Mathematics Education (Secondary Levels)

Dissertation Project of Marie-Elene Bartel

Diagnosing and Supporting Students' Conceptualization Processes with Video Vignettes [Begriffsbildungsprozesse von Schüler/innen mit Videovignetten diagnostizieren und unterstützen]

Diagnoses are of great importance in everyday school life for the control of teaching-learning processes and thus indispensable for everyday teaching (Horstkemper, 2004). This suggests the promotion of the corresponding competence among prospective teachers. To enable them to analyze and support students' learning processes, we designed and developed the computer-based learning environment ViviAn (video vignettes for the analysis of teaching processes). ViviAn is used in large-scale courses on mathematics didactics to illustrate the theoretical knowledge taught there, as well as to enable students to use their diagnostic skills in analyzing student work processes.

Weinert (2000, p. 16) views diagnostic competence as "a set of skills for continuously assessing the knowledge level, learning progress, and performance problems of individual students as well as the difficulties of various learning tasks in the classroom so that didactic action can be based on diagnostic insights."


When Weinert speaks of diagnostic competence, he is obviously referring - according to Praetorius and colleagues' (2012) view of the term - primarily to the partial aspect of learning process-related diagnoses. Teachers must be able to recognize in the classroom "where the individual learner is in his or her learning process and what assistance and feedback the learner needs" (Praetorius et al., 2012, p. 137). This statement already indicates that diagnoses alone are not sufficient to positively influence the learning process of students. Further steps, such as a fitting additional explanation on the part of the teacher, must follow (Schrader, 2013). The complexity of teaching and the complexity of the learning process-related diagnoses described above suggest that the relevant competence should be promoted in universitiy teaching programs.

With this in mind, we developed the ViviAn learning environment based on video vignettes taken from our "Math is More" student lab. In order to enable a satisfactory learning process-related diagnosis of the observed process, further information of the learning situation is usually required in addition to the video data. Therefore, as Lampert and Ball (1998) did in the U.S., we provide students with supplementary information in addition to the video vignette. Students are given "diagnostic assignments" that focus on specific aspects of student learning. In the context of this work, this involves a focus on concept formation processes of the fraction concept. The relevance of this aspect is made clear by the fact that concept formation is a central aspect of mathematics education (Hischer, 2012) and, at the same time, an insufficient understanding of the fraction concept is considered to be the cause of many problems in fractions (Hischer, 2012).

In the context of the large-scale event "Didactics of Number Range Extensions", the effectiveness of the learning environment will be reviewed. In this context, among other things, it will be investigated by means of an experiment whether the ability to make learning process-related diagnoses (concept learning of fractions) can be increased by working with ViviAn and whether these abilities can be promoted better by working with ViviAn than by working with transcripts. Furthermore, it should be found out whether students perceive ViviAn as a practical learning opportunity and whether they are interested in working with it.



Hischer, H. (2012). Grundlegende Begriffe der Mathematik: Entstehung und Entwicklung. Struktur, Funktion, Zahl (Springer Studium). Wiesbaden: Springer [u.a.].

Horstkemper, M. (2004). Diagnosekompetenz als Teil pädagogischer Professionalität. Neue Sammlung, 44 (2), 201–214.

Lampert, M. & Ball, D. L. (1998). Teaching, multimedia, and mathematics. Investigations of real practice (The practitioner inquiry series). New York: Teachers College Press.

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 (S. 115–146). Bad Heilbrunn: Klinkhardt.

Schrader, F.-W. (2013). Diagnostische Kompetenz von Lehrpersonen. Beiträge zur Lehrerinnen- und Lehrerbildung, 31 (2), 154–165.

Weinert, F. E. (2000). Lehren und Lernen für die Zukunft - Ansprüche an das Lernen in der Schule. In Pädagogische Nachrichten Rheinland-Pfalz 2, 1-16.


[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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