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Mathcad White Paper: Modelling Science Learning at Utah State University

    Physics department takes integrated approach to teaching and learning with Mathcad

    “The communication of ideas from one user to the next is so intuitive using Mathcad. It’s incredibly powerful, too.”

    Professor JR Dennison of Utah State University has been using Mathcad for research in surface science and physics of materials for more than 15 years. With half a dozen students, his current research involves electron emission, amorphous materials and absorption of rare gas atoms on carbon. Over the last few years two of his students used Mathcad to carry out all their calculations for their theses.

    “Mathcad version 2 caught my eye in 1986,” Dennison recalled. “I loved the fact that it combined active math and documentation in the same place. It’s really what you see is what you get. The communication of ideas from one user to the next is so intuitive using Mathcad. It’s incredibly powerful, too. One of my master’s students wrote all his calculations in Mathcad. They took quite a while to number crunch, because they were so extensive, but very little time to write up and debug.”

    And that’s just the tip of the iceberg…

    “We use Mathcad in our department in a fairly structured and coherent way. All physics majors, including those studying to become high school teachers, learn Mathcad in a sophomore level course called ‘Introduction to Scientific Computing.’ It’s a three credit hour class, and almost all of that time is devoted to working in Mathcad. Our goal is to provide them with the “tools of the trade” early in their academic career, so they can hone them in subsequent upper division coursework and undergraduate research.”

    The course originated with a statewide call for proposals for distance learning models in 1995. Dennison and longtime collaborator, Professor Mark Riffe, garnered a Utah Higher Education Technology Initiative Grant with their proposal.

    “Originally, the material was targeted at the Algebra-based level for high school teachers, but it quickly became apparent that the course was well suited to our majors, too.”

    The course combines fundamental problem solving methods with physics principles in worksheets collected as a Mathcad E-book. In 1997, the course using the E-book was adopted as a requirement for all physics students.

    “Now we’re starting to get interest in the course across campus – in computer science and engineering. About a third of the students are from computer science. It’s one of a couple classes Computer Science students can use to fulfill their high-level programming requirement. In Scientific Computing they have a chance to play with the math. It’s an excellent experience for them, and we get a lot of positive feedback.” The course is now taught three times a year, more than any other course offered in the physics department.

    One former student who ended up at ATK Thiokol Propulsion said that they develop their extremely sophisticated numerical code in Mathcad, using it as a computational ‘bread board’; they make everything work in the Mathcad environment first, before moving over to FORTRAN or some other high speed language. Dennison says, “The time they save in development is well worth coding it in two different languages. Computer Science students taking the Scientific Computing course get a similar ‘bread boarding’ experience.”

    Once students complete the Scientific Computing course, they’re ready to use Mathcad in other classes in the Physics department.

    “We use Mathcad in a course called ‘Introduction to Wave Phenomenon,’ a sophomore/junior level course, which is really an excuse to teach mathematical physics, including an introduction to numerical methods, symbolic math, differential equations, matrices, and complex analysis. Student evaluations rate the Mathcad component as one of the very best parts of this challenging class.”

    Students are also exposed to other Mathcad intensive resources to enhance their learning. Dennison says, “We make particular use of the Mario Ancona book, Computational Methods for Applied Science and Engineering: An Interactive Approach and Visual Electromagnetics with Mathcad by Keith W. Whites; they dovetail nicely with the mathematics that we introduce in the Waves course.”

    Use of Mathcad is extended in other upper division classes, particularly in the upper division lab courses. Most instructors in upper division classes such as Electricity and Magnetism, Classical Mechanics, Optics and Thermodynamics assign problems expecting students to have Mathcad skills at their disposal. Dennison notes, “The numerical and symbolic capabilities dramatically extend the level of sophistication of problems that can be treated, bringing the coursework much closer to complex real-world problems.”

    In addition to faculty, graduate students, and undergraduates, Professors Dennison and Riffe have turned local secondary school teachers on to Mathcad. Each year, they lead the Physics Department in an Amusement Park Physics outreach program called USU Physics Day at Lagoon.

    “We started it 14 years ago, and now we average over 5,000 high school and middle school students at the annual Lagoon Day event. A key part of the extensive amusement park physics curriculum we’ve developed for local middle and high school teachers, to use before or after the event, are Mathcad simulations of marble roller coasters, playground equipment, and amusement park rides. Physics Day has turned out to be a fun and popular activity and a great way to maintain contact with teachers. The whole department participates, including a majority of the faculty and a bunch of students.”

    Sponsors include Boeing, Clark Planetarium, Dupont Holographics, Mathsoft, the Navy, Raytheon, S&S Power (a roller coaster builder), ATK Thiokol Propulsion, Rocky Mountain and Idaho NASA Space Grant Consortiums, and Utah State University. The event is run jointly with the Idaho National Energy and Environmental Laboratory.

    Dennison notes that their outreach program, both the Lagoon Day event and in-service training done during the summer, have encouraged a lot of physics activity in the local schools.

    “A teacher at one nearby school told me, ‘If I can announce over the intercom that the Physics students are going to Lagoon, I’ll double my enrollment. And I can’t teach ’em physics unless they sign up for the class.’ That school has gone from one part-time physics teacher to three full-time physics teachers over the last fifteen years.”

    In fact, Utah State has a very rigorous teacher education program that involves future teachers in science activities at the department level. “The program is excellent,” says Dennison. “The physics teaching majors and even composite science teaching majors really know what they’re doing. All physics instruction for the future teachers is going on in the Physics department rather than in the education program. So, all education majors are active in the department and get involved. In fact, there’s a lot of cross-over between physics majors and physics teaching majors, until they finally decide what direction to take.”