Combining Sealey, Von Korff & Rebello, Jones, and Swidan & Yerushalmy into a Comprehensive Decomposition of the “Integral with Bounds” Concept
Abstract/Description:
Previous calculus education work on integrals, including definite integrals and accumulation functions, has created useful theoretical frameworks that decompose the “integrals with bounds” concept into constituent parts. Yet, each framework focuses on distinct aspects of the integral and leaves certain parts implicit. Further, definitions and operationalizations are absent in many of these frameworks. This theoretical paper contributes by: (a) pulling together the various pieces in these frameworks into a comprehensive decomposition of the integral concept, (b) explicitly defining the processes and objects within it, and (c) operationalizing the processes and objects within each of the numeric, graphical, and symbolic representations. This comprehensive framework is useful for researchers, curriculum or task writers, and instructors alike to have a more complete picture of the elements that make up the integral concept.
Presenters:
Steven Jones and Brinley Stevens, Brigham Young University