Video-based online mathematics instruction with GeoGebra: a visual learning analytics-supported study to enhance open educational resources and practices

Abstract

Open Educational Resources (OER) have the potential to enhance equity in education. Many regions and education systems thus prioritise integrating these low-cost or free resources into mathematics teaching and learning. However, teachers face challenges when integrating OER into their instructional practices to prepare students for educational success. They need frameworks and guidelines to use OER and related practices (i.e., Open Educational Practices; OEP). Accordingly, we conducted a year-long synchronous online teacher professional development programme, during which teachers learned to reuse/adapt the provided GeoGebra applets and use GeoGebra features to create and integrate OER into their teaching practices. In this study, we aim to develop GeoGebra-oriented and theoretically supported guidelines for OER design and OEP tailored to mathematics teachers. To this end, we analysed teachers’ GeoGebra artefacts and their corresponding micro-teaching videos through the lens of Visual Learning Analytics (VLA) within Mathematics Discourse in Instruction (MDI) framework. In total, 650 talk turns from 14 GeoGebra-supported micro-teaching videos were analysed alongside experts’ comments. GeoGebra's interactive tools (e.g., sliders and check boxes) used in the teachers’ OER were identified, and the insights provided by VLA were explored. Based on our findings, we formulated guidelines for video-based online mathematics instruction with exemplification and explanatory talk. For example, greater integration of exemplification into teaching practices can be promoted by leveraging GeoGebra's features for observation, measurement, and construction tasks. These implications for OER design and OEP potentially contribute to equitable and quality education, in line with Sustainable Development Goal 4.

1 Introduction

Open Educational Resources (OER) are learning, teaching and research materials in any format and medium that reside in the public domain or are under copyright that have been released under an open license, that permit no-cost access, re-use, re-purpose, adaptation and redistribution by others (UNESCO, 2019). They have the potential to improve educational equity by allowing teachers and students worldwide to access and reuse these low-cost or free resources at any time (Adil et al., 2024; Lo et al., 2022). In the post-pandemic era during which many individuals are facing economic challenges, various regions and education systems have prioritised the integration of digital tools and OER into mathematics teaching and learning (Lo et al., 2025; TLS and Kusumah, 2022). GeoGebra, a free dynamic mathematical application, is suitable for creating OER in the form of digital applets featuring interactive and dynamic elements (Lo et al., 2024; Pant, 2021; Seto et al., 2025; Yao, 2024). GeoGebra's tools (e.g., sliders) enable teachers to guide students in exploring, visualising, and gaining a deeper understanding of mathematical relationships (Lo et al., 2024; Yohannes and Chen, 2023). To facilitate the integration of OER into teaching practices, the concept of Open Educational Practices (OEP) has emerged (Tlili et al., 2025). OEP encompass activities that include searching for existing OER, designing and adapting OER, and developing problem sets and examples for specific educational contexts (Van Allen and Katz, 2023). Notably, teachers need to develop essential skills to engage in OEP (Tlili et al., 2023), thereby overcoming barriers to the use of OER (Adil et al., 2024).

2 Theoretical framework

Huang et al. (2020) proposed a theoretical framework for OEP, illustrating the relationships between OEP and (1) OER, (2) open teaching, (3) open assessment, and (4) open collaboration (Figure 1). In this framework, these relationships are afforded by technology, which serves as an enabling condition facilitating the development of OEP. In this study, we focused on OEP and OER (Section 2.1), supported by GeoGebra and its functionalities (Section 2.2). To extend the existing theoretical framework, we incorporated the MDI framework and the VLA technology (Section 2.3) as additional dimensions (Figure 1). The integration of these additional dimensions into the original framework has the potential to enable an objective analysis of the interactions between OEP and OER afforded by enabling technology.

Figure 1

2.1 OER and OEP

OER are defined as teaching, learning, and research materials available in various formats or media, which are either in the public domain or protected by copyright and released under open licences (UNESCO, 2019). These licences facilitate unrestricted use, reuse, repurposing, adaptation, retention, and redistribution by third parties (Tlili et al., 2023). OER have the potential to promote educational equity by providing teachers with readily available and adaptable resources, which aligns with the United Nations’ (2021) Sustainable Development Goal 4 (Huang et al., 2024). However, Harvey and Bond (2022) found that some teachers are concerned about the effectiveness of OER in enhancing student learning outcomes in secondary mathematics education. These concerns can be categorised into resource-related concerns and practice-related concerns, as shown in Table 1. The resource-related concerns can be further categorised into content-level and presentation-level. At the content level, concerns about content quality echo the findings of Tlili et al. (2023), who noted that not all OER meet the required standards for accuracy, coherence, and pedagogical effectiveness. In addition, some teachers have found that using OER poses challenges and requires adjustments in instructional practices when transitioning from textbooks (Harvey and Bond, 2022). At the presentation level, Irvine et al. (2021) found that inappropriate text order and layout in OER can pose problems in understanding the information conveyed. To address these challenges, efforts are needed to develop materials that facilitate their integration into teaching practices and to improve the quality and comprehensibility of OER (see Section 2.2).

