Implementation of Discovery Learning Models to Improve Students Mathematic Learning Outcomes

: The aims of this research was describing about implementation of discovery learning model to increase students mathematics learning outcomes. It was a quantitative research with one shot case study design. Subjects of this research were students of X th TEI 1 SMK Negeri 1 Driyorejo for the academic year 2021/2022. Data collection technique using three essay questions with data analyze technique include validity test and completeness test of Minimum Completeness Criteria. In this research, students are given 6 steps of discovery learning. There are stimulation, problem statement, data collection, data processing, verification


Introduction
The Law No. 20 of 2003 article 13 (Undang-Undang Nomor 20 tahun 2003 pasal 13) concerning education states that education is a conscious and planned effort in order to create a learning atmosphere.The planned learning process must involve students actively in developing their potential.Students' self-potential development is expected to be able to cover aspects of spirituality, religion, ability to control oneself, personality, intelligence, noble character, and the necessary skills (Muhari, 2017).Especially in Mathematics, students can develop the ability to measure, calculate, find and solve everyday problems.
The achievement of learning objectives can be seen based on the level of success and completeness of student learning outcomes.According to Siregar (2017), for some students mathematics is still considered a difficult and boring subject, so students are less interested in mathematics which causes students to have low scores below the Minimum Completeness Criteria.Minimum Completeness Criteria are learning completeness criteria determined by the education unit.
Results of interviews with Mr. Sutejo, S.Pd., M.Pd.as a Mathematics teacher at SMK Negeri 1 Driyorejo, information was obtained that student learning outcomes were below 75.This can be proven by 70% of students who scored below the Minimum Completeness Criteria.In fact, every student must reach the Minimum Completeness Criteria in order to achieve complete learning.One of the causes of student learning outcomes under the Minimum Completeness Criteria is because the models, methods, and learning media used are less innovative, so students are not interested in participating in learning.According to Mr. Sutejo, teacher competence in learning is also one of the reasons why students' scores are below the Minimum Completeness Criteria.
Based on literacy studies conducted by researchers and referring to the condition of students at SMK Negeri I Driyorejo, the solution offered to improve student learning outcomes is to use the Discovery Learning learning model.Ananta (2016) states that Discovery Learning is a learning method that can encourage students to ask a question and can formulate their own answers, as well as conclude general principles from an experience.According to Jerome Bruner in Wedekaningsih et al. (2019) said that Discovery Learning is a learning model that makes students think to ask questions and draw conclusions from an experience.Discovery Learning has characteristics among other learning models, namely: 1) problem solving, 2) about students, and 3) combine all the information held.The advantages of this learning model are that students become more active in learning activities, students are easier to solve problems in everyday life, and train students to learn on their own.So learning using discovery Learning will make students motivated so that they can improve their learning outcomes, especially in mathematics.
In addition, Hanafi (2016) said that the discovery learning model requires students to participate in making many decisions about what, how, and when something should be learned.Discovery learning plays a role in developing students' active learning methods by finding and investigating themselves so that the material to be delivered is easier to understand.The use of the discovery learning model will change the learning conditions that were originally passive to active and change the habits of students who only receive information from the teacher to find information on their own.
Research conducted by Ismah et al. (2018) states that the discovery learning model can improve mathematics learning outcomes on set material.Another study conducted by Wedekaningsih et al. (2019) revealed that the application of the Discovery Learning learning model can improve critical thinking skills and student learning outcomes in mathematics.
In this study, the Discovery Learning learning model was implemented on the subject matter of trigonometry because from the results of the second semester teacher assessment, the student learning outcomes in this material were 70% of students overall have not experienced mastery learning.Trigonometry material can be applied using the Discovery Learning learning model, because in this material students find it difficult to understand various things related to how to complete calculations using formulas.
Another research from Ali (2019) says that when he compared learning methods between traditional teaching methods using the activities that are based on teaching and inquiring through the discovery learning method in teaching the unit "If It Weren't For The Pressure?" to seventh-year elementary students can enhances the students' success and perception of inquiry learning skills.
Based on the results of the background, the formulation of the research problem is: how are student learning outcomes using the discovery learning model?

Method
The type of research that will be used in this research is quantitative research.The research design is One Shot Case Study Design which is a study without a comparison group and without a test at the beginning.In this study, researchers conducted research on 35 students of class X TEI 1 SMK Negeri 1 Driyorejo on Trigonometry and will be conducted in the even semester of the 2021/2022 academic year.
The instruments used in this research are syllabus, lesson plans, evaluation instruments.Syllabus, lesson plans, evaluation instruments used to determine students' abilities after being given a discovery learning model.The types of instruments used include assessment rubrics, questions, and post tests.
The data collection technique used a test method which included a written test in the form of a description of 3 questions.This written test aims to determine student learning outcomes after being given a discovery learning model.
The data analysis technique used descriptive statistical analysis which was used to describe the data resulting from the post test.The data analysis techniques used include: 1) validity test, 2) Completeness test, 3) calculating the average (mean), and 4) post-test result category.

