Challenge
Professor Matthew Westerhoff wanted a tool to improve his students’ understanding of mathematical concepts and to keep them from getting overwhelmed.
Solution
Westerhoff adopted Maple to create a more efficient learning environment and increase students’ comfort with the subject matter. He requires students to use it so they can gain proficiency with a computational software tool.
Result
Since introducing Maple, Westerhoff has observed improved conceptual understanding among his students. In addition, in courses where Maple is used, the average course grade and average final exam grade are significantly higher.
Using appropriate technology in the classroom can have an overwhelming impact on education. Proper digital tools can create a more streamlined learning process and enhance students’ understanding of the subject matter. This is especially true in mathematics courses, where students are regularly dealing with complex materials. Matthew Westerhoff, a professor at Northern Virginia Community College (NVCC), uses Maple to improve his students’ conceptual understanding. Maple’s many features and powerful math engine allow students to work through complex calculations and functions quickly and efficiently.
Teaching at NVCC since 2005, Westerhoff first used Maple when he was a student. His courses required him to learn basic commands and features, including plotting 2-D and 3-D functions, and calculating derivatives and integrals of complicated expressions, which were invaluable in his learning. Westerhoff’s positive experiences with Maple prompted him to use Maple in his teaching and in his research projects as well. “Maple makes work more efficient and saves time on difficult calculations,” Westerhoff said. “You can quickly complete calculations that would take hours to do by hand. At the beginning of the semester I tell my students that using Maple does three things: it helps them develop greater focus, makes them more attentive to detail, and allows them to become familiar with using a computational tool. The first two skills are critical for learning mathematics.”
Students in Matthew Westerhoff’s class work through Calculus problems using Maple.
Westerhoff uses Maple extensively in various courses, including Calculus, Linear Algebra, and Differential Equations. He requires his honors students to learn Maple so they can understand how to effectively use a computational software tool and apply it to solving math problems. “Compared to other math software, Maple handles symbolic calculations better and the help options provide detailed examples,” he said. “I like Maple because of how detailed it is when it comes to performing calculations, as well as the many available options it has for graphing functions. I also like the MapleCloud feature where users can share their Maple creations with each other.”
The graphics in Maple are something Westerhoff finds extremely useful in his classroom, as they allow him to plot systems of equations and visualize planes in three dimensions, which is very beneficial in a linear algebra course. In his Calculus courses, he uses Maple’s Riemann Sums and Volume of Revolution tutorial packages because of the interactive graphics they provide. “The tutorial packages let you choose the type of numerical integration scheme you want,” he said. “The slope fields section in the DE tools package is also an excellent tool for my Calculus and Differential Equation courses because it allows students to visualize the slope fields of the function.”
Students in Matthew Westerhoff’s class work through Calculus problems using Maple.
The first Maple assignment that Westerhoff gives his students is a tutorial on how to use Maple. The main purpose of this assignment is to get the student comfortable with using the software. It consists of commands that students have to type in and execute. Other Maple assignments consist of problems related to the topics being discussed in class that students must use Maple to solve. Some of the assignments require them to modify or tweak a Maple code to make it solve a provided problem of interest. “Most of the students enjoy using Maple, especially those pursuing careers in a STEM field,” Westerhoff said. “Many of the students tell me that once they became comfortable with Maple, they started finding and appreciating numerous benefits from it.”
Since Westerhoff introduced Maple, students are able to grasp concepts better. By using Maple, students become better prepared for handling the rigors of a course. In courses where Westerhoff’s students use Maple, the class average and final exam average are significantly higher compared to courses where students were not assigned Maple assignments. “In addition to doing better, students are getting the opportunity to use a computational tool that they will most likely use as they go further into their academic studies and into careers in industry,” Westerhoff said.
Westerhoff recently had two of his students work on a possible application of the Brachistochrone Curve. The problem involves finding the fastest descent path possible between Point A and Point B in a spatial environment. One possible application of this involves a drainage pipe. The calculation of the arc length of the drainage pipe is one of the major components needed for design purposes. Due to the complexity of the equations, Maple was used to implement and solve the customizable length of the drainage pipe which is used to calculate the approximate rate of flow. One of the students presented his work at the VMATYC (Virginia Mathematical Association of Two Year Colleges) conference. This was the first time that a student had presented their work at a VMATYC conference.
The school is planning to host a Maple Training Day to promote Maple’s capabilities and further train current users. Maple has great value, and Westerhoff and his colleagues hope to see it adopted for more widespread use at the college. “Maple has been an invaluable resource for us,” he said. “It’s beneficial to both instructors and students and we want to see those benefits realized on a larger scale.”
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