Mathematical Modeling in the Social and Life Sciences

CHAPTER 13

Paired-Associate Learning

The mind is slow to unlearn what it has been long in learning.

—Seneca

I. The Learning Problem

The study of learning has been a basic concern of psychology for more than a century. There is a vast literature of books and articles developing different theories or presenting the results of learning experiments involving human and animal subjects. In his chapter, we will examine a very simple model of a particular kind of learning situation. The model was developed by Gordon Bower (and independently by R. R. Bush and F. A. Mosteller) around 1960 in the early days of mathematical learning theory. Mathematical model building for learning processes has had a rich and varied history during the past 50 years; the current “state of the art” has advanced quite far beyond the material we will study. Bower's work is worth examining for us because it shows how a number of predictions can be deduced from a simple model and because it illustrates an actual use of the absorbing Markov chains studied in Chapter 11.

Bower examined a learning problem exemplified by a task familiar to most students. Suppose you are studying for a vocabulary test in your Swahili course. You must be able to translate into Swahili a prescribed list of 25 English words. This learning situation demands the following:

1. You must learn the Swahili words. This includes proper pronunciation and spelling.
2. You must learn to match the correct Swahili word to the appropriate English word.