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Pre-service mathematics teachers’ engagement with dynamic geometry software: Technological actions, challenges, and perceptionsAbstract
Dynamic geometry software (DGS) tools, such as GeoGebra (GGB) and Geometer’s Sketchpad (GSP), are widely promoted for supporting mathematics learning. However, their effective use remains challenging for pre-service mathematics teachers (PMTs), who often struggle to translate digital affordances into pedagogically meaningful practice. Despite growing interest in DGS integration, little is known about how different platforms shape PMTs’ instructional decisions, especially during professional training. This study aimed to investigate how PMTs engaged with GGB and GSP by analysing their technological actions, challenges, and evolving perceptions during collaborative task design in a professional development context. Data were collected from 56 PMTs in 14 groups during a semester-long course on teaching mathematics with technology. A mixed-methods approach was used to analyse mini-lesson videos, lesson plans, DGS materials, and reflective notes. The results revealed that PMTs employed more technological actions in GSP than in GGB, especially in the function-based action category. Technical and pedagogical challenges varied across platforms, with GGB posing greater issues in classroom orchestration and GSP in usability. Reflective data revealed distinct shifts: GGB users grew from unfamiliarity to competence, while GSP users adopted more evaluative stances toward classroom implementation. Effective use of DGS in teacher education requires not only technical training but also scaffolded pedagogical planning and reflection. Balanced exposure to different tools can help PMTs develop adaptive, content-sensitive instructional strategies with technology.
Keywords
dynamic geometry software
pre-service teachers
technology use
mathematics education
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1. Introduction
With the rapid advancement of information and communication technology (ICT), its integration into mathematics education has been emphasized in national curricula and policy documents worldwide (e.g., MOE, 2022). Although both students and teachers now have widespread access to various hardware and software tools (e.g., Fan et al., 2022a; b), the effective implementation of ICT in mathematics classrooms remains challenging (e.g., Sinclair & Yerushalmy, 2016), particularly when it involves dynamic mathematical technologies (Clark-Wilson et al., 2020).
Given that teachers play a critical role in shaping student learning (Lerman, 2001), preparing them to use technology effectively is one of the most pressing issues in mathematics teacher education (e.g., Bowers & Stephens, 2011; Bozkurt & Koyunkaya, 2022; Brown, 2017). A recent review by Thurm et al. (2024) on professional development (PD) for teaching mathematics with technology noted a growing emphasis on pre-structured/guided math-environments and general tools (e.g., PowerPoint), marking a shift from earlier research that predominantly focused on dynamic geometry software (DGS) such as GeoGebra (GGB), Geometer’s Sketchpad (GSP), and Desmos (e.g., Driskell et al., 2015, 2016).
Although scholarly attention to DGS has declined in recent years (St Omer et al., 2025), several studies continue to highlight persistent challenges in its classroom use. These include (1) a lack of confidence or competence in leveraging its dynamic features (e.g., Clark-Wilson & Hoyles, 2017); (2) limited and often superficial integration (e.g., Fan et al., 2022b); and (3) difficulty in selecting appropriate tools to capitalize on their affordances (Ulusoy & Giri-Yildiz, 2024). For example, Fan et al. (2022b) observed that most mathematics teachers relied heavily on PowerPoint slides, rarely using more complex digital resources such as DGS—even though DGS has demonstrated strong potential for supporting exploration, visualization (Jones, 2005), and improved learning outcomes (Chan & Leung, 2014).
Designing mathematically meaningful tasks with DGS is complex (Ratnayake et al., 2020) and integrating these tools into instruction demands substantial time and planning. Consequently, many in-service mathematics teachers struggle to create, adapt, and implement DGS-based lessons effectively (Ulusoy & Giri-Yildiz, 2024). This highlights the importance of supporting pre-service mathematics teachers in developing task-design competencies involving DGS prior to entering the profession (Komatsu & Jones, 2019), as their early experiences with technology strongly influence future classroom practices (Xie, 2023). Further complicating this landscape is the increasing variety of tools categorized as DGS, despite significant differences in their functionalities. Sinclair and Yerushalmy (2016) have called for greater research attention to such differences, noting that mathematics teachers must navigate an expanding and uneven field of digital resources. Furthermore, to effectively use and integrate technology into teaching, mathematics teachers need to cultivate proficiency and understanding of both the educational technology itself and the subject matter, i.e., mathematics (Yildiz & Arpaci, 2024).
In response, this study investigates how pre-service mathematics teachers engage with two widely used DGS platforms—GeoGebra (GGB) and Geometer’s Sketchpad (GSP)—during a one-semester professional training course. It explores their actual technological actions, the technical and pedagogical challenges they encounter, and how their perceptions evolve through collaborative task design. This study was guided by the following research questions:
RQ1. How do pre-service mathematics teachers utilize different categories of technological actions across GSP and GGB?
RQ2. What technical and pedagogical challenges do pre-service mathematics teachers encounter when using GSP and GGB?
RQ3. How do pre-service mathematics teachers’ perceptions toward GSP and GGB evolve in PD?
