The results of students' geometry skills tests, administered before and following the learning period for experiment and control class, are outlined in Table 2. It is ndicates that the experimental class achieved a higher average score in geometry skills compared to the control class. Both groups improved geometry proficiency; however, the experimental class demonstrated greater progress. According to the N-Gain classification, the experimental class falls into the 'effective' category with an N-Gain score of 0.78 (78%), while the control class achieved an N-Gain score of 0.57 (57%). These results suggest that the experimental class experienced a more substantial improvement than the control class.

The results of the normality test show that the significance values for the N-Gain data of the experimental and control classes were 0.65 and 0.25, respectively, both exceeding 0.05. This indicates that the data in both groups are normally distributed. In addition, the homogeneity test using SPSS yielded a significance value of 0.88, which is also greater than 0.05, indicating that the data from both classes are homogeneous.

Given that the data are normally distributed and homogeneous, the t-test was utilized to test the hypothesis of mean difference. The SPSS output is presented in Table 3. According to the t-test results in the Table 3, the significance value (Sig.) is 0.000, below the 0.05 threshold. This indicates that the alternative hypothesis (Ha) is accepted, meaning there is a significant difference in the improvement of geometry skills between students in the experimental and control groups. Additionally, the average N-Gain for the experimental class is higher than that of the control class. These findings suggest that geometry learning using the Geogebra application has a more positive impact on enhancing students' geometry skills than learning without the application.

Based on posttest data, students' geometry skills were grouped into high, medium, and low categories. In addition, one student from each category was chosen as a representative. An interval-based representation of the experimental class group's posttest score distribution is used. The distribution of scores is divided into three groups: high, medium, and low, based on the experimental class students' geometry competence scores (Rahmawati, 2020). The outcomes of data processing to categorize student scores are: 1) 80 ≤ score ≤ 100 (High Category); 2) 60 ≤ score < 80 (Medium Category); and 3) 0 ≤ score < 60 (Low Category). Based on this classification, the posttest score information for the two groups is displayed in Table 4.

As shown in Table 4, over half of the students are categorized as having high-level geometry skills. Nevertheless, nine students were identified as needing further analysis to better support the development of their geometry abilities. To gain comprehensive insights, analysis will be conducted across all skill categories. One student from each category will be selected for in-depth analysis of their work and follow-up interviews. Three students, each representing a different geometry skill

category, will have their problem-solving work analyzed. These selected students will also participate in interviews to provide additional information regarding their learning process and performance. Five types of errors are outlined in accordance with Newman's procedures, namely (1) reading, (2) comprehension, (3) transformation, (4) process skill, and (5) encoding (Noutsara et al., 2021) Zinc, 2020 (Suseelan et al., 2022). This category is a foundation for analyzing students' mistakes in solving geometry-related problems.

Table 5 presents an analysis of the errors the 23 experimental class students made, categorized using Newman’s procedure. Table 5 demonstrates that, with 55 errors, students make the most mistakes on question 4. Based on the error categories, all 23 students were found to have made mistakes in the encoding category. A deeper analysis also reveals many errors in process skills, with 17 out of 23 students experiencing difficulties in this area. Process skill errors refer to applying the correct steps to solve problems. This indicates that students who struggle with process skills will likely produce incorrect final representations of their answers. A similar pattern is observed with other types of errors. For instance, transformation errors, mistakes in converting mathematical information into different forms, can lead to subsequent errors in both process skills and encoding.

Interestingly, the distribution of student errors based on Newman's procedure follows a sequential pattern: reading errors are the least frequent, followed by errors in comprehension, transformation, and process skills, with encoding errors being the most prevalent. This pattern suggests that when students begin making mistakes at the reading stage, they are more likely to encounter difficulties in the subsequent stages. This occurs because an inability to accurately read key information or understand the question makes it difficult for students to progress through the problem-solving process and produce a correct final answer.

Question number 4 is the question with the most student-solving errors. This problem is a question of logic indicator geometry skills, which means that, in general, students still have difficulty using logical and deductive reasoning in understanding, analyzing, and solving geometry problems, so they apply the wrong steps to solve them and write the incorrect final result. Furthermore, question number 3 is also a question that has many mistakes in its completion by students. This question is about geometric thinking skills of drawing indicators; it indicates that students still struggle to use geometric drawings in general or perform geometric constructions from various perspectives as a communication tool to explain geometric concepts or answer questions related to geometry.

