Motivation for Involving Undergraduates in Research
Textbook problems in most disciplines are extremely useful in helping students learn and practice concepts and techniques. Modeling problems found in the real world may be no harder to solve than those problems found in textbooks, however, they are usually harder to identify and to isolate. Textbook problems nearly always offer exactly the right amount of information needed for a solution, rarely more, rarely less. In addition such problems are nearly always written in a consistent language that is used throughout the textbook, and they usually follow quickly after the presentation of a solution technique appropriate for the problem. Perhaps this accounts for some of the difficulty students often have in transferring knowledge from one course to another, such as a student in a geology course who is not able to interpret the meaning given by an earthquake travel-time graph (used to determine the distance to the epicenter of the quake) even after having encountered similar graphs in a precalculus class. The truth is that different disciplines use different terminologies even to represent the same ideas, so the problems that arise in these different disciplines are naturally packaged in different ways. Worse, problems which arise in the real world do not come packaged at all.