2. Literature Review and Analytical Framework
2.1 Mathematics Teachers’ Use of DGS
Over the past two decades, DGS has become an influential tool in mathematics education, offering dynamic manipulation, multiple linked representations, and interactive features that support mathematical reasoning, visualization, and exploration (Jones, 2005; Laborde, 2002). DGS environments, such as GGB, GSP, and Cabri, enable students and teachers to construct geometric objects, manipulate them through dragging or sliders, observe invariant properties and mathematical relationships, and cultivate flexible and fluent perseverance on problem solving (Romero Albaladejo & García López, 2024; Sinclair & Yerushalmy, 2016; Straesser, 2002; Yorganci & Subasi, 2025). These affordances have led to increasing advocacy for the integration of DGS into both pre-service and in-service teacher education, as a means to deepen conceptual understanding and encourage inquiry-based learning (Chan & Leung, 2014; Misrom et al., 2020).
Mathematics teachers employ DGS for various instructional goals, including visualizing functions (Takači et al., 2015), constructing geometric arguments (Jones, 2005), and exploring transformations (Hollebrands, 2003). Research has documented a range of technological actions afforded by DGS, such as constructing points or segments, measuring angles or distances, performing transformations, and manipulating control elements like sliders and checkboxes (Aparı et al., 2022; Jones, 2005). However, teachers’ actual use of DGS tends to focus on a narrow set of functionalities—primarily basic drawing, measuring, dragging, and sliders—while more advanced features such as conditional constructions or dynamic linkages remain underused (Drijvers et al., 2010; Ulusoy & Girit-Yildiz, 2024). Although this limited use may reflect considerations of familiarity or instructional efficiency, it also raises questions about whether teachers are fully leveraging the affordances of DGS to support deeper student’ mathematics learning.
Mathematics teachers demonstrate varied preferences for specific DGS platforms, shaped by factors such as accessibility, prior experience, and perceived pedagogical utility. GGB is widely favoured among pre-service teachers due to its free availability, localized language support, and integration into coursework (Akkaya, 2016). Its symbolic features—such as the ability to enter equations, coordinates, and algebraic definitions—further enhance its appeal for visualizing algebraic concepts (Karaarslan et al., 2013). In contrast, Cabri is often selected for its capacity to model 3-D geometric structures (Akkaya, 2016). Despite the distinct advantages of each platform, teachers do not always integrate DGS meaningfully into instruction. Some use it primarily as a time filler or for supplemental purposes (Martinovic & Zhang, 2012). This reflects a persistent gap between the affordances of DGS and its actual classroom integration. As DGS platforms continue to diversify—with differences in interface design, symbolic capabilities, and instructional flexibility (Sinclair & Yerushalmy, 2016)—comparative research is needed to examine how these differences influence instructional decisions. Such insights can inform the design of pedagogical training and guide the development of future tools more closely aligned with classroom needs (Prieto-González & Gutiérrez-Araujo, 2024).
2.2 Technical and Pedagogical Challenges in Using DGS
In practice, mathematics teachers often face technical and pedagogical challenges when working with DGS. Technically, they may encounter difficulty navigating software interfaces, executing intended constructions, and managing unexpected system behaviours (Clark-Wilson & Hoyles, 2017; Ratnayake et al., 2020; Sinclair, 2003). These difficulties are intensified when teachers attempt to design dynamic mathematical tasks that go beyond routine procedures, particularly for those new to technology integration (Ulusoy & Girit-Yildiz, 2024). Software-specific affordances further shape the nature of these challenges. For instance, GSP requires more manual control over object dependencies, which may add complexity for users when constructing tasks or modifying diagrams (Sinclair & Moss, 2012). Similarly, studies report that GGB poses difficulties in translating mathematical expressions into the software (Doruk et al., 2013), and its input bar commands are especially challenging for users with no prior programming experience (Wassie & Zergaw, 2019). These technical barriers influence not only how teachers interact with DGS, but also their instructional strategies and comfort levels when integrating technology into mathematics lessons.
From a pedagogical perspective, a major challenge lies in aligning the use of DGS with instructional objectives while achieving mathematical depth. Research has shown that DGS is often employed as an isolated demonstration tool rather than being integrated into a conceptually grounded or inquiry-oriented learning sequence (Ulusoy & Girit-Yildiz, 2024; Yiğit-Koyunkaya & Bozkurt, 2019). Both teachers and students may place excessive emphasis on visual or procedural aspects of tasks, thereby neglecting deeper mathematical reasoning (Hölzl, 1996). In some cases, tasks are shaped more by the functionalities of the software than by epistemic goals such as generalization or justification (Jones, 2005). Classroom orchestration also presents considerable difficulties. Teachers frequently report challenges in handling technical issues and maintaining classroom control during technology-enhanced lessons, which in turn influences their orchestration strategies and their willingness to adopt student-centred approaches (Drijvers et al., 2010). Observations of microteaching sessions further indicate that many pre-service teachers struggle to implement their intended orchestration strategies—for example, planning to integrate screen-based and board-based explanations but ultimately reverting to conventional board work (Ulusoy & Girit-Yildiz, 2024). These challenges underscore the need for explicit support in planning and managing the integration of technology into instruction.
