I have attended several lectures in analysis, linear algebra and "higher mathematics for computer science students" in two universities in Germany. None of the professors giving these lectures provided lecture notes. Therefore the students had to copy what was written on the blackboard while at the same time trying to understand the material.
The sequence of a lecture was usually:
- Professor arrives and gives a short salutation and very brief recapitulation of the last lecture
- Professor immediately continues where we left off and starts writing proofs, lemmas, etc. on the blackboard while explaining the material in parallel. Rarely he stops to clarify something.
- When he has filled all three blackboard, he stops to erase one or two of the blackboards while usually continuing to explain what he just wrote down or introducing the next concept.
- He continues with the now empty blackboard.
- The whole process repeats from step 2 until 1.5 hours have passed.
I found it impossible to copy the blackboard and at the same time understand the material he was trying to teach. During the few breaks (question or blackboard cleaning) that we had I was frantically either trying to understand the proof or was squeezing my eyes trying to decide whether an index is i or j and was making sure to not copy i instead of i+1 or i+j by accident.
Although he did encourage us to ask questions and did answer them when someone did, the general pace was so high, that it hardly gave me some time to catch up.
When asked why there are no lecture notes, all professors said something along the lines of: "You can learn/memorize better if you hear and write the proofs yourself." While I agree that having multiple input channels helps memorizing, in practice, all that most students could do was to barely copy what was written on the blackboard, there was no time to understand. I felt like the students were "demoted" to human copy machines because this is all what most could manage to do.
Considering all this:
- Is there really proof that not providing lecture notes and forcing students to frantically copy the blackboard is beneficial for learning math?
- OR Are these professor just too lazy to create proper lecture notes?
- OR Is my perception warped and I was in the minority and just too stupid to study math?