Result and Discussion
Researchers conducted research on Monday, May 23, 2022 at SMK Negeri 1 Driyorejo.This study was conducted to determine the students learning outcomes using discovery learning.Collecting data in this study using the test method.The validity test is carried out to determine whether an instrument is valid or not.The test instruments tested have been tested for validity by expert validators in their fields.The experts who tested were mathematics lecturers at STKIP Bina Insan Mandiri as many as 2 experts.
In the Minimum Completeness Criteria, the researcher calculates the percentage of students who are above the Minimum Completeness Criteria.The formula used refers to chapter 3. From the calculation results above, it can be seen that 89% or 31 students whose scores are above the Minimum Completeness Criteria.Meanwhile, 11% or 4 students scored exactly on the Minimum Completeness Criteria score.Subekti et al. (2019) in their research says that Minimum Completeness Criteria determines a measurement of the quality of learning in the educational unit.It usually determine each school by observe the abilities of their students.So that learning mathematics using discovery learning models X th TEI 1 SMK Negeri 1 Driyorejo for the academic year 2021/2022 can be categorized very well.
The discovery learning model requires students to find their own understanding of a problem.The characteristics that exist in Discovery Learning are: (1) problem solving, (2) student-centered, and (3) combining all the information they have.The syntax carried out by researchers when teaching and learning process using the discovery learning model are: (1) Stimulation (provider of stimulation), (2) Problem Statement, (3) Data Collection, (4) Data Processing, (5) Verification, and ( 6) Generalization (drawing conclusions).
After carrying out the teaching and learning process using the Discovery Learning learning model, the researcher gave a post test to students in the form of 3 essay questions.From the research results for the post test class X TEI 1, it is known that there is an increase in student learning outcomes after using the Discovery Learning learning model.This can be seen in the Minimum Completeness Criteria, which is known that students achieve completeness if students get a score more than 75.
The first research conducted by Cintia et al. (2018).She said that the level of learning in students was considered successful if there were 80 of students who achieved the standard of completeness minimum criteria more than 65.The second study from Sulfemi et al. (2019) said that students had achieved complete learning when they achieved a score of 85 with the Minimum Completeness Criteria score more than 75.
Another study conducted by Puspitasari et al. (2019) in their states that research is considered complete if it meets the minimum standard of completeness criteria, which is 75.These results are in accordance with the theory put forward by Sudjana (2004) which says that learning outcomes are changes in individual behavior in the cognitive, affective, and psychomotor fields.From the theory stated above, it can be concluded that student learning outcomes can be known after going through the learning process.After the teaching and learning process and doing the post test, it was calculated that there were 89% of students who scored.And there are as many as 11% of students whose grades are right on the Minimum Completeness Criteria, this happens because the students who not take part in the teaching and learning process from beginning to end due to being late for class and there are some students who not focus when participating in the teaching and learning process so that the material obtained only partially more than 75.
Then the results of the post-test of students' mathematics are categorized into several criteria according to Table 1 Categories of Post-Test Results.After being categorized according to the table, the results showed that there were 0 students with a percentage of 0% who were in the low category.Students who are in the medium category are 30 students with a percentage of 86%.And there are 5 students with a percentage of 14% in the high category.
The average score of class X TEI 1 students after the post test was 77.6.Based on Table 1 Assessment Criteria for Average Student Scores, it was found that the average score of X TEI 1 students was in the good category.So it can be concluded that all students are said to be successful in using the discovery learning model.It is in accordance with the research that conducted by Wardani et al. (2018).They are taking research samples, namely SDN 1 Kaligentong as a core elementary school, SDN 2 Urutsewu as a distant impact elementary school, and SDN 3 Urutsewu as a close impact elementary school.The purpose of this study was to determine the differences in learning outcomes using the problem based learning (PBL) model in the experimental class and discovery learning learning models in the control class.The class of experiment has a value of 49.18 and increased to 73.76.As for the control class has a value of 50.12 and increased to 80.12.In this study, the experimental class and the control class both experienced an increase.
The second study conducted by Surur et al. (2019) said that there was a significant difference in learning outcomes between the experimental class and the control class.The experimental class that uses the discovery learning model has a score of 8.2500 and the class that uses the direct teaching model has a score of 7.0968.This shows that the class with the discovery learning model is more suitable for use in learning mathematics.
The third study conducted by Siantruri (2020) showed that in the first cycle there were 71.79% of students who completed individually and in the second cycle there was an increase in completeness to 100%.This shows that students' mathematics learning outcomes in the second cycle increased compared to the first cycle.
The fourth, another study from Wedekaningsih et al. ( 2019) also showed that there was an increase from cycle I to cycle II.In the pre-cycle, the average was 60, in the first cycle, the average was 70, and in the second cycle, the average was 81.This proves that the application of the Discovery Learning model can improve critical thinking skills and student learning outcomes.
