Flipped learning is a model in which direct instruction moves from the group learning space to the individual learning space and the resulting group space is transformed into a dynamic, interactive learning environment in which the educator guides students as they apply concepts and engage creatively in the subject matter (Bergmann & Sams, 2012). As shown by a systematic review article done by (O’Flaherty et al., 2015), the application of Flipped Learning can improve students’ learning experience by creating more dynamic interactions. In addition, the application of this model can improve students' learning achievements ((Rotellar & Cain, 2016), ;(Sharma et al., 2015) ; (Sutama et al., 2020)). Briefly, the Flipped Learning model was implemented in three stages: before-class, in-class, and after-class activities (Network, 2014) (see Figure 1. for the design). Previous studies that examined the application of the Flipped Learning model found that the basis of Flipped Learning applications is the use of learning videos in the before-class activity stage, in which students are asked to see and summarize the information they obtained from the video ((Davies, 2013) ;(Hwang et al., 2015); (Lin et al., 2019)). Based on these studies, we believe that students are not actively involved in concept construction. However, students’ active involvement in constructing their knowledge can make the learning process more meaningful (Agra et al., 2019). Therefore, the Flipped Learning model must be improved to involve students' activity by improving their learning independence.

Independent learning is a condition in which students are responsible for their learning because all learning can, in any case, only be carried out by the students themselves, and because they need to develop the ability to continue learning after their formal education ends (Littlewood, 1999)(Tanti et al., 2020). Hubbard states that highly independent learners complete their homework, actively participate in classroom activities, regularly seek advice from teachers, and frequently visit Self-Access Centers or libraries (Hubbard, 1994). The aforementioned definitions can shed light on the term independent learning. People with high learning independence tend to be confident about managing their learning (Firdausy et al., 2019)(Sakai et al., 2010)(Usuki, 2000). Little states that independent learning is not an attempt to alienate students from their learning environment or self-study, but is "an ability to take charge of one's learning" (Little, 1996). In addition, (Little, 1996) stated that independent learners can possess the ability to make decisions concerning all aspects of learning, namely (1) determining the objectives, (2) defining the contents and progressions, (3) selecting techniques and methods to be used, (4) monitoring the procedures used, and ( 5) evaluating what has been acquired. From the five parameters, it can be seen that a lack of learning independence is an obstacle for students in acquiring knowledge, mainly if the subject studied has abstract objects, such as mathematics.

Mathematics taught at the university level has a very high level of abstraction, including plane geometry analytics, advanced calculus, statistics, abstract algebra, real analysis, and numerical methods (Sierpinska et al., 2008). These topics are challenging enough to study online, especially if they are learned using the Flipped Learning model, which does not actively involve students in independently acquiring their knowledge. Thus, the learning process becomes more challenging. Considering the importance of mathematical mastery and the Covid-19 pandemic that forces learning to be implemented in a blended mode, media that can be integrated into the Flipped Learning model are needed to increase students' independence in learning mathematics. GeoGebra is an integrated medium.

GeoGebra is a dynamic software that combines the concepts of geometry, algebra, and calculus in its optimization, and can help visualize abstract mathematical objects ((Fatahillah et al., 2020); (Ishartono et al., 2016); (Judith & Markus, 2008)). Furthermore, the software is user-friendly. Therefore,

it does not require specific computer expertise ((Hohenwarter et al., 2009); (Klemer & Rapoport, 2020)). Previous studies have shown that GeoGebra can increase students' analytical abilities and activeness in mathematics learning ((Hermuttaqien et al., 2019); (Kholid et al., 2022); (Kllogjeri, 2010); (Kristanto et al., 2016); (Septian et al., 2019); (Yamin et al., 2021)).

