Using a Companion Web Site to Enhance Learning
in a Numerical Methods Course
By Nora Strasser
Wichita, KS 67213
(316) 295 – 5879
fax: (316) 295 – 5404
While teaching Numerical Methods, I realized that the students in the course were learning to program, but they weren’t using the current technologies for anything else. In fact, many students struggled with the computer programming and that became the focus of the course. I wanted to find a way to refocus the course on the mathematics and still provide students with the opportunity to explore many of the methods using computers. Since the course Numerical Methods exploits the relationship between Mathematics and computers, I thought that having a companion web site would enhance student learning.
The companion web site was developed so that students could experience interactive learning about Numerical Methods. It was also developed as an easy way to distribute Mathematica notebooks to the students. It was relatively easy to develop a web site that met these two goals by using Blackboard. These two aspects of the web site also led to the increased emphasis on the mathematics involved.
General Web Site:
The web site consisted of several pages that students could access. These pages included: Announcements, Syllabus, Faculty Information, Assignments, and Course Documents. The Announcements page automatically opened whenever a student entered the site. This page contained any current information that students needed to know about the course and assignments.
The Syllabus page contained information that was normally included in the hard copy of the syllabus that was handed out on the first day of class. The topics included course policies, grading, and outcomes. Students could also download and print a complete copy of the syllabus in case they had lost theirs.
The Faculty Information page contained information about the instructor of the course. This information included the instructor’s name, title, office location, phone number, email address, and picture.
The Assignments page contained the assignments that related to the use of the web site and their due dates. Most of these assignments directed students to the Course documents page. The assignments included running Java Applets, and using the Mathematica notebooks.
Finally the Course Documents page contained links to the Java Applets and Mathematica notebooks that students needed to use to complete their assignments. The Course Documents page was arranged by topic. By choosing a topic, the student was taken to a page that contained the links to the various Java Applets associated with that topic and to the Mathematica notebook associated with that topic.
The java applets were used to provide students with the ability to interact with Numerical Methods on the web. Most of these allowed students to change various aspects of the problem and see what happened. These applets usually provided a geometric interpretation as well as a numerical one.
Instead of writing new applets, the applets included were found using a search engine. One of the best search engines on the web is Google.com. By putting in key words, a java applet demonstrating a particular method could be found. For example, if you wanted to demonstrate the Secant method you could use the key words, java, applet, and secant. Several applets were usually found and then the best or the one that provided the insight that was needed could be used. Sometimes there were several links for one topic. The difficulty with linking to these sites is that they needed to be constantly checked to make sure that these sites still existed.
The Mathematica Notebooks were written to allow students to use the Mathematica Programming language to explore each Numerical Technique. Each notebook contained a description of the Numerical Method used, an example, an assignment, and a program. The students were required to do the assignment using and modifying the given program. Mathematica is available for student use on the computers in the Friends University computer lab. Students needed to use these computers to run the Mathematica notebooks and do their assignments.
Students benefited from having the companion web site. Many students commented that they were better able to understand the methods due to the enhanced visualization provided by the Java Applets. The traditional classroom emphasizes the students’ ability to actually use these techniques. However, the understanding of how and why a method works is usually not emphasized. The Java Applets allowed students to gain a deeper understanding of how and why the methods work.
The Mathematica notebooks allowed students to investigate the solution of problems using numerical techniques without the extensive programming knowledge that is usually required. Students at Friends University are introduced to Mathematica in their Calculus courses, so they are already familiar with the language. In order to investigate the Numerical Techniques, all they needed to do was modify the existing program. The emphasis can be placed on the mathematics involved instead of on the programming skills.
For an introductory Numerical Methods course, the combination of a traditional classroom setting with the advantages of a companion web site worked well. Students in the class could concentrate on the mathematics involved. The java applets helped them to understand how and why the methods worked. While the Mathematica notebooks provided students with the opportunity to investigate methods on their own. Even students lacking in computer programming skills were able to succeed in this course and understand the Numerical Methods.