2.3 Teacher Perceptions of and Attitudes toward DGS
Teachers’ perceptions and attitudes toward DGS are central to their instructional decision-making and technology integration practices. Research has consistently demonstrated that beliefs about a tool’s perceived usefulness, ease of use, and instructional relevance significantly influence whether and how teachers adopt it in the classroom (Pierce & Ball, 2009; Stols & Kriek, 2011). These perceptions not only affect adoption intentions but also shape the quality and depth of actual usage.
Many pre-service mathematics teachers initially report low confidence in using DGS, often due to limited prior exposure or apprehension about its technical complexity (Hew & Brush, 2007). However, research indicates that targeted training and structured professional development (PD) can lead to substantial positive shifts in perception. For instance, studies have shown that training can significantly improve pre-service teachers’ beliefs, motivation, and emotional readiness to teach with digital tools (Akkaya 2016; Reinhold et al., 2021). Participants in these PD programs commonly express increased willingness to incorporate DGS, provided it does not overburden their already limited preparation time (Yildiz & Arpaci, 2024).
Furthermore, teacher attitudes toward DGS tend to evolve through hands-on experience. Segal et al. (2021) emphasize that active engagement in designing and implementing DGS-based tasks fosters greater appreciation of the software’s pedagogical affordances. Similarly, Gulkilik (2023) and Ratnayake et al. (2020) note that well-structured microteaching experiences help pre-service teachers align their technology use with instructional goals and increase their self-efficacy. These findings support the view that sustained, practice-based training plays a key role in developing the dispositions necessary for effective and confident use of DGS in teaching mathematics.
2.4 Analytical Framework
To systematically examine how pre-service mathematics teachers (PMTs) engaged with dynamic geometry software (DGS), this study employed a multi-dimensional analytical framework that integrates both theory-informed and data-driven approaches. The framework was structured to address three core aspects aligned with the research questions: (1) the nature of technological actions taken during instruction, (2) the types of technical and pedagogical challenges encountered, and (3) the evolution of PMTs’ perceptions of DGS through reflective engagement.
The classification of technological action (TA) types in the Dynamic Geometry Task Analysis Framework proposed by Trocki and Hollebrands (2018) served as an important conceptual reference for developing our coding scheme. Recognizing that similar TAs may be enacted through different tools and interfaces in GGB and GSP, we adapted the scheme based on the official user manuals and support documentation of each platform (see Supplementary information). Using individual software operations as the unit of analysis, all observed TAs in the video-recorded mini-lesson presentations were coded and categorized into three overarching types: command-based, drawing-based, and function-based actions. Frequencies were then tallied for cross-platform comparison. This structure enabled a detailed analysis of how PMTs leveraged DGS affordances across varying mathematical topics and software environments.
To investigate the technical and pedagogical challenges PMTs faced, we employed a grounded theory approach (Charmaz, 2006) to analyse mini-lesson videos and associated teaching artifacts. Initial open coding was followed by focused coding through collaborative discussions among three researchers, culminating in two emergent thematic categories: (1) software usability and affordances-related issues, and (2) constraints related to lesson design and instructional implementation. Special attention was given to the instructional contextual in which these challenges emerged and how they shaped classroom orchestration choices. Coding reliability was ensured through iterative consensus-building.
Finally, PMTs’ reflective notes were thematically analysed to trace shifts in their perceptions of GGB and GSP use. Grounded theory again guided the coding process, with categories developed inductively and refined through multiple analytic cycles. The resulting codes captured changes in attitudes, emotional readiness, and expectations for future technology integration. The triangulation of video data, lesson plans, digital materials, and reflections supported a robust and nuanced understanding of how beliefs and instructional strategies co-evolved throughout the professional development process.
3. Methods
3.1 Study Context
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This study is part of a broader research project aimed at enhancing pre-service teachers’ use of technology and their beliefs about teaching mathematics with digital tools. The study was conducted within the context of a university-based mathematics education technology course at a university in Zhejiang, China. This elective course spanned 16 weeks (one semester), consisting of four weekly sessions totaling three hours. It was offered during the penultimate year of the mathematics education program, as the final year is primarily dedicated to teaching practicum and thesis preparation. The participating pre-service mathematics teachers (PMTs), who were being trained to teach middle and high school mathematics, were drawn from two classes comprising a total of 56 students (25 males and 31 females). A
Informed consent was obtained from all participants prior to their involvement in the study.A
The overall design of the training program was guided by six design principles for effective professional development in teaching with digital mathematical tools (Barzel & Biehler, 2020): competence-orientation, participant-orientation, stimulation of cooperation, case-relatedness, diverse instructional formats, and reflective documentation. The intervention was structured into three modules: (1) Module 1 focused on GSP training (weeks 1–7); (2) Module 2 focused on GGB training (weeks 8–13); and (3) Module 3 introduced other digital mathematical tools, including Excel, TinkerPlots, and calculators (weeks 14–16).PMTs were assigned a collaborative group task that included designing and delivering a mini lesson using either GSP or GGB, developing an accompanying lesson plan, and writing reflective notes on the experience. After the completion of Module 1, a schedule was implemented in which two groups presented their mini lessons each week. GSP groups presented first to ensure foundational proficiency before GGB groups delivered their lessons. The outputs—mini-lesson videos, lesson plans, teaching materials, and reflective notes—serve as the primary data sources for this study.
