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Learning Statics by Studying Worked Examples

Introduction

The traditional way to learn in a problem-solving course such as statics is to solve a large number of homework problems. This approach is often inefficient and frustrating because students spend so much time searching for the solution that little time is left for learning the principles that will enable them to solve other related problems. Research in cognitive science has shown that under certain conditions, studying worked examples is a better way to learn than solving problems1-9. The purpose of the present paper is to bring this work to the attention of a wider audience and to report on the writer’s experience in implementing worked examples in a course in statics. Because the writer’s approach is based strongly on a particular subfield of cognitive science called “cognitive load theory” (CLT), the paper will begin with an outline of CLT drawn from publications by several researchers closely identified with the theory2,5,8.

Outline of cognitive load theory

1. CLT is derived from information-processing models of cognitive architecture. A number of such models have been proposed, some quite elaborate10-12. Almost all contain at least two key elements that CLT treats as fundamental to the ability to learn: working memory and long-term memory. Working memory is what we are conscious of; it consists not only of a place for temporary storage of information but also an executive system that processes information. Long-term memory is stored information that we are not conscious of but that we can retrieve and move to working memory when the need arises.

2. A fundamental finding of cognitive science—and crucial for the worked example approach—is that working memory is very limited. The number of “chunks” of information that working memory can contain is, as expressed in the title of a widely cited article, “The magical number seven plus or minus two” 13.

3. Long-term memory, on the other hand, appears to be essentially unlimited. Learning “may be defined as the encoding (storage) of knowledge and/or skills into long term memory in such a way that the knowledge and skills may be recalled and applied at a later time on demand”2.

4. One key concept in CLT is “schema” acquisition. A schema is an element of long- term memory that a) although it may refer to multiple pieces of data, may be brought into working memory and treated as a single “chunk” of information, and b) contains information about how the data will be used. A chess master seeing a particular configuration of chess pieces on a board will recall the appropriate schema from long- term memory that will match the configuration on the board and will inform the master which are the best moves14-15. Upon seeing a textbook problem in electrical circuits, an experienced physics teacher recalls the schema that both categorizes the problem and informs the teacher what principles of circuit analysis to use. The very word “schema”

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Rossow, M. (2008, June), Learning Statics By Studying Worked Examples Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3347