As previously explained, online mathematics learning, one of the impacts of the Covid-19 pandemic, is challenging for students because of limited interactions with teachers and access to existing mathematics props. Therefore, student independence in learning mathematics online is a crucial aspect that needs improvement. Learning independence in question has all the limitations that exist: students can construct their knowledge independently based on the learning resources/media provided by the teacher. In the flipped learning model scheme, one of the crucial phases that forms the basis for implementing this model is the pre-class activity phase. As explained previously, this phase gives students the flexibility to prepare for in-class activities. The form of preparation involves independently constructing their understanding through the learning media provided by the teacher. Therefore, this phase can be optimized by integrating mathematics learning media that can increase student activity using their analytical abilities to construct their mathematical experience independently. Under these conditions, GeoGebra acts as an escalator of students’ independence by constructing their mathematical understanding independently.

Some of the characteristics of GeoGebra that are suitable for integration into the flipped learning model in the implementation of online mathematics learning are interfaces that make it easier for students to manipulate objects displayed in GeoGebra-based learning media. Features such as lines, points, fields, and other mathematical objects can help students manipulate displayed mathematical objects. In addition, the completeness of the tools in GeoGebra makes it easier for teachers to design visualizations of the mathematical topics being taught. Another feature of GeoGebra is that it is available on various websites. Therefore, the level of accessibility of this device is high, making it easier for students to access it anywhere. An exciting aspect of the GeoGebra website is that it can also act as a learning management system (LMS), where all GeoGebra-based learning media can be arranged in a series of learning activities.

The strengthening of the role of GeoGebra in the syntax of flipped learning is not only a learning medium but also an investigative medium of a concept. Therefore, the integration of GeoGebra in this study does not stand alone, but is complemented by investigative questions. In principle, investigative questions serve as a complement to GeoGebra, where it is through these questions that students conduct various investigations that lead to a concept. This is in accordance with the framework of mathematical tasks in 1998Smith & Stein () pada framework of high-level demands ( mathematics). The framework consists of six points: (1) requires complex and non-algorithmic thinking; (2) requires students to explore and understand the nature of mathematical concepts; (3) demands self-monitoring; (4) requires students to access relevant knowledge and experiences and make appropriate use of them while working though the task; (5) requires students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions; and (6) requires considerable cognitive effort and may involve some level of anxiety for the student because of the unpredictable nature of the solution process required.

Few studies have examined efforts to strengthen students' learning independence in mathematics at the university level during the pandemic. Houston and Lazenbatt used peer tutoring to increase students' independence in mathematics. However, that study was conducted before the pandemic began (Houston & Lazenbatt, 1996). (Saputra & Fahrizal, 2019) showed that using GeoGebra improved university students' learning independence in mathematics. However, the study was not conducted under online learning conditions.

Previous studies have investigated the integration of Flipped Learning model and GeoGebra, such as; (1) (Nuraeni et al., 2021), who developed a learning tool on the flipped learning model assisted by GeoGebra to improve the mathematical representative skills of secondary school students in Indonesia, (2) (Ishartono et al., 2022) who studied the integration of GeoGebra into Flipped Learning model to improve students’ self-regulated learning, and (3) (Andriani et al., 2022) who integrated Flipped Learning and GeoGebra to improve students’ critical thinking skills during online learning. However, there is a lacuna in studies which examine how the integration of GeoGebra and Flipped Learning increases students' independence in learning mathematics during the Covid-19 pandemic.

In the context of online mathematics learning, the independence of learning mathematics becomes essential for students because all the limitations of place and time require them to actively construct their own understanding of mathematical concepts based on the learning resources provided by teachers (Liaw et al., 2007), especially during the Covid-19 Pandemic which requires them to study the materials remotely instead of being surrounded by their teachers/tutors. The present study is critical because its results reveal steps to increase students' independence in learning mathematics online. This will benefit practitioners, researchers, and stakeholders in mathematics education, particularly in improving the quality of online mathematics learning.

