18. juli 2021

Probability, Combinatorics, and Lesson Study in Danish High School

Probability, Combinatorics, and Lesson Study in Danish High School - Investigating inquiry-based education and teachers’ professional development using the Anthropological Theory of the Didactic [26.1 MB]

IND's studenterserie nr. 101. Specialerapport. Matematik.

Claus Axel Frimann Kristinson Bang, 2021.

Vejleder: Carl Winsløw


The aims of this thesis are, firstly, to investigate the potential of lesson study as a tool for teachers’ professional development, and as a means for developing and sharing didactical techniques and didactical knowledge. Secondly, to study inquiry-based teaching on the subjects of combinatorics, probability theory and the binomial distribution. Lesson study combines both teacher cooperation and knowledge exchange, and teaching through problem solving and is thus a natural object of study to analyse these questions. The theoretical part of the thesis introduces two theoretical frameworks, the Theory of Didactical Situations, and the Anthropological Theory of the Didactic. This part also covers the mathematical contents, namely combinatorics and probability theory at the level of the Danish high school curriculum. These subjects are analysed and discussed using relevant didactical literature. The empirical part of the thesis is centered around data collected from a lesson study cycle on combinatorics. This case study concerns a team of four teachers in a Danish high school that plans, holds, and reflects upon, two research lessons in conjunction with university researchers, as a part of the TIME project. The data is then analysed in detail using the ATD. In particular the mathematical organisations of the students and the didactical organisations of the teachers are investigated. The problem in the case concerns codes, so a particular focus is on the multiplicative principle, counting trees, partial lists and the combinatorial formulas. It was found that inquiry-based education could be beneficial when teaching these subjects because of the particular problems that combinatorics and probability poses to the students. The analysis of the case also found that the participants discussed and shared a large number of didactical techniques. The thesis thus concludes that lesson study, as a form of paradidactic infrastructure, has the potential to enable teachers to share and develop their didactical knowledge, including knowledge of students’ praxeologies.