The Four Factors of Problem-Solving Performance

Decades ago, education researcher Alan Schoenfeld sought to understand the traits and behaviours of high-performing mathematics students. In 1985, he published a page-turning thriller called Mathematical Problem-Solving. There he describes the following factors of problem-solving performance:

Resources are things that you know. They are necessary, but you can never predict what you'll need to know in future. Trying to learn everything in advance is futile.

Heuristics are procedures, tactics and rules of thumb. They are a little more valuable. You can use them to acquire knowledge on-the-fly and exploit patterns. But you cannot try everything. You must be strategic to succeed with limited time and energy. That's why control is crucial.

Control is executive decision-making. It's how you decide to use resources and heuristics. Problem solvers with good control face the crux of the problem, instead of retreating into busywork. They also take a break when they need one. They are efficient and self-aware.

Beliefs are the invisible ideas that shape your view of the problem. Beliefs create blindspots, causing you to overlook the obvious. Even if you are strong in every other factor, beliefs can block the way.

When it comes to improving your problem-solving performance, control and beliefs are the high-value targets. But how do you improve these factors?

There are many answers to this question, but I can boil them all down to two words: Be systematic. Structured thinking of any kind combats the bias and reactivity that creeps into adhoc problem-solving. Personally, I use Thinking Mathematically.