Based on the aforementioned description, researchers have considered it necessary to develop a learning syntax that integrates GeoGebra into Flipped Learning to increase students' independence in learning mathematics during the Covid-19 pandemic. However, to date, no syntax has accommodated these efforts. Thus, the question is, what syntax can accommodate the improvement of students' learning independence when studying mathematics online? This study aims to fill these theoretical gaps by developing a syntax for the GeoGebra-based Flipped Learning model to increase students' independence in mathematics learning during the Covid-19 pandemic.

This first phase is critical to the entire development process because the outcome of this phase becomes the foundation for the next phase. Therefore, at this stage, several analyses were conducted, such as a cognitive analysis of students based on Bloom's Taxonomy, analysis of the existing learning resources related to GeoGebra, analysis of the best mathematical learning strategies to use online, learning independence, and appropriate learning media for students based on aspects of GeoGebra and online learning.

This phase is based on the analysis and exploration phases in which the information obtained is developed into components of the intended syntax. The validity of each component is tested by two experts. The validation results are analyzed quantitatively (validation sheet data) and qualitatively (suggestions and input validators). Quantitatively, the results of the validation sheet are then analyzed using Cohen's Kappa inter-rater formula to test the reliability of the two designated validators and Aiken's Coefficient Value formula to test the content validity index (CVI) (Ishartono et al., 2022)(McHugh, 2012). Qualitatively, the inputs obtained from the validators become evaluation materials that must be periodically revised. At this stage, there is an iterative process in which the components are consulted again by the validator to assess the revision results after the revision process is completed.

Once the component is completed, it is constructed as the initial design for a GeoGebra-Based Flipped Learning syntax. Next, the syntax is validated in theory by two experts, where the validation results are analyzed just like the component validation process that has been done before. The iteration process also occurs in the construction stage, where, after the revision process is carried out, the design is consulted again by the validator.

Furthermore, in theory, design validation is implemented during the learning process. In this study, implementation was carried out at a private university in Central Java, Indonesia, and involved 125 second-year undergraduate students. The students consisted of 98 female and 27 male students who have been learning mathematics for two years. University selection is based on the availability of facilities that support the mixed learning process, such as Internet capacity, sufficient computers, and the completeness of the mathematics laboratory.

This implementation was conducted in two meetings on the plane geometry analytic course, which aimed to identify obstacles during syntax design implementation. In addition, it was used to see how significantly the design has been developed to increase student independence in mathematics learning during online learning. Two instruments are used to obtain the data:

observation sheets to see and record obstacles during the implementation process, and questionnaires to assess students' learning independence based on the criteria developed by (Little, 1996). The observation process was carried out at each meeting as an iteration of the evaluation process, whereas the questionnaire was only administered at the end of the meeting. The questionnaire uses a Likert scale ranging from 1 (strongly disagree) to 4 (strongly agree), combining negative and positive questions. Questionnaire items on learning independence are adapted from instruments developed by (Hidayati & Listyani, 2013). The instrument items are presented in Table 1.

This stage is performed by evaluating the results obtained in the second stage, which are the results of observations related to implementation constraints and the questionnaire results distributed to students. The observational results are analyzed qualitatively, and the questionnaire results were analyzed quantitatively. The iteration process is also carried out at this stage based on the results of the obtained observations. If an obstacle is identified in the developed syntax, it is fixed and piloted again. After obtaining the results of the quantitative and qualitative analyses, a reflection on whether the application of GeoGebra-based Flipped Learning can significantly increase students' independence while studying mathematics online is conducted. This stage is based on a Normalized Gain (N-Gain) test to determine the effectiveness of improving students’ learning independence during online mathematics learning (Bao, 2006). The results are categorized using the category table from (Meltzer, 2002).

At this stage, the authors conduct a literature review on the syntax aspect of the Flipped Learning model, aspects of learning independence characteristics, aspects of mathematical topics that will be used as the basis for GeoGebra media development, and aspects of GeoGebra itself. The first aspect analyzed is the syntax aspect of the Flipped Learning model. This model is implemented in three stages: (1) the pre-class (asynchronous) stage, where teachers provide learning materials for students to learn; (2) the in-class (synchronous) stage, where teachers deepen students' understanding through exercises to work on questions or implementation of learning models based on higher-order thinking skills (HOTS); and (3) the post-class (asynchronous) stage, where teachers evaluate the learning outcomes of students in the form of feedback or additional projects (Murillo-Zamorano et al., 2019).

