A professional development course inviting changes in preservice mathematics teachers' integration of technology into teaching: the lens of instrumental orchestration

The integration of Information and Communication Technologies (ICTs) in education is transforming how students learn, particularly in mathematics. Effective use of ICTs hinges on teachers' ability to orchestrate technology effectively, a concept known as 'instrumental orchestration.' This involves the intentional and systematic organization and use of available artifacts (like GeoGebra) to guide students' learning processes, specifically their 'instrumental genesis'—the transformation of an artifact into a cognitive instrument. Existing research highlights the importance of instrumental orchestration but lacks sufficient studies exploring how teacher training can improve it. This study addresses this gap by designing and implementing a professional development course aiming to explore its influence on preservice mathematics teachers' instrumental orchestrations within a GeoGebra environment. The research questions focus on the changes in the types, frequencies, and details of instrumental orchestrations after the course, and the specific course elements that contributed to these changes.

The literature review establishes the theoretical foundation for the study, focusing on instrumental genesis and orchestration. It draws upon the work of researchers like Trouche, Guin, and Drijvers, who have defined and elaborated on the concept of instrumental orchestration, highlighting its four key components: a set of individuals, a set of objectives, a didactic configuration, and a set of exploitations of this configuration. The review also discusses the evolution of the definition of instrumental orchestration, incorporating the concept of didactical performance. The review emphasizes the crucial role of teachers in guiding students' instrumental genesis and the importance of teacher training in fostering effective instrumental orchestrations. The use of GeoGebra as a dynamic mathematics software is also highlighted, focusing on its affordances for creating meaningful learning environments and supporting different roles of ICTs in education as identified by researchers like Roschelle et al. Previous studies exploring instrumental orchestrations in various ICT contexts are reviewed, underscoring the need for focused professional development programs that directly address teachers' instrumental orchestrations rather than just their knowledge of technology.

This study employed a mixed-methods approach involving 26 preservice mathematics teachers from a Chinese university. A professional development course was designed and delivered online, incorporating theoretical instruction (instrumental approach), practical demonstrations (GeoGebra), two rounds of simulated teaching practice, peer feedback, and group discussions. Participants chose a secondary school mathematics topic and developed a lesson plan integrating GeoGebra. Data collection involved video recordings of simulated lessons, GeoGebra files created by participants, teaching design documents, questionnaires, written interviews, self-reflection reports, and transcripts of online discussions. Qualitative data analysis used NVivo software for coding and thematic analysis, focusing on the types and frequencies of instrumental orchestrations observed in the simulated lessons, based on a pre-defined framework that categorized orchestrations and their components (didactic configuration and exploitation modes) within the GeoGebra environment. The inter-rater reliability for coding was assessed using Kappa coefficients, ensuring high consistency (>0.72). Quantitative data on orchestration frequencies were analyzed to identify changes before and after the course. Three participant cases were selected purposively for detailed qualitative analysis to showcase a variety of changes and experiences. These cases were selected after data collection based on the richness of the data and representativeness of the overall changes observed.

The key findings reveal that the professional development course significantly influenced the preservice teachers' use of GeoGebra in their teaching. While the types of instrumental orchestrations remained relatively consistent (primarily Technical-demo, Guide-and-explain, and Explain-the-screen), the frequency of their use increased significantly for all three participants. Detailed analysis of three case studies (two female, one male) revealed substantial changes in the details of instrumental orchestrations. In terms of *didactical configurations*, all three participants exhibited improved GeoGebra layouts in their second simulated teaching, incorporating more interactive elements like sliders and buttons and structuring the interface for better clarity and flow. Changes in *exploitation modes* were evident in the increased use of various techniques (dragging, measuring, constructing) and a more sophisticated management of mathematical tasks. Participants demonstrated a more targeted approach to questioning and explanation, suggesting an improvement in their pedagogical content knowledge (PCK). Although changes in *didactical performance* were difficult to objectively assess in the simulated teaching setting, participants' reflections suggested an increased capacity for improvisation and responsiveness to student needs. The analysis identified three key elements within the professional development course that contributed to these changes: 1) *Theoretical support*: The introduction of the instrumental approach provided a strong theoretical framework for understanding technology integration. 2) *Technical support*: Proficiency in using GeoGebra software was crucial for effective implementation. 3) *Community support*: The peer teaching, group discussions, and "Same Content Different Designs" activity fostered collaboration and shared learning.

The findings demonstrate that the professional development course was effective in improving preservice mathematics teachers' instrumental orchestrations, specifically enhancing their ability to integrate technology purposefully and effectively into their teaching. The increased frequency of instrumental orchestrations, coupled with qualitative changes in their design and implementation, highlights the course's impact on their teaching practices. The identification of theoretical, technical, and community support as crucial elements underscores the importance of comprehensive teacher training that goes beyond simple technical skills. The results align with previous research emphasizing the need for teachers to understand the process of instrumental genesis and to anticipate students' interactions with technology. The study's findings also suggest a positive correlation between teachers' PCK and the quality of their instrumental orchestrations. This highlights the interconnectedness of content knowledge, pedagogical knowledge, and technological proficiency in effective technology integration. The impact of social influence on teachers' attitudes towards technology integration also warrants further investigation.

This study demonstrates the effectiveness of a professional development course in improving preservice mathematics teachers' instrumental orchestrations. The course's success was attributed to the combination of theoretical, technical, and community support. While the study's findings are valuable, future research should focus on validating these results in real classroom settings to assess didactical performance more accurately, examine the generalizability of the findings to a larger and more diverse population, and develop a more quantitative approach to measuring the level of instrumental orchestrations. Further research is also needed to explore the interplay between instrumental orchestrations and teachers' PCK more thoroughly.

The study's limitations include the relatively small sample size (26 preservice teachers), the reliance on simulated teaching settings (lacking real students), and the difficulty in objectively assessing changes in didactical performance. The online nature of the course might have influenced the types of orchestrations observed, and the specific choice of GeoGebra may limit the generalizability of the findings to other technologies. The subjective nature of qualitative data analysis could also influence interpretation. Further research in real classroom settings with a larger and more diverse sample is needed to address these limitations and enhance the generalizability of the findings.