Title:

Problem solving from textbook examples

There has been a great deal of research into students' use of examples when solving problems in textbooks. Much of this work has been within the framework of analogical problem solving (APS). Indeed many researchers believe they can build adequate models of how students learn and solve exercise problems by analogy to worked examples. In the first part of this thesis I argue that this view of problem solving from examples is inappropriate and often misleading. Most students learning a subject for the first time tend to imitate examples. Imitative Problem Solving UPS)is a weak form of analogical problem solving. APS accounts assume that a solver has a representation of an earlier problem in memory. The difficulties involved are accessing that source problem and adapting it to solve the current one. WS does not assume t at the source is represented in memory, and even when the source example is available( as in textbook examples), the student may not understand it well enough to be able to adapt it to new situations. The second part of the thesis presents an interpretation theory for analysing both texts and the behaviour of solvers using those texts to solve exercise problems. The third part applies the interpretation theory to the solution explanation of a simple algebra word problem. Where an example problem fails to map directly onto an exercise problem, or where inferences have to be made to understand it, the solver win be unable to imitate the example and hence will have difficulties in proportion to the mapping inequalities between the two problems. That is, the interpretation theory allows us to predict precisely where solvers will have difficulty using an example to solve an exercise problem of the same type. The final part presents experimental tests of these predictions. The results confirm that the interpretation theory analysis can correctly identify possible areas of difficulty for the student due to a) the way an example problem is structured, and b) the nature of the transfer task.
