The use of technology and visualization in calculus instruction.

摘要

This study was inspired by a history of student difficulties in calculus, and innovation in response to those difficulties. The goals of the study were fourfold. First, to design a mathlet for students to explore local linearity. Second, to redesign the curriculum of first semester calculus around the use of technology, an emphasis on visualization, and the use of local linearity to introduce the concept of the derivative, while delaying formal limits until later in the semester. Third, to design a framework to assess learning outcomes on the derivative. Fourth, to assess the impact of the course on the learning and attitudes of students. The study also aimed to assess the impact of learner characteristics, the role of technology, and the role of visualization, as they related to learning and attitude outcomes.;The development and justification of the local linearity mathlet, the redesigned first semester calculus curriculum and the framework to assess derivative proficiency are reported. A mathlet is a computer application typically accessed over the internet which allows exploration of a specific mathematical concept. Students in this study developed a robust knowledge of the derivative as measured by the framework. Overall they demonstrated facility with stating definitions, finding the derivative and tangent lines, determining non-differentiability, and optimization. They demonstrated these proficiencies in multiple representations. Prior knowledge in rate and slope as well as proficiency translating between mathematical representations were significant determinants of eventual calculus proficiency. Spatial ability and prior knowledge of function were weaker predictors. There was clear evidence that the use of mathlets and graphs had a positive impact on student learning, and students were very positive about their use in this course. They experienced minimal changes in attitude regarding mathematics and technology in general, except for visually oriented students, who had very positive changes in attitude. The students in the experimental group were significantly more positive about their experiences using technology to learn calculus than students studying calculus with a traditional curriculum and labs using Maple which were not discussed in lecture.