Exemplary design and research results in the DoMath project

In the following, we present exemplary insight into some results of the Design Research project focusing on teachers’ professional development. Regarding the design, we briefly discuss two of the design elements implemented, evaluated and successively adapted over the course of the design cycles. In terms of the research results, we discuss obstacles in the teachers’ professionalization process which lead to refinements of the local theory for noticing and fostering students’ mathematical potential. As both types of results are intertwined, they are described first before being illustrated by an exemplary analysis of a transcript.

Design Results

Design element video clips from participants' classrooms

In line with other professionalization approaches (e.g. Sherin & van Es, 2009; Empson & Jacobs, 2008), the project uses video clips from the participating teachers’ classrooms which are intensively discussed by groups of teachers. The collective video analysis aims at promoting discussions among the teachers, in which they deepen their own understanding of mathematical potential by collectively negotiating which student utterances or actions can be interpreted as situational seeds of potential and which interactions by the teachers could have possibly lead to fostering them (for a detailed description of a video clip cf. Rosike & Schnell, 2017). Even though the analysis takes place in a laboratory setting to allow for in-depth inquiries, the clips are taken from real classroom activities to facilitate the transferability of acquired noticing skills into the teachers’ everyday practice. The clips are selected by the research team in terms of student interactions showing high levels of cognitive activities, productive discussions or other seed of mathematical potential. However, the captured working processes are often non-linear and can be interspersed with less productive phases or incorrect approaches, which allow for a large variety of analytic perspectives.

Design elements focus question and diagnostic categories

The collective discussion of classroom video clips allows for a variety of settings such as letting the teachers pick relevant scenes themselves vs. pre-picked scenes or developing an analysis focus during the meeting vs. pre-given focus questions (cf. van Es & Sherin, 2006). Results of van Es and Sherin (2006) point out that a less focused discussion enables the teachers to adopt more diverse perspectives with a broader scope of different aspects that are considered. A pre-given focus question, on the other hand, leads to a narrower perspective with insights on a more in-depth level, e.g. into student thinking. Both - the narrow as well as the broad perspective - are valuable for a comprehensive account of the classroom interactions.

In the project DoMath, the first video club meetings in Design Experiment Cycle 1 did not immediately aim at directing teachers’ noticing of potential. Instead, the first goal was to identify in-service teachers’ conceptions of mathematical potential as a starting point to complement the theoretically derived facets and aspects (cf. Table 9.1). However, teachers kept a deficit-oriented mode for a long time, which hindered them in seeing any seeds of mathematical potential at all. Thus, after the first mini cycles, we introduced the focus question “What kind of potentials can you discover in the students’ processes?” which was repeated by the researchers throughout the discussion session. Furthermore, to facilitate the focus on potential under the cognitive facet (cf. Table 9.1), additional scaffolding material was provided which included didactical categories for grasping typical cognitive processes when working on open-ended tasks. For example, the Stair Number Exploration in Figure 9.2 was discussed together with the categories for cognitive activities in that figure.

As the following analysis will exemplify, the effect of the focus question and categories was substantial in the second cycle: from the first PD session on, the second teacher group adopted more of a process perspective in mainly nondeficit modes. The categories allowed the teachers to focus their attention on the processes rather than the products and give them a language to distinguish different moments in a refined way.

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