The finite-to-finite strand of a learning progression for the concept of function: A research synthesis and cognitive analysis

In this paper we report validation efforts around the finite-to-finite strand of a provisional learning progression (LP) for the concept of function. We regard an LP as an empirically-verified account of how student understandings form over time and in response to instruction. The finite-to-finite strand of the LP was informed by literature on students’ thinking and learning related to functions as well as the Algebra Project’s curricular approach, which is designed for students who are traditionally underserved by mathematics education. Developing and validating an LP is a multi-step, cyclic process. Here we report on one step in this process, an item and response analysis. Data sources include 680 students’ responses to 13 multipart computer-delivered tasks. Results suggest that revisions to the items, associated scoring rubrics, and in some instances the LP are warranted. We illustrate this task, rubric, and LP revision process through an item analysis for a selected task.