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

Abstract

ABSTRACT 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.