Dr. Steven Furino, Assistant Dean for Online Studies in the Faculty of Mathematics at the University of Waterloo wanted to provide students with access to flexible and engaging courses, resources and opportunities to practice mathematics online.
To achieve this goal, the University of Waterloo partnered with DigitalEd, a local software company, to develop a new content authoring and deployment tool for science, technology, engineering and math (STEM) subjects called Möbius.
Until recently, rendering mathematics on the web was a challenge. Beyond the problems associated with mathematical exposition, teachers were limited to asking multiple choice questions or questions with numeric answers. Dr. Furino wanted a platform with the ability to execute a variety of interactive questions and problem-solving formats that could be used at every level of university mathematics.
Thanks in part to Möbius, the University of Waterloo now has over 60 fully online mathematics courses, and has launched a Financial Analysis and Risk Management online degree.
Möbius is a platform for creating and delivering online STEM courses, including lessons, interactive learning activities, hands-on exercises and assessments, both formative or summative for grades, integrated directly into the University of Waterloo’s learning management system (LMS), D2L’s BrightSpace.
Utilizing the Möbius platform at the University of Waterloo sparked innovation in three ways: pedagogically sound deployment, technically sophisticated delivery for teaching complex STEM subjects and novel administration practices.
The online STEM courses are designed and created as a team effort, involving the subject expert (faculty member) and staff at the Centre for Extended Learning (CEL), which includes Online Learning Consultants, Developers, Quality Assurance/LMS Specialists, Copyright Specialists, Digital Media Developers, student support and Project Managers. Many CEL staff have a STEM background. This team effort allows for the deployment of sound pedagogical and quality practices when creating STEM courses with Möbius.
As Dr. Furino puts it, “you only learn mathematics by doing mathematics”. Möbius can ask sophisticated questions and ask for sophisticated answers beyond multiple choice. It has the capacity for formula input, sophisticated 2D and 3D plotting, free-response questions, creation and interaction with free-body diagrams, geometric inputs, interaction with graphs, algorithmic questions and adaptive questions.
STEM courses have their own requirements when it comes to assessment. Teaching by testing gives students the opportunity to practice important concepts by interacting with problems and solutions, and testing their understanding by answering questions that are graded instantaneously. Throughout the entire lesson, students remain actively engaged with the narration, visualizations and interactivity and receive constant feedback that helps to solidify their understanding of the course material.
To see an example of content built in Mobius visit: https://open.math.uwaterloo.ca/
Student practice for matrix multiplication. Algorithmically-designed free response question.
- When users click "How Did I Do?", they see customized feedback.
- Users can click "Try Another" once reviewing the feedback to generate a new set of values and try the question again.
- Although not evident in this example, the math engine is calculating the correctness of students' responses.
Möbius’ high-powered engine drives sophisticated STEM questions and answers. This engine, in combination with interactive applications and powerful assessment features, provides students with an abundance of instant and personalized feedback.
There are 15 different STEM-focused question types, the ability to design questions algorithmically (meaning you can create a single question and the software generates different values for the same type of questions so students can attempt the same question multiple times with different values), and adaptive questions that provide students with custom paths through questions and assignments based on their current level of understanding.
To see an example of an adaptive question visit: https://open.engineering.uwaterloo.ca/3/assignments/6/1
Example of an adaptive question
- If users get a quiz question incorrect, they are presented with a simpler question that breaks the original question down into smaller steps.
Möbius also provides analytical information focused around student and content performances to ensure aspects of the educational experience are optimized to their full potential. Instructor dashboards provide insight into student understanding and help to highlight areas of course content that need revision or modification based on student understanding and grasp of concepts.
From the administrative side, the Faculty of Mathematics has full support and buy-in for the online courses from senior management. Online development is built into the University’s strategic plan with the necessary funding for support. They developed a math authoring group called the Digital Assets Group (DAG), comprised of 6 faculty members from the faculty of mathematics to build online courses and assist other faculty to author courses online.
Another novel approach is the availability of the online resources. The University of Waterloo made a number of the classes open access at Open Waterloo. There are collections of open online resources for learning under the subjects: open engineering, open math, open science, open computer science, financial literacy and K-12 resources. They also have the option for math for credit courses where anyone can enrol in a math course (for a fee) without enrolling into a program.
Benefits and Outcomes
The main benefit of using Möbius is fulfilling student demand for engaging courses, resources and opportunities as well as access and flexibility as students are increasingly taking online courses. For those who prefer to study online or who cannot come to campus – international students, students involved in the University of Waterloo’s co-op programs and most recently, the response to COVID-19 – online learning is a mechanism to support thousands of students at a distance. Most importantly, faculty and student acceptance of the platform is high.
Möbius allows for extra practice and instant feedback. Practice questions are placed at reinforcing points within a lesson so students have a greater chance at concept retention. Students can make multiple attempts to questions since Möbius generates different values for the same type of questions, and provides low-risk practice where students can try again if they get it wrong. Providing immediate feedback to the students helps them understand where they stand with the course material.
Möbius replaces textbooks and therefore lowers costs to students. It is also mobile friendly with STEM resources as HTML files, meaning they present all users with a consistent learning experience regardless of what device or browser they are using. The resources are innately more accessible for those who rely on assistive technologies to navigate through web-based content.
Through the University of Waterloo’s direct contact with the Möbius product manager and key members of the Möbius development team, they have the ability to influence the tools' key features and, to some degree, the way in which they are designed and implemented.
Challenges and Enhancements
Faculty members in mathematics biggest concern when Möbius was implemented was if online study or studying with digital assets was comparable to face-to-face or with a textbook. There were some barriers to overcome such as faculty resistance and accepting digitally supported learning as a valid method of learning. The Centre of Extended Learning is continuing to work with faculty to improve online teaching practises, enhance instructor presence and keep student engagement high.
Other challenges include:
- Online collaboration. It is challenging to create online group activities in STEM.
- An Internet connection is required to access Möbius. There is no desktop version of the platform.
- Accessibility to Chinese students due to the Chinese firewall blocking content. They have to find local servers to host the platform.
- All of the features are not available on smart phones.
- Steep learning curve for authoring and lots of technical jargon. DigitalEd is working on the usability of the authoring environment, back-end development tools and enhancements in areas such as analytics and integration.
There are many possibilities for Möbius the University of Waterloo is exploring:
- Selling resources for professional development for corporations.
- Sharing resources and collaboration across institutions – offer courses in niche STEM subjects that smaller institutions don’t offer.
- Translate resources into different languages.
- Proctoring exams online.
For Further Information
Assistant Dean, Online Studies
Faculty of Mathematics
University of Waterloo
Online Learning Consultant
Centre for Extended Learning
University of Waterloo