Table 6 describes the errors made by experimental class students, selected randomly from each geometry skill category, as analyzed using Newman’s procedure. Table 6 summarizes student errors categorized into high, medium, and low levels. It can be observed that students in the low geometry skills category tend to make numerous mistakes on nearly all question items. Overall, students view items 3 and 4 as presenting a higher difficulty level, whereas item 5 is generally considered easy.

Figure 3 displays the excerpt of a high category student's answer in question number 4, the geometric skills question with logical indicators. In Figure 3, students categorized under the high

level of geometry skills demonstrate a generally structured problem-solving process, such as presenting information in a sequence, starting from identifying what is known and being asked, and proceeding to solve the problem. However, analysis of responses to question number 4, which measures logical reasoning skills, reveals that some students still experience difficulties in applying deductive logic when analyzing geometric relationships. Specifically, one standard error lies in their inability to interpret and relate plane shapes' properties. In this case, students failed to describe the characteristics of shapes such as rectangles and rhombuses and did not construct a proper Venn diagram to visualize their relationships. This indicates a gap in understanding that rectangles and rhombuses are exceptional cases of parallelograms. A rectangle, for example, is a type of parallelogram in which all angles are 90 degrees, while a rhombus is a parallelogram where all sides are of equal length. Although all rhombi and rectangles are parallelograms, not all parallelograms are rectangles or rhombi due to specific defining features. Misunderstanding this hierarchy reflects incomplete conceptual knowledge.

The encoding error identified in this group refers to incorrect conclusions drawn by students. One student stated, "I feel that my answer is correct. However, there is a lack of confidence because I should have written down the properties of the parallelogram and the rectangle one by one so that the relationship is visible. Still, I forgot to remember the properties of the plane shape." This reflects a partial understanding that students can logically reason and recognize similarities between properties, but their ability to recall and articulate specific characteristics is still limited.

Another student admitted, "I need to relearn the definition and properties of each plane shape because I feel like I have forgotten a lot." This suggests that even high-performing students require more practice recalling, writing, and organizing geometric properties. This skill can be strengthened by encouraging students to write down regularly and group shape properties, followed by making logical conclusions based on these groupings. Writing activities, as supported by (Santos & Barbosa, 2023)), and (Žakelj & Klancar, 2022), significantly influence the improvement of students’ geometric concept mastery, structure mathematical reasoning, and build connections between concepts. Students can better visualize, describe, and justify geometric ideas through writing while reinforcing their comprehension through verbal and visual representations.

Figure 4 shows the excerpt of a medium category student's answer in question number 4. In Figure 4, students in the medium geometry skill category possess a basic understanding of geometric concepts, they still experience substantial difficulty performing tasks requiring deductive and logical reasoning. In question number 4, which assesses the ability to analyze and establish relationships

between properties of plane shapes, these students generally follow an orderly process in solving the problem and attempt to illustrate relationships using Venn diagrams. However, their responses reveal conceptual gaps, particularly in understanding the classification of geometric figures. For example, students often fail to recognize that a rectangle is a special case of a parallelogram, despite claiming to remember the properties of plane shapes. As one student stated, "I forgot that a rectangle can be considered a special case of a parallelogram. However, I remember the properties of a plane shape." This indicates their memory of properties is fragmented and poorly connected to broader geometric classifications.

A standard error found in this group is related to encoding the process of forming and articulating correct conclusions. One student mentioned, "I feel confident in the answer I wrote in question number 4. I think this question is quite difficult because there are many properties in each plane shape." Despite an incorrect conclusion, this confidence suggests surface-level familiarity rather than deep comprehension. Students may recall specific properties but struggle to analyze them logically or connect them meaningfully within geometric structures.

Although using GeoGebra in learning helps make abstract relationships more concrete, students in this category still face challenges in optimally applying the tool. Their difficulties likely stem from a tendency to memorize geometric facts without truly understanding the underlying relationships. Analytical thinking, especially in geometry, requires extended, meaningful practice that promotes lasting conceptual retention.

