Department of Physics
Condensed Matter Seminar

Statistics, like physics, is a subject in which a relatively small number of fundamental ideas and principles distill and impose a compact, coherent structure on a powerful body of knowledge. In each case, the power stems not only from the enormous range of the knowledge’s applicability but also from the way in which its structure facilitates its use in novel situations. In each case, it is also difficult to help students develop the kind of coherent understanding that is the foundation for flexible problem solving. For them, too often, problem solving remains a matter of attempts to match new situations superficially to recalled worked examples, of equation- or formula-hunting and of purely formal computation. In the study to be discussed, a method of promoting deeper understanding without sacrificing basic skills was assessed in the context of statistics. College students worked alone or in pairs to learn about the chi-square formula in statistics. Half of the students (randomly assigned) were given a lesson, a set of practice problems, and a final example. The other half were given the practice problems first, then the lesson, and then the final example. This second group had to invent formulas to try to solve the practice problems. On a posttest, the students who worked in pairs to invent solutions before receiving the lesson showed a greater understanding of how to adapt their knowledge to solve novel problems. They also showed more awareness of when a particular formula did not apply. The process of collaborating to invent solutions is thought to help students notice key features of problems and prepare them to appreciate how they work in the expert formulation.