The Art of Problem Posing

This book presents some very interesting views that could be used to gain insight into any problem by starting out with Level zero with an hypothesis of What If?

This level should be able to be used by all levels of mathematics students from K - 12 and beyond.

The next stage is to list all the attributes that make up level zero, the given hypothesis. Attributes
are simply a thorough listing of what is given in detail, such as powers,+,-,=,>,<, and what some people might say is obvious.

Level 2 is to review all the attributes and ask, What If Not?, that is what if this were not true. As you ask this question things may open up and change the view of your original problem. This level may require higher thinking and would be excellent to pose to all your students K-12 to see how they are thinking. You may find some wonderful insight from the younger grades as they do not find a predisposition in their thinking.

This whole new way of looking at the problem from a different perspective may now cycle into some new attributes for each what-if-not question asked about the previous level attributes. This expansion and cycling will expand the future avenues of investigation that you may wish to pursue. To pursue these may require higher level mathematics and challenge even the brightest students.

This explosion in questions can take you off track so it is important to go to level 2 and then to return to solve the original question and then to pursue the other avenues. This procedure can be cycled over again into level three questioning of ,what -if and what -if not until you see no further sensible questioning.

Now all your questions need to be analyzed and answered to see the many possibilities that you have created for you to investigate which is level 4.

Your hypothesis started out so simple and manifested itself into a network of possibilities. Choose carefully the pursuit of these addition direction to analyze as you must not loose site of your original objective.

This method of what if and what if not can be very powerful in uncovering new ideas, but it can also be a huge consumer of your time. Choose wisely and prioritize those additional directions that you may wish to analyze, so that they do not distract you from the current work at hand.