In the recent time, the fact that the use of Computer-assisted Instruction (CAI) in the classroom becoming more frequent is undeniable. The use of CAI could provide imaginary tools visualized in computer on which the tools could bridge the students understanding in the real class. In fact, this approach help the students during the class in visualizing and (2) calculating mathematical problems. One example of CAI in mathematics lesson is called Digital Geometry Software (DGS). The use of Digital Geometry Software (DGS) provide opportunity for the students in making sense of geometric representation of the algebraic manipulation. This visualization using DGS, help the students in making relationship of visualization on algebraic manipulation.

One topic in mathematics that is visually unable to be taught promptly to the students is integral calculus. in integral issue, most of the students consider the integral as anti-derivative relation concept. In fact, those understanding is proven to give drawbacks for the students understanding of integral. It is suggested to deliver the context on which integral is developed and applied consequently. Therefore, the use historical aspect of the integral development may become a good starting point in delivering integral concept. Nevertheless, providing a good visual and context may be the main challenge in teaching integral calculus.

Based on the historical development, integral calculus is developed by progressing through the idea of infinitesimal. In details, ancient mathematician had troubled themselves in solving area of curved shape plane figure using the idea of the method of exhaustion and the method of indivisible. In the end, the Riemann Sum conclude the historical development of integral calculus. That is where the DGS take a part for assisting the teaching in the class. One of simple DGS used in the academics that can support visualization and contextualization of integral calculus is Geogebra. Geogebra provide an opportunity to the students in exploring multiple representation on graph and function in practical ways. The Geogebra user interface may provide direct comparison on both visual and context of integral directly. Thus, in this paper we present the use of Geogebra in reconstruct Integral Calculus reinvention historical based learning.

 

 

The implementation of Geogebra help the students to understand the historical development of integral calculus through reinvention activities. By using Geogebra, the stduents translate the idea of the method of exhaustion and the method of indivisible as the approximation in estimating the area of curve line plane figures (see Fig 1 and Fig 2). The Riemann Sum as the stepping stone before the idea of integral calculus is introduced were visualized perfectly using Geogebra as partitioned approximation (see Fig 3). The problem in this implementation is that the various student’ ability in using Geogebra.