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Motivation In the mid-90's, the CU-Boulder Applied Math Department attempted to teach Mathematica and Calculus at the same time in order to increase student understanding of Calculus; however, students were simply overwhelmed. As a result, a faculty-student project was begun to create some simple and effective software tools to help students visualize concepts in Calculus and Differential Equations. SUN Microsystems' Educational Services lent their support to this academic initiative and offered Java training to those involved; this partnership flourished and eventually led to the development of the Mathematics Visualization Toolkit (MVT), a collection of Java applets that were designed and created jointly by CU faculty, graduate and undergraduate students. Approximately thirty students (including several Korean exchange student interns) will have participated in this project by the end of this summer.
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Background The department of Applied Mathematics at the University of Colorado at Boulder is responsible for teaching Engineering students. Our students are highly motivated and very hardworking. A goal of the software was to have the students "play" and by playing learn that some Calculus concepts reoccur. For example, finding Riemann sums, lengths of curves and volumes of solids of revolution are essentially the same task.
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Learning Activities MVT is designed as a supplement to what happens in the calculus classroom. It is designed to allow the faculty and students to explore math concepts without a huge investment of their time. Connecting with students is a key to motivating learners. A goal of a good teacher is to motivate the students to learn on their own and MVT facilitates this.
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Impact of Use on Teaching and Learning The MVT project not only helped to solve the original problem but it led to a number of related benefits. The undergraduate and graduate students who became involved in the project learned a lot about real-world math and computer science applications and became thoroughly engaged in their learning processes. They had opportunities to incorporate their software design, numerical analysis and programming skills in a challenging and professional environment. They took ownership in the project and developed a sense of pride in the outcomes, especially upon hearing other students declare how much they enjoyed using MVT. In addition, the experience that they gained in working on the project and in collaboration with SUN Microsystems has led to a number of job and graduate school offers from interested parties in technology, industry and academia. Altogether, this has been a very fruitful example of student and faculty collaboration and academic/corporate partership. Learning Assessment is one of the things that we still need to do. There is a national dialogue that is currently taking place and the Department of Applied Mathematics at the University of Colorado-Boulder wants to participate in the discussion.
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Tips for Teaching One of the goals of this software project was to empower students and teachers. MVT is a mathematics supplement that was designed to be "sticky," i.e., to draw people back to it for continued use. We want students and faculty to play with MVT and learn some of the key ideas from the Calculus. Investigation is one of the primary features that MVT affords to both students and faculty. As students use the resource, questions for further investigation naturally arise.
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Reflections Having students who are well trained in mathematics and computing working on a multigenerational project is very exciting for all of the participants: graduate students, undergraduate students and faculty. The MVT team recently packaged its first set of 1000 CD's and distributed them to teachers and students both at CU and beyond. Students like the functionality of MVT but they also want enhancements that help them play with the material that shows up in our vector calculus courses. For this summer (2005), we have plans to do some further work in the areas of vector calculus and differential equations. A future hope is to have MVT included with a Calculus textbook(s) so that more students will be able to benefit from the project. We also hope to expand MVT and develop it into one of the premiere teaching aids in mathematics. The effort expended by faculty and by students on the MVT software project is significant. As Departmental resources have been taxed by other needs, we are actively seeking additional funding to help us sustain this unique effort. We welcome inquiries from interested parties.
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