# Entwicklung und Evaluation von Unterrichtsmaterial zu Data Science und mathematischer Modellierung mit Schülerinnen und Schülern

Sube, Maike; Walcher, Sebastian (Thesis advisor); Frank, Martin (Thesis advisor)

*Aachen (2019)*

Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2019

Abstract

Today, students live in a world strongly influenced by digitisation and data. In order to solve real-word problems with data, knowledge of mathematical modelling and methods from the field of data science are necessary. At the moment, teaching data science is not explicitly provided within teaching guidelines. However, initial ideas can already be found in didactic research. In order to make a contribution to this discourse, the dissertation will illustrate the development and evaluation of teaching materials for data science and mathematical modelling with high school students by focussing on questions about "privacy of data in social networks" and "evolutionary distances". For this purpose, background information on data science and mathematical modelling is given (Chapter 2). Chapter 3 deals with "privacy of data in social networks" and Chapter 4 considers "evolutionary distances". Both chapters include an introduction into the mathematical (and biological) background and a description of the teaching materials as well as a didactic reflection on it. In addition, first empirical results from tests of the materials and an outlook on further work steps are presented. The topics are prepared in a subject-related didactic way: Existing methods and models are elementarily presented or linked; aspects of data science and mathematical modelling are underlined as well as applied and analysed to real data. This will be done on the topic of privacy of data following from a master's thesis by expanding the existing investigations. For the topic of evolution, the mathematical work is newly invented. Different models for distance calculation and phylogenetic tree creation are combined to form a comprehensive model and are edited. The results of the application to a data set are evaluated in great detail. Additionally, the influence of the underlying assumptions is discussed. This part of the work is addressed to those readers interested in mathematics and biology on university level. In particular, it serves teachers in mathematics or biology as supplementary material for the treatment of working materials. The teaching material, which has been developed based on this, is presented and evaluated within this work. The topic of privacy of data can be dealt within the context of an Abitur examination with high school students in advanced courses for mathematics from the 11th grade on. The topic evolution is intended as a project day for high school students of mathematics from the 9th grade on or for high school students in an advanced biology class. The materials show a balance between the fulfilment of given framework conditions (e.g. the curriculum) and further didactic quality criteria: The materials can be seen as innovative; the problems are authentic, relevant and demonstrate the main aspects of mathematical modelling. They show data science and mathematical modelling in complementary form. In addition, problem-oriented concepts can be created, which are worked on as actively and independently by the students. The fact that the concepts are appropriate for the target groups is theoretically supported by reference to the curricula and practically by initial tests.

### Identifier

- DOI: 10.18154/RWTH-2019-10240
- RWTH PUBLICATIONS: RWTH-2019-10240