INTRODUCTION Representation is one of the Process Standards that the Principles and Standards for School Mathematics [4] lists as useful for obtaining and applying mathematical skills and concepts. The ability to clearly and accurately represent mathematical ideas is key to analyzing real world problem situations. The National Council of Teachers of Mathematics (NCTM) advocates that K-12 mathematics courses should incorporate all aspects of mathematical representation. One significant aspect is to "use representations to model and interpret physical, social, and mathematical phenomena" [4, p. 67]. This is fundamental to understanding the connections between concepts and applications and is the heart of mathematical modeling. The Committee on the Undergraduate Program in Mathematics (2004) [2] has recommended that a mathematics degree include a course that focuses on real-world mathematical applications. They recommend that the course emphasize all aspects of the solution process from the development of a model to the interpretation of the numerical values the process yields. Mathematical Modeling is a semester-long course at Virginia Commonwealth University that emphasizes building accurate models and analyzing model solutions. With a focus on problems that reflect real-world situations, this college course incorporates many of the NCTM (2000) guidelines on the development and use of mathematical models. To meet state certification requirements, this is a required course in the degree tracks for pre-service middle and high school mathematics teachers. Each semester, the class is also comprised of students preparing for careers in operations research, engineering, or other mathematics-related fields. This diverse population provides for a dynamic learning environment and an opportunity for all students to realize the importance of mathematical modeling to a variety of career paths. To present students with a more accurate picture of the role technology plays in modern applications of mathematical models, student versions of state-of-the-art software play an integral role in our course. This use of technology adds its own set of challenges to course instruction, however, and previous offerings of the course have shown that emphasis unintentionally shifts from the modeling process to software specifics. Certain subgroups of the student population tend to have more difficulty with the technical aspects of working with software programs than others. For example, in our experience pre-service teachers tend to exhibit higher levels of computer-related frustration than Engineering majors. With an interest in keeping the focus of our course on the important aspects of the modeling process, we designed a series of video tutorials to help students master the software details (i.e. the entry locations for numerical values, the steps to perform a certain function, etc.) that must be understood before they can successfully use the software to develop mathematical models. The modeling course, the video tutorials, and an assessment of the usefulness of the tutorials are described below. We hope that our work will inspire others to design tutorials for courses in which software plays a significant role and there is a need to get students up-to-speed quickly on the technical details of how to use a software tool. MATHEMATICAL MODELING COURSE The textbook for the course is Spreadsheet Modeling and Applications - Essentials of Practical Management Science1 [1]. As the title reflects, a spreadsheet software program - Microsoft Excel - is the tool used to develop mathematical models. The course is taught in a computer lab where all class presentations, examples, and assignments take place with the use of technology. Each student has access to a computer for the entire class period. Occasionally the instructor uses Microsoft PowerPoint presentations to highlight important aspects of the mathematical content being covered in a class session. …
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