3.2 Research Instrument: Collaborative Group Work Task
Table 1 outlines the design of the collaborative group work task, organized around seven mathematical topics from functions, geometry, and applied mathematics. Each area contains two topics, while the seventh topic is a mixed topic that integrates content from both functions and geometry. For each topic, specific content is provided along with suggested references from the People’s Education Press textbooks or other sources. It should be noted that groups are free to consult alternative versions or supplementary materials as needed.
Topic | Content | Hint | Area |
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1: Quadratic functions | Exploring quadratic functions and equations | Hint from textbooks: “Exploration of properties of quadratic functions”, “quadratic functions, quadratic equations and inequalities.” | Function |
2: Trigonometric functions | Exploring the graphs and properties of trigonometric functions | Hint from textbooks: “Examining the properties of sine and cosine functions using the unit circle.” | Function |
3: Graph transformation | Exploring the properties and applications of rotation | Hint from textbooks: “Rotation.” Additional hint: Interesting exercises and exam questions related to rotation. | Geometry |
4: Regular polygons and circles | Exploring regular polygons and circles | Hint from textbooks: “Exploring conditions for four points to be concyclic.” | Geometry |
5: Wheel path | Exploring mathematical reasoning behind wheel paths | Hint from textbooks: “Discussion on the mathematical reasoning behind circular wheels.” Additional hint: Investigating wheel paths of different shapes, such as triangles or squares. | Application |
6: Optimization | Exploring shortest path problems under fixed perimeters | Hint: Real-life applications involving shortest paths under axial symmetry, such as moving a ladder against a wall to maximize the area of the triangle formed. | Application |
7: Geometric understanding of mathematical formulas | Exploring sine and cosine laws | Hint: Geometric proofs of sine and cosine laws, in addition to vector-based approaches. | Mixed (Function + Geometry) |
Each pair of groups was required to select the same mathematical topic and reach a consensus on the teaching content. After this joint decision, each group independently developed its own lesson plan and delivered a 10-15-minute mini-lesson using either GSP or GGB. To ensure balanced software exposure, if one group selected GSP, the other group in the pair was required to use GGB, and vice versa.
In addition to the lesson plan and mini lesson, each group was required to submit a reflective note as a sub-task. The reflective note focused on the group’s perceptions of using DGS and addressed two main aspects: (1) their attitudes toward GSP/GGB and any changes observed throughout the semester; and (2) their expectations regarding the use of technology in their teaching practicum and future instructional practice.
3.3 Data Collection and Data Coding
Data were collected in 2023. The 56 PMTs were organized into 14 groups of four members each. Groups were labelled using the letter “G” (e.g., G1 for Group 1). Each group was required to submit materials within one week of their presentation. Four types of group-based data were collected, resulting in 14 sets for each type: (1) lesson plans, (2) GSP/GGB teaching materials, (3) mini-lesson videos recorded by the instructor, and (4) reflective notes.
For data coding, the primary focus was on the mini-lesson videos, which were analysed alongside the corresponding lesson plans and digital mathematics teaching materials to enable a comprehensive coding of collaborative group work. Figure 1 illustrates a sample coding from G6’s task.
Fig. 1
Coding of collaborative group work for a GGB task
Regarding technological actions, the two researchers adapted the tool categories provided in the GGB manual and the GSP reference centre (Supplementary information). Individual function operations were treated as the smallest unit of analysis. A binary coding scheme was applied to identify the presence (1) or absence (0) of specific actions, which were then categorized into three overarching groups: command-based, drawing-based, and function-based actions. For example, in Fig. 1(a), the PMT clicked a button labelled “Formula Method,” which was coded as “Button” and categorized under action object tools in the function category. Interrater agreement was 100.0%, indicating high reliability.
To examine technical obstacles and pedagogical problems, we focused on the specific instructional contexts in which the technological actions occurred and annotated notable incidents.
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Grounded theory was used to develop initial codes, followed by researcher discussion to resolve discrepancies and finalize a codebook for consistent application. For example, in Fig. 1(b), clicking the “Formula Method” button produced a formula that appeared excessively large, irregular, and disorganized. This suggests that the PMT struggled with formatting and layout controls, resulting in poor visual presentation of mathematical content during instruction. This instance was coded as “ineffective management of instructional visuals.” After reviewing all items, final codes were assigned. To ensure reliability, three researchers jointly coded each item using the finalized codebook, achieving 100% agreement. Consistent with the above procedures, grounded theory was also used to code the reflective notes, resulting in similarly high interrater reliability (100%).3.4 Data Analysis
Guided by the research questions, we adopted a mixed-methods approach that integrated both quantitative and qualitative analyses.
To address the first research question, we quantified and compared the technological actions performed in GSP and GGB tasks during the collaborative group work. This analysis aimed to identify distinctive patterns and commonalities in the categories of technological actions observed in authentic teaching contexts, as well as to examine how these patterns varied across different mathematical topics and platforms.
