An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure

A robust finding of past research is that the number types involved in a problem statement strongly affect the solution process and the difficulty level of problems with a multiplicative structure. To account for these number type effects Fischbein, Deri, Nello & Marino (1985) have put forward the theory of the primitive intuitive models of arithmetic operations. This theory specifies that every arithmetic operation (e.g., multiplication) is associated with a primitive intuitive model (e.g., repeated addition), which intervenes in the process of selecting the operation needed to solve a word problem. In an attempt to unravel the number type effects on solving multiplicative problems, a study was carried out in which student-generated word problems for given number sentences were used as data to test a series of hypotheses and predictions that were derived in a straightforward way from the theory of the intuitive models. Although the results are fairly consistent with the basic hypothesis of the theory, the investigation also shows that at a more specific level this theory cannot sufficiently account for a number of empirical observations. The study also points to the necessity of continued research aimed at a better understanding of the cognitive processes involved in studentsʹ modeling of situations by multiplicative operations.