School of Mathematics

Mathematics Today article - Hybrid Education: A Student Centred Approach

This article originally appeared in the December 2020 edition of Mathematics Today

Hybrid Education: A Student Centred Approach
By Danny Walker and Reuben Wheeler

In preparation for the challenges of a year of teaching during the COVID-19 pandemic, the School of Mathematics at the University of Edinburgh created the ASID project (Assist, Support, Implement, Deliver). By recruiting 4th and 5th year undergraduate and PhD students, course organisers had access to a resilient and adaptable support structure for developing a response to these challenges.

The School recognised that there would be significant hurdles to overcome in making the transition to hybrid teaching. Some of these hurdles could be foreseen: adapting course materials for computer aided assessment; ensuring all course materials are digitally accessible and of high quality; developing expertise in, and advice for, the creation of video content; and determining a suitable digitally-mediated alternative to traditional workshops. Naturally there were likely to be other unforeseen challenges, and the diversity of experience and expertise among the digital creation assistants allowed these to be addressed effectively.

The project was established during lockdown and the greater portion of it was undertaken remotely, with participants joining from 10 countries. The number of tasks meant that digital creation assistants established effective working relationships with many of their colleagues. A keen sense of camaraderie was soon felt, supported by an active programme of social activities, which is reflected in the quality of the teams' output and the feedback they provided. In this way, the success of the project motivated the digital content assistants to develop guidance on effective remote working, and on digitally mediated social experiences, which has been made available to staff and students.

The responses from course organisers were overwhelmingly positive. Prof. Miguel F. Anjos, Chair of Operational Research said:

"I was impressed by the team's enthusiasm, creativity and ability to deliver so well on what was initially a set of rough ideas. They made suggestions that influenced the design of the setup, and that will influence how the course is delivered."

Dr. Charlotte Desvages, Lecturer in Mathematical Computing said:

"The task went really well and I'm very happy with the work. The [Digital] Creation Assistant reached out over Teams and we had a continuous discussion about the task. They were very responsive in implementing changes and even creating extra material at my request."

Case Study: Programming notebooks

The digital creation assistants were tasked with designing and updating teaching resources which utilise Jupyter notebooks. These programming notebooks can provide a new flavour of teaching and assessment, and increased demand for online material has made resources like these invaluable.

Jupyter notebooks can be used to create interactive versions of lecture notes and it is relatively straightforward to render a notebook from a LaTeX source. A student accessing a notebook has the freedom to add their own code and comments, and can be prompted to explore the content they are learning via coding exercises or written discussion. Notebooks can also be designed to provide students with live feedback and tools like nbgrader can digitally mark their work.

Using notebooks facilitates the continuous assessment of programming skills, which are not well suited to traditional exam-type assessment. This relieves pressure from students' exams and encourages continuous engagement with learning materials. Additionally, students are likely to support the introduction of continuous autograded assessment amidst the uncertainties of a pandemic. Although initial implementation may take some effort, tools like nbgrader make the future maintenance of this kind of digital assessment very low.

There are many courses in the mathematical sciences in which programming has frequently been taught. Scientific computing sees numerical methods, statistics and their applications as obvious areas for its inclusion. Consequently, those students labelled as 'applied mathematicians' typically graduate with at least some exposure to programming.

This tradition clearly excludes students of 'pure mathematics', those focusing on algebra or geometry, for example. However, using Jupyter, one can run SymPy, a Python library designed for symbolic algebra, or SageMath, a largely Python based language built with the intention of exploring topics such as algebra, geometry, combinatorics and graph theory.

The tools mentioned here are currently being utilised at the University of Edinburgh.

Dr. David Jordan says "live feedback on computer algebra programming tasks serves an important need, of checking basic comprehension"

Dr. George Kinnear feels that "this year the students are more engaged with the lab notebooks"

The value of these tools for both instructors and students is now clear. Their application will be further improved through continued use.

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