A Preliminary Validity Evaluation of a Learning Progression for the Concept of Function

Abstract

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity of an LP cannot be taken for granted, however. LPs evolve from a synthesis of multiple research studies, subject-matter expertise, and standards documents. They are working models of student development that may require revision in light of critique and empirical evidence. The formulation of an LP is an iterative process in which expert feedback is elicited, data are collected, and the LP is revised accordingly. We developed an LP for the concept of function both because the concept of function is challenging to attain and because it is central to the study of algebra and higher mathematics. We report early findings with respect to the validity of the concept of function LP, based on small-scale cognitive interviews and expert reviews.