The next aspect analyzed is the characteristics of the students' learning independence. According to (Hidayati & Listyani, 2013), six indicators reflect students' independence in learning: (1) being independent, (2) having confidence, (3) being disciplined, (4) having a sense of responsibility, (5) having initiative, and (6) conducting self-control. These six factors form the basis for developing questionnaires to determine the level of students' independence in learning mathematics.

The third aspect studied is the topic used to develop GeoGebra-based teaching media. In this study, the developed syntax is implemented in university-level mathematics subjects. Therefore, the chosen topic was the circles contained in the course of the plane geometry analysis. The selection of this topic is based on its suitability for GeoGebra applications that accommodate geometry and the record of assessment results in the previous academic year at a private university, where students' scores were relatively low in this course in 2020 compared to those in the previous years.

The last aspect analyzed is the GeoGebra software, which used GeoGebra 5.0. This software can be easily used to illustrate abstract mathematical objects such as geometric objects. In addition to the offline version of GeoGebra, researchers can use the GeoGebra applet version, which can be accessed at the following link https://www.geogebra.org/m/p7yypye4. Initially, GeoGebra-based learning media were designed using GeoGebra 5.0. Subsequently, a validity test was conducted using the media. The last step is uploading the files onto the applet so that students can operate and manipulate them online (Nisiyatussani et al., 2018). Of course, GeoGebra-based learning media do not stand alone but include investigative questions that lead students to a concept that must be mastered. These questions function as scaffolds for students to construct their knowledge independently. This condition is based on the results of Kristanto et al. 2016b(), who combined investigative questions in computer software-based learning media to direct students toward understanding concepts.

The authors began this stage by designing a GeoGebra-based Flipped Learning syntax component to increase students' independence in mathematics learning, assessment instrument designs to assess GeoGebra-based learning media, and questionnaires to assess college students’ level of independence in mathematics learning. The first design was the syntax of the GeoGebra-based Flipped Learning model to increase the independence of college students in mathematics learning. The syntax was designed based on Little's five learning-independence aspects in the previous explanation (Little, 1996). In addition, two aspects distinguish this syntax design from existing syntax. It does not use video as the basis for delivering materials in the pre-class activity stage, but uses GeoGebra, which is equipped with investigative questions. In addition, in-class activities are implemented offline using the existing syntax. This phase is then implemented online (synchronously) in the syntax design. Subsequently, the researchers detail a GeoGebra-based mathematical learning media design that can increase students' independence in mathematics learning, focusing on circles. Indeed, as presented at the analysis stage, the media are equipped with investigative questions that lead students to the concept circle.

The author designed a questionnaire to assess students' independence in learning mathematics and determine their level of independence. This was a modification of the questionnaire developed by (Hidayati & Listyani, 2013). The questionnaire used a four-point Likert scale of 1 for "strongly disagree," 2 for "disagree," 3 for "agree," and 4 for "strongly agree" (Suharsimi, 2006). Furthermore, the questionnaire results are analyzed quantitatively using SPSS 23 to observe an increase in the average level of student independence in mathematics learning. The questionnaire was distributed using Google Forms to collect data.

This stage was accomplished by developing a syntax based on the previously designed components, and the development results were subjected to internal validation by involving two experts in the field of educational technology from one of the private universities in Indonesia. The validation process was conducted using a walk-through interview model in which the components that had been prepared were then commented on directly by the two experts and given input on improvements. The validation aspects included (1) conformity of the syntax with the model used, (2) suitability of the learning media (GeoGebra) used in the syntax, and (3) conformity of the syntax with the learning sequence in the classroom (Indartono, 2019). Inputs from both experts are used to improve the syntax, and the results are shown in Table 2.

