Student’s Mathematics Ability in Written Communication Based on Van Hiele's Theory and Gender

This study aims to determine the ability to analyze students on geometry learning by applying Van Hiele's theory to elementary theory to grade V elementary school students. The background of this researchis the author found an indication of the low ability to analyze learners in elementary school. This article aims to provide a proposal for Van Hiele Theory in geomtery learning. The method of this research is through literature study, which is collecting data from various books, articles, and research results to obtain the information being researched. research results to obtain information that is being researched. The approach used in this research is qualitative, which is to collect descriptive data from previous research as a source of research. as a source of research. The data that has been obtained is analyzed and concluded so as to get conclusions from several previous studies to answer how to provide proposals for the ability to analyze students through Van Hiele's theory in learning geometry. The results of the literature study This literature study shows that Van Hiele's theory has an important role in helping the teachers to develop learning methods that are suitable for geometry material, by going through the stages of geometry learning based on through the stages of learning geometry based on Van Hiele's theory, namely: 1) Recognition stage; 2) Analysis stage; 3) Deduction stage; 4) The accuracy stage. With this it can be concluded that Van Hiele's theory can help students and teachers in the process of learning geometry by going through the stages that have been proposed by Van Hiele stages that have been put forward by Van Hiele. In this case, the teacher can apply Van Hiele's theory to students starting from the introduction stage by using concrete media that is commonly found in the classroom. Introduction stage by using concrete media that is commonly found around, up to the analysis stage, namely the around, up to the analysis stage, which is the stage of students to analyze in depth about the observed flat shapes.

Geometric writing ability is part of written mathematical communication abilities that focus on representing mathematical ideas in written form. Research observations show that this ability is still relatively low among eighth-grade students. The Geogebra-assisted Problem-Based Learning model is considered effective in encouraging active student engagement. Van Hiele's theory was chosen to classify students' geometric thinking stages. The purpose of this study was to describe the geometric writing ability of eighth-grade students based on Van Hiele's theory through the application of the Geogebra-assisted Problem-Based Learning model. The method used in this study was descriptive qualitative. The population in this study were eighth-grade students of SMP Negeri 32 Purworejo in the 2024/2025 academic year, with a purposive sampling technique. The instruments used included the Van Hiele geometry level test questions and interview guidelines. Data analysis was done by reducing the data, presenting the data, and drawing conclusions/verification. The results of this study are (1) the Van Hiele geometry level test results show that most students are at stage 2 (informal deduction), and (2) there are differences in students' geometric writing abilities based on groups, with the upper group able to achieve three of the four indicators, the middle group able to achieve two of the four indicators, and the lower group only able to achieve one of the four indicators. Based on these results, it is found that Van Hiele's theory, the PBL model, and Geogebra can help develop students' geometric writing ability.

This research is a literature study with a qualitative approach. This research is motivated by the importance of students' understanding of the material properties of quadrilaterals. The purpose of this study is that researchers want to find out whether Van Hiele's theory and contextual approaches are effective in increasing the understanding of fifth grade elementary school students about the material properties of quadrilaterals. Van Hiele's theory is a theory that is specifically used in the field of geometry which has 5 stages of learning, namely the information stage, the directed orientation stage, the explicitization stage, the free orientation stage, and the integration stage. While the contextual approach emphasizes on 7 contextual components, namely: (1) Constructivism, (2) Asking, (3) Finding, (4) Learning Society, (5) Modeling, (6) Reflection, (7) Actual assessment. So that learning is obtained through knowledge and experience or the real world, improving students' higher order thinking processes, student-centered, active students, critical, creative, problem solving, students learn in a fun, exciting, not boring, and use various learning resources. The results of this study indicate that there is an increase in students' understanding of the material properties of quadrilaterals by using Van Hiele's learning theory and contextual approach.

Geometry is one of the important subject in mathematics. One of the objectives of learning geometry is the students can gain confidence about their mathematical abilities and be able to communicate mathematically. However, in their practices students are still having difficulty understanding geometric material and students’ mathematical communication skills are also still low. Considering the importance of geometry learning, the students’ mathematical communication ability need to be improved to achieve geometry leaning goals. In this study, geometry learning devices were developed based on the Van Hiele Theory with the purpose to produce a product consisting of lesson plan and students worksheet to develop students’ mathematical communication ability. The development model used is Model Plomp. Based on the results obtained in small group stage, there is increase in students’ mathematical communication ability seen from the result of working the questions every meeting. Then, an analysis the questionnaire of students who obtained practical category. So that, it can be conclude that geometry learning sets based don Van Hiele Theory practical can be used to increase Students Mathematical Communication Ability in Class VII Junior High School.