The findings suggest that integrating the GeoGebra application with consistent writing activities can support students in this category. Students are encouraged to describe known information, construct logical steps, and formulate their own conclusions through writing. This process not only strengthens understanding but also enhances memory and conceptual clarity. As highlighted by ((Chasanah & Usodo, 2020) ; (Kazemian et al., 2021)), writing in mathematics, especially in geometry, is a critical tool for developing deeper conceptual understanding, analytical skills, and reflective thinking. Writing allows students to connect theory with practice, articulate their reasoning, and engage more actively with geometric ideas ((Graham et al., 2020); (Santos & Barbosa, 2023)).

Figure 5 presents the excerpt of a low category student's answer in question number 4. Students in the low geometry skill category demonstrate considerable challenges in applying logical and deductive reasoning, as demonstrated in their responses to question number 4, which assesses their ability to analyze and understand relationships between the properties of plane shapes. One major issue is their inability to transform the information provided into a broader context. Specifically, they struggle to group and relate properties using Venn diagrams. A clear example is a student’s statement: "I do not understand how to read Venn diagrams and what they have to do with the properties of parallelograms and rectangles." This reflects a fundamental gap in understanding

the diagram's purpose and the conceptual relationships between different geometric figures.

Regarding process skills, students in this category often do not write down the steps needed to solve the problem. Their responses typically include what is known and what is being asked, indicating some willingness to engage with the task. However, they fail to use the necessary reasoning or analytical steps to bridge the gap between known information and a logical conclusion. One student admitted, "I forgot the properties of plane shapes and did not understand how to see the relationship between the two shapes." This suggests a lack of recall and a weak conceptual structure related to geometric classifications.

Encoding errors are also common, as students often provide incorrect or incomplete conclusions due to confusion or a lack of understanding. One student stated, "I believe my answer is wrong because I do not understand." This reveals a lack of confidence rooted in conceptual uncertainty, particularly in distinguishing and relating the properties of parallelograms, rectangles, and other plane shapes.

The students' inability to complete this task can be attributed to limited experience with abstract reasoning and inadequate exposure to representational tools such as Venn diagrams. Although these tools were introduced in previous lessons, students showed difficulty applying them independently. Therefore, to support students in this category, a more meaningful and structured learning approach is essential, one that helps build foundational understanding while developing abstract and logical thinking skills. Geometry inherently involves abstraction and generalization, and logical skills enable students to recognize patterns and apply general principles across different geometric contexts.

Integrating the GeoGebra application into learning provides a powerful solution to this challenge. Through dynamic visualization, GeoGebra allows students to explore relationships among geometric properties concretely and interactively. Using GeoGebra helps provide representational support, allowing students to understand better and generalize geometric relationships (Seloane et al., 2023). To maximize its impact, GeoGebra should be accompanied by scaffolded writing and reasoning tasks, enabling students to see relationships and articulate them clearly and accurately. This approach can gradually strengthen both their logical reasoning and conceptual understanding.

Figure 7 displays the excerpt of a high category student's answer in question number 3, the geometric skills question with drawing indicators. In Figure 7, students in the high category demonstrated a strong understanding of geometric concepts and problem-solving strategies, as shown in their responses to question number 3, which involved calculating the area of a rectangle based on given information. The student approached the problem systematically, beginning with interpreting the question, constructing an accurate geometric drawing, and outlining the steps clearly. This reflects the student’s achievement in the drawing indicator, which involves using geometric representations or constructions to communicate and solve problems. The drawing

included all relevant dimensions and elements, helping to simplify the task and clarify the reasoning process. The student stated, “I’m confident I wrote the correct answer. At first, question number 3 seemed difficult, but after I drew each part based on the given information, it turned out to be very easy.”

Despite the structured approach and confident execution, the student made a crucial error in the encoding phase, specifically in the final step of the calculation. The student mistakenly substituted the length of the rectangle as five units instead of the correct value, 11 units, which resulted in an incorrect computation of the rectangle’s area. This type of error suggests a lapse in attention to detail rather than a lack of conceptual understanding.