In addition to resource-related concerns, Table 1 shows that teachers express practice-related concerns, including an overemphasis on certain selected examples and practice problems, while insufficient basic practice opportunities are offered for certain concepts (Harvey and Bond, 2022). To address these issues, appropriate teaching methods must be adopted for OER (Zulaiha and Triana, 2023). To facilitate integration, the concept of OEP has been introduced to promote the incorporation of OER into innovative teaching approaches (Tlili et al., 2025). OEP can diversify and improve educational materials, which requires teachers to adapt to new paradigms of curriculum delivery (Shareefa et al., 2023). Specifically, OEP go beyond simply creating and (re)using OER to provide active and engaging learning experiences using OER, including open assessment, open collaboration, and open pedagogy (Zhang et al., 2020a). Therefore, the development of comprehensive teaching frameworks and guidelines for OEP is essential to help mathematics teachers balance the emphasis on knowledge presentation and working examples, which essentially relate to their discursive practices (see Section 2.3).

2.2 Geogebra and its functionalities

GeoGebra is a dynamic mathematical application suitable for teachers and students of all education levels. Recognised as an effective tool for developing OER in mathematics (Pant, 2021), GeoGebra's functionalities can address some of the resource-related concerns identified by Harvey and Bond (2022). At the content level, GeoGebra can supplement textbook activities by facilitating rapid and accurate geometric constructions (Hidayat et al., 2023) through features such as lines, segments, angles, and circles, which simulate tangible tools such as rulers, protractors, and compasses (Birgin and Topuz, 2021; Florio, 2022). To help teachers guide students in understanding mathematical concepts, GeoGebra's text annotation features allow for detailed descriptions and explanations of mathematical steps and concepts within GeoGebra applets (Huang et al., 2024). To visualise complex relationships, its animation and manipulable features, such as dragging, can provide visual insights into complex relationships and enhance conceptual comprehension (Hidayat et al., 2023). For example, Emul et al. (2022) used GeoGebra to solve geometric locus problems through dragging functionalities. They found that teachers were successful in generalising, conjecturing, and proving by observing the visual structures created in GeoGebra. Regarding its manipulable features, the GeoGebra applets created in Lo et al. (2024) and Seto et al. (2025) provided several sliders for students and teachers to change their corresponding values (e.g., the coefficients of a parabola and a circle). Both studies found that these applets significantly improved students’ mastery of mathematical concepts. At the presentation level of resource-related concerns, GeoGebra's flexibility allows teachers to customise the layout, display options, and interactive tools according to the complexity and nature of specific mathematical problems (Siregar, 2025). Furthermore, it can integrate various mathematical domains, including geometry, algebra, spreadsheets, graphs, statistics, and calculus, into a user-friendly interface (Rahmadi et al., 2021).

2.3 The MDI framework and the VLA technology

As Avila et al. (2020) suggested, researchers can use learning analytics tools to examine the impact of OER implementation in teaching practices. With visualisation technology, VLA can serve as an analytical tool to provide visual insights into learning analytics and enhance the understanding of the complexities inherent in discourse data (Lo and Chen, 2025). To observe and evaluate teachers’ practices with the OER they have developed, our VLA platform developed by Chen (2020) is capable of visualising teachers’ MDI. As noted in Lo and Chen (2025), the VLA platform enables the transcription, coding, analysis, and visualisation of video discourse through various representations, such as graphs and statistical data. Researchers first transcribed teachers’ micro-teaching videos into written transcripts and divided them into talk turns. Each talk turn was then categorised into one of four categories derived from the MDI framework. Subsequently, the researchers identified which of these talk turns pertained to the use of GeoGebra. Figure 2 shows that our VLA platform can display a video recording (Figure 2), categorise talk turns (Figure 2C), and present video dialogue transcripts (Figure 2B) synchronously. In Figure 2C, each row on the x-axis features bubbles of different sizes, where the size of a bubble corresponds to the number of words in a talk turn. Specifically, larger bubbles indicate talk turns containing more words. This VLA platform can thus facilitate a comprehensive analysis of teachers’ use of OER and their discursive practices.

