Developing Resources for Student Success in Online Linear Algebra at Carleton University, Ottawa, Ontario
In 2013, Dr. Kevin Cheung, Associate Professor in the School of Mathematics and Statistics at Carleton University in Ottawa, Ontario, Canada was looking for strategies to improve his face-to-face course in Linear Algebra. The particular challenge of the course was the diversity of knowledge and skills among students, as those taking the course were mostly from life sciences rather than mathematics, physics or computer science.
Dr. Cheung was considering the use of technology and his discussions with the Director of the School and his Dean led to a connection with Patrick Lyons, Director of Teaching and Learning, who recommended a pilot using online learning.
With the support of an instructional designer from Teaching and Learning, Professor Cheung redesigned the face-to-face course for online delivery, with the course launch in Winter 2014 term.
The initial design of the pilot included weekly quizzes, as well as mid-term and final exams, but no homework due to concerns about collecting the homework and ensuring it originated from each designated student. Student results from the pilot course were comparable with those of students in the face-to-face class and the pilot was considered successful.
After this first offering, with the help of Ontario government funding for the redevelopment of online courses, a number of new approaches and resources were added to the design. Data from the pilot indicated students waited until the last minute to complete the quizzes, rather than using them as tools for learning.
To counter this, students now complete two weekly quizzes. The first quiz contains basic rather than challenging or complex questions based on that week’s topic; students are required to achieve a grade of 70% on this first quiz before they can access the second, more comprehensive, quiz. In addition, students are allowed five attempts at both the basic and more comprehensive quizzes, with the system recording the highest marks achieved. This strategy encourages students to repeat exercises for better understanding and mastery – and to earn higher marks.
Another realization from the pilot offering of the course was mid-term exam results were lower than expected. To counter this, homework is now part of the online resources. Students enter digits from their student numbers to generate homework exercises – with each assignment using different numbers in the problems so students have to complete their own work. This process was recently improved to simplify student access to the homework exercises. Students can also get the solutions to their specific question sets once they submit their assignments, offering further tools for analysis of their strengths and gaps.
In Winter 2015, a further innovation was introduced to generate examples and exercises based on student requests, especially in areas of learning difficulty. These are personalized assignments in that random sets of numbers are generated in each example so students can develop and verify their understanding through numerous exercises applying appropriate mathematical principles. Student response to this tool confirms its usefulness as they ask for more and more examples.
The overall course structure is built around weekly topics, featuring 7 – 10 short videos interspersed with easy questions provided for student practice rather than assessed for marks. Teaching Assistants lead weekly tutorials, in-class or synchronous online sessions. Student choose which style of tutorials they wish to take.
Dr. Cheung made his course notes available to other Carleton professors who teach this course; each of them prepares individual videos and quizzes. Students use the course notes and are not required to buy a text. The final exam is the same for all sections of the course regardless of the style of delivery.
Benefits and Outcomes
Dr. Cheung reports that, although withdrawal rates are higher in the online course, final grades achieved are comparable to those in face-to-face classes. His experience demonstrated online learning does not work for everybody; it offers advantages to many and should be continually available to students.
In a pre-course survey, some students report a preference for online learning, many due to scheduling conflicts while others feel they learn better.
The data logs for online quizzes show the number of student attempts at questions and provide insight into their difficulties, allowing for faculty responses and changes in explanations and examples. Using this information for course revisions, Dr. Cheung saw a reduction in student questions posed on the course forum.
Dr. Cheung characterized working with Teaching and Learning as “a pleasure – they are there no matter what I ask them for.” He also received a Carleton University award for his work with this course – the 2018 Excellence in Blended and Online Teaching Award.
Challenges and Enhancements
The online exercise generator was developed manually, using handwritten and coded questions rather than electronically generated. If the course were to be scaled up, it would need a better platform. He is exploring options that do not depend on third-party platforms.
The provision of immediate, detailed, and personal feedback is extremely difficult, especially anticipation of problems and personalized explanation concerning specific errors and correct procedures. Extensive research and preparation of feedback are required, as well as continuous review to ensure ongoing links between feedback and student errors and needs.
The preparation of personalized assignments is very time consuming as all questions must be verified for clarity and accuracy. Having reduced requirements for traditional teaching allows time for more quality technological innovations, which is better for students.
Maintaining student motivation week after week in a 12-week course is challenging, especially with online learning, as there is no strict timetable of attendance and little peer group support.
Expectations of independence on the part of first-year students may be too high. As Dr. Cheung describes this: “it is more of a student psychology than an educational design issue. A course can be easy to work with and include accessible, practical exercises, but it is hard to provide an online push for attention and completion.”
Dr. Cheung sees the availability of online courses bringing new students to the university, often from other institutions during summer term. The offering of online courses is no longer optional but needs to be part of a college or university strategy. Carleton University has long been a leader in technology for educational delivery, moving from television based delivery to digital. He would like to see regular events for the sharing of insights and experiences among faculty using online learning and with those new to the field.
For Further Information
Dr. Kevin Cheung
School of Mathematics and Statistics
Carleton University, Ottawa, Ontario, Canada