Resumen de How do widely-used calculus textbooks introduce the concepts of definite integrals?

Dae S. Hong, Dennis Kwaka

• This study explores opportunities to learn definite integrals in three widely-used textbooks in the US, Definitions, worked examples, and exercise problems were coded using research based cognitive resources in definite integrals to examine if widely-used textbooks provide students with opportunities to explore how two quantities are related to show area under a curve or other contexts. The results show that initial introduction, worked examples, and exercise problems all provide limited opportunities for students to explore the multiplicative relationship between two quantities (integrand and differential) and adding small pieces to understand definite integrals. Although students may be able to solve integral problems using anti - derivatives, it is possible that they may not understand the definite integral conceptually (knowing why the definite integral gives the area under a curve) or be able expand their understanding to other contexts. Implications of these results are also discussed.