Meanings, Reasoning, and Modeling with Definite Integrals: Comparing Adding Up Pieces and Accumulation from Rate
Abstract/Description:
Approaches to integration based on quantitative reasoning have largely developed along two parallel lines. One focuses on continuous accumulation from rate, with accumulation functions as the primary object. The other focuses on summing infinitesimal bits of a quantity, with definite integrals as the primary object. No work has put these two approaches in direct conversation with each other, which is the purpose and contribution of this theoretical paper. In this paper, we unpack both approaches in terms of meanings and reasoning. Because modeling is a key motive for using quantitatively-grounded approaches in the first place, we then analyze and discuss each approach’s method of modeling two example contexts.
Presenters:
Steven Jones, Brigham Young University and Rob Ely, University of Idaho