Mathematics Education (Secondary Levels)

Dissertation Project of Dr. Moritz Walz

The Dissertation was Completed in 2020.

Dissertation [german]

Diagnostic Competence and the Design of Learning Environments. [Diagnosekompetenz und die Gestaltung von Lernumgebungen]

Diagnostic competence and the design of mathematical learning environments are two important skills for mathematics teachers. Both are essential for student-centered instruction. Since teachers need to assess their students' abilities and performance in order to design appropriate mathematical learning environments, higher diagnostic competence leads teachers to design more adequate learning environments in which potential sources of errors and misconceptions are prevented.

Influence of Diagnostic Skills on the Design of Learning Environments.

Teachers need to (1) correctly assess the level of knowledge a learner has already achieved and (2) support the learner and provide adequate support if necessary. Trained diagnostic skills are a fundamental requirement for teachers to implement appropriate real-time interventions. Furthermore, they are useful in developing learning environments to prevent potential sources of error and student misconceptions.

Theoretical background

It is important for good teaching that teachers can respond to student actions in real time (cf. Randi & Corno 2005). The teacher's diagnostic competence has a positive impact on students' learning gains in mathematics classrooms (cf. Brunner et al. 2013). Teachers often have to diagnose their students "on the fly", which means that they have only little time to diagnose the respective problems in order to be able to implement an adequate intervention (Wiliam & Thompson 2007). For this reason, teachers' diagnostic skills need to be developed during their studies at the university.


We plan to measure the diagnostic skills of mathematics teaching students using Vivian, a video- and computer-based learning and testing environment for diagnostic skills. Students then design or revise a mathematics learning environment in the "Math is More" mathematics lab at the Landau campus. The learning environments are aligned with the curriculum and are each tested by a class of students. During the revision, the students are interviewed regarding their conception of the mathematical learning environment. We then film a group of four students testing the station. The students who designed the mathematical learning environment watch in real time and intervene if they feel that further work cannot productively take place without intervention. This is processed into video vignettes and group members discuss and reflect on the interventions made. In doing so, students need the interconnectedness of the different areas of professional knowledge in order to act adequately and as a basis for their argumentation. This is followed by a qualitative analysis of the videos.

Expected results

We expect that students who have practiced their diagnostic skills with ViviAn will (1) be better able to grasp students' problems and (2) design better math learning environments.


Brunner, M., Anders, Y., Hachfeld, A., Krauss, S. (2013). The Diagnostic Skills of Mathematic Teachers. In Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers. Results of the COACTIV Project (pp. 229-248). New York: Springer.

Randi, J., Corno, L. (2005). Teaching and learner variation. In Pedagogy – Learning for Teachers. BJEP Monograph Series II, 3 (pp. 47-69). The British Psychological Society.

Wiliam, D. & Thompson, M. (2007). Integrating assessment with instruction: What will it take to make it work? In C. A. Dwyer (Hrsg.), The Future of Assessment. Shaping Teaching and Learning (pp. 55–82). Mahwah, NJ: Routledge.


[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.]

Go to top