Difficulties in learning geometry relate to spatial abilities. Students with good spatial skills will be able to solve geometric problems. In helping students overcome difficulties in learning geometry, they used the Van Hiele's learning theory. This qualitative descriptive study aimed to describe the spatial perception ability in solving geometric problems based on Van Hiele's theory in terms of mathematical ability. The subjects in this study were three junior high school students with high, medium, and low math abilities. Subjects were given a spatial ability test and an interview twice. The triangulation time and subject was carried out to test the credibility of data. Based on the results of data analysis, students with high, medium, and low math abilities were able to observe objects from different perspectives. Subjects with medium math abilities were able to observe the object from different perspectives. However, subjects with high and low math abilities have some difficulties in observing objects from different perspectives.

Mathematics learning must be facilitated by students' skills in conveying their creative ideas and the teacher's skills needed to provide constructive learning. One of the abilities that can develop students' thinking skills in learning geometry is spatial ability. Mathematical spatial ability pressure in the field of geometry and is important for students to master. The importance of spatial abilities requires students to have good mathematical spatial abilities. Because learning mathematics cannot be separated from geometry, so with good spatial abilities, mathematical abilities will also be good, especially in the field of geometry. The form of an effort to find out students understand geometry material is by using van Hiele's geometric thinking theory so that they are able to overcome students' difficulties in learning geometry. Van Hiele's stages consist of the visualization stage, the analysis stage, the abstraction stage, the deduction stage, and the rigor stage. ). In this study, we wanted to know the spatial abilities of students at the level of visualization (0) and analysis (1) from van Hiele's theory, namely students' initial ability to recognize geometric elements/components.

Mathemathical communication ability is one of the mathematical abilities that need to be developed for students, so that students are able to solve mathematical problems and other sciences as well as being able to provide logical, systematic, critical and open reasoning skills needed in everyday life. The results of the literature study and preliminary study state that students' communication abilities are still low. This is because students are less active in the learning process and are not used to expressing mathematical ideas. Therefore, a learning device based on Van Hiele theory is designed which is expected to later be able to improve students' mathematical communication skills. This research is a development research by adapting the development model of Plomp consists of 3 phases, namely preliminary research, prototyping phase, and assessment phase. The research subjects were class VII students of SMPN 13 Padang. At the preliminary research phase needs analysis, curriculum analysis, analysis of the characteristics students, and concept analysis. In the prototyping phase, the design of lesson plan and students worksheet based on Van Hiele theory, then formative evaluation is carried out to determine the validity and practicality of the product. In the assessment phase an assessment is carried out with limited practicality and effectiveness. Practical data is obtained from the implementation sheetof lesson plan, teacher practical questionnaire, students practical questionnaire. Effectiveness data obtained from student learning outcomes in the formof a final test to see the mathematical communication abilities of students. The results showed that learning sets based on Van Hiele theorywere valid, practical and effective. Valid because it meets the criteria valid in terms of content and construct. Practical because it is easy to use and understand, the allocation determined is very efficient, interesting, and contributes to learning. Effective in terms of its potential impact on the communication ability of mathematical learners.

