Analysis of Student's Spatial Ability in terms of Van Hiele's Thinking Stages in Problem Based Learning

Mathematics plays an important role in the development of science and technology in everyday life. Especially at school, Mathematics is one of the main subjects studied at every level of education from SD / MI, SMP / MTs, SMA / MA to tertiary institutions. In addition, mathematics is also a requirement with values that can shape the personality and character needed to face an era that demands professionalism. Based on this, mathematics needs serious attention. The Indonesian government has made various efforts to improve the quality of teaching and improve student mathematics learning outcomes, because mathematics is a very important science in every level of education pursued by every Indonesian citizen. The government's efforts are to develop curricula, provide training to teachers, complete educational infrastructure and even improve teacher welfare. Along with the development of the internet, learning strategies have shifted and various information and communication technology-based learning strategies have emerged from the e-learning Abstract


II. Research Methods
The subjects in this study were journal articles on the analysis of students' spatial abilities in terms of van hiele's thinking stages in problem-based learning. The object of this research is the provision of a problem-based learning process. Researchers are the main research instrument. So in this study, researchers act as planners, implementers of data collectors who then interpret the data that has been collected. In conducting research, researchers collect as much data as possible so that the research results are accurate. Apart from that, researchers began to read and understand several previous studies or journals about research on students' spatial abilities in terms of van hiele's thinking stages in problem-based learning. In this study, researchers used a type of literature study research, namely a series of activities related to the library data collection method, Mahmud (2011). In this study, the analysis technique used was the Miles and Huberman model. Data analysis activities, namely data reduction display data and conclusion drawing/verification.

Results
From several sources, experts who expressed their opinion about spatial abilities, namely some of the opinions above stated how important it is to master spatial ability in mathematics learning is one of the factors that influence student learning success. This is emphasized by Indriyani, (2013) that spatial abilities also have an influence on students' mathematical abilities. This means that if the student's spatial ability in mathematics is high, then the student's ability to do mathematics is generally high.
Several previous studies that have conducted research with the same title have obtained different results as one of the previous researchers. According to Sari (2013) who conducted a study entitled Analysis of Student's Spatial Ability and Self-efficacy in Cooperative Learning Using Jigsaw.
Students' thinking processes on spatial abilities are divided into 3 categories, namely high, medium, and low. In this study, after applying the teaching and learning process determined by the researcher, eating can show the level of students' spatial abilities which will be shown in the following Based on the results of the math spatial ability test on 34 students, the students' spatial ability levels were divided into three categories. 5 students out of 34 students involved in this study were selected for the interview based on their Mathematical spatial abilities.
The results of the test were corrected by the researcher and further classified in the Van Hiele geometric thinking level distribution table. The criteria for students to be able to answer an item correctly is if the student gets a minimum score of 8 or gets 80% of the maximum item score on that item.

Figure 1. Distribution Results Diagram for Van Hiele Geometry Thinking Class VII B MTs
Darussalam Jabon Based on Figure 1, it can be seen that the highest distribution of students is at level 2 based on Van Hiele's level of thinking, while at level 0 and level 1 only about half of the students who have level 2.
The subject of this study was then given a test of students' mathematical problem solving abilities on the rectangular material and then analyzed according to Van Hiele's geometric thinking level. The following is the student name and coding data provided by the researcher for analysis.

a. The Abilities Obtained by the Subject Level 0 (Visualization)
In carrying out the problem-solving plan, subject A1 was unable to solve the problem according to the question's instructions because in the preparation of the settlement strategy there was still something missing. Subject A1 was in the rechecking stage, unable to check the results of his answers again and unable to convince himself that the results of the solutions were correct. Based on the discussion, students in group level 0 (visualization) note that in understanding the problem can be done correctly, but in compiling the plan for completion, implementing the plan for completion, and re-checking the answer cannot be done correctly.

b. The Abilities Obtained by the Subject Level 1 (Analysis)
In carrying out the problem solving plan, subject A2 is able to solve the problem in accordance with the solution strategy by using the correct settlement steps and the calculation process for each step is also correct. Subject A2 at the rechecking stage, has not been able to re-check the results of his answers, is unable to determine how the steps are in re-examining the results of his work. Based on this discussion, students at level 1 (analysis) note that in understanding the problem, compiling a solution plan, and implementing the problem solving plan have been done correctly. However, students have not been able to check the results of their answers again even though the calculations have been done correctly.

