Mathematische Module für Chemiker : Zielgruppenspezifische, interaktive Lehr-Lern-Einheiten
Hirshman, Markus; Walcher, Sebastian (Thesis advisor); Liauw, Marcel (Thesis advisor)
Dissertation / PhD Thesis
Dissertation, RWTH Aachen University, 2020
With mathematics being an integral part of all natural sciences, it is a neccesary foundation for chemistry students if they aim to advance further into their field of expertise. Different fields of chemistry will use different mathematical methods, which necessitates that at the beginning of a chemistry program a broad basis containing both analysis and linear algebra should be laid. While the former is covered in two courses at the RWTH Aachen University, the latter is underrepresented in terms of available courses with linear algebra only being taught in a combined course "Mathematische Methoden und Symmetrie (in der Chemie)" for students in their third semester. The aim of this thesis is to create a Blended Learning Environment, which contains the neccessary contents of linear algebra for chemistry students as well as group theory for the determination of so-called point groups of a given molecule and imparts them in a succinct and target-oriented manner. This environment will be implemented within the organisational framework of the course "Mathematische Methoden und Symmetrie (in der Chemie)", which are defined by the module handbook for the Bachelor's degree Chemistry programme of the RWTH Aachen University. Therefore this thesis focuses on the creation of new teaching material as well as new teaching practices. The material developed here is based on an analysis of the students' current knowledge of those mathematical methods, which can be assumed to be known by a student starting his studies at university. The groundwork for this analysis are the Bildungsstandards Mathematik by the Kultusministerkonferenz as well as, due to the location of RWTH Aachen University, the Kernlehrplan Mathematik für die gymnasiale Oberstufe des Landes NRW. Additionally, a selection of applications from different chemical disciplines which draw on various contents of linear algebra, was created in collaboration with Prof. Arne Lüchow, Prof. Ulrich Englert and Prof. Marcel Liauw. Based on this analysis as well as results concerning different study types and the requirements of a blended learning environment, new material is developed and presented in this thesis. It consists of different gradations for the different phases of blended learning, which can be roughly divided into two parts. For the participants of the lecture "Mathematische Methoden und Symmetrie (in der Chemie)" a teaching text was written, which offers a detailed and application-oriented introduction to linear algebra and the determination of point groups of molecules. However, this text is too extensive to be used as accompanying material for the lecture. Therefore, in cooperation with Prof. Lüchow, a content catalog for the allocated six lectures was prepared and then used to create six short modules accompanying the respective lectures acting as a lecture script. Furthermore, additional material emphazising computational abilities was created for selected methods of linear algebra. This material acts on a different teaching/learning level and aims to ensure a minimum standard for the processing of exercise and exam tasks. A third level of teaching/learning is addressed by supplementary material, which provides further explanations and motivations for seleceted concepts of linear algebra that would be too time-consuming and therefore will not be covered during the lecture. If students have difficulty understanding these basic concepts, they can use this material to comprehend the contents of the respective lecture. These learning materials are supplemented by a glossary, which serves as an orientation aid for the students in their virtual classroom and contains the most important terms of the lecture. Due to the organisational framework of the course "Mathematische Methoden und Symmetrie (in der Chemie)", which does not provide students with homework or small group exercises, a collection of comprehensive online exercises was implemented as the second part of the developed material. These exercises provide students with a possibility to practice the concepts taught during a lecture as well as receiving personalised feedback. The new learning management system at the RWTH Aachen University, RWTHmoodle, provides teachers with the opportunity to use STACK, which implements the computer algebra system Maxima to create and evaluate these online exercises. Solving practice problems is an integral part of learning mathematics, which is emphasised by these online exercises. In accordance with the requirements of blended learning, these parts interlock and are not to be used as stand alone materials. This material, particularly the online exercises, now provides an effective, application orientated and, in terms of the organisational framework, low personnel expenditure way of teaching linear algebra, which nevertheless has a high degree of mathematical accuracy.