The purpose of this study was to: (1) finding out the difficulties experienced by mathematics education students in solving geometric reasoning problems based on van Hiele's theory; (2) identifying the factors causing difficulties experienced by students in solving geometric problems based on van Hiele’s theory; and (3) determining the steps that need to be taken to overcome the students' difficulties in solving geometric reasoning problems based on van Hiele's theory in the Transformation Geometry Course. The students' difficulties in solving geometric reasoning problems based on van Hiele's levels will give an idea of the indicators of geometrical reasoning abilities that are still low, so that the right alternative solutions are obtained. This type of research is descriptive research with a qualitative approach. The research subjects were 28 students who programed geometry transformation courses. The instrument in this study was a test instrument, namely geometric reasoning abilities of students as many as 5 questions consisting of 5 levels of ability, namely visualization, analysis, abstraction, formal deduction, and rigor. While the data analysis techniques in this study used descriptive analysis. Collecting data in this study used interview techniques and written tests. The results showed that from the five indicators of geometric reasoning ability, for the visualization level, there were 26 people who achieved the optimal score with a percentage of 92.9. Seen at the level of analysis still not reached optimally with a percentage of 21.4 or only 6 people who achieved the optimal score, while the level of abstraction, formal deduction, and rigor has not been achieved. Difficulties experienced by students at the level of analysis, abstraction, formal deduction, and rigor. The causal factors experienced by students based on the results of interviews obtained information that students have difficulty answering questions due to several things including; students have forgotten about the material being taught, when they learn they understand but are less interested in developing, feel unsatisfied so they expect concrete media, need to be trained in many questions, and follow up to students. From this information, an appropriate alternative is needed, for example using van Hiele's theory to familiarize students with reasoning skills.

Every student has different abilities, this difference is due to the different stages of ability that students have. The purpose of this study was to describe students' thinking skills based on Van Hiele's learning theory. The subjects of this study were 15 students of class VIII SMPN 2 Makale. The instruments used were test descriptions and interviews. The results showed 93% who had the ability to think at the introductory stage (stage 0), 80% of students who had the ability to think at the stage of analysis (stage 1), 33% of students who had the ability to think at the sequencing stage (stage 2), and 20% of students. who has the ability to think at the deduction stage (stage 3). Thus, the thinking ability of iclass VIII students of SMP Negeri 2 Makale based on Van Hiele's theory on cube and block material reaches stage 3 or the deduction stage.

In implementing the 2013 curriculum, Higher Order Thinking Skills (HOTS) must be integrated into learning activities. Similarity are sub material of similarity and congruence that students must learn. In fact, the higher order thinking skills of junior high school students in similarity material is low. To overcome this problem, it is necessary to develop a learning materials for learning in the form of plane similarity according to the level of student thinking in geometry, which is based on Van Hiele's theory to improve students' higher-order thinking skills. Van Hiele's theory was chosen because it suggests the development of students' thinking in learning of geometry occurs through five levels sequentially so that learning devices can be developed according to the level of van Hiele students. The purpose of this research is to obtain a description of the learning materials of plane similarity based on van Hiele theory based on van Hiele theory to improve students' high-level thinking skills that are valid, practical, and effective. This type of research is a research development using the 4-D model proposed by Thiagarajan then simplified to a 3-D model. Validation of learning devices, participant observation, questionnaires, and tests are the data collection techniques used. The results showed that the RPP, LKS, and THB were said to be valid then, the learning materials was declared valid; the management of learning is said to be good, the overall evaluation on the validation sheet of the learning materials is stated to be used, and the percentage of active student activities at the second meeting and the third meeting respectively is 91.25% and 91.25% then, the learning kit is declared practical; and the percentage of positive responses of students by 71% and an increase in higher order thinking skills seen from the results of the N-Gain pretest and posttest of 0,728 categorized as high then, the learning device is declared effective. Keywords: learning materials, plane similarity, van hiele’s theory, higher order thinking skills.

The ability to think geometrically is hierarchical so students need to master the initial level of thinking before they are going to the next level. Geometry learning strategies need to consider the level of students' thinking abilities. Assessment with paper-based tests has weaknesses in terms of practicality and does not develop students' technological literacy in the digitalization era. This study aims to analyze the need for the development of a website-based instrument to assess the geometric thinking skills of elementary school students referring to Van Hiele's theory. This research is a literature review with a qualitative approach. The articles reviewed in this research are articles that discuss thinking skills based on Van Hiele's theory with research subjects of elementary school students and published from 2021 to 2023. Data were analyzed by Miles and Huberman's interactive model. The results showed that a web-based instrument for assessing the geometric thinking abilities of elementary school students based on Van Hiele's theory was needed to systematically assess students' geometric thinking abilities then could be followed up with learning activities according to students' abilities. The level of thinking of elementary school students assessed is from visualization to abstraction which is adapted to the material and curriculum of the elementary school.