To address the second research question, we identified and categorized the challenges encountered by PMTs when teaching with GSP and GGB, focusing on two dimensions: (1) software usability and affordances, and (2) lesson design and implementation. Frequency counts and thematic comparisons were used to reveal the nature of these technical and pedagogical challenges, along with the contrasts and overlaps between the two DGS platforms.
To address the third research question, we conducted a thematic analysis of PMTs’ reflective notes to examine their lesson design strategies, attitudes, and expectations regarding the use of DGS. This analysis highlighted both evolving perspectives and shared concerns across participants.
4. Results
4.1 Comparison of Technological Actions in GSP and GGB
Table 1 shows different types of technological actions the pre-service teachers employed in their GSP or GGB tasks. Specifically, GSP tasks involved significantly more technological actions than GGB tasks, both in total count (GSP: 274; GGB: 205) and in the diversity of tool types. For nine tool types—such as point tools—GSP consistently showed higher frequencies. This pattern also holds across the three categories: commands, drawing, and function, with GGB showing 3, 16, and 186 actions, respectively, and GSP showing 5, 44, and 225. Despite this disparity, the two tools display a similar distribution: actions in the function category overwhelmingly dominate, followed by drawing, while commands are used least and involve only function-related commands.
Topic | DGS | Technological Actions | Total 1 | ||||||||
Commands Category | Drawing Category | Function Category | |||||||||
C | PT | LT | CAT | MET | TT | MOT | AOT | GT | |||
Quadratic Function | GGB | FC (3) | Point (1) PO (1) | Line (2) | / | / | / | Move (13) | Button (12) Slider (2) | SI (5) | 6/39 |
GSP | FC (5) | Point (7) | / | / | / | / | Move (4) | Button (20) IB (19) | S/HO (1) ZO (1) D/R (4) SI (5) | 5/66 | |
Trigonometric Function | GGB | / | / | / | / | / | / | Move (1) | Button (4) CB (3) Slider (5) | SI (4) | 3/17 |
GSP | / | / | / | / | / | / | Pen (10) Move (5) | Button (16) | D/R (1) ZO (2) SP (15) | 3/49 | |
Graph Transformation | GGB | / | Point (1) | Segment (1) PB (1) | / | / | / | / | Button (20) CB (16) Slider (8) | SI (1) FS (1) | 4/49 |
GSP | / | Intersect (1) MC (2) Point (4) | Segment (5) PL (2) | / | Angle (1) | RPT (7) | Move (1) | Button (1) | SP (3) | 7/27 | |
Regular Polygon and Circle | GGB | / | / | Segment (3) PL (1) | CCP (1) | Angle (1) | RPT (1) | / | Button (4) Slider (1) CB (14) | / | 5/26 |
GSP | / | / | Segment (4) PL (1) | CCP (2) | Angle (1) | RPT (2) | Move (7) | Button (9) IB (1) | D/R (1) | 7/28 | |
Wheel Path | GGB | / | MC (1) | Locus (1) | / | / | / | Move (8) | Button (1) Slider (2) | SI (7) SP (4) | 5/24 |
GSP | / | / | / | / | / | / | Move (5) | Button (40) | / | 2/45 | |
Optimization | GGB | / | / | / | / | / | / | Move (1) | Button (3) CB (19) | / | 2/23 |
GSP | / | Point (2) | Line (1) | / | / | RPT (2) | Pen (5) Move (8) | Button (22) | SP (5) | 6/45 | |
Geometric Understanding of Mathematical Formula | GGB | / | / | / | / | / | / | Move (4) | Button (7) | ZO (1) SI (2) SP (13) | 3/27 |
GSP | / | / | / | / | / | / | Pen (2) Move (2) | Button (8) | SP (2) | 3/14 | |
Total 2 | GGB | 3 | 4 | 9 | 1 | 1 | 1 | 27 | 121 | 38 | 205 |
3 | 16 | 186 | |||||||||
GSP | 5 | 16 | 13 | 2 | 2 | 11 | 49 | 136 | 40 | 274 | |
5 | 44 | 225 | |||||||||
| Note. (a) “C” refers to commands; “PT” refers to point tools; “LT” refers to line tools; “CAT” refers to circle and arc tools; “MET” refers to measurement tools; “TT” refers to transformation tools; “MOT” refers to movement tools; “AOT” refers to action object tools; “GT” refers to general tools; “FC” refers to function commands; “PO” refers to point on object; “MC” refers to midpoint or center; “PB” refers to perpendicular bisector; “PL” refers to perpendicular line; “CCP” refers to circle with centre through point; “RPT” refers to rotate around point tool; “IB” refers to input box; “CB” refers to check box; “S/HO” refers to show/hide object; “ZO” refers to zoom out; “D/R” refers to delete/revoke; “SI” refers to switch interface; “SP” refers to switch page; and “FS” refers to font size. (b) The format X/X in the “Total 1” column indicates the number of types of technological actions used versus the total number of actions recorded. | |||||||||||
Within the drawing category, certain tools were used in only a limited range of topics. For example, circle and arc tools, measurement tools, and transformation tools appeared in just 1, 2, and 3 topics, respectively—specifically involving circle with centre through point (3 uses), angle (3 uses), and rotate around point (12 uses). In contrast, sub-tools such as button and move were used frequently, accounting for 167 (34.9%) and 59 (12.3%) actions, respectively. Notably, button was applied across all topics, though its implementation varied between platforms. Due to differences in functionality, the switch page feature was unique to GSP, while an equivalent operation in GGB was performed via switch interface.
