A resource for introducing students to the integral concept

ABSTRACT

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students to the integral concept. The resource addresses a number of challenges when introducing the integral: (1) choosing an appropriate, intuitive context which gives meaning to the symbols in the integral expression; (2) aiding the transfer of the integral expression to different contexts via using the Riemann sum in an informal way so that students can see and interpret the rectangles which are inherent in this sum; and (3) the gradual formalizing of the Riemann sum and its linkage with the Fundamental Theorem of Calculus. The resource has been used over a number of years at this university amongst first-year undergraduate science and engineering students. Anecdotal evidence would suggest that the resource is beneficial.

KEYWORDS:

• Integral calculus
• Riemann sum
• transfer
• teaching ideas

Acknowledgements

Funds from the Irish Research Council helped to develop this resource. Special commendation is also due to Assoc. Prof. Dr. Brien Nolan, Head of the School of Mathematical Sciences at Dublin City University, and associated with the Centre for Advancement of STEM Teaching and Learning (CASTeL) at Dublin City University, who offered invaluable help and advice in the design of the resource as well as to the drafting of this article. Any opinions, findings, or conclusions expressed in this document are those of the author only, and do not necessarily reflect the views of the Irish Research Council.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Richard A. Hoban http://orcid.org/0000-0002-7368-7566

Additional information

Funding

This work was supported by the Irish Research Council.