Independence in Secondary Probability and Statistics: Analysis and Task Design
IND's studenterserie nr. 112. Specialerapport. Matematik.
Jonas Uglebjerg, 2023.
Vejleder: Carl Winsløw
Abstract
This thesis is written on the subject of Mathematical Didactics. The intention of this thesis is to examine how conditional probability and independence should be taught such that students acquire solid knowledge about the subject that is conceptualized in a non-misleading way. This thesis contains a presentation of the place of conditional probability and independence in curricula and textbooks today and within the past 15 years. This is followed by a review of preliminary theory on how misconception can be avoided in conditional probability and independence. This review is used to design a teaching course of five lessons of 55 minutes, that aims to prevent students from forming misconceptions and to increase students’ linguistic and formalistic abilities. This didactic design is made within the framework of the Theory of Didactic Situations, which is also explained. The developed design has been tested on a second-year class in a Danish upper secondary school. The thesis
contains an a priori analysis, which was made before this design was tested, and an a posteriori analysis of the collected data and observations. Based on this, it can be concluded that it takes more than five lessons to deconceptualize the students’ misconceptions. It can also be concluded that it is possible to increase the students’ linguistic abilities, but it requires changes in the teaching design and a new study to be able to conclude that the students’ formalistic abilities can be improved.