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Prof. Dr. Vogel, Markus

Professor; Fak. 3 - Mathematik
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PH Heidelberg
Im Neuenheimer Feld 561
69120 Heidelberg

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Projekte

Alle20232022202120202019201820172016201520142013201220112010
Fak. 3 • Mathematik
Projekt-ID:842
Dissertation
abgeschlossen

„Analyse und Förderung von Transformationsprozessen beim Umgang mit multiplen Repräsentationen in der Mathematik“
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Publikationen

Alle20222021202020192018201720162015201420132008200720062005
VortragPeer Review

Improving pre-service teachers’ diagnostic judgments regarding task difficulties in the domain of fractions and angles. A process-oriented investigation with eye-tracking

Schreiter, S., Vogel, M., Rehm, M. & Dörfler, T. (2022). Improving pre-service teachers’ diagnostic judgments regarding task difficulties in the domain of fractions and angles. A process-oriented investigation with eye-tracking. Bolzano, Italy (online).

Abstract
Twelfth Congress of the European Society for Research in Mathematics Education
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Fachlich vs. instruktional: Welche Aufgabenmerkmale werden bei der Schwierigkeitseinschätzung von Bruchrechenaufgaben identifiziert und evaluiert? Eine Studie mit Eye-Tracking Stimulated Recall Interviews

Schreiter, S., Vogel, M., Rehm, M. & Dörfler, T. (2022). Fachlich vs. instruktional: Welche Aufgabenmerkmale werden bei der Schwierigkeitseinschätzung von Bruchrechenaufgaben identifiziert und evaluiert? Eine Studie mit Eye-Tracking Stimulated Recall Interviews. In: Klein, P., Graulich, N., Kuhn, J. & Schindler, M. (Hrsg.), Eye Tracking als Methode in der Mathematik- und Naturwissenschaftsdidaktik: Forschung und Praxis (S. 159-175). Heidelberg: Springer Spektrum, Berlin.

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ArtikelPeer Review

Changing between representations of elementary functions: Students' competencies and differences with a specific perspective on school track and gender

Sproesser, U., Vogel, M., Dörfler, T. & Eichler, A. (2022). Changing between representations of elementary functions: Students' competencies and differences with a specific perspective on school track and gender. International Journal of STEM Education, 9, 1-18.

Abstract
Background

Functional thinking is characterized as a specific way of thinking in relationships, dependencies, and changes. Hence, beyond mathematics, it is also crucial for other (STEM) disciplines as well as for everyday situations. In particular, dealing with different representations of functions and changing between them are core function-related competencies, which are correspondingly needed for the formation of appropriate concepts and flexible problem-solving in various situations. Therefore, this study investigated students’ (N = 856) competencies related to representational changes of elementary functions and, in particular, assessed which changes are especially easy or difficult for students. Moreover, possible school track and gender differences were investigated by performing DIF analyses within the framework of Rasch modeling. The data were gathered using a paper–pencil test administered after the students had completed the teaching unit on linear functions in their mathematics lessons.

Results

Altogether, students were found to have limited competencies related to representational changes of elementary functions. There was no clear pattern regarding the types of representational change that were difficult or easy for them. Moreover, girls performed better on purely mathematical tasks, whereas boys did better at a complex modeling and problem-solving task. Classes from the academic track produced better results in tasks with a situational context compared to their peers from non-academic tracks, who performed relatively strongly on purely mathematical tasks.

Conclusions

These findings imply that various representations and representational changes should be included in lessons on functions to support students in building a rich concept of function and flexible problem-solving skills, thus fulfilling curricular requirements and responding to didactical considerations. In particular, the teaching of functions should be more balanced by mixing tasks with and without a situational context and the corresponding representational changes. These findings should motivate teachers, in particular those teaching non-academic tracks, to give a more prominent role to situational contexts in their lessons on functions in order to foster their students’ learning and build a bridge between mathematics and real-world situations.
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ArtikelPeer ReviewDeutsch

Die Rolle des Wissens angehender Mathematiklehrkräfte beim Diagnostizieren schwierigkeitsgenerierender Aufgabenmerkmale. Erkenntnisse aus Eye-Tracking Stimulated Recall Interviews.

Schreiter, S., Vogel, M., Rehm, M. & Dörfler, T. (2022). Die Rolle des Wissens angehender Mathematiklehrkräfte beim Diagnostizieren schwierigkeitsgenerierender Aufgabenmerkmale. Erkenntnisse aus Eye-Tracking Stimulated Recall Interviews. Journal für Mathematik-Didaktik, 43(1), 101-133.

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