Level 1 Analysis Level 0 Visualization
Level 2 Deduction

c. The Abilities Obtained by the Subject Level 2 (Informal Deduction)
In carrying out the problem solving plan, the A3 subject is able to solve problems according to the correct resolution strategy and the correct calculation process. Subject A3 is in the rechecking stage, is able to check the results of their answers again and is able to convince themselves that the results of their solutions have been done correctly. Based on this discussion, students at level 2 (informal deduction) note that in understanding the problem, compiling a problem-solving plan, executing the solution plan, and checking again can be done correctly and the calculation process is also carried out correctly.
Siagian (2019) conducted a study with the title analysis of the difficulty of solving geoetric problems for class VIII students of SMP Methodist 7 Medan in terms of van Hiele's theory of thinking assisted by Macromedia Flash. This research is a qualitative descriptive study. Learning carried out assisted by macromedia flash.
The research data were obtained directly from the research subjects, namely in the form of work sheets on the students' geometry problem-solving abilities, the results of the learning media questionnaire test results and recorded interviews. The data that will be presented in this research are Van Hiele's geometry thinking level, the level of students 'geometry problem solving ability, and a description of the researcher interview with students.Then from the existing data, data triangulation is carried out to analyze students' difficulties in solving geometric problems which refer to the patron of problem solving difficulties. Students 'geometry. Through the data analysis, it can be concluded that new findings are drawn. Conclusion is to describe the students' difficulties in solving the geometry problems under review and student work sheets and researcher interviews with students.

Figure 2. Diagram of the Level of Troubleshooting Ability
In Figure 2, many students who have a minimum level of gometric mass solving ability are 13 students and many students who have a low level of geometric problem solving ability are 13 students because there are many students who have a low level of geometric problem solving ability, which shows that there are still many students who do errors in solving geometry problems. So it is necessary to explore the difficulties experienced by students who make mistakes in solving geometry problems.
Nur'ani Muhassanah (2014) in his research entitled Analysis of students' geometric skills in solving geometric problems based on van hiele's level of thinking. The qualitative research method is a case study type, which analyzes students' geometric skills in solving geometry problems based on van hiele's level of thinking in depth.
Researchers determine the research subjects using purposive sample. To determine the subject, the researcher gave a placement test to 28 students of class VIII SMP N 16.
Based on the results of the analysis on the results of interviews conducted 18 times 9 subjects, the characteristics of students' geometric skills in solving geometry problems were obtained based on van hiele thinking level for level 0 (visualization), level 1 (analysis), and level 2 (informal education).

Discussion a. Geometry Skills at Level 1 (Analysis) 1. Visual skills
It can only determine the type of flat shape of a quadrilateral based on the appearance of its shape and the properties it has, in explaining the properties of a quadrilateral based on the image it can explain the specifics which include the number of sides, side size, angle size, side alignment, and the relationship between the two angles. facing the same size, and cannot explain the relationship between the various types of rectangular images.

Verbal skills (descritive skills)
Can group the correct names for given quadrilateral images, can describe / define a quadrilateral based on the properties it has from the number of sides, side size, angle size, number of angles, side alignment, and cannot formulate sentences that indicate the relationship between the rectangular images.

Drawing skills
Be able to construct images according to the characteristics and properties given such as two parallel lines, two perpendicular lines and determine a point in a line, and able to construct other rectangular images related to the given rectangular image and can describes the properties of the quadrilateral starting from the side dimensions.

