How robust are intuitive conceptions? Insights from production tasks regarding arithmetic operations.

Abstract

Intuitive conceptions are known to be prevalent among young learners and can impose constraints to knowledge acquisition. Data even suggest that instruction does not eradicate them, but the phenomenon has rarely been quantified. In this study we raise the question of how robust intuitive conceptions are. Moreover, we look at how persistent they are long after instruction of the studied notions. Production tasks concerning the four elementary arithmetic operations were used for measuring the degree to which they prevail and impose constraints among adults, 131 bachelor students as well as 168 high-school and 57 mathematics teachers. The findings revealed that in most cases (88.93%) participants evoked examples that are congruent with an intuitive conception. This was observed for all the arithmetic operations and population involved in the study. Even when explicitly prompted to find incongruent cases, they failed on two thirds of the cases. The educational entailments of these findings are discussed.