Algebraic symbols play an important role in school mathematics. In this paper it will be shown, in which ways algebraic symbols enable learners to think algebraically in non-routine problems. This issue is addressed on the basis of an analysis of theories about algebraic thinking and the concept of agency. It is shown that such symbolic algebraic thinking includes ﬁnding an algebraic approach, acting intentionally in an algebraic way, and reﬂecting algebraically. Intentional algebraic actions describe a student’s capability to both act on relations in the original mathematical context (non-symbolic intentional actions) and to act in the context of its symbolic representation (symbolic intentional actions). By being able to change the mode of action between these two modes students can think algebraically in more elaborate ways.