Level of Ability in Geometry Problem Solving
The Number of Students 4. Logical skills Be able to understand the conservation of the shape of a rectangular image in various positions by mentioning the type of each image, be aware of the similarities of several quadrilateral images starting from the same shape as rectangles and the number of sides, and be able to mention the differences in rectangles and realize that properties can be used to distinguish types of rectangles , starting from the size of the side, the size of the angle and the number of sides that are parallel.

Applied skills
Can relate information (physical objects) given and develop it in a geometric model (without using scale), can explain the geometric properties of physical objects, and can use geometric models in solving problems.

b. Geometry Skills at Level 2 (Informal Education)
1. Visual skills The visual skills possessed include the subject being able to group and determine the type of rectangular shape in each image based on the properties of each image, in explaining the properties of a rectangular shape based on the image can explain specifically which includes the number of sides, side size , the alignment of sides, the size of the angles, the relationship between two facing angles of equal size, the number of angles, the relationship between adjacent angles totaling 180o, and can explain the relationship between various types of rectangular images based on the properties of each image and recognize the general nature of various types of rectangular images by sorting out which ones fall into the general nature or not.

Verbal skills (descritive skills)
Subjects can classify the correct names for the given quadrilateral images, can describe / define a rectangular shape based on the properties they have from the number of sides, side size, angle size, number of angles, side alignment, and the relationship between the two angles. facing the same size, the relationship between adjacent angles has 180o number of angles, and can formulate a sentence that shows the relationship between the quadrilateral based on the general properties possessed by the quadrilateral.

Drawing skills
Subjects are able to construct images according to the characteristics and properties given such as two parallel lines, two perpendicular lines and determine a point in a line and are able to construct another rectangular image related to a given rectangular image (rectangle , square, right-angled trapezoid) is even able to make guide lines to form another rectangle (line of ranks), and can explain the properties of the image of the rectangle it forms.

Logical skills
Subjects can understand the conservation of the shape of a rectangular image in various positions by mentioning the type of each image, realizing the similarities of several rectangular images starting from the same shape as rectangles, the number of sides, and the number of angles, can mention the difference in rectangles and realize that properties can be used to distinguish the type of rectangle, starting from the size of the angle, the size of the side and the number of pairs of sides that are parallel, and can use the properties of a rectangular drawing to determine a class of rectangles contained in other types of rectangular classes.

Applied skills
The applied skills possessed by each category of van Hiele's thinking level are different, where there are similarities and differences in the applied skills possessed by each level. According to Harina et al (2018) conducted a study with the title knowing the geometric development of students. This type of research is a descriptive study with a qualitative approach. Data collection techniques in this study consisted of two methods of test and interview. The instrument used was a test consisting of 25 multiple choice items. Data analysis used Miles and Huberman's model. The results showed that the geometric thinking level of mathematics education students was at level 0 (visualization), level 2 (analysis), level 2 (informal deduction), and level 3 (formal deduction). On the other hand, no one has yet reached level 4 (rigor). The number of students who were difficult and could not be classified or identified was significant enough to be at the pre-visualization level (before visualization). Table 5 shows the results of the data analysis on the level of development of students' geometric thinking. Based on Table 5, most of the mathematics education program students are at level 1 (analysis). Only a few students (2.15%) have met level 3 (deduction), while there are no students who meet level 4 (rigor) (0%), and 30.67% are not at the level of van hiele geometry development. This data shows that most of the development of students 'geometric thinking is at the level of analysis, namely understanding the concept of geometry is carried out by informal analysis of parts of geometric objects, students' ability in deductive thinking is still weak. For the sixth semester, all geometry courses consisting of geometry, space geometry, field analytic geometry, space analysis and transformation geometry are expected to be at a higher level than these results. Especially if the student has taken an optional course in the geometry system. Ideally, their level of geometric development is already at the top level. This shows that learning activities in geometry courses need to be improved so that the development of students' geometric thinking can be boosted. In table 6, the percentage of the highest transition level at the pre-1 level (preanalysis) is 17.2% and the lowest percentage at the pre-rigor level is 1.08%. Students who have reached the transitional level can increase their geometric level through learning that supports increased geometric thinking. In addition, students who are at the transitional level, there are also students who have difficulty classifying their level of geometric thinking as many as 75 students (40.32%). This is because the respondent is not serious in working on the questions given so that they answer randomly or cheat while working on the questions, or it could be because the development of their geometrical thinking has not met any level in Van Hiele's theory. Analysis of the Spatial Ability of Class VII Students of SMP N 2 SAWIT in Solving Quadrangular Material Questions Based on Van Hiele's Thinking Level The research data were obtained through three methods, namely the test method, interview method and documentation method. The test was held on Monday, August 7 2017 in class VII D which was attended by 21 students. The test is in the form of an essay which consists of 3 questions. The selection of subjects in this study was taken from 21 students of class VII D who took the written test and were classified based on the minimum completeness criteria (KKM) as follows. Through this grouping, 3 students were selected as research subjects, namely one student from the high spatial ability category, hereinafter referred to as an undergraduate student, one student from the medium spatial ability category, hereinafter referred to as a master's student, and one student with low spatial ability furthermore. referred to as doctoral students.

