The Notion of Reducing Abstraction in Quadratic Functions

Abstract

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the concepts (O. Hazzan and R. Zazkis, Reducing abstraction: the case of school mathematics, Educ. Stud. Math. 58 (2005), pp. 101-119). Reducing abstraction as a theoretical framework has been used for explaining students' thought process in areas of advance mathematical topics in collegiate mathematics. By analysing two tenth-grade algebra honour students' ways of thinking on quadratic functions, this article shows how the notion of reducing abstraction can be used for analysing students' mental processes in secondary school mathematics and provides insights into students learning about graphs as well as reports two different strategies on translation tasks as an act of reducing the level of abstraction: one provides an effective method, while the other becomes misleading.