Figure 2

3 Methods

This section first describes the research context (i.e., a year-long synchronous online teacher professional development programme), followed by the teachers who participated in this study and the experts involved in the evaluation of their OER and OEP. It then details data collection and analysis methods.

3.1 Research context

This study was conducted as part of a year-long synchronous online teacher professional development programme for mathematics teachers in China. This programme comprised eleven lessons, including 10 two-hour fully online training lessons and one concluding lesson. Throughout the programme, the teachers were introduced to the knowledge and skills needed to create their own teaching applets using GeoGebra (e.g., the use of sliders). In terms of OEP, the teachers were guided on how to adapt and incorporate existing GeoGebra applets into their teaching practices, with specific examples (see https://www.geogebra.org/m/a7s2hpc8 for a review) created by the instructor and his team.

3.2 Participating teachers

Forty in-service secondary school mathematics teachers from eight schools participated in our teacher professional development programme. The participants were recruited through the research team's prior connections in Mainland China. Their participation was voluntary. Their teaching experience ranged from 1 to 36 years (M = 18.2; SD = 8.2). After completing the 10 training lessons, they were encouraged to design and create their own OER using GeoGebra or to reuse/adapt the sample applets mentioned in Section 3.1. Subsequently, they video-taped how they used the OER in their teaching practices. Each video was limited to a maximum duration of 15 minutes. Notably, the submission of their videos and GeoGebra applets was voluntary to avoid imposing additional workload and burden on the teachers. Among the 40 teachers, 14 submitted their work to demonstrate their teaching approaches. One should therefore exercise caution when interpreting these data, as the artefacts voluntarily submitted by these teachers might reflect higher levels of technological and pedagogical proficiency as well as greater motivation. According to Ando et al. (2014), this sample size was sufficient for a study primarily using qualitative approaches.

3.3 Experts involved in the evaluation

To evaluate the quality of teachers’ OER and OEP, five education and subject experts, ranging from Assistant Professor to Full Professor, were invited to provide their feedback. These experts had relevant expertise in mathematics, mathematics education, and technology-enhanced learning, thereby ensuring a comprehensive and informed evaluation. The chair of the expert panel initially collected written feedback on each artefact, which was subsequently synthesised by consolidating similar comments. The resulting set of comments and suggestions was organised into four categories: (a) supportive, (b) critical, (c) suggesting alternatives, and (d) proposing refinements. This synthesised feedback was then circulated among all panel members, who had reviewed, agreed upon, and endorsed the final version for our subsequent analysis (see Section 3.4).

3.4 Data collection and analysis

The data were collected from three major sources: (1) GeoGebra applets adapted and/or created by the teachers, (2) their corresponding micro-teaching videos, and (3) the experts’ comments and suggestions. To address RQ1 regarding the interactive tools used by the teachers when adapting and/or creating their OER, the GeoGebra applets were categorised according to different GeoGebra features (e.g., the “Slider” feature). In each category, we present a representative example for illustration. To address RQ2 regarding the insights provided by VLA into OEP, the teachers’ micro-teaching videos (named MTV-01 to MTV-14) were transcribed and then analysed using the MDI framework (Adler and Ronda, 2015) to code their mathematics instruction. The analysis involved identifying talk turns associated with specific coding categories in MDI framework (comprising examples, tasks, naming, and legitimations, as described in Section 2.3). These talk turns were subsequently mapped to relevant GeoGebra features, if utilised. We used the GeoGebra applet created by Seto et al. (2025) as an illustrative example. The researchers demonstrated various “Examples” to facilitate students’ exploration of quadratic graph features through their OER, using the “Slider” feature to manipulate the coefficients of x², x, and the constant term. In the present study, we further employed the VLA platform to observe teaching practices with OER and to provide guidance for the enhancement of OEP. Some representative talk turns and rationale for our coding are presented in the Appendix.

