THE CONCEPT OF ACCUMULATION IN CALCULUS

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The prevalence of area-under-a-curve and anti-derivative conceptions over Riemann sum-based conceptions in students’ explanations of definite integrals (2015, background): “They might better understand how the definition of the definite integral and the FTC fit together (see [9,17]), since they would be in a better position to see how the accumulation notion of the integral (see [4]) leads to an anti-derivative.”
CONCEPTUAL ANALYSIS OF MATHEMATICAL IDEAS: SOME SPADEWORK AT THE FOUNDATION OF MATHEMATICS EDUCATION 1 (2008, background): “Homogenous rate of change entails the characteristic that constant rate of change entails change and accumulation simultaneously (Thompson, 1994a; Thompson & Silverman, 2008).”
Ideas foundational to calculus learning and their links to students’ difficulties (2021, background): “As Thompson (2008) insisted, “It takes 12 years to learn calculus”.”
Learning the integral concept by constructing knowledge about accumulation (2014, background): “If we know the value of Fa(x)for every x (the accumulation value) and we know that the derivative of Fa(x) is the integrand f(x), we obtain the main relationships of integration in a nutshell (Thompson and Silverman 2008).”