A reflection on Star and Seifert’s operationalisation of flexibility in equation solving

My interest in flexibility in equation solving comes from a research agenda whose aim is the study of flexibility in the teaching and learning of algebra. Several researchers have proposed operationalisations. One of the most relevant of these is the one proposed by Star and Seifert (2006). In this operational definition, flexibility is knowing multiple solution procedures to a problem and having the capacity to generate new and more efficient procedures to solve it. Even though this definition has had an impact on the research on flexibility (e.g., Xu et al., 2017), there are calls for a more comprehensive account (e.g., Ionescu, 2012) given flexibility’s contribution to efficient problem solving.

Here I offer a reflection about flexibility in equation solving that extends the definition by Star and Seifert. To this end, I offer examples of equation solving that suggest that there is a need for another property in the definition, to deepen both the investigation of students’ flexibility in equation solving and its fostering in teaching. I add ‘connections’ because when performing transformational activities, students make a number of procedural connections.