In the process of learning mathematics, especially geometry, teachers must pay attention to the level of ability possessed by students. Van Hiele suggests that there are five stages of thinking that students will go through in learning geometry: the visualization stage, the analysis stage, the informal deduction stage, the deduction stage, and the rigor stage. Each stage of thinking will be passed by students sequentially without passing any of the previous stages. This study aimed to identify and describe the geometric thinking stages of high school students. The first is based on van Hiele's theory. The research method used in this research is descriptive quantitative. This research was conducted at MTs (Madrasah Tsanawiyah) An-Nur, Cirebon City, with a population of 318 students and a sample of 72 students selected using a purposive sampling technique. The data collection technique used is in the form of a Van Hiele geometric thinking stage test with 25 multiple choice questions divided into five subtests. The results showed that 29.17% of students were in stage 1 (visualization), 25% of students were in stage 2 (analysis), and 6.94% of students were in stage 3 (informal deduction). There are still students who have not entered the van Hiele geometric thinking stage (at stage 0), namely 13.89%. As for the students who could not determine their van Hiele geometric thinking stage, as many as 25%. The highest stage achieved by students was stage 3 (informal deduction), so no student reached stage 4 (deduction) and stage 5 (rigor). In general, the geometric thinking stage of MTs (Madrasah Tsanawiyah) An-Nur students is at stage 1 of van Hiele's geometric thinking.

The purpose of this research is to describe, identify and analyze students' spatial intelligence in working on geometry problems according to Van Hiele's theory. The method used in this research is descriptive research with a qualitative approach. This research was conducted at SMP Negeri 2 Tarakan. The research instrument used was the Van Hiele geometric thinking level test and spatial ability test, interview guides and documentation. Prior to use, the test, an interview guide, was first validated. The data analysis technique will be used in 4 stages, namely collecting, reducing, presenting, and concluding all the data obtained. The results of this study are that students with high spatial intelligence (KST) are at the level of informal deductive thinking (level 3) where at this ability students are able to know the relationship between shapes. While students with moderate spatial intelligence (SCC) are at the level of analytical thinking (level 2), namely the ability to know and mention the properties of flat shapes. Students with low spatial intelligence (KSR) are at the level of visualization thinking (level 1). In conclusion, it is important for teachers to know students' abilities in learning geometry by paying attention to the level of geometric thinking, being able to use the Van Hiele Geometry learning model, increasing spatial intelligence and van Hiele levels can be done through training involving geometric media or software (geogebra).
 
 Keywords: spatial intelligence, geometry, level of thinking, Van Hiele

This study aimed to determine the effect of applying van Hiele's theory using a Think Pair Share (TPS) cooperative learning model on students' mathematical thinking levels. Following the research objectives, the researchers used experimental and quantitative research methods. In this study, two sampling techniques were used, namely using, purposive and random samples. Based on the sampling technique, class VIII F is the experimental class, and class VIII G is the control class, with 32 students each. Based on the results of the analysis, it was found that the level of students' mathematical thinking after the implementation of van Hiele's theory used the TPS type cooperative learning model with an average post-test score of 63.38, which was considered sufficient, and based on the results of hypothesis testing using t-test calculations, t-count = 3.825 > t-table = 2.04. This means that applying van Hiele's theory utilizing a Think Pair Share (TPS) cooperative learning model affects the level of students' mathematical thinking.

Abstract: Due to difficulties in learning geometry, the teacher plays an important and active role in creating students who have good problem solving skills. The teacher also has to test the level of geometrical thinking of students based on Van Hiele's theory to find out the students understanding about geometry material, so the teacher can overcome the difficulties of students in learning geometry. This research is designed to explore and describe the process of geometry problem solving based on Van Hiele's theory. Therefore this research used descriptive exploratory. It used qualitative approach. The subject of this research is limited to University of Muhammadiyah Sorong students which obtained the level of visualization, analysis, informal deductive and will be analyzed based on the gender. Data of this research is 1) Geometry Van Hiele Test; 2) Problem Solving Test; 3) Interview. The conclusion of this research is: 1) At the level of male visualization thinking is to identify problem and determine goal using language problem. While at the level of women visualization, it reached on determining goal, ; 2) the level of male analysis thinking is able to pass five steps in problem solving by using own language but are less systematic. While level of female analysis thinking is able to pass five steps in problem solving systematically; 3) level of male deductive formal thinking is to pass five steps problem solving systematically and using own language. While level of female deductive formal thinking is able to pass five steps problem solving systematically and explaining by using own language.