My teaching philosophy is based on the following two facts, that distinguish the possibilities of teaching today from only a few decades ago:
Information is easy to access and provided by many different institutions.
For example, consider the groundbreaking RSA encryption scheme that I teach in my introductory class to modern cryptography. This first public-key encryption scheme is used by any device when accessing emails or websites securely. Only a few decades ago, my lecture would have been the only source for students to learn about the breathtaking invention. Today, the students may listen to my lecture or watch Ron Rivest’02 ACM Turing Award Lecture, where he tells the history behind the invention of the RSA encryption scheme, freely accessible on youtube. Thus, whenever a student wishes to learn a particular subject, many videos, lectures notes, and original research papers are online available.
Nowadays, we can use many different technologies to support individual learning. Starting with classic methods such as books, lecture notes, exercise sheets, (board) presentations, accompanying videos, and introductory podcasts. In the future, we will use AI methods to generate dedicated exercises based on the personal knowledge and progress of the student.
These two points raise the following fundamental question: What is the benefit for a student to attend my lecture? The answer to this question goes back to Einstein’s vision of teaching: “Education is not the learning of facts, but the training of minds to think”. With the ready availability of knowledge and advances in technology, Einstein’s words carry even more weight today than they did then. My lectures support student learning by giving them a well-structured approach to a topic and practicing independent learning through a process that I will explain in the following.
Structure of my classes
My classes combine three elements, beginning with a self-study period, followed by guided learning, and ending with an independent learning phase:
Self-study, accessibility, and structure
In the self-study phase, the students obtain a work plan for each week together with written lecture material that lists the required prerequisites of each unit (such that the students may potentially repeat them), precise goals, and an outline of how the topic fits in the class. The material consists of written lectures notes, introductory podcasts, and accompanying teaching videos. This material completely replaces the regular (board) presentation and I assume that the student studied everything and prepared open questions before the guided learning class.
I call the first in-person meeting the guided learning phase, and it consists of two parts. In the first part, open questions from the self-study phase are discussed, followed by a specific problem, which is worked on together. This task is structured so that the knowledge learned from the first phase is first deepened and then slightly expanded. In addition, approaches to solving the problem are discussed together, and I then explain to the students how I approach the problem. The main idea of this part is to encourage (self)-thinking.
The last part is comparable to a classical exercise session. The students receive a weekly exercise sheet with three different problem types. The first one deepens the knowledge gained from the first two parts. The second problem set is slightly advanced and requires transferring a given approach to a new setting. The last problem set is extremely challenging and can only be solved by developing novel techniques. This problem set is marked and targeted for future Ph.D. students. After one week, the students present and discuss the solutions with their fellow students in class.