For both RQ1 and RQ2, the experts’ comments and suggestions were used for triangulation. First, all comments and suggestions for each artefact were combined into a single dataset. A qualitative content analysis was conducted to identify similar and overlapping narratives across the artefacts. The synthesised feedback was then coded deductively into four categories adopted by the expert panel chair: (a) supportive (affirming strengths, effective design, or clear verbal instructions), (b) critical (identifying weaknesses or issues), (c) suggesting alternatives (proposing different approaches to framing mathematical ideas or presenting examples), and (d) proposing refinements (recommending concrete improvements to the OER or OEP). Following coding, the narratives in these four categories and across the 14 teachers were examined to identify common patterns in the experts’ perceptions of GeoGebra-supported OER and OEP. Representative narratives from each category were selected to illustrate typical examples of expert feedback, with particular emphasis on how these comments aligned with or complemented the analysis of teachers’ GeoGebra applets and micro-teaching videos. Notably, the content analysis aimed to provide GeoGebra-oriented guidance for the improvement of OER and OEP, rather than to compare or rank the quality of individual artefacts. To ensure coding accuracy and reliability, the transcripts were double-coded by the first and second authors. The coding discrepancies were resolved through discussion until a consensus was reached. To enhance transparency and trustworthiness, direct quotations from experts’ feedback were included to demonstrate a clear audit trail from data to interpretation (Eldh et al., 2020). Therefore, some data were translated into English for reporting purposes.

4 Findings

Table 2 provides an overview of the 14 GeoGebra applets and their corresponding micro-teaching videos, with a description of their topics and the GeoGebra features used. As indicated in Table 2, only one artefact (MTV-12) related to a statistical topic, whereas others focused on topics related to geometry and measurement (n = 7) and numbers and algebra (n = 6). The findings are structured according to each research question.

4.1 RQ1: what interactive GeoGebra tools did the teachers use when adapting/creating their OER?

All teachers in this study integrated the dynamic features of GeoGebra into their OER development (see Table 2), including “Slider,” “Point,” and “Check box.” These resources were designed to support the teaching and learning of geometry and algebra.

4.1.1 The “Slider” feature

The “Slider” feature can be used to animate geometric constructions in geometry teaching (e.g., MTV-03, MTV-05, and MTV-14). For example, the teacher in MTV-03 (Figure 3A) used the provided GeoGebra applet to demonstrated the construction of an angle congruent to a given angle using a compass and straightedge. The “Slider” feature was used to control and visualise the sequential steps of the construction process. The teacher allowed the students through each step, as displayed on the GeoGebra applet, providing a clear demonstration of the construction process.

Figure 3

In addition to facilitating geometric constructions, the “Slider” feature can be used to manipulate the positions of mathematical objects (e.g., MTV-09 and MTV-10). For example, the teacher in MTV-09 (Figure 3B) created a GeoGebra applet using the “Slider” feature to control the position of point P to demonstrate various configurations of triangle APC. Point P was moved sequentially from point A to point D, then from point D to point C, illustrating how the triangle's shape and area change with the movement of point P. In the teaching of algebra, the “Slider” feature can be used to change the numerical values or parameters of examples. For example, Figure 3C shows that the teacher in MTV-09 created a GeoGebra applet using the “Slider” feature to change the cycling speed of a person and its animation to introduce the concept of speed.

4.1.2 The “Point” feature

When teaching geometry, some of the teachers used the “Point” feature to illustrate locus and geometric relationships (e.g., MTV-08 and MTV-13). Figure 4A shows that the teacher in MTV-13 created GeoGebra applets placing point F as a moving point on the line segment BC. In addition, point E was defined as the intersection of the curve y = k/x and the line segment AC. Point C’ was used to represent the symmetry of point C. As point F moved from point B to point C, the locus of point C’ was displayed (see Figure 4). As our experts noted, “This OER enable students to observe the geometric transformation in real time and deepen their understanding of symmetry.”

Figure 4

When teaching algebra, the “Point” feature can be used to represent numbers as points on the number line and compare the number directly. For example, in MTV-04 (Figure 4B), as the point moved to the right, the corresponding number increased; conversely, when the point moved to the left, the number decreased. As our experts indicated, “This GeoGebra applet helps students intuitively understand the concepts of number size and order.”

4.1.3 The “Check box” feature

The “Check box” feature can be used to toggle the visibility of mathematical objects. For example, the teacher in MTV-01 (Figure 5A) based on the provided GeoGebra applets, further added the “Check box” to control the display of the calculation process of the area and other relevant objects.

