal to help it (reduce the number of starving children by 10%).With that understanding of problem solving, let’s talk about the steps that can get you there.The five problem solving steps are shown in the chart below: However this chart as is a little misleading.Before we talk about the stages of problem solving, it’s important to have a definition of what it is.Let’s look at the two roots of problem solving — problems and solutions.