At this stage, the learning media are developed according to the design described in the design stage. Media development was based on indicators of the topic of the circle being taught. These are (1) compiling equations of circles and using them in problem solving, and (2) determining the equation of the tangents of circles that meet specific criteria. In addition, the media are developed using investigative questions that direct students to construct their knowledge independently. After the development process was completed, it was validated by two mathematics learning experts from a private Indonesian university. The experts validated the content and media aspects. The results of the validation assessment conducted by the two experts were then used to assess inter-rater reliability using Cohen's Kappa formula. The test results are presented in Table 3. The table shows that the reliability level is 0.89, indicating that the reliability levels of both validators were highly rated. The content validity was tested using Aiken’s content validity index (CVI). The average CVI obtained for the content aspects is 0.81, categorized as valid, and the average CVI for the media aspects is 0.79, categorized as valid. Based on these results, the developed GeoGebra-based learning media can be used in the learning process. The GLMIQ can be accessed at the following link https://www.geogebra.org/m/xb7psqnw. The Conformity of GeoGebra-based flipped learning with the mathematical task framework proposed by (Smith & Stein, 1998) is presented in Table 4.

In this study, two types of questionnaires were developed: pre- and post-test. Both questionnaires are based on the aspects of learning independence presented by (Hidayati & Listyani, 2013). What distinguishes the two questionnaires is that the pre-test questionnaire focuses more on students’ experiences regarding aspects of their independence in constructing their knowledge, and the post-test questionnaire focuses on students' experiences related to improving their learning independence during the study of mathematics based on the GeoGebra-based Flipped Learning (GbFL) model (see Table 5).

After development, the questionnaires were validated by two experts in learning evaluation from a private university in Indonesia. The validity test results were then used to test the reliability levels of both validators using Cohen's kappa inter-rater reliability test, where the result was 0.811, which can be categorized as a strong level of reliability. The validity results were then used to conduct a validity test using the Content Validity Index Aiken's Coefficient Value obtained by each point of the two questionnaires developed, which had a good level of validity with the lowest score of 0.77.

This stage was held online for two meetings: the sixth (April 16, 2021) and the seventh (April 23, 2021). The authors collaborated with a lecturer who enabled the course to carry out the learning process according to the syntax developed in each meeting. The implementation begins with a pre-

class activity where teachers provide GeoGebra-based learning media on the topic circle to students through the LMS that has been set. Then, in the in-class activity stage, the lecturer validates and deepens students' understanding of the topic of the circle. Figure 3 shows a sample of an in-class activity in which the lecturer validated students’ understanding of tangents drawn from points outside a circle. Finally, lecturers evaluated and enriched the students in the post-class activity stage as an additional task to strengthen their understanding.

The authors first distributed a pre-test questionnaire to students on a pre-class activity in the sixth meeting to measure students' independence level in knowledge construction. Meanwhile, for the post-test questionnaire, the authors administered it to the post-class activity at the seventh meeting. The questionnaires were distributed using Google Forms for easier analysis. All questionnaires were then analyzed as materials at the evaluation stage.

This stage is based on the process of applying Gb-FL in the previous phase. Based on the observations made, the obstacles found are technical problems, namely, the lack of solid Internet networks owned by students or computers that are less supportive of operating GeoGebra online. For the rest, there are no constraints related to the syntax order developed.

Next, the authors collected the results of the students’ pre- and post-test questionnaires. The collected data were analyzed descriptively using SPSS 23. The results of the pre-and post-test questionnaires are shown in Table 6. The table shows that the average student response score for each aspect of the pre-test was above 1.5, whereas in the post-test, it is above 2.5. When viewed from the normalized gain test values, all aspects are categorized as medium. According to (Meltzer, 2002), the medium category indicates that syntax effectively increases students' learning independence in each aspect assessed.