Figure 5

In addition to points and triangles, the teachers in MTV-03 and MTV-05 used the “Check box” features in provided GeoGebra applets to control the visibility of angle measurements (Figure 5B). This functionality helped to demonstrate the angular congruence between two angles. For displaying distance measurements, the “Check box” feature can be used to show the lengths of line segments. For example, the teacher in MTV-02 (Figure 5C) used the “Check box” feature in a provided GeoGebra applet to display the sum of the lengths of line segments AC’ and BC’ to illustrate the condition in which the shortest distance occurred.

4.2 RQ2: how does VLA provide insights into the development of OEP?

The teachers produced micro-teaching videos in which they used the provided GeoGebra applets or their created GeoGebra applets to teach mathematics. The talk turns in these videos were analysed using the MDI framework (Adler and Ronda, 2015), as outlined in Section 2.3. All of the teachers incorporated exemplification and explanatory talk into the MDI framework. Table 3 shows that 43.4% of the talk turns fell into the “Tasks” category, representing a higher percentage than “Examples”, “Naming”, and “Legitimations”. The majority of these talk turns were related to the use of GeoGebra features and thus were classified into three subcategories, namely observation, measurement, and construction. As our experts suggested, “In addition to using the MDI framework via the VLA platform to evaluate the comprehensiveness of teaching practices, the framework can serve as a guide for teachers in adapting and developing OER and associated instructional practices.” In the following sections, we present our findings regarding each category and subcategory, along with the experts’ comments.

4.2.1 Examples

All of the micro-teaching videos demonstrated that the teachers incorporated multiple examples to support their instructional content. More than 50% of the talk turns used for examples relied on Microsoft tools (e.g., PowerPoint) and/or PDF documents. Regarding GeoGebra features, the teachers used functions such as “Point” and “Slider” to present and demonstrate different variations in their examples (see Table 4).

The teachers primarily used Microsoft tools rather than GeoGebra features. As the experts remarked, “Most teachers have become accustomed to using Microsoft tools for online classes. In addition, certain graphics, such as complicated function relationship images, were challenging for the teachers to replicate using GeoGebra within the limited timeframe [of the professional development programme].” Regarding the GeoGebra applets used in MTV-10 (Figure 6B), the experts pointed out that “In the absence of accompanying text descriptions and guidance, these applets as standalone OER are unlikely to be sustainably used by other teachers.”

Figure 6

In contrast, the experts appreciated that the teacher in MTV-09 was able to integrate the “Text” feature into her OER to describe her examples and enhance student understanding during teaching. In their words, “Teachers from other schools can directly adopt these OER to present the topic without needing supplementary materials. This integration [of GeoGebra applets and text descriptions] enhances both the instructional effectiveness and the applicability of OER.” In addition, the integration of dynamic features such as “Slider” enabled the teachers to present multiple scenarios through interactive adjustments of numerical values. Taken together, the VLA of the video data shows that the teacher in MTV-09 was able to refer to the “Text” feature [Figure 7 (A1)] in her GeoGebra applets (Turn 13, Figure 7B) and use the “Slider” feature [Figure 7 (A2)] to change the values of the variables to increase the variations of the example. Specifically, she manipulated the sliders that controlled the distance, speed of the two people, and time, while allowing the students in exploring different cases, such as where person A was faster than person B and vice versa. The experts observed that this practice with OER allows students to experience a variety of scenarios. In addition, they have more opportunities to deepen their understanding of the formulas involving these variables. Most importantly, for less proficient students, teachers can provide simpler numerical values tailored to their level.

Figure 7

4.2.2 Tasks

When assigning tasks involving observation, measurement, and construction, most of the teachers used GeoGebra features (see Table 4). The “Point” feature was the most frequently used tool during observation activities, while the “Slider” feature was most commonly used in construction activities. Tasks related to measurement had the fewest talk turns, with a few teachers using the “Angle” and “Distance or Length” features.

4.2.2.1 Observation

Regarding tasks involving observation, most talk turns focused on the using of the “Point” feature to demonstrate dynamic animation. For example, the VLA of the video data indicates that the teacher in MTV-02 employed a provided GeoGebra applet and used the “Point” feature [Figure 8 (A1)] to illustrate various positions corresponding to different lengths (Turn 7, Figure 8B) and identify the minimum sum of lengths [Figure 8 (A2)]. During the demonstration, she moved the “Point” from left to right, allowing her students to observe that the sum of the lengths [Figure 8 (A2)] decreased and then increased. As our experts noted, “Illustrating a moving point on a blackboard is difficult. By using GeoGebra's dynamic features, the teacher did a great job guiding students in interactively observing the movement, making the abstract situation more tangible and enhancing their understanding through visual animation.”

