SOME LEARNING MODELS FOR ARITHMETIC TASKS AND THEIR USE IN COMPUTER BASED LEARNING
Pat Woods, James R. Hartley · British Journal of Educational Psychology · 1971
S ummary . There are many advantages in having the computer individualise instruction by generating teaching material when it is needed, at a level which suits a pupil's particular competence. This requires valid models of task difficulty, and this paper describes such models and the experiments to validate them, for practice tasks in arithmetic computation. Using criteria of probability of success and rate of working for each column of an addition task in vertical format, analyses of variance of experimental data reveal main effects of digit size and number of rows. Following a formal development of the model a least squares analysis derives a function which, for the experimental data, relates those variables to the criteria. These are used by the computer to generate examples so that a pupil works at any specified level of success. Methods of implementation and decision making together with some preliminary results are given. These are extended by describing an experiment with subtraction tasks in which two competing models were used to describe pupils' success and working levels. These analyses and experiments show the complexity of the decision making which is needed for adaptive teaching and which exploit the computer's capabilities.