When analysed by topic, technological actions appear to be shaped by the openness and specificity of the task design. However, no consistent differences between the two software platforms were observed, except in inquiry-oriented tasks. In Wheel Path, pre-service teachers using GGB employed five tool types across two categories, while those using GSP used only two types within one category. A similar pattern occurred in Optimization, where GGB users engaged two tool types in one category, compared to six types across two categories in GSP. These disparities suggest that inquiry-based tasks may prompt more varied tool use depending on the platform, a distinction not evident in more structured, non-inquiry tasks.
Overall, more technological actions were observed in GSP tasks, with the function category being the most frequent and the commands category the least. Some sub-tools appeared exclusively in one software. Additionally, the mathematical topic influenced both the type and frequency of actions.
4.2 Technical Challenges and Pedagogical Issues in Using GSP and GGB
Table 2 presents the challenges encountered by pre-service teachers when using GSP and GGB for mathematics instruction. The data are categorized into two domains—technical challenges and pedagogical challenges—reflecting issues related to software learning and usability as well as instructional planning, explanation, and interaction. Key findings are summarized below.
1. Technical Challenges | GSP | GGB | |
|---|---|---|---|
1.1 Software Learning and Operation | 10 | 8 | |
Insufficient mastery of software functions | 9 | 6 | |
Error in executing instructional design | 1 | 2 | |
1.2 Interface and Usability | 15 | 5 | |
Difficulty with annotation control | 3 | 0 | |
Difficulty inputting mathematical language | 1 | 1 | |
Difficulty adjusting/repositioning objects | 5 | 2 | |
Lack of efficient reset functionality | 3 | 0 | |
Inefficient multi-page navigation | 1 | 1 | |
Interruptions caused by frequent tool switching | 2 | 1 | |
2. Pedagogical Challenges | GSP | GGB | |
2.1 Lesson Planning and Task Design | 4 | 0 | |
Lack of consideration for students’ prior knowledge | 1 | 0 | |
Incoherent task sequencing | 1 | 0 | |
Overuse of leading questions | 2 | 0 | |
2.2 Instructional Clarity | 17 | 18 | |
Inaccurate instructional explanations | 7 | 6 | |
Ineffective explanation strategies | 10 | 12 | |
2.3 Technology Integration in Teaching | 11 | 18 | |
Inefficient instructional workflow design | 5 | 2 | |
Ineffective management of instructional visuals | 4 | 9 | |
Failure to implement technological elements | 2 | 7 | |
2.4 Classroom Interaction and Feedback | 4 | 3 | |
Lack of timely feedback | 2 | 0 | |
Limited teacher-student interaction | 1 | 2 | |
Insufficient time for student cognitive processing | 1 | 1 | |
In terms of technical challenges, pre-service teachers encountered more usability-related difficulties when using GSP (15 cases) than GGB (5 cases). These included problems with adjusting the position or size of objects, adding annotations, and resetting actions. For instance, five participants struggled to reposition shapes or points in GSP, leading to delays in demonstrating mathematical ideas. In addition, insufficient mastery of software functions—such as setting appropriate slider ranges or linking multiple objects to create dynamic relationships—was a common problem in both GSP tasks (9 cases) and GGB tasks (6 cases), suggesting that while the tools are easy to learn at a basic level, achieving deeper fluency—particularly in combining functions for instructional purposes—remains challenging for both platforms.
Pedagogical challenges were more frequently observed in GGB tasks, particularly in relation to the integration of technology into instruction. Participants often struggled to manage visual representations effectively (9 cases in GGB vs. 4 in GSP), such as aligning dynamic elements with explanatory text or avoiding overlaps that made key content difficult to read. Additionally, several pre-service teachers chose not to use GGB when explaining critical concepts, despite having prepared digital materials, and instead reverted to traditional blackboard-based explanations (7 cases in GGB vs. 2 in GSP). These difficulties suggest that while GGB offers more advanced functionalities, it also imposes greater cognitive and pedagogical demands, which may discourage novice teachers from fully engaging with the platform during live instruction.
Instructional clarity emerged as a prominent challenge across both platforms. The subcategory ineffective explanation strategies had the highest number of coded instances within the pedagogical domain (10 in GSP and 12 in GGB). In many cases, teachers presented mathematical concepts without clearly linking their digital actions to the intended ideas, or failed to pace their explanations in ways that allowed students to follow visual changes. These findings indicate that even when technical procedures were executed successfully, the ability to communicate mathematical reasoning effectively through digital representations remained a significant hurdle.
Additionally, a few instructional issues were observed only in GSP-based tasks. For instance, some pre-service teachers posed highly directive questions to lead students toward pre-scripted dynamic demonstrations, while others combined unrelated visual effects into loosely connected instructional sequences. These behaviours suggest a tendency to design lessons around available tool functions rather than instructional goals. Similar patterns were not observed in GGB-based tasks, which may be due to the limited sample size or the fact that some participants chose to avoid using technology when explaining complex mathematical concepts.
