Multivariable Calculus: Interactive Digital Space for Online Learning

Concurrent Session 2
Streamed Session

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Brief Abstract

This session showcases cross-campus collaboration efforts to create an asynchronous, interactive, student-oriented math course that provides an inclusive and accessible learning experience for all types of learners who are keen to explore the wonders of multivariable Calculus. This digital space is complemented with other "teachnology" and pedagogy choices to increase student engagement and create strong teacher presence.


Burcu earned her B.Sc. in Mathematics at Bogazici University and MMath in Pure Mathematics at the University of Waterloo (UW). She is a lecturer in the Digital Assets Group (DAG) in the Faculty of Mathematics. Burcu taught many online courses (mainly, Calculus and Linear Algebra) for the University of Waterloo before joining the faculty. Prior to her role at UW, Burcu worked as a full-time instructor in the Department of Mathematical Sciences at the Florida Atlantic University(FAU). At FAU, Burcu created and taught many online courses. She has a special interest in learning te(a)chnologies. In her free time, she likes doing yoga, traveling, playing board games as a family, and doing arts and crafts with her daughter.
Amanda earned her MMath and PhD (Systems Design Engineering) at the University of Waterloo. She is currently a member of the Digital Assets Group in the Mathematics Undergraduate Office. Amanda's current work on digital asset development is focused on linear algebra and calculus courses. She is passionate about teaching and is eagerly exploring the possibilities offered by online learning. In her spare time, Amanda enjoys knitting and reading.

Extended Abstract

This presentation describes the creation of interactive digital space for online learning in the context of a second-year multivariable calculus course. The course design represents a departure from previous traditional, video-based, asynchronous online mathematics courses at the institution. With a strong emphasis on student-centred learning,  an innovative combination of mathematical software encourage active learning, universal course design principles support the learning process and increase retention, and the interactive digital space provides a safe learning environment where students thrive.

At the end of the presentation, participants will:

  • Understand how the needs and unique challenges of this project were met and overcome.
  • Describe the course design goals and how they were achieved while reflecting on their applicability to their own courses.
  • Describe the course delivery goals, how they were executed, and consider how to implement similar techniques in their own teaching.
  • Explain how various course design elements impacted student learning and student course perception.

How to take online learning for university courses to the next level? This was the challenge posed to the course design team for a second-year university multivariable calculus course. A team of instructors, online learning consultants, software developers, programmers, and quality assurance experts incorporated evidence-based best practices for online course design and pushed the limits of existing technologies to produce an innovative, iterative, sustainable, reusable, flexible, and student-centred calculus course.

At the start of the project, the team identified the unique needs and challenges for this project, which mainly revolved around identifying teaching tools able to handle sophisticated calculations, produce interactive 3D visualizations, and allow for user interaction in accordance with accessibility principles. 

To address these challenges, the team used Möbius, an online platform designed for STEM courses, and the institution's Learning Management System (LMS) to create an interactive digital space for online learning.

The Möbius courseware included an interactive textbook with 15 modules and an accompanying set of auto-graded assignments; complementary learning components included short targeted videos, various opportunities for student-instructor interactions, a discussion board, scaffolded written assignments (including reflection pieces), and an organized LMS structure.

In addition to the above needs, the course design team-oriented course development around three core principles:

  • Design for all students
  • Put students in charge of their own learning
  • Use the attraction of technology to its full potential to increase student curiosity. 

These principles were implemented through the strategic use of course design elements, learning technologies, and complementary learning components, all of which will be discussed in detail during the session. In particular, we will focus on universal design principles (Troop et al., 2020), active learning techniques, facilitating the Testing Effect (Greving & Richter, 2018), and mitigating the Dunning-Kruger effect (Kruger & Dunning, 2000).

The course delivery itself was also executed with three core ideas in mind:

  • Create strong instructor presence 
  • Foster metacognition skills
  • Manage the teaching resources efficiently for online courses

Discussion around course delivery goals will touch on the various types of online teaching presence (Moradi et al., 2018), ways of promoting metacognition skills (Tanner, 2012), and tips for teaching as a team.

To provide the student perspective results from several student course perception surveys will be presented. Overall, students had a positive learning experience in the course and reported that the course design elements contributed to their engagement and learning.

This session will provide several opportunities for audience engagement. Participants will take an "interactive digital spacewalk" to experience the Mobius interactive textbook. They will be invited to reflect and share their thoughts on the ideas presented by the speakers and how to incorporate them into their own courses throughout the presentation. Participants will also be provided with a copy of the presentation slides.