February 11, 2013

Linear Algebra and Vector Geometry – Not Yet Fun and Games

This text was initially published by Profweb under a CC BY-NC-ND 4.0 International licence, before Eductive was launched.

Within the catalog of the Anglophone sector at Cégep à distance, the mathematics course Linear Algebra and Vector Geometry (201-105-RE) has been one entry that has loomed menacingly for many of those required to take it. The course is part of the Humanities with Mathematics program and is a prerequisite for access to university programs in Business Administration. The challenge for the course’s developers and tutors was to make it interesting for students in Humanities, given that the content is rather abstract (you can easily make a very theoretical course) and the main applications of the principles presented in most manuals are in engineering and computer science.

You have to go through this whole formal process of course development where you design from the final exam backwards.

From the start, the priority of the design team was to find linear algebra and vector geometry applications in the various fields of humanities or to make them relevant to everyone’s daily life in order to generate interesting and even fun (yes, you read that right) scenarios. This Linear Algebra and Vector Geometry course, however, has had several technological and pedagogical challenges, only starting with the motivation of students. Our content experts, Stephen Newbigging and Mike Besner of Vanier College, showed great creativity in this regard, and students now have the opportunity to hone their math skills on behalf of auto workers, adventure sports entrepreneurs or Egyptian tomb raiders. There are numerous examples related to student interests which provide training opportunities and encouragement to produce regular summaries of the content of the lessons. Contrary to popular belief, mathematics achievement is not innate: it is closely related to the time put into it!

Information technology should also make the course more enjoyable. Videos featuring the content experts demonstrating methods of problem solving are available on the course website (watch for our presence at the Emmys next year!), and online exercises are available on the WeBWorK platform, recently installed at Cégep à distance. WeBWorK is an Internet-based system for generating and delivering problems to students.

How to recognize eigenvectors in matrix transformations

How to use Cramer’s rule

Its advantages include immediate feedback, in the form of hints as well as complete solutions, and the possibility of allowing several attempts to answer a problem. WebWork is used by many colleges and universities in English-speaking Canada and the United States, including Vanier College in Montreal, where our content experts teach. Several articles about WebWork have appeared in Profweb. As with all Cégep à distance courses, there is an online study guide available to students which explains all aspects of the course in great detail.

Good courses incorporate technology when it will help learners master the material. Good courses take the needs of their students into account.Both Stephen and Mike, our content developers, felt that the rigor of the true competency based approach to education at Cégep à distance changed the way they think about all of their courses. As Stephen put it, You have to go through this whole formal process of course development where you design from the final exam backwards. In traditional math instruction, you tend to have a body of content that you cover, and then you test what you taught. Both teachers recommend the competency based approach because it can make you more aware of the logical flow of your teaching. I’m sure we can all remember taking tests as students that had little to do with the material that the teacher taught. That does not happen at Cégep à distance.

In terms of evaluations, our technological ambitions were hindered by an important obstacle, symbolic mathematical language is not always easy to communicate in electronic documents or by internet and requires a lot of effort not related to the subject on the part of students doing assignments, this is why we chose to use course option 75 (paper assignments). Currently we have various solutions for everyday communication with the tutor such as taking a picture of the problem, using an online “electronic whiteboard” (eg. Twiddla) and, of course, that old standby – paper and the mail!.

In conclusion, we realize that although technology can provide many advantages in education, it remains just a tool. Good courses incorporate technology when it will help learners master the material. Good courses take the needs of their students into account and good courses evaluate the material that has been presented in the course in a fair and balanced manner. Even if this course does not make you love mathematics, if it can make you laugh and even occasionally make you say “wow”, while making the concepts that you are being evaluated on easily understood, we at Cégep à distance can feel that the enormous amount of work that has been put into bringing Linear Algebra and Vector Geometry to life for our students has been worth the effort!

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