ABSTRACT
WHAT IS A PROBLEM? This book is about learning to solve problems, so first I shall describe what a problem is, that is, what is being solved. There are many conceptions of a problem. The word “problem” derives from the Greek problema, meaning obstacle. The word “problem,” as used in this book, refers to a question or issue that is uncertain and so must be examined and solved. Everyday life and work are filled with uncertain situations for which no resolution is immediately known. What route should I take to work to minimize traffic congestion? How can we afford an addition to the school building? How can we accelerate the collection of receivables? What will be the most effective method for marketing our new product to the target group? How can we increase fatigue strength to this material without increasing cost significantly? Which medical-insurance program should I select? These are all questions about situations that are currently unknown and therefore need resolution. Those problem situations vary from algorithmic math calculations to vexing and complex social problems, such as mitigating violence in the schools. For me, finding or solving the problem must have some social, cultural, or intellectual value. That is, someone believes that the problem is worth solving. “Problems become problems when there is a ‘felt need’ or difficulty that propels one toward resolution” (Arlin, 1989, p. 230). That is, someone believes that the question is worth answering. If no one perceives a need to answer the question, there is no problem. This latter attribute may eliminate most formal, in-school problems
from the category of real problems because students often do not perceive a need to find the unknowns to the types of problems posed in schools. However, because their teachers do perceive such a need, they are normally regarded as problems.