Such mistakes highlight the importance of developing students’ habits of double-checking and validating their final answers, even when the problem-solving process appears to be correct. While students in this category generally show advanced problem-solving and visualization skills, they still benefit from being encouraged to practice careful verification of calculations. With continued practice, including structured reflection and feedback, students at this level can further refine their precision and accuracy in mathematical problem-solving.

Figure 8 shows the excerpt of a medium category student's answer in question with drawing indicators. Students in the medium category show a moderate level of understanding in solving geometry problems, but still make procedural and conceptual errors that affect the accuracy of their final answers, as shown in Figure 8. In question number 3, the student successfully applied the drawing indicator, which involves using geometric diagrams or constructions to interpret and solve problems. The student could represent the word problem with an appropriate drawing, indicating an ability to visualize the scenario geometrically. As noted in their statement, “At first, I had difficulty drawing the trapezoid, but after trying, I felt confident that my drawing was correct. I enjoy solving problems that involve diagrams.” This reflects a positive attitude toward visual problem-solving and a developing skill in geometric representation.

However, an error occurred in the process skill aspect, specifically when the student incorrectly applied the formula for the perimeter of a trapezoid by substituting the wrong value for line AB. This mistake led to an incorrect final result. The miscalculation suggests that while the student could interpret the diagram, they lacked precision in applying the correct measurements. Additionally, the student made an encoding error by incorrectly calculating the area of rectangle ABCD. Although they expressed confidence in their answer, “I’m confident that my answer was correct, but it turns out there was a mistake in calculating the length of the sides,” the outcome revealed gaps in executing the final steps of the problem.

Overall, students in this category need more consistent practice with procedural accuracy and self-monitoring strategies. They benefit from being explicitly encouraged to review their work after solving problems and to carefully extract and record the given information before proceeding to calculations. Reinforcing these habits can help bridge the gap between correct conceptual understanding and accurate execution, enabling students to improve their confidence and mathematical precision.

Figure 9 demonstrates the excerpt of a low category student's answer in question with drawing indicators. Students in the low category exhibited significant difficulties in understanding and solving geometry problems, particularly in question 3, which assessed the drawing indicator's ability to use geometric diagrams or constructions from various perspectives to communicate and solve problems.

The student demonstrated an apparent lack of comprehension regarding the geometric context and terminology used in the question. As expressed in their statement, “I wasn't sure what was meant by the trapezoid leg length being equal to the length of sides AD and EF. I think I need to review the definition,” the student did not understand that the legs of a trapezoid refer to its non-parallel sides. This fundamental misunderstanding prevented them from grasping the core concept needed to solve the problem correctly.

The student failed in complete the transformation stage to represent the problem information in diagrammatic form. They could not create a visual sketch of the trapezoid based on the data provided in the problem. Their confusion is reflected in the statement, “I was confused about how to draw trapezoid ABEF. I became unsure about drawing it after reading that one of the bases had to be side AB. That sentence confused me.” This indicates a struggle with interpreting spatial and relational information, which is critical in geometry.

The student also made errors in the process skill domain by misapplying the formula for the perimeter of the trapezoid and substituting incorrect side lengths. This procedural mistake suggests that, beyond conceptual misunderstanding, the student had not internalized the necessary formulas or how to apply them appropriately. They admitted, “I'm not confident in my answer; the question was too difficult and I forgot the formula,” signaling a need for more foundational practice and support.

Lastly, the encoding error was evident in the incorrect calculation of the area of rectangle ABCD. Despite knowing the formula, the student struggled to apply it due to a lack of clarity in interpreting the problem. As they explained, "I know the formula for a rectangle, but I had trouble understanding the question," it became clear that conceptual confusion interfered with successful problem-solving.

Students in this category face challenges: difficulty comprehending geometric terms and relationships, inability to translate textual information into visual form, and procedural weaknesses in solving standard geometry problems. To support these students, instructional strategies should strengthen conceptual understanding by explicitly teaching geometric definitions and relationships. In addition, consistent practice in visualizing and drawing geometric figures, combined with scaffolded guidance in writing down relevant information, can help bridge the gap between understanding and application. Training students to organize information systematically, symbolically, and diagrammatically will enhance their ability to interpret problems and develop accurate solutions.