Study and Research Paths in Discrete Mathematics
IND's studenterserie nr. 92, 2020. Specialerapport. Matematik.
Vejleder: Carl Winsløw
The present thesis presents and analyses two teaching designs within the field of discrete mathematics. The purpose was to explore the suitability of discrete mathematics for inquiry-based teaching. Study and research paths (SRP) - the design tool of the Anthropological Theory of the Didactic (ATD) - was used to design the two teaching sequences. The first SRP aimed to generate the core combinatorial techniques from the current Danish STX-A-level curriculum. Prior to the design of the SRP, a synthesis of the existing didactical literature on combinatorics was conducted. This literature synthesis identified common student difficulties and attempts to ameliorate these. To determine what constitutes the subject of combinatorics in upper secondary school, the didactic transposition from scholarly knowledge to knowledge to be taught was studied. The determined praxeologies identifies the combinatorial knowledge to be taught. Based on the synthesis of the didactical literature and the determined knowledge to be taught, an SRP of five lessons was designed. The SRP was based on the generating question “How could you construct a secure password?”. An a priori analysis was conducted to determine the questions and answers likely to be produced by the students during the lessons. An a posteriori analysis was conducted based on empirical observations from the first lesson. The second design consisted of two lessons and the topics were immunisation strategies and the friendship paradox, motivated by the 2020 coronavirus outbreak. Prior to the design, a content analysis was conducted in which the three strategies random, targeted and acquaintance immunisation were described. Some of the content of the analysis was transposed into an SRP based on the generating question ”Who should get the vaccine?”. The design is intended as a supplementary topic in discrete mathematics in upper secondary school. The focus of the SRP was the friendship paradox and its implication for immunisation strategies. Another a priori analysis of the teaching design was conducted. The present thesis contributes with inquiry-based teaching material in discrete mathematics for empirical testing. Further, the two designs represent suggestions of how to meaningfully incorporate study and research paths in upper secondary school.