Figure 8

4.2.2.2 Measurement

Regarding tasks involving measurement, the teachers used the “Angle” and “Distance or Length” features as mathematical tools, similar to using a protractor or ruler in a traditional classroom. For example, the VLA of the video data indicates that the teacher in MTV-05 employed a provided GeoGebra applet that used the “Angle” feature (Figure 9A) as a protractor to measure the angle (Turn 15, Figure 9B). He used this measurement to demonstrate that the central angle is twice the measure of an inscribed angle subtended by the same arc. Similarly, in MTV-14, the teacher explained: “We can demonstrate that the angles and lengths are equal by indicating that the angles measure 90 degrees and that the corresponding lengths are equal” (Turn 34). As our experts confirmed, using GeoGebra's “Angle” and “Distance or Length” features for measurement enhances accuracy and facilitates a more streamlined teaching process.

Figure 9

4.2.2.3 Construction

In the context of construction tasks, most talk turns involved the use of the “Slider” feature to animate points, lines, or circles. For example, the VLA of the video data indicates that when teaching how to construct an angle bisector using a compass and straightedge, the teacher in MTV-03 employed a provided GeoGebra applet to direct her students to construct each step sequentially through the “Slider” feature (Figure 10A). In her words: “In the next step (of the slider), we take point M and point N as centres and draw two arcs with a radius equal to half the length of segment MN.” (Turn 22, Figure 10B). Our experts noted that the “Slider” feature works similarly to a video slider. This allows teachers to manipulate it to guide the instructional process effectively without having to manually graph each step. In addition, the experts indicated: “The text descriptions serve to remind the teacher to follow a step-by-step approach. This use of OER demonstrates their applicability, as even novice teachers, who are teaching this process for the first time, can rely on the guidance provided in the “Text” to facilitate teaching.”

Figure 10

4.2.3 Naming

When analysing talk turns related to naming, the selection of GeoGebra features varied according to the specific focus of the lesson. The teachers selected different GeoGebra tools to effectively support their instructional objectives. For example, the teacher in MTV-05 used the “Polygon” and “Circle” features to clarify the concept of a cyclic quadrilateral. By dynamically constructing the quadrilateral ABCD with its four vertices constrained to lie on a circle, the teacher stated: “Then, this ABCD, with its four vertices all on the circle, is called a cyclic quadrilateral.” (MTV-05, Turn 11). Similarly, when teaching symmetry properties, the teacher in MTV-13 used the “Reflect about Line” and “Reflect about Point” features to demonstrate symmetry properties. Through the dynamic construction of point C’ as the reflection of point C (see Figure 4A), she explained: “So, based on the symmetry properties, we know the relationship between this line and EF. EF must be the perpendicular bisector of segment CC’, right?” (MTV-13, Turn 15). As our experts suggested, “While several teachers successfully linked GeoGebra constructions to the appropriate mathematical terminology, other constructions lacked explicit textual definitions or formal statements embedded in the applets, which may limit their reuse by other teachers.”

4.2.4 Legitimations

In the analysis of talk turns related to legitimations, the majority of the teachers used Microsoft tools (e.g., PowerPoint), which they are accustomed to using in online teaching contexts. In addition, writing boards were used to support the explanations. Regarding the GeoGebra features, the teachers primarily used functions such as “Text” to present their teaching (see Table 5). For example, as shown in Figure 5A, the teacher added the “Text” feature to display the equation for calculating the area of triangle APO in a provided GeoGebra applet. The experts observed that she also used the “Check box” feature to control the visibility of the equation. When she presented triangle APO, she hid the equation. As she explained the method for determining the area of APO, she used the “Check box” feature to show the corresponding equation. This approach facilitated a clear presentation and guided the calculation steps. Our experts noted that presenting the calculation process through the “Text” feature enhanced the comprehensiveness of the applet. They further recommended that, “Suggested answers to the examples displayed in the GeoGebra applets should be provided, as some novice teachers may not be familiar with these answers.”

