Guided Discovery Learning to Improve Students'

. Classroom Action Research aimed to assess the mathematical representation ability and collaboration in understanding circle material by implementing the guided discovery learning model. The data collection took place in April 2023 at SHS 6 Yogyakarta, involving 35 students from XI science. The research comprised two cycles, with a diagnostic test conducted in the first cycle focusing on the equation of a circle, particularly the position of points and lines related to the circle. In the second cycle, the diagnostic test concentrated on tangents to the circle. Data were gathered through tests, interviews, and questionnaires. The findings indicated that guided discovery learning effectively enhances both mathematical representation ability and collaboration. The average scores for the pre-cycle test were 78.87, for cycle I were 79.17, and for cycle II were 85. Moreover, the percentage of students achieving a score of 75 or higher increased from 60% in the pre-cycle to 71% in cycle I and further rose to 77% in cycle II. Regarding collaboration skills, in cycle I, 23 students were categorized as having medium-level skills, and 12 were classified as having high-level skills. In cycle II, the distribution changed with 16 students falling into the very high category, 12 in the high category, and seven in the medium category.


INTRODUCTION
Mathematics is a field of knowledge that can be used to improve the ability to think logically, critically, and rationally.It can be achieved but requires understanding and competence in mathematics (Sinaga, 2016).One of the goals of mathematics learning at all levels of education is to improve students' mathematical abilities.Students can better understand and apply the concepts they have learned in various contexts if this ability is developed.They can use it in various situations.
Representation is a model or form that replaces a problem to help find a solution to the problem, usually shown using images, words, or mathematical symbols (Jones & Knuth in Sabirin, 2014).According to NCTM (2000), the first conducted by Mulyaningsih, Marlina, and Effendi (2020), revealing a tendency among students to approach questions with a lack of attentiveness and precision in execution.Additionally, students exhibited limited proficiency in problem-solving through graphical representations, hindering their comprehension of presented information.Consequently, an imperative arises for implementing instructional practices incorporating elevated cognitive challenges, encompassing sophisticated questioning techniques and increased integration of mathematical representation indicators within the learning process.
Based on the results of students' daily tests and observations made in class Apart from that, when writing mathematical symbols, sometimes students write them incompletely, so it can be concluded that students' symbol representation abilities still need to be improved.Apart from representational abilities, based on interviews with mathematics teachers and observations of mathematics learning, information was obtained that students only group with close friends and tend not to want to change groups.It shows that students' collaboration skills are still lacking.Therefore, there needs to be a learning breakthrough that can improve students' representation and collaboration abilities.
One alternative to improve students' representation and collaboration abilities is to use the guided discovery learning model.Guided discovery learning is scientific learning which aims for students to solve problems in groups using the steps of simulation, problem statement/identification, data collection, data processing, verification, and conclusion (Simamora, Saragih, Hasratuddin, 2019;Shieh & Yu, 2016;Yang et al. al., 2010;Yerizon et al., 2018;Alfieri et al., 2011).
Therefore, researchers are interested in conducting classroom action research using the guided discovery learning model to improve students' mathematical representation and collaboration abilities.The collaboration questionnaire created by researchers was scaled from 1 to 5 with scale information: 1 = very inappropriate; 2 = not appropriate; 3 = not suitable; 4 = appropriate; 5 = very appropriate.The criteria for students' collaboration abilities were divided into five categories: deficient, low, medium, high, and very high.

RESULTS AND DISCUSSION
The researcher performed a diagnostic test in the pre-cycle stage using circle     In the verbal representation aspect, initially, the lowest score was 0, then increased to 50, meaning that all students had begun to develop in the verbal representation aspect.If we look at the average obtained, all aspects have increased.The following also presents the completeness of students' grades.It suggests that students' demonstration of responsibility requires further enhancement and improvement.
In cycle I, mathematical abilities increased compared to pre-cycle, but mathematical abilities in the verbal aspect were lower than in the other two aspects.
Meanwhile, for students' collaboration abilities, the indicator showing an attitude of responsibility is also lower than other collaboration ability indicators.So, based on this reflection, the researcher retook action by conducting research in cycle II.

