Danijela Damjanovic and Kristian Bjerklöv KTH Mathematics

We are the coordinators for two "big" courses in mathematics: SF1624 Algebra and Geometry, and SF1625 Calculus in One Variable, that are taken by most of the KTH students. This year we explored and used the benefits of the distance education while trying to keep the best features of the old set up of the course. The changes we made in our courses under the new circumstances are numerous.

Changes
A big challenge was the lectures, which had to be given via zoom. In the live zoom lectures the teachers exploited the different possibilities offered in zoom in order to engage the students in thinking and working during the lecture. These include chat room, zoom polls and breakout rooms. The main motivation in using extra zoom tools was to maintain contact with the students, so as to mimic the usual classroom environment. Our classes are large, so this was not easy, but when students are divided into smaller groups, fruitful discussions can develop. One important reason for having live zoom lectures, compared to only recorded films, is to make the interaction possible. We also believe that live-streamed lectures encourage the students to work continuously with the course. Before the start of the academic year our colleague Lars Filipsson completed the video library for the two courses: he created video lectures for essentially each topic. These lectures, which are available on the course homepage, cover the basic material. We recommend the students to watch the film before coming to a live zoom lecture. 

As for exercise sessions, in the first period they were in the classroom, while now, as we write this, they are also moving to zoom. Having exercises in the classroom in the first period was a part of the requirement from KTH administration regarding first year students. To be able to keep distance in the classrooms, we had to increase the number of rooms. This implied that the teaching assistants often had to have exercise sessions in more than one classroom, at the same time! Because of that, the format of the exercises was slightly changed with more focus on students working with the problems themselves, with the possibility to ask questions. To offer the option of learning by observing an assistant solving a problem, we have pre-recorded exercise sessions by our colleagues Frida Svelander and Lars Filipsson. Frida and Lars have really done a wonderful work in creating these films.

Recently, in accordance with the recommendations, we had to act fast and move all the exercise classes to zoom. Sometimes we had to change the plans for teaching the morning just before the class: if a student in the group reported being ill, we had to cancel all the classroom teaching. The fast changes between classroom- and distance teaching were a challenge for us. We have a huge number of assistants, many of them have not got training and technical tools (i-pad and i-pen) in order to start overnight to hold exercises on zoom. Having continuous examination in these courses is crucial for achieving good results. In the previous years we had weekly tests in the classroom, in connection with the seminars, which were proctored by teaching assistants. But now we do not have such an option. Instead, we now assign weekly homework sets to the students. The questions in the homework sets are constructed to cover the most important topics in the material for the given week. The goal of these problem sets is twofold. One goal is to encourage the students to work continuously with the course material. Even more importantly, we want students to learn how to write and present their solutions to mathematical problems. A drawback with the homework problems, compared to the test in the classroom, is that the former does not prepare the students for the real situation on an exam, where one has to solve problems alone, without aids, and with a limited amount of time.

Wonderful work of the teachers
We are very grateful to our colleagues for their fast reactions under these changed circumstances. Everybody involved in the courses have worked hard to try to make the best of the situation. The pre-recorded lectures and exercise sessions by Frida Svelander and Lars Filipsson have been crucial for compensating for the changes in teaching.

We need more support from KTH
The exams we had in October were in the classrooms. Even though we had experience with examination during the spring term, which was proctored via zoom, the on-campus examination was a more sound option for the following reasons. The first one is that zoom proctored exam requires a large number of well-trained proctors, which in principle is not guaranteed by the SCI exam administration; concerning upcoming zoom exams we are already informed about this lack of resources. Another reason is that the exam has the usual format which the students are used to and for which they prepared for, which reduces stress. Lastly, we believe that having exams on campus is a more legally secure form of examination.
The biggest issue with the exam was the lack of IT support for grading. Giving that corona was on the rise, grading on paper a thousand paper copies of the exam was too risky an option. The Canvas "SpeedGrader" option, which we used in April, was not set up by the IT department to deal with exams submitted on paper. This issue was resolved thanks to Tommy Ekola who came up with an ingenious internal temporary solution which allowed us all to grade on-line. This took a lot of effort and time, and thus postponed grading into the period two, which resulted in prolonged grading time even more so, since people started teaching and having other obligations. Timely support from the IT department would have been greatly appreciated. We are very grateful to Tommy for his fantastic work.

Conclusion
The whole Department of Mathematics has worked hard to provide the good quality of teaching. We are thankful for the help and support we are getting from all the faculty members, teaching assistants and our administration. Learning mathematics is an evolutive process and getting answers to questions in real time is essential. Having lively communication with fellow students and lecturers is central for acquiring knowledge in mathematics. Regardless of our efforts to expand the use of various digital possibilities in distance education, the quality of immediate contact with students and classroom discussions is irreplaceable. We would appreciate more technical help from KTH, in particular, with the digitalizing / conducting the digital examination: scanning the exam papers and adapting the format for on-line grading. After all, we are a technical university! 

We will continue to strive to achieve high standards of teaching through the means we have available under given circumstances.