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

The study addresses how preservice mathematics teachers integrate ICT—specifically GeoGebra—into teaching through the lens of instrumental orchestration. Instrumental orchestration refers to the teacher’s intentional and systematic organization and use of artifacts to guide students’ instrumental genesis. Despite its importance, little is known about how to develop teachers’ orchestrations through professional development. Purpose: to examine whether a designed professional development (PD) course can change preservice teachers’ instrumental orchestrations and to identify course elements that invite change. Research questions: (RQ1) After participating in a PD course, what are the changes in the types, frequencies, and details of instrumental orchestrations preservice mathematics teachers used? (RQ2) What elements in the PD course invite changes in preservice mathematics teachers' instrumental orchestrations? The study is significant for improving technology integration practices and guiding teacher training.

Theoretical framing uses instrumental orchestration (Guin & Trouche; Trouche; Drijvers et al.) comprising didactical configurations, exploitation modes, and didactical performance. Prior work identified nine whole-class orchestration types (Technical-demo, Explain-the-screen, Guide-and-explain, Discuss-the-screen, Link-screen-board, Spot-and-show, Sherpa-at-work, Board-instruction, Work-and-walk-by). GeoGebra (GGB) is a widely used dynamic mathematics tool supporting conceptual exploration and inquiry. An analytical framework tailored to GGB was constructed: didactical configurations (GGB layout, involved tools, arrangement), exploitation modes (roles of GGB, techniques—dragging, measuring, constructing—and task management), and didactical performance (ad hoc decisions). Related literature highlights the need for teacher guidance of instrumental genesis, the frequency of certain orchestrations (e.g., Technical-demo), and the potential of PD structured around orchestration concepts. The framework draws on classifications of techniques (dragging, measuring, constructing) and roles of ICTs (developing conceptual understanding, practicing problem solving, inquiry, communication/collaboration, doing mathematics).

Design: A PD course was designed and implemented online over six days, integrating theory, demonstration, practice, feedback, and guidance. Participants: 26 Chinese preservice mathematics teachers (age 20–22) in a 4-year bachelor’s program; all had prior basic proficiency with GeoGebra and no prior exposure to instrumental genesis/orchestration concepts. Procedure: A month prior, five technology-suitable topics were provided (algebra and geometry). Participants selected one topic, prepared a 45-minute design (simulated delivery ~25 minutes), and were grouped (5 groups; 5–6 per group). PD schedule included: first round of simulated teaching (Day 1); sessions on instructional design and GGB proficiency (Day 2); introduction to the instrumental approach and cases of instrumental geneses/orchestrations (Day 3); problem discussion/feedback and group independent discussion (Day 4); GGB document sharing (Day 5); second round of simulated teaching (Day 6). Data collection: documents (lesson designs, slides, GGB files, course slides), transcripts of online discussions, daily reflections, summary reports; questionnaires; computer screen recordings of simulated lessons; written interviews and follow-up clarifications; supplementary chat logs (Table 5). Analysis: Transcribed two simulated lessons per participant and coded in NVivo against the nine orchestration types (Table 1). Each sentence was checked; multiple codes possible per sentence; triangulation with designs, questionnaires, and interviews. Two coding rounds separated by >3 months; inter-rater agreement via NVivo Kappa per node >0.72; discrepancies resolved by discussion. Quantitative comparison of types and frequencies across rounds; qualitative analysis of changes using the GGB orchestration framework (Table 3) focusing on didactical configurations, exploitation modes, and didactical performance. Three illustrative cases (T1, T2, T3) were purposefully selected for depth and heterogeneity after data review.

