The Students–Professors Problem—The Reversal Error and Beyond

This paper first introduces and reviews the existing research on the well-known “students–professors (S/P) problem”, which was first formulated in 1979. Next, it presents an empirical study of Danish upper secondary students’ answers to two mathematical modeling versions of the S/P-problem; a mathematization version (296 students), and a de-mathematization version (658 students). Besides reproducing several previously reported findings, e.g., the so-called reversal error, the study identifies new error types not previously reported in the literature. The mathematical modeling perspective adopted, along with a mixed-methods design, give rise to new potential explanations of the reversal error as well as explanations of the new error types. Our study shows that interpreting the linguistic formulation of the S/P-problem statement is not only related to language but is intrinsically of a mathematical – and cognitive – nature as well. Altogether, there is still more to be said about the S/P-problem forty years after its emergence.