Primitive Model of Partitive Division: A Replication of the Fischbein et al. Study

We present a replication study of one of the most renowned seminal works in the field of mathematics education, i.e., the Fischbein et al. (1985) study on implicit models of multiplication and division in solving word problems. The original instrument was administered to a sample of 902 grade 7 students, proposing some methodological variations. The discussion focuses on four items involving partitive division of integer numbers, and results are compared to the original study: the main results of the original study are confirmed, but we contribute further with considerations on the statistical significance of differences observed in item difficulty. Finally, through our new methodological approach, we broaden the results of the original study by analysing students’ behaviour on the basis of their general arithmetical problem-solving ability. Students with medium-level ability are more influenced by the primitive model than those with lower ability.