• Types vs frequencies: Across three focal cases, orchestration types observed remained limited (primarily Technical-demo, Guide-and-explain, Explain-the-screen; with rare Discuss-the-screen and Work-and-walk-by), but total frequencies increased markedly after PD. Technical-demo increased the most. Quantitatively (Table 6): T1 total 28→48 (+20); T2 12→23 (+11); T3 37→121 (+84). Technical-demo counts: T1 14→23 (+9); T2 5→10 (+5); T3 17→67 (+50).
• Didactical configurations: Main changes were in GGB layout and tool usage. T1 added a 3D visualization of a plane truncating a cone; more sliders/variables and clearer on-screen data. T2 enriched interactivity (sliders/buttons/angle tool) to dynamically show folding/cutting paper to form isosceles triangles. T3 streamlined controls (fewer checkboxes), expanded to general power functions with input boxes and sliders; added group work, shifting to a mix of whole-class and group arrangements.
• Exploitation modes: Roles of GGB consistently supported inquiry-based learning and conceptual understanding, with added roles such as doing mathematics and collaboration (T3). Techniques expanded: more diverse dragging (wandering/guided/dummy locus), added measuring (perceptual/validation) for T2, robust constructions throughout; additional interface techniques (moving view, buttons, checkboxes). Task management became more explicit and content-specific, with increased questioning, explanations, and finer task subdivision (e.g., T3 splitting integer vs fractional exponents; T1 refining question prompts).
• Didactical performance: Changes were difficult to observe due to simulated, peer-based teaching and lack of real-time contingencies; minor ad hoc issues varied by session. Nevertheless, artifacts and reflections indicated likely increased improvisation and student interaction in authentic settings.
• PD elements inviting change: Evidence pointed to three supports: (1) theoretical support—introduction to the instrumental approach and cases of instrumental geneses; (2) technical support—GGB proficiency (as foundational, especially for novices); (3) community support—Same Content Different Designs (peer observation of differing designs for the same topic) and structured discussions/feedback within groups and class. These influenced revisions to GGB files, techniques employed, and task management strategies, and shifted attitudes toward technology integration (notably T2).

Findings answer RQ1 by showing that while orchestration types used by preservice teachers did not diversify in the simulated, online context, their frequency of orchestration actions increased substantially, accompanied by richer didactical configurations and exploitation modes in GGB. This aligns with literature noting the prevalence of Technical-demo and underscores the potential of PD to intensify and refine orchestration practices. For RQ2, PD components offering theoretical framing (instrumental approach), peer design comparisons (Same Content Different Designs), and collaborative discussion/feedback were key levers for change, consistent with prior work on communities of practice and the value of anticipating instrumental geneses. The study also indicates interplay between orchestration development and growth in pedagogical content knowledge (more content-specific prompts, structuring, and explanations), suggesting fruitful integration of orchestration theory with knowledge frameworks such as TPACK and PCK. The online, peer-teaching format likely constrained observation of didactical performance and certain orchestration types (e.g., board-related or student-presenting types), indicating context dependency in orchestration manifestation.

After the PD course, preservice teachers showed substantial increases in orchestration frequency—especially Technical-demo—while types remained largely unchanged in the online simulation setting. Notable qualitative changes included more informative GGB layouts, expanded techniques (dragging, measuring, interface controls), and improved task management with more content-specific questioning and structuring; changes in didactical performance were hard to capture without real students. Effective PD elements comprised theoretical support (instrumental approach and cases), technical support (GGB proficiency), and community support (Same Content Different Designs and structured discussions). The study proposes and validates an analytical framework for instrumental orchestrations in a GGB environment and suggests adapting the PD content for in-service teachers. Future research should investigate orchestration in real classrooms, develop quantitative scoring for orchestration quality, and analyze the relative influence of PD components; exploring links between orchestration development and PCK proficiency levels is also recommended.

• Sample and generalizability: 26 participants with three focal cases reported; limited representativeness.
• Context: Simulated online teaching without real students; absence of a physical board constrained observation of certain orchestration types; didactical performance changes were difficult to detect.
• Measurement: No quantitative scoring of orchestration levels; relative impacts of different PD components not isolated.
• Topic variation: Multiple topics used; although analyses were within-teacher, topic-specific affordances may still influence outcomes.