Prof. Dr. Pohl, what do you do in your innovation professorship?

The most extensive activity is redesigning the lecture notes for analysis. On the one hand, the script should be suitable for self-study by the students, either as part of reading assignments when using activating teaching methods or for reworking the content in traditionally held courses. On the other hand, it should show students that mathematics does not just fall from the sky, but that much has to be laboriously worked through. This aspect remains hidden in most of the textbooks I know.

I am also designing a new course in which students will learn how mathematics learning works. These activities are supplemented by formative assessments, which students can use to assess their own level of knowledge.

How could other teachers, students and researchers (at OTH) benefit from your projects?

First of all, I evaluate the innovations implemented in the script and the course. These results can serve as food for thought for lecturers.

The revised script is to be published as a textbook on analysis, which will benefit students at OTH and other universities. I would like to transfer the basic ideas to the teaching material for the "Analysis for Computer Scientists" course, and the analysis courses in other engineering degree programs can also use these ideas.

What motivated you to want to realize a teaching innovation?

My observation of students' difficulties in the introductory phase of their studies. I noticed two things in particular: Firstly, students find it difficult to work precisely in mathematics. Secondly, I keep hearing the comment "I might be able to understand it, but I would never have thought of it on my own."

Why do students in the introductory phase of their studies often have difficulties with mathematical working methods in higher education and are unable to assess their learning progress correctly?

On the one hand, the difficulties arise from the substantial difference between math at school and math at university. At school, predetermined recipes are often applied in a variety of tasks without thinking about why the recipes apply and how these recipes are created. At university, the emphasis is on understanding the concepts and deriving procedures. In short, school is about "doing the math", whatever that means, and college focuses on "why". Students are unable to properly assess their learning progress for two reasons: Firstly, they have no experience of the new approach to mathematics. Secondly, the mathematics seems to be quite simple when presented by the lecturers. To exaggerate, you could say "the better the explanations, the easier the students find the content - and the less they see the need to learn."

Where does your teaching innovation professorship come in? What resources do you want to use to help students and support them at the start of their studies?

I will include some innovative elements in the script that will make self-study or revision of analysis courses easier. Firstly, I invite students to "invent" key terms and concepts using examples. This preparation is intended to support understanding of the exact definitions given afterwards. In the proofs and examples, I show the difference between "brainstorming" and the mathematically cleanly written result. This makes it clear to the students that in the representations found in textbooks, the way in which mathematics is created has been thoroughly blurred and is no longer visible. This provides an answer to the question "How do you come up with that?" and relieves students of the attitude "I would never have thought of that myself". Formative assessments of various kinds are used to promote self-assessment.