Mathematics Education (Secondary Levels)

Dissertation project by Dr. Patrizia Enenkiel

Materials for the doctorate completed in 2021

Title: Promoting Diagnostic Skills with Video Vignettes and Feedback - Group Work Processes for Determining Lengths, Area and Space Contents [ Diagnostische Fähigkeiten mit Videovignetten und Feedback fördern - Gruppenarbeitsprozesse zur Bestimmung von Längen, Flächen- und Rauminhalten]

Digital version of the dissertation [german]

Promoting process-oriented diagnostic skills in teacher trainees.
Concept formation of learners in geometry.

Diagnostic competence is a central component of teachers' professional knowledge (cf. Brunner et. al 2011). In order to adequately support a learner in his or her learning process, a teacher must have ideas about which learning difficulties and misconceptions hinder learning and be able to identify them in students (cf. Praetorius et. al 2012). Furthermore, diagnostic skills are essential for teacher judgment that meets the quality criteria of objectivity, reliability, and validity when assessing student performance (cf. Helmke 2003).
In order to prepare student teachers for this requirement in the teaching profession, they should already be given the opportunity to develop and, if necessary, further develop their diagnostic skills during their education.

In the course "Didactics of Geometry" students should develop their diagnostic skills in the area of geometric concept formation.

Concept formation is an essential component in mathematics education. Especially in geometry, the building of a conceptual understanding plays a particular role. Vollrath & Roth (2012) give verifiable skills that can be used to determine whether a concept has been grasped by students. In order to diagnose the learning status of the learners' concept formation process individually, the students' characteristics are compared with these capabilities. Based on this, it will be decided which measures are suitable to support and promote the learner individually.

With the help of ViviAn, a digital video tool developed at the University of Landau, it will be examined whether the diagnostic competence in the area of geometric concept formation can be promoted by teacher trainees and what influence the feedback has, which the students receive after the diagnosis. The students will work with video vignettes that show students in group work phases working on a geometry station. Appropriate diagnostic assignments are created for the corresponding video vignettes, which students will work on. In addition to the video vignettes, information about the learning environment is available to students via buttons. This gives the opportunity to investigate how ViviAn is used by the students.


Brunner, M.; Anders, Y.; Hachfeld A.; Krauss, S. (2011). Diagnostische Fähigkeiten von Mathematiklehrkräften. In: Kunter M.; Baumert J.; Blum, W.; Klusmann, U.; Krauss, S.; Neubrand, M. (Hg): Professionelle Kompetenz von Lehrkräften. Ergebnisse des Forschungsprogramms COACTIV. Münster: Waxmann, S. 215-234

Helmke, A. (2003). Unterrichtsqualität. Seelze: Kallmeyer

Praetorius, A.-K.; Lipowsky, F.; Karst, K. (2012). Diagnostische Kompetenz von Lehrkräften: Aktueller Forschungsstand, unterrichtspraktische Umsetzbarkeit und Bedeutung für den Unterricht. In: Lazarides, R. (Hg.): Differenzierung im mathematisch-naturwissenschaftlichen Unterricht. Implikationen für Theorie und Praxis. Bad Heilbrunn: Klinkhardt. S. 115 – 146

Vollrath, H.-J.; Roth, J. (2012). Grundlagen des Mathematikunterrichts in der Sekundarstufe. 2. Aufl. Heidelberg: Springer.


[This dissertation was written and is only available in german. Our summary was translated by our website team. Possible quotations have been translated in accordance with scientific regularia.]

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