B. Cycle II
Based on the reflection results in cycle I, researchers and teachers discussed again to design various things needed and preparations for learning cycle II.Things that are needed and must be prepared include a lesson plan different from Cycle I with continuing material, students' worksheets, learning assessments, and test or post-test questions that will be tested in Cycle II.The material used in cycle II is the tangent line to a circle whose tangent point is known and the tangent line to the circle whose gradient is known.
At the action stage, researchers carry out learning using the lesson plan that has been designed.Cycle II was carried out with three learning meetings, namely two learning meetings and one cycle 2 test meeting.The cycle 2 test meeting was   So, based on this reflection, the researcher only needed to take action until cycle II.
In the pre-cycle, there were 21 students (60%) who completed it; in the first cycle, there were 25 students (71%) who completed it, while in the second cycle, there were 27 students (77%) who completed it.Students' collaboration abilities from cycle I to cycle II can be seen based on collaboration ability indicators that have not experienced a significant increase.
After the teacher identified why these ability results tend to remain constant, this is due to, among other things: 1) students are bored of working in groups because, in every mathematics subject, both interest and mandatory, many tasks are done in groups; 2) group members who change frequently; 3) students feel bored using Desmos.Apart from that, the use of cellphones, laptops, and tablets to complete students' worksheets makes the distraction of using these devices to open other applications outside of learning also high; 4) mathematical material is increasingly abstract so that the formulas to be found become more difficult so that group discussions are difficult to build; 5) the teacher determines the selection of group members, this causes students not to be in the same group as their close friends.in cycle I, it was 79.17; and in cycle II, it was 85.In addition, the percentage of students' score completion also increased from pre-cycle where 60% of students completed, in cycle I there was 71%, and in cycle II increased to 77%.
Guided Discovery learning can also improve the collaboration skills of class XI students at SHS 6 Yogyakarta on circle material.In cycle I, there were 23 students in the medium category and 12 in the high category.However, after cycle II, students' collaboration abilities increased very significantly.There were 16 students in the very high category, 12 in the high category, and 7 in the medium category.
research used the type of Classroom Action Research.In classroom action research based on the model of Stephen Kemmis and Robyn McTaggart, there were four stages: planning, action, observation, and reflection.At the planning stage, researchers designed learning by applying guided discovery learning to circular material.

A
. Cycle IResearchers and teachers discussed preparation.The Lesson Plan used the discovery learning model, learning materials, student worksheets, learning assessments, and mathematical representation ability test questions, which were tested in cycle I.In cycle I, the teaching material was the position of points and lines relative to the circle.In cycle I, researchers divided students into nine groups, each with four students.The researcher will divide these nine groups into Category One and two categories.The group with category one will identify the position of the point on the circle based on the picture.Meanwhile, the group in category two will identify the position of the point on the circle based on their similarities.Below is a presentation of the student worksheet researchers used in cycle 1 in Figures1 and 2. The students' worksheet was designed using the Desmos application.

Figure 2 .
Figure 2. Students' worksheet cycle 1 students' collaborative proficiency across various facets when juxtaposed with the outcomes from cycle I.Additionally, scrutinizing the five collaboration ability indicators reveals that the fourth criterion, specifically indicative of a responsible attitude, persists as the least developed compared to the remaining indicators.The results of cycle II show a significant increase in each indicator of mathematical representation.In cycles I and II, verbal representation had the lowest average compared to symbolic and visual representation.Symbolic, verbal, and visual mathematical representation indicators have a high average related to collaboration ability.The indicator of active collaboration ability has the highest average, while the lowest is the ability to demonstrate an attitude of responsibility.

