Scaffolding, abstraction and emergent goals

This study examines the role of scaffolding in the achievement of a mathematical abstraction by focusing on emergent goals. An activity-theoretic approach to abstraction in context is taken. The examination is carried out with regard to the verbal protocols of two 17-year-old students working on a task related to the graphs of y=f(|x|). This examination suggests that abstraction is likely to be achieved through satisfaction of several emergent goals. These goals are observed to be contingent upon four parameters: the scaffolder's interventions, students, tasks, and prior emergent goals. Dynamic and dialectical interrelationships amongst these parameters are discussed with regard to the students ' verbal protocols.