Calculus & Technology: Conceptual Explorations and Applications
Kellie Keiser, Lehigh University, United States
Lehigh University . Awarded
Graphing calculators made their first appearance in classroom settings in the early 1980's and have grown to have a valuable place in the instruction of mathematics. The technology has advanced to a point where the calculators are more similar to software programs that have been available on the computer, but are far less expensive compared to the price of a computer and the accompanying software. Many experts in the field of mathematics education advocate the use of graphing calculators. In fact, the National Council of Teachers of Mathematics (NCTM) advocates the integration of graphing calculators into the classroom beginning at the elementary school level.
One of the areas of concern with the implementation of lessons in the classroom using graphing calculators is that not all instructors share the same pedagogical view on how the graphing calculators should be used and, therefore, do not use the graphing calculators in the same manner. Since there are no standards for implementation, graphing calculator usage is varied from classroom to classroom. It has been shown in studies discussed in this document that student performance in mathematics is linked to student ability to model mathematical situations graphically, numerically, and algebraically. With this in mind, the graphing calculator activities Exploring the Relationship Between Average and Instantaneous Rates of Change with the TI- nspire CX Handheld and Exploring the Relationship Between Derivatives and Integrals with the TI-n spire CX Handheld were created to help students discover two major concepts in Calculus, the derivative and the integral.
The results presented in this document represent a small sample of students taking an introductory college- level Calculus course. Although results appear to indicate that student competency in graphical, numerical, and algebraic modeling, as well as technological competency, may be linked to student success in the graphing calculator lab activities, more research on a larger sample group of students will need to be completed to substantiate the results. In informal discussions with students while they were completing the lab activities, many of the lower-performing students attributed their inability to complete the labs without assistance based on the fact that they were initially unable to link the graphical, numerical, and algebraic representation together to draw the correct conclusions. When students had completed the labs and results were discussed as a group, this lower-performing group was able to see the connections between the different representations and was able to understand the concepts that were being explored.
Without the use of a graphing calculator, explorations like those presented in this document would be very difficult to implement. The graphing calculator allows students to perform computations that would require a great deal of time and would detract from the overall purpose of the labs. In addition, the data collection features on the graphing calculators allow students to explore data in the world around them, allowing them to make mathematical connections by focusing on topics that are important and meaningful to them. The graphing calculators not only carry out mathematically difficult computations, which are often time-consuming, they also allow students to easily represent data graphically, numerically, and algebraically. As the graphing calculator continues to make its way into the mathematics classroom and students are able to explore mathematical models in multiple representations, researchers are optimistic that student performance in mathematics will continue to improve.
Keiser, K. Calculus & Technology: Conceptual Explorations and Applications. Master's thesis, Lehigh University. Retrieved February 22, 2019 from https://www.learntechlib.org/p/120178/.
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