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OPTES+ – A Mathematical Bridging Course for Engineers
Anna-Katharina Roos, Gerhard Götz, Hans-Georg Weigand, Jan Wörler
To cite this version:
Anna-Katharina Roos, Gerhard Götz, Hans-Georg Weigand, Jan Wörler. OPTES+ – A Mathematical Bridging Course for Engineers. Eleventh Congress of the European Society for Research in Mathe- matics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. �hal-02422676�
OPTES+ – A Mathematical Bridging Course for Engineers
Anna-Katharina Roos1, Gerhard Götz2, Hans-Georg Weigand3 and Jan Franz Wörler3
1University of Würzburg, Germany; [email protected]
2DHBW Mosbach, Germany; [email protected]
3University of Würzburg, Germany; [email protected];
[email protected] Keywords: Bridging course, engineers, competencies.
Introduction
Many students perceive the transition from school to university mathematics as problematic.
Existing studies not only discuss difficulties broadly but promise that so-called bridging courses can help to reduce the gap between school and higher education. Also for students studying science, technology, or engineering (STE), mathematics is an important prerequisite for successful studies.
For them, mathematics is mainly used as a tool for other subjects. We focus on these STE-students, who have a high heterogeneity with regard to their mathematical knowledge before entering university. Taking this phenomenon into account, creating a bridging course in mathematics especially for this group of students is important in order to build a common level of mathematical knowledge, which professors can take for granted and rely upon when students enter university.
The OPTES+-project – optimizing the self-study phase
OPTES+ is a project funded by the BMBF (Ministry of Education and Research) that includes several universities in Germany working together to reduce the drop-out rate in STE-related subjects. The heart of the project is an online mathematics course, similar to a traditional mathematics book, but enriched with additional interactive elements. The whole course is implemented in the open source learning management system ILIAS. All the material offered by OPTES+ will be accessible for universities and other educational institutions in the future. The contents of the course are based on the experience of the involved lecturers and the cosh-catalogue (Cosh group, 2014), a catalogue written by representatives of schools and universities to list the minimum requirements in mathematics that students should have when starting their studies in economy or a STE-related subject at university. Moreover, as engineering per se often requires the application of mathematics, not only mathematical knowledge is important, but also the development of mathematical competencies. Weinert defines mathematical competencies as an individual’s available or learnable cognitive abilities and skills to solve certain exercises, as well as the connected willingness and ability to use the solutions in variable situations in a successful and responsible way (Weinert, 2001). For that reason, apart from the mathematical contents, the bridging course should also concentrate on mathematical competencies, which leads to the following questions.
Research Questions
(Q1) Which model can be used to describe the learners’ mathematical competencies and simultaneously provide a basis for differentiation within the course?
(Q2) How can the chosen competency model be implemented into the online course?
(Q3) How could, after the construction and implementation of the model, an evaluation and reflection of it take place as a step of design-based research?
The Ability Matrix
We decided to take the HarmoS-model (Huber, Späni, Schmellentin, & Criblez, 2006;
Schweizerische Konferenz der kantonalen Erziehungsdirektoren [EDK], 2011) as foundation for constructing our own model – the so-called Ability Matrix (AM), as the aspects of action used in the HarmoS-model seem to fit well the competencies the future engineer students should acquire.
Figure 1 illustrates the AM.
Figure 1: The Ability Matrix
Outlook
While (Q1) and (Q2) concentrate on theoretical considerations that are answered by the construction and usage of the Ability Matrix, we plan to run a pilot study in January and February 2019 to answer (Q3) and to investigate if the chosen competency model and its implementation are suitable for our setting. To do so, we will compare the measured competencies before and after the course to see if the attendance of the course (including the feedback the students get by the visualization of the Ability Matrix) brings any improvement of the students’ competencies. Based on the results of this pilot study we will evaluate the used competency model and reflect on possibilities of adjusting it.
References
Cosh group (2014). Mindestanforderungskatalog Mathematik (Version 2.0). Retrieved September 1, 2018 from https://lehrerfortbildungbw.de/u_matnatech/mathematik/bs/bk/cosh/katalog/.
Hubner, C., Späni, M., Schmellentin, C., & Criblez, L. (2006). Bildungsstandards in Deutschland, Österreich, England, Australien, Neuseeland und Südostasien – Literaturbericht zu Entwicklung, Implementation und Gebrauch von Standards in nationalen Schulsystemen. Aarau, Switzerland:
Fachhochschule Nordwestschweiz.
Schweizerische Konferenz der kantonalen Erziehungsdirektoren (2011). Grundkompetenzen für die Mathematik – Nationale Bildungsstandards. Retrieved September 1, 2018 from http://www.edk.ch/dyn/12930.php.
Weinert, F. (2001). Vergleichende Leistungsmessung in Schulen – eine umstrittene Selbstverständlichkeit. In F. Weinert (Ed.), Leistungsmessungen in Schulen, (pp 17–32).
Weinheim: Beltz.
