Designing and Using a Self-Paced Linear Algebra Course

After more than 10 years of teaching Linear Algebra in the traditional way and seeing students struggle with the pace of the course every single semester, we decided to develop a hands-on self-paced course, stop lecturing, and let the students learn by doing.

This decision was based on our long-term successful experience with using self-paced, instructor-assisted courses in other areas including computer programming, 3D modeling, and data analytics.

The new course is public. Any instructor can create a copy and use it as-is, or adjust it for his or her needs. The course allows students to learn actively, by reading and solving problems rather than by sitting, listening, and taking notes.

Students work through detailed interactive online coursework, and they must demonstrate mastery of each concept before advancing to the next one. Their understanding of the material is validated each step of the way by instant feedback from the software platform.

Interactive Matrix App

An integral part of the course is a Linear Algebra App which allows the students to quickly enter matrices on their touch devices, and manipulate them using elementary row operations.

NCLab Matrix App
NCLab Matrix App

Watch a short video which shows how the Matrix App is used to create the reduced echelon form of the above augmented matrix.

In-Classroom Use and Online Teaching

In the classroom, the instructor interacts with students one-to-one and helps them learn most efficiently. In remote instruction, NCLab provides the instructor with a detailed real-time overview of each student’s progress, so again s/he can assist each student most efficiently.

We have been using the course both in the classroom and for online instruction with remarkable success. The majority of the students became more engaged, they learned the material better, enjoyed the course more, and the average scores have improved by 21% compared to our prior traditional classroom instruction. In this paper we share our experience with creating the coursework, as well as with using it as a self-paced, instructor-assisted course at a tier-1 research university.

Student Testimonials

Student response to this type of self-paced instruction is overwhelmingly positive.

“Having never dealt with Linear Algebra, the format of this class has been extremely helpful in my success as a student. Being able to tackle the class at my own pace, collaborate with peers, and receive direct help from the professor in real time has been an invaluable experience.”

–Mathew Neill, student

Many more student testimonials can be found at the course page.

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