THEME: TAL2023 - The thinking classroom

About 90 students are enrolled the course, and the course is organized around a four-hour lesson every week throughout the semester. In addition to Henrik Skov Midtiby, two student instructors are attached to the course. The form of the exam is a three-hour written test where you solve math problems with paper and pencil.

In each lesson, the students work 35-45 minutes in the thinking classroom. Here the students are divided into approx. 30 groups of 3 people. All groups (i) are given a math problem of a type they have not encountered before, which they must solve together; (ii) are allocated a whiteboard surface on which they can write (in practice Magic Chart foil that can stick to the wall) and then the students stand in groups around their own 'board'. The tasks have a character that requires the students to think about the solution strategies, and they are thus not typical tasks, for which you know the solution route. The groups are new from lesson to lesson and are randomly put together by the teacher. The group size of three has been carefully chosen on the basis that everyone should be able to speak up and contribute and 'speak mathematics', and no one should be able to slip out or hide in the work. The idea is also that the changing working communities should contribute to binding the cohort together socially. It has been shown that it is important that the 'boards' allow for erasing. It gives greater creativity and courage in solving the task, that you can just wipe it out and try a new approach. The groups pick up one task at a time and solve as many tasks as they can achieve within the time frame. This ensures that all groups are occupied and provides the opportunity for differentiated teaching.

The teaching method was introduced from the first lesson, and five minutes into the first lesson the students worked in the thinking classroom. It has been a desire to show the students from the very beginning of their studies that university teaching is activating and participant-oriented.

The intentions of the Thinking Classroom are, among other things, that you want all students to think and speak mathematics through active participation, and thereby acquire the subject's reasoning and as a result increase the students' in-depth understanding of the subject's issues. The thinking classroom is thus a mean to also get the 'weak tail' involved. But the teaching style also ensures that the students get far more feedback on their professional contribution from their peers. The teacher and the two teaching assistants go around between the groups and help here and there if necessary and give feedback. But perhaps more importantly, the teachers constantly get a lot of feedback from the students' conversations and attempted solutions on the boards about their understanding of the material, difficult threshold concepts, pitfalls and misunderstandings of the material, all of which are used in the subsequent joint teaching.

The thinking classroom is here embedded in a course format that is based on the principles of the flipped classroom. Before each lesson – ie. no later than the week before - the students are given a lesson note that describes which chapter in the textbook to read, which videos to watch and which tasks to complete before the next lesson. The students can thus come prepared to the lessons, which most also do according to Henrik Skov Midtiby

The course and its individual components have been evaluated very highly by the students at the end-of-course evaluation, and the students also emphasize that working in groups with many different fellow students has contributed to quickly getting to know your fellow students well, which has contributed positively for the well-being of the students in the first semester. This in itself is a benefit of the teaching style, says Henrik Skov Midtiby, who is currently eagerly awaiting to see whether the redesign of the course also has the expected impact on the exam results.

Watch the two youtube-videos for more information on the Thinking Classrooms :

• En anderledes måde at lære matematik på with Henrik Skov Midtiby and students on using the Thinking Classrooms. Produced by Mie Karoline Jørgensen, TEK Communication, SDU.
• Peter Liljedahl: Building Thinking Classrooms