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| Department of Mathematics |
| Technology | Group Projects | Writing to Learn | Undergraduate Research |
From calculus I to advanced calculus, in linear algebra and modern algebra, and in all other courses in the curriculum, the goal of the professors at Grand Valley is to engage students in mathematics in and beyond the classroom. We are a department committed to excellence and innovation in instruction, and this page aims to describe some of the ongoing efforts of faculty and students.
The incredible power of the technology of handheld calculators and desktop computers has made many new learning tools available to students. Through the use of such computational devices, students at Grand Valley have the consistent opportunity to explore mathematics and make conjectures in the classes they take. In addition, calculators and the computer program Maple enable students to see powerful results in difficult problems that may be inaccessible by hand. Especially in calculus, faculty makes extensive use of laboratory assignments designed to allow students to make key discoveries independently. Such hands-on work in the classroom is one important way that students are actively involved in the learning process. To see examples of some of the activities students engage in that use technology, check out our Calculus Archive, especially the various Lab Activities that are available there for Math 201 and Math 202.
Several faculty have also grown interested in ways that technology can be used to improve the learning of mathematics beyond calculus. In some classes, such as linear algebra or differential equations, this may involve extensive use of Maple. Other classes integrate even more specialized software. Dr. Paul Fishback has been active in the mathematics community in promoting the program F(z), a package specifically designed for the study of functions of a complex variable. In addition to using F(z) in his Math 402 course, he has also developed a web page devoted to resources for teaching complex variables that includes information on a variety of technology-related approaches.
Java applets are yet another marvelous technological tool that can assist in the demonstration of deep mathematical ideas. Many of us have become involved in using laboratory activities centered on applets; most of the applets that we use are creations of Dr. David Austin. You can check out some his work in this area at Calculus Demonstrations or Java Demonstrations; a must-see for every linear algebra teacher is his grid applet, which shows the effects of a linear transformation on a grid in the plane, and the dynamic way this changes when one alters entries in the matrix of the transformation. Links to many of his applets are collected here.
Group projects are another means by which students may deepen their understanding. These assignments often demand significant independent study and investigation, and result in impressive reports and written work. In recent years, some instructors and students have used the web as a means to publish their work in these projects. Currently available for viewing are projects from Math 341 (Euclidean Geometry) course, and Dr. Ed Aboufadel's special topics class on The Enigma Machine.
Faculty at Grand Valley also strive to show students genuine applications of mathematics. Through courses in linear algebra, Dr. Aboufadel and Dr. Steve Schlicker have engaged many of their students in projects on wavelets. This powerful mathematical tool finds applications in fingerprint compression for the FBI, as well as other types of audio and data compression, and is used in a wide range of disciplines from music to geology. In addition to the projects available at the previously noted link, these professors' curricular developments in the area have led them to author a textbook, Discovering Wavelets, which will be published in late 1999. The book is designed for an undergraduate audience through a problem- and project-based introduction to the ideas in linear algebra that lie behind wavelet analysis.
The group projects at some of the noted sites above demonstrate another important aspect of mathematics at Grand Valley: many courses involve extensive writing to explain the mathematics being studied. Writing to learn through group projects, in-class assignments, and even daily homework, is an attribute found in many instructors' courses. Beginning in calculus I, students are encouraged to strive to communicate their understanding in complete sentences with the meaning of their work explained; through such work, learners find that they are expected to do far more than simply manipulate the symbols of the subject.
In addition to using writing as a learning tool in calculus and other courses, the department offers a specific course focused on mathematical writing, Math 210 (Communicating in Mathematics). This unique course is designed as an introduction to abstract mathematical reasoning, as well as to the particular skill of proof writing. The course carries a special SWS designation (supplemental writing skills) that informs students beforehand that extensive writing assignments will be a part of the course. Through in-class critique, review of journal articles, submission of proofs in draft form, and other approaches, students are introduced to the subtle complexities of mathematical writing, as well as prepared for future courses in the major. Another useful resource is Dr. Ted Sundstrom's Guide to Mathematical Exposition, a collection of suggestions for writing well that he uses in when he teaches Math 210. In fact, Dr. Sundstrom's long-standing efforts in developing curricular materials for this class have led him to write a textook, titled Mathematical Reasoning and Writing, published by Prentice Hall and is in use here and at other universities and colleges.
Several faculty have also experienced extensive involvement in undergraduate research. Grand Valley has won a continuing National Science Foundation grant as a Research Experience for Undergraduates site.(See the REU page for details.) Undergraduate research has also often been funded by the Student Summer Scholars (formerly Summer Undergraduate Research Projects in the Division of Science and Mathematics). In all of these projects, students work closely with faculty over an entire summer, getting a significant stipend to conduct their mathematical investigation. These efforts can extend into the coming school year, and have resulted in student presentations at national conferences, as well as publications in various journals. Descriptions of some of these projects are available for the interested reader to review. The department has a strong desire to engage more students in such activity and faculty will continue to invite students to participate in these sorts of projects.
Recently the department began a multi-year project to include activities from the National Science Foundation's exemplary K-12 curricula in our core curriculum. View more about this project here. The goal is to make the courses more relevant to our preservice teachers and to all students taking the courses.
Whether in a project in an introductory calculus course, or doing advanced work in an undergraduate research project, the goal of faculty members remains constant: engaging students in hands-on study of mathematics with an emphasis on developing understanding of the beauty and power of the discipline. The above examples are just some of the interesting things happening in the department; to learn more, any interested person can simply ask a faculty member.