What Can Be More Challenging than Square-Rooting from Squared Things?

Roots is one of these mathematical topics that students encounter multiple times in their studies of mathematics. Growing from the commognitive framework, this study is concerned with intra-commognitive conflicts where the same discursant develops incommensurable discourses on 'the same' mathematical object (square roots, in this case) and endorses seemingly conflicting narratives about it. These conflicts were explored among eleven preacademic students who worked individually on a multiple-question assignment asking them to extract square roots from squared numbers and expressions. Three intra-commognitive conflicts are presented in this paper: a conflict of perfect squares and squared inputs, a conflict of stand-alone and incorporated roots, and a conflict of expressions and equations.