Understanding Meaningful Arithmetic Operations in Word Problems: A Computational Model and Task Design

In the context of arithmetic word problems involving multiplication and division relationships between quantities, a typical arithmetic situation leads to two multiplications and four divisions. This paper introduces an educational framework for a meaningful and integrated interpretation of both operations in such situations. It is based on the ‘tri-quantitative proposition model’, a computational approach representing problems with two existential and one relational propositions. Additionally, this paper describes a problem-posing task designed using this model. Preliminary evaluations with teachers and university students were conducted to assess the task’s effectiveness. The results of these evaluations, which are reported here, suggest the usefulness and advanced nature of the proposed framework and task design.