Claremont Physics Professor Uses Maple to Teach Complex Course Material

Défi

Professor Scot Gould’s courses require students to spend a significant amount of time developing models and calculations. He wanted a tool that allows students to review materials and complete assignments with minimal time and effort.

Solution

Gould introduced Maple into his courses because it provides students with the necessary tools to complete complex problems and work through challenging course materials.

Résultat

Students have welcomed the use of Maple due to its simplicity and user-friendly interface. Gould observed that even when the option of using other tools was available, students found they were more productive when using Maple.

When dealing with courses that involve complex systems and formulas, it is essential to find teaching tools that easily handle detailed and intricate calculations, while simplifying the process to minimize time and effort for the students. This avoids costly time spent on learning how to use the tools themselves, and allows students to place greater focus on understanding the principles by working through and solving the actual problems. For Scot Gould, the level of difficulty in his courses is such that a great deal of time is spent on models and calculations. He uses Maple to deliver a variety of science courses, as Maple provides a convenient educational tool that doesn’t require students to spend valuable time and effort learning the tool itself.

A professor of physics, Gould has taught a variety of subjects in his 26-year career. He works in the W.M. Keck Science Department, a science campus associated with Claremont McKenna, Pitzer, and Scripps Colleges in California, and his courses also include students from nearby Harvey Mudd College and Pomona College. Currently, Gould is teaching within a science program called the Accelerated Integrated Science Sequence (AISS). He works with a biologist and a chemist to deliver a year-long combined course that provides potential science-major students with an introduction to all three science disciplines. The instructors use Maple to support course delivery because it offers the greatest mathematical and pedagogical value. “Maple continues to be heavily used in AISS since it provides the best pedagogical bang for the buck,” Gould said. “It is a valuable teaching tool for students who would normally not be exposed to solving real biological or biochemical problems using computers during their first year of college.”

In AISS, students work on systems that field experts typically don’t see until graduate school. Maple allows them to work through these complex problems in an interesting way that keeps the students engaged. “Maple has a low activation barrier in getting started on these problems,” Gould noted. “If a student can write a mathematical equation, they can easily visually code it into Maple. And by being able to create their own equations to model a system, they learn mathematics beyond what most first-year students cover, some computer science and the consequence of mechanisms affecting their system (i.e. the science). Maple is a great tool for integrating principles and processes.”

*Students at the Keck Science Department of Claremont McKenna, Pitzer and Scripps Colleges work through an assignment using Maple.*

Gould chose Maple after considering a number of options. Early in his career, he began experimenting with various types of mathematics software, attempting to find a tool that was both productive for solving algebraic problems, and that would require minimal effort on the part of the student. The latter was essential, as he did not want to spend a significant amount of time in his course teaching programming. Initially, Gould settled on Mathcad^{®}, but he found that his colleagues were using either Maple or Mathematica^{®} for numerical analysis in their physics and engineering research and courses, so he decided to try those solutions as well. Ultimately, Gould found Maple to be superior due to its advanced features, its stability and a programming language that was the easiest to learn. “While I saw Mathematica as a powerful product, the students told us Maple is easier to read and learn,” he said. I initially moved to Maple for upper division courses and since then, I have moved all of my courses to Maple. ”

In Gould’s experience, many professors are impressed by Maple’s capabilities when they are first introduced to it, even those who have previously used another software tool. “Other physicists have viewed my classes, seen how the students are able to easily generate vector field plots or animations of physical systems, and asked, ‘What is this software you are using?’” Gould said. “They really like how Maple expands the types of problems that can be addressed.” Gould has also noticed that chemistry instructors who typically use other tools now allow students to choose, since many students have gained experience with Maple.

Students like the simplicity of Maple, such as having the ability to modify values and equations directly in the worksheet and re-calculate values with one click, and the fact that systems with many unknowns can be solved algebraically with sufficient opportunities to input the required number of unique formulas. “I like the fact that so many problems in special relativity, quantum mechanics, and classical mechanics can be solved by the students – many more problems than one finds in a typical textbook,” he said. “We can work on real problems and not a set of synthetic examples.”

In addition to physics problems, Gould has students use Maple to solve chemical kinetics problems such as Michaelis-Menton. Rather than giving students an equation and describing the system to them, Gould starts by having the students propose models for the system using first order rate equations. “The students code into Maple, use it to solve the equations and then generate plots to see how the system evolves with time,” he said. “And if their model doesn’t make sense, they can go back and modify the equations. Our goal is to have students learn science the way scientists do science.”

Gould also recounts a course he delivered on mathematical and computational techniques for physics and engineering majors which used MATLAB^{®}. He pushed students who were headed to engineering school to use MATLAB more due to the fact many jobs use that particular tool. “Initially 12 students started with MATLAB and 12 started with Maple. By the end of the semester, all but one student had switched to Maple,” he said. “It simply was a consequence of the students realizing they were more productive using Maple.”

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