Hypothetical Learning Trajectory (HLT): A Lens on Conceptual Transition between Mathematical “Markers”

in Researching and Using Progressions (Trajectories) in Mathematics Education

Abstract

In this chapter I introduce a distinction between two research types, marker studies and transition studies, that I find useful in developing and categorizing hypothetical learning trajectories (hlts). I stress the latter type as one closely related with the third element in Simon’s (1995) definition of hlt. To further depict the linkage between hlt and transition studies, I discuss the starting points and development of hlts, including a model of learning as cognitive change – reflection on activity-effect relationship. I follow those sections with a description of four ways in which I find hlts that specify conceptual transitions to be useful.

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