Mathematics Education (Secondary Levels)

Dissertation Project Rita Kittel

Developing Teacher Trainee's Diagnostic Skills with the Help of Videos. How do Students Deal with Function Graphs?

[Diagnostische Fähigkeiten von Lehramtsstudierenden mit Hilfe von Videos fördern Wie gehen Schüler/innen mit Funktionsgraphen um?]

Diagnosis is an essential part of the teaching profession. Students' levels, progress, and difficulties must be continually diagnosed in the classroom. The teacher training program, which is supposed to prepare the prospective teachers for the future profession in the best possible way, must therefore also build up or promote the diagnostic competencies of the students. The purpose of this study is to investigate whether the diagnostic competencies of student teachers can be promoted with the help of video vignettes. The diagnostic focus is on the mathematics content area of Functional Relationships. This is present in mathematics classes across all grades and is also essential for understanding and talking about connections and developments in everyday life as well as in science.


Theoretical background

The construct of diagnostic competence includes, among other things, those skills that are needed to assess the performance level or problems of students and to recognize learning progress (Schrader, 2009; Weinert, 2000). However, such knowledge should not only be gained at certain points in time, for example through class tests, but continuously during the learning processes of the students in order to enable timely and appropriate action. In the classroom, however, this occurs under a certain pressure to act (Praetorius et al., 2012), which can lead to cognitive strain, especially at the beginning of the teaching activity. To counteract this, early support should take place during the study period of the teacher.

Functional thinking is composed of three main aspects: Assignment, change behavior or covariation, and function as a whole (Malle, 2000; Vollrath, 1989). Furthermore, it is characterized by the use of and the change between different forms of visualization. The three aspects of functional thinking are best illustrated by the representation of the function as a graph. However, especially the change between the situation and the graph of the function is often fraught with errors, because here often overlaps with everyday ideas occur (Nitsch, 2015).

Methodological approach

In an intervention study it is to be investigated whether special facets of the diagnostic competence of student teachers - namely those relating to the handling of function graphs - can be promoted by the processing of video vignettes. The support is to take place in the learning environment ViviAn, since both the thematically selected video sequences and the work assignments of the students as well as their solutions can be integrated in it. This is an attempt to create a high degree of realism. Furthermore, ViviAn offers the possibility to present diagnostic assignments in order to focus the students' attention.



Malle, G. (2000). Zwei Aspekte von Funktionen: Zuordnung und Kovariation. mathematik lehren (103), 8–11.

Nitsch, R. (2015). Diagnose von Lernschwierigkeiten im Bereich funktionaler Zusammenhänge. Eine Studie zu typischen Fehlermustern bei Darstellungswechseln. Wiesbaden: Springer.

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

Schrader, F.-W. (2009). Anmerkungen zum Themenschwerpunkt Diagnostische Kompetenz von Lehrkräften. Zeitschrift für Pädagogische Psychologie 23 (34), 237–245.

Vollrath, H.-J. (1989). Funktionales Denken. Journal für Mathematikdidaktik (10), 3–37.

Weinert, F. E. (2000). Lehren und Lernen für die Zukunft - Ansprüche an das Lernen in der Schule. Bad Kreuznach: Pädagogische Nachrichten Rheinland-Pfalz.


[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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