Ever wondered how we solve problems? I recently took a course called ‘education psychology’, where we study how the brain works when it comes to teaching and learning. A module on problem solving in particular caught my interest, so I thought I would write about the key things I learnt.

According to Roger H. Bruning a **problem **exists when our current state differs our desired state. If we look at this idea more broadly, we can understand a problem as situation that needs to be dealt with and overcome

Problems can be defined in even greater detail when we divide them into seperate categories; ill-defined and well-defined problems.

** Ill-defined** problems can be solved in different ways. Because an ill-defined problem has multiple solutions it means that there is no one direct method to solve it. Examples of ill-defined problems include; poverty, hunger, plastic waste.

In contrast, **well-defined** problems have only one correct solution and a guaranteed method for finding it. Example, turning a light on in a dark room, mathematical equation.

### Now that we know what problems are, lets look at problem solving!

I’m not going to lie – it’s pretty abstract, but fret not, I’m going to break it down for you! Broadly, we can understand problem solving as “*a **conscious, deliberate process **governed by a naturally occurring sequence of steps” *(John Dewey, 1910). Specifically problem solving can be seen as the need to **move from a current state** **to a desired state.**

Confused? So was I! But then I discovered this theory called ‘The Problem Space Theory’ (1972) which suggests that **people ***solve problems*** by searching in a ***problem space***. **

Lets say we have a problem (image below).

Now lets break down this problem according to the Problem Space Theory.

First up is the **initial or current state – **this is the starting position, where the learner first encounters the problem.

At the other end of the problem is the **goal state **i.e. the resolution of the problem.

The little dots that take up the space between the **initial** and **goal** state are **operators. Operators **are actions, decisions and choices we make in order to move from one state to another i.e. how we solve the problem.

**Constraints** are restraints or restrictions placed on operators – this could be an algebraic rule or a limitation such as time, money or a restriction placed on a task by a teacher.

Hopefully I have sparked your interest on problems and problem solving. Feel free to get in touch with me to learn more! You can read all about the psychology of problem solving.

-Miss Mileto