Learning with technology
Technology provides us with exciting new ways to teach and study mathematics. In the last half century, advances in computing have completely redefined the way we collect, compile, and analyze data. Problems that may have taken days to calculate by hand in the past can now be solved by computers in a matter of seconds. Interactive software such as GeoGebra also gives us new ways to illustrate mathematical knowledge. I used this program to create a lesson entitled Using Riemann Sum and Integration to Find the Area Under a Curve, which can be downloaded using the link below. Integration is often taught using the concept of Riemann sums; this GeoGebra lesson enables us to look more closely at how Riemann sums can be used to approximate the process of integration. Sliders used to control parameters in the lesson allow students to experiment with the number of rectangles under the curve. Students should be able to see that dividing the area into smaller shapes will give an answer that more accurately reflects the one found by integrating, which should lead to a more intuitive understanding of the integration process.