4 phases:
- Understand the problem - see clearly what is required
- Find connections and make a plan
- Carry out the plan
- Look back at the completed solution - review and discuss
“To devise a plan, to conceive of the idea of a solution is not easy. It takes so much to succeed: formerly acquired knowledge, good mental habits, concentration on the purpose, and one more thing: good luck. To carry out the plan is much easier; what we need is mainly patience.”
“…by reconsidering and examining the result and the path that led to it, they could consolidate their knowledge and develop their ability to solve problems.”
“There remains always something to do; with sufficient study and penetration, we could improve any solution, and, in any case, we can always improve our understanding of the solution.”
Where do I start?
Start with the problem statement
What can I do?
Isolate the principle parts of the problem
A problem to prove has a hypothesis and a conclusion A problem to find has data, conditions, and an unknown
If a problem is very complex, you may distinguish great and small steps. Consider the great ones first and get down to the smaller ones after.
Looking back
start with the solution consider the solution from various sides scrutinize the method that led you to the solution