Maximum Likelihood Estimation
Maximum Likelihood Estimation
Subject Matter Didactic Analysis and Didactical Design
IND's Studenterserie nr. 129, 2025, Speciale i Statistik & Didaktik
Cæcilie Bøje Pedersen
Vejleder: Carl Winsløw
Abstract:
This is a thesis within the didactics of statistics and mathematics that investigates how to introduce likelihood functions and maximum likelihood estimation in Danish upper secondary school. The thesis examines how the topic can be meaningfully communicated to strengthen the content of statistics and create links between statistics, probability and mathematics.
Since likelihood functions and maximum likelihood estimation as topic is largely unknown in the context of upper secondary education, and that very little didactic literature exists on the topic, the purpose is to carry out a new didactic transposition. This is done by analysing the content of likelihood functions and maximum likelihood estimation and by developing a textbook chapter. The analysis consists of a subject matter didactic analysis conducted within the theoretical framework known as ‘Stoffdidaktik’. The analysis use the tools ’aspects’ and ’Grundvorstellungen’ to describe the content and explore which competencies students might acquire to understand the topic. Furthermore, the analysis identify subject-didactic perspectives used to legitimize likelihood functions and maximum likelihood estimation as knowledge to be taught. In total, four subject-didactic perspectives are identified that support the teachability of the topic. Secondly, to organize the didactical design, an analysis of the textbook chapter using the theoretical framework of the ’Anthropological Theory of the Didactic’ is conducted. This analysis consists of an institutional analysis of the conditions that must be considered when implementing likelihood functions and maximum likelihood estimation in teaching practice. It was found that the topic places high demands on both teachers and students in terms of qualifications and prior knowledge, due to its theoretical nature. Finally, the analysis includes an a priori analysis on the praxeological organization and the task design. This analysis offers a proposal for how a didactical design on likelihood functions and maximum likelihood estimation could be introduced in upper secondary school. However, it also identifies several heuristic difficulties related to task design, which teachers should be aware of when using the textbook chapter.