Finally, while relatively less frequent, challenges related to classroom interaction and feedback were observed in both GSP- and GGB-based tasks. In several cases, pre-service teachers became overly focused on operating the software and overlooked opportunities to check students’ understanding or respond to their questions. Others failed to provide adequate processing time after dynamic demonstrations, moving on before students could make sense of the visual transformations. These instances suggest that the use of digital tools, while beneficial for visualization, may at times compromise instructional responsiveness if not carefully managed.
4.3 Attitudes and Future Intentions for Using GSP and GGB
Reflections on attitudes and future intentions were provided by 12 groups in total, although one group did not respond to the prompt on attitudes. As a result, attitude-related data were drawn from 11 groups (GGB: 5; GSP: 6), and future intention data from all 12 groups (GGB: 5; GSP: 7).
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Regarding attitudes toward using GSP and GGB, participants reported a clear disparity in initial familiarity with the two tools. A majority of GGB groups (80%) expressed concerns about their ability to use the software effectively or noted limited prior experience. In contrast, only one GSP group indicated unfamiliarity with GSP, suggesting that pre-service teachers were generally more confident and experienced with it at the outset. Nevertheless, through repeated use and guided exploration, participants reported gradually becoming more proficient with both tools, which enabled more purposeful integration into instructional planning and delivery.A
Building on the initial differences in familiarity, participants described distinct ways of responding to the challenges of using each tool. For GGB, one group emphasized the importance of decomposing complex tasks into smaller, manageable components. They noted that working collaboratively helped improve both task design and individual learning outcomes, reflecting a process of adaptation to a previously unfamiliar platform. In contrast, two GSP groups—despite being more experienced with the tool—highlighted specific limitations in its classroom usability. They pointed out that managing animations and page transitions in GSP required multiple steps, making it less efficient during live instruction. As a result, they suggested supplementing GSP with tools like PowerPoint or Flash, which allow for smoother transitions and easier control through keyboard navigation.Despite these differences, nearly all groups recognized the pedagogical value of dynamic geometry software. Participants highlighted its capacity to represent abstract mathematical ideas dynamically, facilitate inquiry-based learning, attract student attention, and foster an engaging classroom environment. As Group 9 noted, “…we found that the robust graphing and visualization features of GGB allow for the rapid and intuitive presentation of mathematical concepts… Teachers can visually demonstrate problem-solving processes, thereby making abstract mathematical ideas more accessible to students.”
When describing their intentions for future use, most groups expressed interest in incorporating DGS selectively, depending on the content to be taught. Topics involving spatial reasoning or graphical representation were seen as especially well-suited. Half of the groups (three from each platform) emphasized the importance of promoting teacher-student interaction through digital tools and guiding students in independent exploration. Additionally, one-third of the groups (two from each platform) highlighted the need to assess students’ prior knowledge, monitor learning progress, and adjust instruction accordingly. While only one GGB group explicitly stated a strong intention to adopt the software in their future teaching, most participants emphasized the importance of aligning technology use with instructional purpose. As Group 5 reflected, “GSP or GGB is more effective for topics involving spatial reasoning or graphical representations, such as problems related to circles, function graphs, three-dimensional shapes, symmetry, and transformations. However, for tasks like theorem proofs or purely computational exercises, traditional teaching methods may still be preferable.”
5. Discussions and Conclusions
This study examined how pre-service mathematics teachers (PMTs) engaged with two widely used dynamic geometry software (DGS) platforms—GeoGebra (GGB) and Geometer’s Sketchpad (GSP)—in a semester-long professional development course. Specifically, we investigated their technological actions, the challenges they encountered, and how their perceptions evolved through collaborative task design. The findings offer several implications for mathematics teacher education and future research.
First, PMTs employed more technological actions in GSP tasks than in GGB tasks. Function-based actions were the most frequently used in both platforms, while command-based actions were used the least. The command-based tools, though potentially powerful for automating complex constructions and facilitating instructional efficiency, were rarely applied. This underuse may stem from PMTs’ limited experience with such tools, their unfamiliarity with scripting-based features, or discomfort with programming logic. This finding supports prior research suggesting that GGB’s input bar commands present challenges for users without prior programming experience (Wassie & Zergaw, 2019). Given the increasing emphasis on algorithmic thinking and programming skills in this digital world (Oda et al., 2021), training programs should incorporate explicit instruction on the pedagogical value and practical use of command-based DGS functionalities.
Second, PMTs used more technological actions in geometry-related tasks than in algebraic or applied mathematical tasks. This may be attributed to the intuitive dynamic affordances of DGS in visualizing geometric transformations and spatial relationships, while algebraic topics is often more familiar and manageable through traditional methods. These findings suggest that professional development should enable PMTs to explore and compare the utility of digital tools across various mathematical domains. Building capacity to match tools with content-specific teaching goals is essential for meaningful technology integration.
Moreover, the most frequently used individual technological action was the “button” feature, often used for toggling visibility or controlling animations. However, pedagogically valuable functions—such as annotation tools, reset buttons, and page transitions—were either missing or difficult to access in both platforms. This highlights a gap between current software functionalities and classroom teaching needs. As Drijvers (2020) notes, collaboration among educational designers, software developers, teachers, and researchers can result in tools that are not only theoretically grounded but also practically useful. Collaborating with mathematics educators and addressing pedagogical demands—such as annotation, pacing, and interactivity—should be a priority in software design.