5 Discussion

In this study, we extend the theoretical framework proposed by Huang et al. (2020) through the integration of the MDI framework and the VLA technology as the additional dimensions of the framework (see Figure 1). With this theoretical foundation, we evaluated in-service teachers’ GeoGebra applets alongside their micro-teaching videos in the context of OEP. The implications are discussed in relation to GeoGebra-supported mathematics instruction, with a focus on the MDI framework (Adler and Ronda, 2015). These implications could inform future development of GeoGebra as a tool and support the creation of a mathematical OER repository, where GeoGebra-using mathematics teachers can contribute and draw upon resources for their teaching practice. Such a repository has the potential to catalyse the development of mathematics resources as OER, and foster an open educational community that supports more inclusive mathematics learning. In addition, we discuss the methodological implications of using VLA in evaluating teachers’ OEP. These implications have the potential to facilitate open assessment and foster open collaboration (see Figure 1) in their teaching practices (Huang et al., 2020). Finally, we discuss the challenges and constraints related to OEP and GeoGebra, thereby implying suggestions to future professional development.

5.1 Theoretical implications: adapting, developing, and implementing OER with a focus on the MDI framework

The MDI framework encompasses examples, tasks, naming, and legitimations (Adler and Ronda, 2015). In this study, tasks were further divided into observation, measurement, and construction (see Section 4.2.2), using a variety of GeoGebra features to adapt and develop OER that guided students through these processes. These approaches align with the findings of Zhang et al. (2020b), who emphasised that functional diversity is a key consideration in OER development. Based on these research findings, we propose four recommendations for developing and implementing OER that support teaching practices.

5.1.1 Enhancing the applicability of OER using GeoGebra's “Text” feature

Most of the micro-teaching videos created by the teachers showed a preference for using Microsoft tools (e.g., PowerPoint) and PDF documents when presenting examples and legitimations. This finding echoed the study by Escola et al. (2022), who reported a high level of satisfaction among secondary teachers regarding the use of Microsoft tools in distance learning. However, the experts in the present study pointed out that when the teachers used text-based materials outside of GeoGebra applets (e.g., Figure 6), these OER were unlikely to support broader adoption by teachers from other schools, especially among novice teachers, who may have difficulty articulating formal justifications or balancing procedural fluency with conceptual explanation due to their limited classroom experience (Ahmed et al., 2020). To enhance applicability, the experts recommended using GeoGebra's “Text” feature when adapting and developing OER, thus allowing detailed information and correct mathematical language to be included directly in the applets (e.g., Figure 7). This recommendation is consistent with Huang et al. (2024), who emphasised that text annotations enable GeoGebra to provide comprehensive descriptions and make them usable as standalone resources.

5.1.2 Promoting inclusivity by using GeoGebra's “Slider” feature for diverse learners

Some of the teachers used the “Slider” feature to facilitate the interactive adjustment of numerical values to demonstrate multiple scenarios of real-life problems (e.g., Figure 7). Consistent with the findings of Lo et al. (2024) and Seto et al. (2025), the experts of the present study noted that this approach can illustrate various case examples. In addition, this design allows teachers to use simpler numerical values to accommodate students with lower mathematics abilities. As Alvarez-Icaza et al. (2025) emphasised the importance of implementing inclusive OEP that address the diverse needs of secondary school students, the GeoGebra applets in this study showcased how teachers may leverage this dynamic mathematical application to achieve this inclusivity.

5.1.3 Enhancing geometric observation using GeoGebra's “Point” feature

Most of the teachers used GeoGebra's “Point” feature for observation tasks to animate dynamic representations of mathematical objects, which is difficult to achieve with blackboard demonstrations. For example, the teacher in MTV-02 used this feature to display various positions of a point, along with the corresponding lengths, which facilitated the identification of the minimum sum of these lengths (see Figure 8). This design and instructional practice were similar to the approach described by Emul et al. (2022), who used GeoGebra's dragging functionalities to solve locus problems. Similarly, Lo et al. (2024) developed a GeoGebra applet to guide students in observing the locus of a moving point while maintaining a fixed distance from a fixed point. They found that using this applet significantly enhance students’ mastery of this type of locus problems. Their empirical evidence echoed the experts’ comments that the teacher in MTV-02 effectively made abstract scenarios more concrete and enhanced understanding through visual animation.

5.1.4 Providing accurate measurements and step-by-step constructions through GeoGebra features

Several teachers used the “Angle” and “Distance or Length” features as mathematical tools, similar to using a protractor or ruler for measurement tasks. These GeoGebra features served as substitutes for traditional measurement instruments commonly referenced in textbook activities (Birgin and Topuz, 2021) and enhanced the accuracy of measurement. In addition, for construction tasks, the teachers frequently used the “Slider” feature to animate points, lines or circles to guide students through a sequential process (e.g., Figure 10). These practices align with Florio’s (2022) findings that these GeoGebra features facilitate the creation of dynamic figures by simulating traditional geometric tools. With the guidance of the “Slider” feature, constructions can be carried out step-by-step. This type of OER allows easy navigation throughout the construction process and thus enhances the efficiency of teaching practices involving multiple steps, such as the construction of an angle bisector (see Figure 10).

