Children’s Acquisition of Arithmetic Principles: The Role of Experience

The current study investigated how young learners’ experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children’s acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children who viewed incorrect, principle-consistent equations and those who viewed a mix of incorrect, principle-consistent and principle-violation equations both showed gains in principle knowledge. However, children who viewed only principle-consistent equations did not. We hypothesized that improvements were due in part to improved encoding of relative magnitudes. In Experiment 2, children who practiced comparing numerical magnitudes increased their knowledge of the principle. Thus, experience that highlights the encoding of relative magnitude facilitates principle learning. This work shows that exposure to certain types of arithmetic equations can facilitate the learning of arithmetic principles, a fundamental aspect of early mathematical development.