A model of how students' definitions of substitution and equivalence may relate to their conceptualizations of algebraic transformation

International audienceThis empirical paper explores students' conceptions of transformation as substitution equivalence by linking it to their definitions of substitution and equivalence. This work draws on Sfard's (1995) framework to conceptualize conceptions of substitution equivalence and its components, equivalence and substitution, each on a spectrum from computational to structural. We provide examples of student work to illustrate how students' understandings of substitution, equivalence, and substitution equivalence as an approach to justifying transformation may relate to one another