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Mathcad in the Chemistry Curriculum
Theresa Julia Zielinski Monmouth University West Long Branch, NJ 07764-1898
Mathcad Documents and Student Learning It is inevitable that the use of symbolic mathematics software and digitally formatted classroom materials will increase rapidly. However, before we go helter-skelter down the path of translating standard textbooks into digital clones, we should reflect on how digital documents can enhance learning, improve learning efficiency, and build learning skills. Enhanced learning can mean greater depth of understanding, fewer misconceptions, and longer retention of knowledge. With digital materials authors are not constrained by page limits. Students using digital documents can be led to explore applications of chemistry that normal classroom and study time would preclude. Content can be presented using hyperlinked layers of increasing mathematical detail. Deeper understanding is fostered when students analyze realistic data sets interactively within a template or document. Visuals such as graphs can be created, modified, and examined interactively. Exploring a topic via digital interaction leads to increased retention and greater understanding of concepts. This observation parallels the success reported for active learning, hands-on–minds-on techniques. Digital documents increase efficiency of learning, allowing students to achieve high levels of mastery of concepts and techniques. By preparing model templates and documents, faculty can reduce de novo data processing, programming, and algorithm development by inexperienced student users. In a symbolic mathematics template or topical instructional document, the programing is complete and accurate. Students need not debug their own original documents, but can instead concentrate on mastering chemistry concepts through the mathematical models created by instructors. This does not mean that students should not create their own documents. Through faculty documents and templates students learn the syntax of the software and become sensitive to the elements of style in document preparation; they can then adapt the faculty created templates to their own projects and reports. As students progress by using many model documents they also gain confidence in their ability to use the software for assignments requiring de novo authoring of reports and homework. A central concern when creating symbolic mathematics templates and instructional documents is to develop students’ critical thinking skills. Perhaps the most effective ways to do this are the Socratic method and active learning. Fully devel-
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oped topical digital documents can include both. Embedded questions can focus student thinking and reflection. Requests for students to practice the concepts by interacting with the document enhance comprehension and retention. Wellcrafted exercises and mastery-level problems develop the ability to apply learned concepts to new situations and create independent symbolic documents. Finally, when students apply skills and techniques they learned from faculty-prepared documents to new problems, choosing the approach, mathematical model, and simplifying assumptions, faculty gain an excellent return on their investment in creating instructional documents. This column introduces two Mathcad documents, each of which provides a fully developed introduction to an important topic. Scott Van Bramer’s introduction to pulsed NMR spectroscopy allows students to explore free induction decay, dwell time vs acquisition time, aliasing, resolution, and signal-to-noise ratios. The document contains many practice exercises and questions that probe student understanding and promote learning. Faculty using the document are prompted to remove the graphs before distributing the materials to students. The excellent and interactive use of graphics will enhance student learning. It would also be possible to use all or parts of the document in classroom presentations. The second document, “Modeling of pH in Natural Waters”, by Sielmann, Andersen, and Keiding, develops the model for the variation of pH in the Simested River in October 1998. The document is an excellent example of equilibrium concepts applied to an environmental question. The focus is the carbonate equilibria in the river and how these translate into fluctuations in pH over time. Exercises are used throughout the document to develop and reinforce understanding. Students also learn how to iteratively solve differential equations. Asking students to participate in model evaluation and leading them to consider other system properties to add to the model fosters the development of critical thinking. The document concludes with a complete set of solutions for instructors, a good set of references, and data tables. It would be relatively easy to replicate the study at any river near any college campus. These documents require Mathcad 6 or higher. PDF files are available for those who wish to recreate the document with their preferred symbolic software platform.
JChemEd.chem.wisc.edu • Vol. 79 No. 4 April 2002 • Journal of Chemical Education
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