Play with it: creativity in problem-solving.

I get it when fiction-writer Dean Wesley Smith says that we have a 'creative voice' and a 'critical voice'. Smith always writes with his creative voice, never with the critical one, not even when rewriting the text, simply because he never rewrites. He says the best work is done with the creative voice (and actually, it is the way to enjoy the process the most).

It is easy to distinguish between the two voices: the critical voice is always finding problems, and difficulties, it is negative, complaining, judging; the creative voice says 'let's play!'. I think this is the best description I have ever encountered about creative voice: 'let's play!'. No judgment, no evaluation, no worries about reaching the objective.

That is why the creative voice is so important: because it does not create barriers, it allows anything to happen; it does not stop action by analysing it, evaluating it, judging its value, measuring its importance. 

The creative voice is the realm of possibility. The critical voice is the realm of limitation.

And this also applies when solving maths exercises (or actually when trying to solve any problem). The best way to find a solution is to access the creative voice. The critical voice is good for revision (and yes, in problem-solving there is a need for revision). 

The four steps of Polya's problem-solving are:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Looking back (examine the solution).

It is in step number 2 where the creative voice has to be set free. After all, how do you devise a plan if you do not know how to find the answer? Well, that is where you have to do this: forget about solving the problem and just play! I am serious here, forget about your objective, let go of your need to get an answer. Just look at the question and play with it. Can you write some parts of the statement differently? Can you write some simple examples? What happens if some parts of the problems are modified? How could this be useful in other settings? Have I seen something similar somewhere else? What are the elements in the problem and how would the problem change if I changed some of them? The person that posed the problem, what did they have in mind? When I look at the problem, what do I wonder?

By becoming detached from the results, by allowing yourself to explore, by allowing yourself to play, you will be surprised how much more you learn, how much easier it is, and, definitely, how much more you enjoy it. Many times, after doing this, the answer pops out of the page by itself.