Sustaining quantitatively-grounded meanings for definite integrals in high school calculus

Although the importance of developing students’ quantitatively-grounded
meanings for integrals is widely acknowledged, there is limited research into
how this can be accomplished in classroom settings. To address this limitation,
I conducted a classroom design study in which I analyzed the collective
development of classroom mathematical practices for establishing quantitatively-grounded meanings for integrals by a Year 12 calculus class. The
findings suggest that the class established ways of approximating the
value of definite integrals and integrals with a variable upper bound by
progressing through the six layers of the Adding Up Pieces framework in
ways that were largely similar to previous findings from studies conducted in
clinical settings. The findings from this study also extend previous research
by documenting the reasoning that students used to partition the domain
and calculate target quantities using the trapezoidal rule, as well as the
difficulty they encountered in developing the accumulation function.