The fifth study conducted by Ismah et al. (2018), showed that the data on learning outcomes of student during the pre cycle, cycle I, and cycle II experienced an increase in the set material.Although there was a slight decrease in cycle II, it did not have a significant impact, but the discovery learning model could increase the learning outcomes on the set material.
The sixth study conducted by Prasasti et al. (2019) showed that in the pre-cycle the number of learning outcomes achieved was only 35%, but there was an increase in the first cycle to 77% and increased to 85% during the second cycle.The application of the Discovery Learning model in this study was able to improve student learning outcomes, especially in the flat material.
The seventh, some study from Trisnawaty et al. ( 2017) also conducted that the assessment instrument based on SSA-HOTS can be applied in learning to train higher-order thinking skills so that it can improve cognitive aspects, psychomotor aspects, and affective aspects.The SSA-HOTS assessment conducted at SMA Muhammadiyah 4 majoring in science had a score of 0.95, 0.83, 0.81, and 0.80 which were in the high category.So that the use of the SSA-HOTS assessment instrument can improve students' higher order thinking skills.
The last research using the discovery learning learning model from Oktaviani et al. (2018).There was an increase from pre-cycle to cycle II.This can be shown in the pre-cycle where the number of students who completed was 34.61%, then increased to 73.07% in the first cycle.Because the indicators of success were not completed, the second cycle was carried out which obtained the number of students who completed 84.62%.This shows an increase in critical thinking skills and student learning outcomes using the discovery learning model.
In this research, students are given 6 steps of discovery learning.In the first step, stimulation, the teacher starts learning by asking various questions and other learning activities that lead to preparation for problem solving.Furthermore, in the problem statement, students are asked to identify problems that are relevant to the topic of the lesson and formulate it in the form of a hypothesis.The third step is data collection where the teacher gives students the opportunity to prove their hypothesis by collecting as much relevant information as possible.In the next step, data processing, students process the data obtained with the guidance of the teacher.Furthermore, in the verification step, students carry out a careful examination to prove the hypothesis and related to the results of data processing.And in the last step, generalization, students draw conclusions from the results.
After observing and assessing the students of class X TEI 1 SMK Negeri 1 Driyorejo, it was concluded that students who previously obtained completeness of 30% experienced an increase to 89%.Meanwhile, the students' average score, which was previously below 75, has now increased to 77.6.So that students experienced an increase of 59%.Svinicki (1998) in his research says that the learning theory behind discovery learning is the cognitive model of learning.This theory focused on what happen in the student's mind.The new information is acquired and then incorporate into student's existing network.After that student's will be create new networks or reorganizing old networks and process it to be a new information.To reach this purpose, student must be constantly notice a new information and ensure in their memory to make relation.With repeated of memory, that new networks will be more strengthened and elaborated until they become well.So we can say that students of class X TEI 1 SMK Negeri Driyorejo have obtained good cognitive learning.It can see frome their score that increased by 59%.
From the tests conducted by researchers, starting from the validity test, calculating the average (mean), and categorizing the students' post test results, it can be shown that the discovery learning model has an influence on the mathematics learning outcomes of students in class X TEI 1 SMK State 1 Driyorejo.The result relate with the research from Marian (2019) that find the learning method used by the teacher has not been able to facilitate students so that the learning process is still not meaningful.It can not yet cover all competency indicators in the school.From that conclusion we can say that if teacher did not used the right learning method, it can make learning process being not meaningful.Zulkarnain et al. (2021) in their research also find that mathematical communication skills of students in mathematics learning can increase using discovery learning model.Another research from Muchlis et al. (2021) also find that discovery learning model can improve learning outcome in trigonometry course.From their research discovery learning also can optimize multiple intelligence activity of students.Batubara (2019) in his research also find that guided discovery learning methods can make students critical thinking ability increase.From all these research we can conclude that discovery learning make all students' ability increase.So we can use these models in the learning process.It is suitable with our research too.From our research we find that this model is able to make student's learning outcomes improve on trigonometry material in class X TEI 1.

Conclusion
Based on the results of the research and discussion that have been carried out and explained in Chapter IV, the researchers can conclude that students' mathematics learning outcomes using the discovery learning learning model have increased, especially in trigonometry material in class X TEI 1 SMK Negeri 1 Driyorejo.Suggestions that can be considered by schools include: (1) To improve student learning outcomes, especially in mathematics, teachers are expected to use various variations of learning models.One that can be used is the discovery learning model, and (2) so that mathematics becomes a subject of interest to students, it is hoped that teachers can provide various innovations in delivering learning materials.

Table 1 .
Category of Student Post Test Results