Abstract: Dieser Artikel stellt den neuen elektronischen Fragetyp STACK zur Formulierung von Mathematik-Aufgaben in elektronischen Tests und eKlausuren vor. Dieser steht als PlugIn für die Learning Management Systeme (LMS) moodle und ILIAS zur Verfügung. Mit diesem Fragetyp ist es möglich, Mathematische Ausdrücke wie Matrizen und Gleichungen als Lösung eingeben zu lassen und die Ergebnisse der Testteilnehmer auf mathematische Eigenschaften zu untersuchen. Bei der Auswertung findet kein Stringvergleich statt, sondern es wird das Computer-Algebra-System (CAS) Maxima, das als Open-Source-Projekt entwickelt wird, verwendet. Außerdem können Fragen randomisiert und differenziertes Feedback gegeben werden.

Abstract: Prior knowledge in mathematics has repeatedly been found related to study success in engineering, making its lack a variable to identify “at risk” students. Not all secondary school graduates are equally prepared to meet the demands of an engineering programme; different school types and mathematics curricula lead to broad differences in basic knowledge. As a remedy, universities offer pre-courses or bridging courses in mathematics, more and more frequently employing e-learning or blended learning programmes. The paper describes the development of an online course for study preparation in mathematics. The design process is accompanied by a research project that analyses both quality of the learning material and performance of the participants. In a multiphase research design repeated evaluations of test results, questionnaire data and statistical information are used to revise and successively improve the programme. The overall goal is to build a pre-course that meets the demands of the group of prospective engineering students. The main research interest is to build a consistent data model that relates students’ personal and demographic backgrounds, prior knowledge in mathematics, and learning outcomes in the pre-course. In the first design phase, or pre-study, the most relevant issues that should be addressed in the further course of the project were identified, applying qualitative methods to question (or confirm) quantitative outcomes. Based on these results, learning material and quantitative tools were modified, and re-evaluated. The final data model for the main study is based on three quantitative sources: pre- and posttest performance, personal questionnaire, and evaluation questionnaire. The results so far reveal a highly heterogenic learner group regarding cognitive and metacognitive variables. While many students are able to close minor gaps via self-study, others lack the ability to self-regulate and need support structuring and monitoring the learning process. Thus different learning scenarios, from self-study to blended learning to online tutoring, were provided and evaluated in 2014. In the article examples for the use of learning analytics in the developmental design process and the latest version of the programme are given. The pre-posttest design’s reliability was increased based on statistical analyses of students’ test results. Test results then could be related to known predictors of mathematics performance, e.g. school grades, or attitude towards mathematics. Analytics were also made accessible for students by relating individual results to the peer group’s overall score. Finally, pretest results were used to cluster students with similar results and assign them to matching learner groups. In the further course of the project the data collected in the pre-course will be related to external datasets, like first year exams in mathematics, and overall study success. It will be investigated if and how these correlate with learning progress in the pre-course and predictive variables like prior knowledge, type of secondary school, or attitude towards mathematics. Findings are incorporated into a joint research project funded by the German Federal Ministry of Education and Research (www.optes.de).