Third, although PMTs generally demonstrated proficiency with basic DGS functions, they encountered difficulty composing technological actions into coherent, mathematically meaningful sequences. Many struggled to connect actions with instructional goals or to break complex tasks into manageable sub-actions. This highlights the importance of not only tool-based training but also the development of pedagogically informed task design strategies. Effective sequencing of technological actions is critical to mathematics instruction and teacher professional growth (Markle & McGarvey, 2025; Pincheira & Alsina, 2022). We recommend that training programs explicitly address how to scaffold complex task design through modular and compositional use of digital tools.
The findings also revealed that some PMTs engaged in what may be characterized as “instrumental use” of technology—employing DGS features without aligning them with teaching objectives or fostering deep mathematical understanding. In several cases, PMTs appeared more focused on demonstrating software functions than on supporting student learning. Additionally, they often overlooked the student perspective, offering limited opportunities for interaction, feedback, or formative assessment. These observations, consistent with prior studies (e.g., Hollebrands & Lee, 2016; Zhu & Xu, 2023), underscore the need for reflective training on pedagogical rationale behind technology use. Teacher education programs should emphasize how digital tools can enhance student learning, rather than be used for their own sake.
Finally, PMTs’ reflective notes showed meaningful changes in their perceptions and intended used of DGS. Those working with GGB progressed from unfamiliarity to comfort and purposeful use, while those using GSP—starting from a place of greater familiarity—moved toward more critical and evaluative engagement. This contrast supports previous findings that prior experience with DGS shapes teachers’ adoption and use of such tools (e.g., Cevikbas & Kaiser, 2021). In addition, many PMTs expressed ambivalence about balancing traditional teaching approaches with technology-enhanced instruction. While most recognized DGS’s value for topics such as spatial reasoning and transformations, they remained cautious about its application to more abstract or procedural content. This finding resonates with Recio et al. (2019), who reported that some PMTs felt disoriented in dynamic instructional environments and preferred the familiarity of traditional reasoning process. These insights highlight the importance of providing opportunities for authentic teaching practice, critical reflection, and peer discussion to support PMT’s instructional decision-making with technology.
This study has several limitations. The use of a convenience sample and reliance on mini-lesson tasks conducted outside authentic classroom environments may limit the generalizability of findings. Moreover, the short duration of the intervention precluded long-term tracking of participants’ development. Future research should examine how PMTs use DGS in actual classroom contexts, particularly how their pedagogical decisions evolve through experience and feedback. Comparative research on different DGS platforms is also needed to better understand how software affordances and constraints influence instructional strategies. Lastly, we encourage stronger collaboration between software developers and mathematics educators to align tool design more closely with classroom realities. Features that support annotation, pacing, page management, and classroom orchestration are critical for making digital tools both mathematically robust but pedagogically effective.
In sum, even though DGS is one of the most helpful and widely used tools in mathematics classrooms, PMTs are still struggling with meaningful DGS integration, highlighting their dependence on simple actions, challenges in designing coherent tasks, and a tendency toward instrumental use. They exhibited varied DGS use, including limited use of advanced features, a preference for geometry tasks, and frequent reliance on basic tools, such as buttons. PMTs’ growth in perceptions varied by their prior familiarity with DGS, emphasizing the importance of authentic practice, reflection, and content-specific decision-making. Therefore, professional development programs should move beyond technical skills and emphasize how teachers can align mathematical goals, pedagogical strategies, and the tool affordances. Furthermore, educational software developers should work closely with teachers and researchers to ensure tool design meets classroom needs. Future research should inform teacher education and software development by examining how different platforms support or constrain instructional strategies in real classrooms.
Competing interests
The authors declare no competing interests.
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Data Availability
The datasets generated during and/or analysed during the current study are not publicly available due to their proprietary nature but are available from the corresponding author on reasonable request.
Ethical approval
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All procedures performed in studies involving human participants was carried out under the ethical guidelines. A
This study was approved by the Academic Committee of the School of Artificial Intelligence in Taizhou University (Approval 20230301). A
Each participant in this research signed an informed consent form. To ensure confidentiality, students’ personal identifiers were removed prior to data processing.Informed consent
All participants were voluntary to participate in this research, and they were informed of the research objective and context.
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Written informed consent was obtained from all participants.A
Funding
declaration
This work was in part supported by the [Science and Technology Commission of Shanghai Municipality] under Grant [22DZ2229014], and [Ministry of Education of China] under Grant [22YJC880035].
Electronic Supplementary Material
Below is the link to the electronic supplementary material
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Author Contribution
YS: Conceptualization; investigation; writing – original draft; formal analysis; writing – review and editing. SL: Conceptualization; investigation; writing – original draft; visualization; methodology; writing – review and editing; project administration. QZ: Data analysis; writing – original draft. YS: Data collection; project administration.
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Acknowledgement
The authors wish to thank Miss Yurong Shen for her assistance at various stages of this study.
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