Table 2 . Pre-Cycle Learning Results in Every Aspect of Mathematical Representation
Based on Table1, the highest and lowest scores from the diagnostic test results in the symbol representation aspect were 75 and 25, averaging 64.11.In the visual representation aspect, the highest and lowest scores were 100 and 25, with an average of 73.21.Meanwhile, the highest and lowest values for the verbal representation aspect were 100 and 0, with an average of 12.86.If we looked at the students' grades and completion based on the Minimum Completion Criteria (MCC) at school, namely 75, several students had not yet completed the minimum criteria.The following data on student completion is presented in Table2.
equation material and interviews.The results of the mathematical representation diagnostic test were divided into three assessment aspects: symbol representation, visual representation, and verbal representation.The results of the mathematical representation ability test in the pre-cycle or initial diagnostic test are presented below.

Table 3 . Distribution of Final Diagnostic Test Scores
Based on Table2, more students were in the complete category than students in the incomplete category.Of the 35 students, 14 (40%) were in the incomplete category, and 21 (60%) were in the complete category.The highest and lowest scores from the final cycle I test were 94.6 and 29.7, averaging 78.87.From this table, many students still had not completed the MCC.Therefore, researchers carry out learning using the guided discovery learning model. of mutual respect, mutual assistance, and responsibility.

Table 3
shows an increase in results compared to Table1, especially in symbolic and verbal representation.In symbolic representation, initially, the student's highest score was 75, but at the end of cycle 1, some got a score of 100.

Table 5 . Distribution of Final Scores for Cycle I Tests Based
on Table4, it can be seen that students' completeness scores in cycle one increased when compared to diagnostic tests.Initially, students' completeness was 60%, which increased to 71%.Apart from that, the average student score also increased from 78.87 to 79.17.In this way, discovery learning can help students improve their representation abilities.Based on the collaboration questionnaire that students filled out, the results of students' collaboration abilities are presented below in Table5.

Table 6 . Results of the Student Collaboration Ability Questionnaire
Upon examination of Table5, it is evident that most students exhibit moderate levels of collaboration abilities, while a subset demonstrates high levels of proficiency in collaboration.Notably, there is an absence of students categorized as having very low, low, or very high collaboration abilities.The ensuing data presents an overview of the accomplishment of indicators about students' collaboration abilities.

Table 10 . Results of the Collaboration Ability Questionnaire for Cycle II Students From
Table9, it can be seen that there is an increase in students' collaboration abilities from cycle I to cycle II.In cycle I, no students reached the very high category; in cycle II, 16 students reached the very high category.In addition, the collaboration criteria are being reduced from 23 to 7 students.It shows that students' collaboration abilities increase after learning using the discovery learning model.Data on students' collaboration abilities based on each indicator is presented below.

Table 11 . Results of the Collaboration Ability Questionnaire for Cycle II Students
Table 10 delineates that there has been no discernible enhancement in Kurniasih and Sani (2014)athematical representation ability of around 17% from the initial condition.It is in line with what was stated byKurniasih and Sani (2014)that guided discovery Pardede (2015)rif (2021) diagnostic tests that most liked tasks done in groups but not too often.It is in line with research conducted byMasruroh and Arif (2021)that If we look at the scores obtained by students on the collaboration skills questionnaire, the scores have increased significantly.In cycle I, there were 23 students in the medium category and 12 in the high category.However, after cycle II, students' collaboration abilities increased very significantly.There are 16 students in the very high category, 12 in the high category, and 7 in the medium category.It aligns with research conducted byPardede (2015), who found that this learning model can improve students' collaboration abilities using media.In the learning that has been carried out, researchers use Desmos media as students' worksheets, which students complete in groups.From this discussion, guided discovery learning can improve students' representational and collaborative abilities in circular material.CONCLUSIONGuided Discovery Learning can improve the mathematical representation abilities of class XI students at SHS 6 Yogyakarta on circle material.The results of the mathematical representation test showed that students' mathematical representation abilities increased; namely, the average pre-cycle score was 78.87;