Multi-use, multi-medium, interactive features for Applied Compositional Thinking for Engineers I (ACT4E I)

For our ETH course “Applied Category Theory for Engineering I” we have created a slides-based book which will serve as a basis for flipped classroom teaching and multi-media learning. We also co-created a trailer film to advertise for our course to a cross-disciplinary audience.

Our goals for this “slide-book” format are:
1) provide comprehensive, concise, visually appealing materials for students to study ahead of each live classroom session
2) have a single searchable and structured PDF with all key information in one place, so that it is user-friendly and can highlight the many interconnections between topics covered
3) stimulate interest, inspiration, and active thinking in students
4) provide students an opportunity to check their learning before live classroom meetings,so that questions and insights may be discussed in-person
5) have a format that can, at a later stage, be supplemented with audio/video narration

Each chapter of our slides book begins with a short introduction, which aims to “hook” the reader with an interesting story, surprising facts, or stimulating puzzles. The introductions also give a brief overview of what will be covered. At the end of each chapter, a quiz section poses simple questions with which students can check their understanding and which serve as a basis for live classroom discussion.

The slides-book is intended as an integral part of the following learning flow. For each weekly topic, students will:
1) read the corresponding chapter in the slides book and engage with the (ungraded) quizzes in their own time, and possibly also engage with the (graded) homework problems for that topic;
2) during live classroom meetings with the lecturer and TAs, the quizzes and other questions will be discussed, in addition to repetition of key aspects of the course content;
3) students solve graded homework sheets, and receive feedback on their solutions (which may also be discussed in-person a week later).

The motivations for this project:
1) attract students from a wide range of technical backgrounds
2) provide students with more flexibility in the pace and style with which they engage with the topics of our course, which take time and work to digest;
3) stimulate active and interactive learning by moving away from formats that prioritize “full frontal” teaching;
4) in the longer term, develop a version of our course that is an online MOOC, in order to reach a broader audience, in addition to our courses at ETH.

Before the creation of the slides book, we conducted limited testing of flipped teaching to see how this approach would work with our course’s topics and materials.

This testing showed the need for concise, well-organized materials, so that students have a clear and user-friendly learning path to follow in their independent study before live classroom
meetings. This especially because the mathematical concepts we teach exhibit a high level of interdependence. Students must understand concept A in order to understand concept B, which is needed for concept C, etc.

Previously, our course was based on frontal slides-based lectures, supported by a work-in-progress textbook. However, our textbook is suboptimal for guiding students through a clear and manageable semester-length curriculum in the flipped format, due to the book’s large breadth and yet-incomplete status. Our slides book now provides a gapless pedagogical path for students to follow, supplemented by in-person interaction, homework sheets, and our textbook which is still present as a reference for further topics, examples, extra exercises, etc.

Our testing of flipped teaching also showed how enlivening and enriching it can be to have classroom meetings where the main focus is animated and flexible exchanges about the material. Here, quiz questions proved valuable as a concrete starting point for discussion, for checking student understanding, and for triggering further questions. Experience has shown that once an atmosphere of enthusiasm and safety is created by the lecturer, for example in the way quizzes are discussed, students are then much less inhibited to voice further questions or comments about the lecture material as a whole.

We are excited to see our slides book in action for the first time this coming semester (using the learning flow described above), and interested to hear student’s feedback about it. Our trailer film has already been in use, both for advertising our ETH course, and promoting the topic of applied category theory more generally.

Dynamically developing materials

The original main aim of this project was to directly create videos based on our lecture slides. This turned out to be unsuitable and overly optimistic, given the current scope and nature of our course. We have learned how time-consuming it can be to create coherent, tightly-interconnected learning materials that should constitute a statically-fixed finished product, rather than being an organically improving set of materials mitigated by commentary from instructors, improved through feedback from students, and repeatedly edited. Due to the interdependent nature of the mathematical concepts in our course, minor changes in one place in our materials can create a cascade of changes that are needed in other places. Furthermore, our definitions and conceptual choices need to be consistent across the various formats we use: slides, homework sheets, and our textbook. Because the conceptual architecture of our course has not yet converged to a stable, unchanging structure, and our textbook is similarly still undergoing morphological changes, it became clear that video was a medium that, in our current stage, is too inflexible and time-consuming. Our slides book, in contrast, can more readily be edited and updated, and it can serve as a stepping stone to possibly producing videos at a later point.

Flipped teaching

Another lesson learned through this project concerns the idea of flipped classrooms. The desire to use flipped learning came from personal experiences of how flipping can make room for much more engaging classroom interactions, and also from the understanding that most of the abstract concepts we are teaching require the learner to pause, think, reflect, write notes, and digest the material at their own pace. Thanks to input from Innovedum’s Andreas Reinhardt, who pointed us to the research of Prof. Manu Kapur at ETH and collaborators, we have gained a more nuanced and evidence-based understanding of flipped teaching (and taken inspiration from their “4F” model). Main takeaways have been the importance of catalysing active thinking and “productive failure” in students’ learning process (the latter term is from Kapur), and how these are integrated in the learning cycle. Such aspects are reflected in our course design through the use of hooks, puzzles, quizzes, live-discussion questions, and weekly problem sheets as graded homework.