On students' understanding of Riemann sums of integrals of functions of two variables

2018

International audience; APOS (Action-Process-Object-Schema) Theory is used to pose and test a conjecture of mental constructions that may be used to understand the relation between integrals of two variable functions over rectangles and corresponding Riemann sums. Interviews with ten students who had just finished a multivariable calculus course showed that the conjectured mental constructions are necessary.