c. Level of Visualization
At the visualization level, undergraduate students are familiar with geometric shapes and are able to name a geometric shape. This is indicated by the student being able to describe a rectangular shape object on the student's answer sheet. This means that students who have high spatial abilities have reached the visualization level.

Figure 4. Students' Answers with Moderate Spatial Ability in Visualization Level
Based on the students' answers from Figure 2, it appears that students who have moderate spatial abilities can already visualize rectangular objects. Students have identified a shape based on the shape or characteristic they know. This means that students with moderate spatial abilities can reach the Visualization level.

Figure 5. Answers of Students with Low Spatial Ability Level of Visualization
Based on the students' answers from Figure 3, it appears that doctoral students can already understand the questions. The student can already visualize the rectangular shape by drawing on the answer sheet. Doctoral students can already identify shapes based on the shape or nature they know. This means that students who have low spatial abilities can reach the Visualization level.
The results of the research above indicate that students who have high, medium and low abilities have reached the Visualization level. This is in line with the results of research conducted by Nur'aini (2015) which revealed that students at level 0 (visualization) on visual skills can only determine the type of flat rectangular shape based on the appearance of the shape; verbal skills, can group the correct name for the pictures given rectangle; drawing skills, only able to sketch rectangular images with labeling of certain parts; logical skills, can understand the conservation of rectangular image shapes in various positions and realize the similarities of several rectangular images; and applied skills, can relate information (physical objects) provided and develop it in a geometric model, in addition to explaining the geometric properties of physical objects. This opinion was later strengthened by research conducted by Wahab (2016) which stated that of the 133 respondents the majority of students had reached level 1 (visualization).

Figure 6. Answers of Students with High Spatial Level of Analysis Ability
At the level of analysis, undergraduate students have memorized the properties of geometric shapes and the attributes of their components. This is indicated by the student being able to do the problem correctly. It means that undergraduate students already understand the questions given. Thus S1 has reached the Analysis level.

Figure 7. Answers of Students with Moderate Spatial Ability Level of Analysis
Based on the students' answers from Figure 5, it appears that students who have moderate spatial abilities already understand the questions. This is indicated by students being able to identify shapes based on their shape or what they know. Students can already describe a geometric shape based on the properties or attributes of its components. This means that students who have moderate spatial abilities have reached the level of analysis.

