Teaching and Learning of Mathematical and Statistical Computing Online

Over the last ten years we have comprehensively embedded computational mathematics in the undergraduate mathematics degree programmes at the University of Leeds, with the philosophy that undergraduate computational mathematics should be as broad as possible rather than focused on specific topics and techniques such as, say, numerical analysis. In particular, we explore examples across both pure and applied mathematics, with an emphasis on open-ended investigation. We focus on a particular language (Python 3), but the pedagogical principles of computer use within mathematics apply very broadly. Having already reconciled the practical challenges of assessing and providing feedback for a large class (320 in our case) with the requirement that students work individually creating substantial pieces of work, we are now faced with needing a new set of solutions when delivering and assessing this course online. We will discuss four practical approaches we will take, and the educational opportunities they present: (a) mathematical content delivered via short prerecorded videos, (b) full-class synchronous code-along sessions, (c) online coding workshops (in groups of around 50) staffed by workshop tutors, (d) assessment (weekly coursework and one timed test). We will primarily use Blackboard Collaborate Ultra as our platform for live sessions, but the basic arrangements we plan would be deliverable across a variety of video conferencing software.

Elwes, R. & Sturman, R, 2020, Developing computational mathematics provision in undergraduate mathematics degrees. MSOR Connections Vol. 18 (2) pp 59—65. https://doi.org/10.21100/msor.v18i2

In this talk we will discuss how Git (a version control system) and GitHub (a remote hosting service for Git repositories) can be integrated into statistics and data science courses. Beyond the advantages and benefits of using a version control system within a course we will discuss how these tools can be used to deliver and collect assignments, promote collaboration, and provide automated feedback to students. We will also discuss the various options for automating the process of interacting with GitHub (e.g. creating student repos) as well as considerations around data protection and privacy.

If we have learned anything from this pandemic, it is that online education is not only a nice geeky add-on to the educator’s repertoire, but a vital component of modern teaching. Traditional online math teaching uses tools to share screens, compute and calculate mathematical examples and lets the students watch the process. Flipped classroom methods are becoming increasingly popular but focus mostly on how students can obtain new content through watching videos and how the instructor can transfer information to students by using technological tools. Arthur Schuchter teaches engineering subjects at the university of Tromsø as well as mathematics, physics and computer science at an Austrian High School. He founded the Coding Club Initiative in Austria, where he uses drones to combine both hardware and software aspects and teach coding holistically in order to increase interest in STEM (Science, Technology, Engineering, Math) and counteract the skilled labour shortage in these fields. The module includes steps such as collaborative shared 3D-Modelling with clara.io, where students create mathematics know-how for matrices, vectors, shaders, physics and trigonometry. We also deal with topics in physics (force, pressure and rotation) and coding (computational-thinking, block-based programming, javascript and Python). The instructor follows a problem-based learning approach and focuses on a self-determined, self-discovered and hands-on approach for students to develop new skills intuitively and efficiently and encourage logically structured thinking. During this project, students learn to create a real-life application with a practical purpose, while going through all stages of developing a product. Students are put in the role of co-educating content generators, thus giving them a more active role, and encouraged to work on their project in teams. Students will therefore develop communication skills as well as structural and computational thinking. Collaborative methods are used to compose educational material together and flip the composing process of the educator by letting student groups create useful mathematical material such as a collection of examples and solutions, FAQs to theories as well as a Handbook of Knowledge (open-book). Before students start with calculating their assignments in math, they have to write down all their ideas and working steps in full sentences. This makes it easier to track down false conclusions and other students can easily follow the idea behind it. Students will learn to formulate goals, solve problems and create a ready-to-use product with the help of “reverse engineering”, the building of cross-references and by using creative thinking.

Programming with Mathematical Applications is a second year elective module for BSc Mathematics undergraduates that teaches programming and related skills using Python, VBA, HTML, MathJax and SQL. The usual class experience is student-led, with students working on activities while the lecturer circulates answering questions and offering advice as needed. In 2020/21, this will be taught entirely online. This necessitates a considerable rethink of the approach, since it does not seem optimal to require all students to work at the same time while connected to a Zoom call in case the need arises for support. Instead, the in-class teaching and support arrangements must be replaced by a remote, online format. This talk will outline the module teaching and learning, how this was adapted for lockdown in 2019/20, and discuss plans to deliver the module in 2020/21.

Since several years an engineer and a mathematician offer the course "Simulation of transportation processes using Matlab" for master students of process and power engineering. This is an interdisciplinary course where the students will get an elementary introduction to numerics and coding in Matlab/Octave, will repeat the modelling of heat flow and steady Rankine processes and combine this in some Matlab scripts. This blended course already engaged the students to work independently but to meet every two weeks for discussion and get support in programming. For the two weeks between the sessions we have prepared learning modules provided in our LMS ILIAS, which the students have to prepare. This is basis for the discussion in the presence meetings. In this learning modules, e.g. the 1d heat transfer was introduced and in parallel the idea of the finite differences of first and second order. For this a loop back was done to the engineering mathematics courses 1 and 2.

All this we turned now into a pure online course, in particular the coding sessions. Some adjustments we have done, so we offered a weekly question hour. The main headline about all is: Getting the students in to action.

At the end we have to state, that this year the students were more active and discussed the models much more deeply then before.

This course is held together with Micheal Wensing (Institute of Engineering Thermodynamics).

Students headed for the modern data-driven workforce need to be able to think and perform flexibly in the context of real-world data. Statistical computing provides students with critical skills that greatly expands their capacity for not only managing and analyzing data, but for engaging in quantitative reasoning and data driven inquiry at the highest levels. To this end, and in the expanding context of virtual classrooms, we will describe an array of resources providing virtual computing support for students, from accessible video content (in R, SAS, Stata, Python and SPSS), to platform-based syntax translated across the major statistical platforms, to personalized on-line support. The resources are part of the Passion-Driven Statistics Initiative that includes a growing network of instructors working to engage students in an empowering data-driven statistics curriculum. Funded by the U.S. National Science Foundation, the curriculum engages students in authentic projects with large, real-world data sets. The model has been used as a statistics course, a research methods course, a data science course, a capstone experience, and a summer research boot camp with students from a wide variety of academic settings. It is aimed at supporting students to move flexibly between data analysis platforms, starting with proficiency with one (a first course) and continuing to build new proficiencies as they encounter new data-driven opportunities and coursework in the future. Resources are available at https://passiondrivenstatistics.com/. Some that have been most useful in the virtual environment include 1) a free e-book, with links to videos 2) translation code aimed at supporting the use of statistical software; 3) a Slack channel for coding and software support and 4) a Coursera course series allowing classrooms from around the world to work together in the Massive Open Online course environment (MOOC) https://www.coursera.org/specializations/data-analysis.