Danish Professors Use Maple to Revolutionize Mathematics Teaching at Technical University

Challenge

Twenty five years ago, professors Steen Markvorsen and Poul Hjorth at the Technical University of Denmark (DTU) sought an innovative teaching tool for mathematics courses. They wanted to incorporate technology into their classrooms to better engage students and have them take greater ownership of their work.

Solution

After testing various mathematics software solutions, they decided on Maple due to its ease of use and relatively low cost, which made it easier to provide all students at DTU with access to the new software tool.

Result

Today, approximately 1,000 first-year mathematics students at the school use Maple as their primary learning tool. Markvorsen and Hjorth have used Maple to shift focus from solving problems to making learning applicable to real life applications. They agree that Maple is helping change the way students approach mathematics and creating a deeper understanding of the theory behind the mathematics. Several departments in the university have now adopted Maple and its use continues to grow.

Professors Steen Markvorsen and Poul Hjorth, both from the Department of Applied Mathematics and Computer Science at the Technical University of Denmark (DTU), believe in revolutionary and innovative ways of teaching, and have used technology in their classrooms for the last thirty years. They’ve been teaching with Maple for 25 years - long before computer technology was embraced in education. Wishing to teach mathematics in an innovative way, they looked into using a variety of different mathematics software. They found that Maple was a great fit - easy to use and cost effective such that the software could be made easily available to all students at DTU.

“Initially, there was some resistance to the new way of teaching and learning because using computers was new,” says Markvorsen. “Now students have adopted it as a way of learning.” Students learn how to use Maple right from the start, using worksheets from the very first week, and continue to use it heavily for the first two semesters. They complete exercises and homework using Maple, and then upload their solutions. Teachers then access these using the campus server to grade assignments and provide feedback.

Currently, at DTU, Maple is the primary tool in the first year mathematics course for about 1000 first year students, covering courses such as Calculus, Linear Algebra, and Geometry. “There is normally a spectrum of competencies when students enter university, so the first few weeks are spent on an overview of core competencies in mathematics,” explains Markvorsen. “Maple is used heavily at this time to learn concepts such as complex numbers or geometry in the complex plane, which are new to most students, but at the same time induce a natural repetition of the elementary high school mathematics. Students use Maple to build their expertise in more advanced math problems through their first year in the university.”

*Figures: Steen Marvorsen uses Maple to develop an intuitive proof of Euler’s theorem for the normal curvatures of surfaces*

At DTU, students use what Markvorsen calls the ‘ownership principle,’ where students are more involved in and take ownership of what they are doing. “Maple is helping change the way students approach mathematics problems by shifting students’ focus from simply solving a problem to a deeper understanding of the theory behind the mathematics,” says Markvorsen. “They can see the fundamentals of mathematics and the intermediate steps before arriving at the final results - this helps them understand the concept and then move into more complex problems. Learning then becomes more interesting than just getting the right answer.”

Markvorsen also encourages experimentation and play using ‘what if’ scenarios. He believes that students are able to learn more by experimenting themselves, also a part of the “ownership” principle. “Learning in Maple, it is easy to relate mathematics to real life applications,” he says. “This allows students to experiment freely and understand how concepts can be applied in a future career or in an engineering problem they are currently dealing with. This is a very important part of learning, and is a real bonus in Maple.”

When they move on to more advanced math courses, and to their engineering and technical programs, students view the use of Maple as an extension of its use in the first year. Other departments such as Mechanical and Chemical Engineering are also using Maple, and Maple is being rolled out to other programs across DTU.

Hjorth feels that Maple enables teaching in a way that was not possible 20 years ago, and students learn using new and innovative problems that are solved easily in Maple. “Some features in Maple are outstanding,” he says. “Its graphing capabilities are excellent. Students can quickly draw accurate plots and graphs, and they understand many concepts which would otherwise have been difficult. For engineering students, the mix of math and engineering concepts in Maple is an advantage.” “Our aim is to shift focus from solving problems to making learning applicable to real life applications,” concludes Markvorsen. “Maple helps tremendously in that. It makes students aware that they are not done with mathematics when they are done with high school, and that mathematics has far greater and deeper impact - not the least in real life applications.”

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