Jack Marr

A Mingled Yarn

The behavior of nonliving and living systems is generally viewed as being qualitatively different. The key difference is often summarized by saying that whereas living systems are complex, nonliving ones are simple. This distinction is often the basis for claiming essential differences in conceptual stances, methods, and theories between scientific fields. I argue first that nonliving systems can display the unpredictable, irreducible, irreversible, and emergent—in sum, complex—properties of living systems. Then I discuss an emerging field called complexity theory, the principles of which offer the promise of bringing quantitative unity to an enormous range of phenomena, living or dead.

Subgoal identification and error analysis in problem solving

Quantitative problem solving is the major ingredient of core pre-engineering physics courses. The analysis of problem-solving behaviors in these courses can provide an important source of information not only about how students approach problems in general, but how their performance might be enhanced through the development and assessment of instructional innovations. We have focused on the electromagnetics portion of our introductory physics sequence. This course has a failure rate exceeding 30%. Thus, any system for enhancing problem solving in this difficult course will significantly impact many students. A principal barrier to successful problem solving is lack of generalization, i.e. the ability to transfer knowledge and skills from one problem to another and to recognize classes of problems. The common tendency is to treat each problem as a separate entity to be approached by rigid application of memorized formulae, or simply by trial and error. Seemingly small changes in requirements or conditions can be met with bafflement. We have approached problem solving in two interlocked ways. One is the systematic analysis and classification of errors that students make when attempting standard problems in quizzes and exams. The second consists of breaking problems down into a sequence of subgoals. The results show that students often improperly identify both the correct operational equations and the appropriate subgoals required for solution. Our analysis is used to teach students more effective problem-solving strategies with a computerized tutorial.

Enhancement of intuitive reasoning through precision teaching and simulations

We have studied how performance on the E&M (Electricity and Magnetism) portion of an Introductory Physics course may be enhanced by the careful choice of the exercises that the students perform. Exercises and homework problems are of two types; direct problems involve little more than the entry of numbers into a basic equation; and indirect problems requiring a solution strategy involving various subgoals which must be identified and achieved. By concentrating first on the development of basic skills through the technique of precision teaching and the use of simple direct problems, we show significant long term performance improvement, particularly among students at risk. We further examine how computer simulations can enhance intuitive reasoning and how the choice of a structured set of homework problems enhanced performance.