Figure 8 Answers of Students with Low-Level Spatial Ability for Analysis
Based on the students' answers from Figure 6, students who have low spatial abilities can work on the questions correctly. However, during the interview session, doctoral students could not answer the questions asked in question number 2b. This is indicated by the student's statement that "Don't understand, sir. Because I'm still confused about the corners, sir. "This means that doctoral students have not been able to identify a shape based on its shape or nature. Students have not been able to describe a geometric shape based on the properties and attributes of its components. This means that students who have low spatial abilities have not yet reached the level of analysis.
Subject 2 who has moderate mathematical ability, the description of Van Hiele's geometric thinking level at the recognition level (0) is that the subject is able to recognize the structure of the shape and name the shape, for the level of analysis (1) is able to realize the properties of the shape. The level of informal deduction (2) is being able to make a statement that there is a shape that is interconnected with other shapes. Subject 3 has low mathematical ability, the description of Van Hiele's geometric thinking level is at the recognition level (0), which is able to visually recognize shape characteristics, and give names.

e. Levels of Informal Deduction
Based on the answers of undergraduate students from the picture above, these students can understand the questions well. Students can compare geometric shapes based on their properties. Students can also solve problems that involve familiar wake-up properties. Students can also apply the formulas and solve these questions on the answer sheet. This means that students who have high spatial abilities have reached the level of Informal Deduction

Figure 10. Answers of Students with Moderate Level of Informal Deduction
Based on the answers of S2 students from Figure 8 it appears that students with moderate spatial abilities are still having difficulty working on the questions given. Students have not been able to compare geometric shapes based on their properties. Students also have not been able to solve problems related to the questions given. This is indicated by students who are still confused about the angles of geometric shapes. This means that students who have moderate spatial abilities have not yet reached the level of informal deduction.

Figure 11. Answers of Students with Low Spatial Ability in Informal Deduction Levels
Based on the answers of S3 students from Figure 9 it appears that S3 is still having difficulty in solving the problems in the questions given. This is indicated by students who cannot do several points on the questions. Students also cannot yet compare geometric shapes based on their properties. This means that students with low spatial abilities have not been able to reach the level of Informal Deduction.
Indicators of informal deduction can only be achieved by students who have high spatial abilities. Undergraduate students can understand the questions well. S1 can relate the properties of a flat shape with its application to the flat shape formulas. Meanwhile, students who have moderate spatial abilities and students who have low spatial abilities have not been able to reach the level of informal deduction. This is indicated by students who have moderate and low spatial abilities who still have difficulty solving problems. This is in accordance with research conducted by Suwito, et al. (2014) which states that the results of this study concluded that students who reach the level three van Hielle level are able to solve geomertial algebra problems correctly by utilizing the deduction of spatial reasoning ability to build geometric structures in axiomatic systems. in solving a given problem. Then this is also in accordance with the results of research conducted by Febriana (2015) which states that students with moderate abilities have difficulty in representing the spatial images in their minds in the field. Meanwhile, low-ability students have difficulty imagining object shapes from different perspectives. This opinion is reinforced by the results of research from Jogymol K. Alex (2016) which reveals that rectangular flat shapes namely rhombus, kites and trapezoid are considered to be problems for students.

f. Analysis of Student Spatial Ability in terms of Van Hiele's Thinking Stages in Problem Based Learning
This research is to determine the analysis of students' spatial abilities in terms of Van Hiele's thinking stages in problem-based learning, after analyzing various sources taken such as books, articles, journals and previous research, we can see that problem-based learning with Van Hiele's thought process. students 'spatial abilities greatly affect the improvement of students' abilities. From several research findings in the field, namely the difficulty of the problem solving process in spatial abilities. And the thinking process of students at Van Hiele's thinking stage still reaches level 3 (deduction).

IV. Conclusion
The Based on the results of data analysis and discussion in this study, the following conclusions are stated: 1. Students' thinking processes on spatial abilities after problem-based learning by following Van Hiele's thought process are categorized into three categories, namely high, medium low as follows: a. Students with high spatial abilities have a process of exploratory thinking, methodical thinking, analogical thinking, abstract thinking, synthesis, serendipity, and recycling of ideas. Students with high spatial abilities also have high imagination. b. Students with moderate spatial abilities have an exploratory thought process, serendipity, analogical thinking, semi-abstract thinking, and recycle ideas and have a moderate imagination. c. Students with low spatial abilities in understanding problems use exploratory, analogical, semi-abstract, synthesis thinking processes and have low imagination.