5.2 Methodological implications: using VLA in evaluating teachers’ OEP

As Avila et al. (2020) suggested, researchers can use learning analytics tools to evaluate how teachers incorporate OER into their teaching practices. In this study, we further integrated visual elements, such as video footage and talk turn bubbles, to visualise the learning analytics of discourse data in our VLA platform (Lo and Chen, 2025). The VLA derived from the micro-teaching videos facilitated the examination of the teachers’ mathematics instruction when using their GeoGebra applets (see Section 4.2). The VLA provided an overview of their OEP by summarising the distribution of mathematics instruction in MTV-01 to MTV-14 across four major categories of talk turns, namely examples, tasks, naming, and legitimations (Adler and Ronda, 2015; see Figure 2). Researchers can therefore gain an initial understanding of whether teachers have addressed all essential aspects of teaching mathematics. For example, the teachers in the study by Xu et al. (2025) tended to overlook exemplification through examples and tasks. In contrast, the teachers in the present study were able to use both examples and tasks in their OEP, representing more than 15% and 40% of their talk turns, respectively (see Table 3). This ability can be attributed to the use of GeoGebra, which enabled them to ask students to engage in observation, measurement, and construction (see Section 4.2.2). At a deeper level of analysis, the VLA allowed researchers to identify how the teachers used each GeoGebra feature to facilitate their exemplification and explanatory talk of mathematical concepts across a series of talk turns (see Section 4.2). Visualising video data from teachers’ OEP can enhance their awareness of aspects relevant to reflection (Xu et al., 2025) and promote peer observation of teaching practices.

5.3 Challenges and constraints related to OEP and GeoGebra

While this study provided the above theoretical and methodological implications, it also identified challenges and constraints related to OEP and GeoGebra. First, only 14 out of 40 teachers who completed the professional development programme voluntarily submitted their artefacts (see Table 2). The relatively low submission rate may be attributed to external factors, including additional workload associated with modifying and/or creating GeoGebra applets and recording videos, along with limited time for resource production in teachers’ schedules. To address these challenges, future professional development programmes could allocate a portion of class time for teachers to develop their own instructional materials (Lo, 2021). Second, our teachers primarily used GeoGebra to illustrate concepts related to geometry and measurement (n = 7) and numbers and algebra (n = 6). Notably, only one artefact (MTV-12) focused on statistics, despite GeoGebra's potential to enhance the teaching practices and facilitate the resolution of statistical problems (Rizkiani et al., 2024). Therefore, future professional development programmes could explore ways to encourage teachers to employ GeoGebra for creating OER related to statistical topics.

6 Conclusion, limitations, and recommendations for future research

Based on the analysis of in-service teachers’ GeoGebra applets and micro-teaching videos, we propose a set of recommendations for the adaption, development and implementation of OER and OEP in mathematics education. Furthermore, we demonstrate the application of VLA in evaluating OEP and highlight its potential to support teacher reflection and peer observation to inform teaching. Despite the contributions of this study, several limitations must be acknowledged. First, the study relied on a subset of teachers who voluntarily submitted artefacts, which might have introduced a positive bias toward more capable or motivated participants. This may limit the generalisability of the study. Second, although our sample size was adequate for an in-depth qualitative analysis, all research participants came from Chinese secondary school contexts. Therefore, further research is required to broaden the applicability of our research findings to other education levels (e.g., primary education) and regions. Third, this study focused on evaluating the teachers’ use in GeoGebra applets and their micro-teaching videos. Future studies could investigate student learning outcomes in terms of mathematical reasoning and conceptual development associated with these OER and OEP. Fourth, the MDI framework and our VLA platform were used to analyse the teachers’ mathematics instruction. Further research is needed to identify suitable frameworks for discourse analysis and to examine the application of the VLA platform in OEP assessment in other subject areas. Finally, this study primarily concentrated on teachers’ technological and pedagogical knowledge related to teaching practices. Future research could adopt additional framework, such as the Technological Pedagogical Content Knowledge (TPACK) framework, to further extend the theoretical contributions to technology integration research.

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