Hiele Theory Research Articles

Level Berpikir Geometri Peserta Didik Berdasarkan Teori Van Hiele pada Materi Bangun Ruang Sisi Datar

According to Van Hiele, in understanding geometry, students need to understand five stages, namely stage 1 (introduction stage), stage 2 (analysis stage), stage 3 (sequencing stage), stage 4 (deduction stage), and stage 5 (accuracy stage). Each student has different geometric thinking abilities. This study aims to examine the geometric abilities of junior high school students in the material of flat-sided geometry according to Van Hiele's Theory. This research belongs to the type of qualitative research with a case study design. It was conducted at three schools in Padang, West Sumatra, Indonesia. The subjects were students of SMP Negeri 1 Padang, SMP Negeri 7 Padang, and SMP Negeri 25 Padang. Data collection was carried out using tests, interviews, and documentation. Data analysis was carried out with the stages of data reduction, data presentation, and data verification or drawing conclusions. The data originality technique was carried out with the triangulation technique, where the researcher compared the test data with the results of interviews with students. Of the 94 students (male = 38, female 56) tested based on the geometric thinking level of Van Hiele Theory, 92.55% of the students reached the Van Hiele thinking stage at the visualization level. As many as 45.74% of students reached the level of geometric analysis, and 6.38% of students reached the level of abstraction. For the level of deduction and accuracy, no one has been able to solve the problem. The results obtained in this study are that most students are still at stages 1 and 2, unlike van Hiele's opinion, which revealed that the level of geometric thinking for junior high school students is at level 3. According to the study results, it is essential to carry out further checks on the level of geometric thinking of junior high school students in other areas.

Development of Geometry Test Based on Van Hiele's Theory in Exploration Profile of Student's Spatial Reasoning Ability Level

Assessment of geometry learning should encourage students to have spatial reasoning abilities. This type of study is research and development to develop a geometry test instrument with Van Hiele's level of thinking to measure students' spatial reasoning abilities. This research and development aim to obtain a valid and reliable test instrument for spatial reasoning abilities. This test has been declared content validity through expert judgment techniques and has been declared linguistically correct by linguists. Based on the results of the field test, the test instrument has a reliability of 0.89. The developed test instrument has a pretty good average distinguishing power estimate. The results of the difficulty level of the developed test are 12.5% items have a very easy, 25% easy, 37.5% moderate, and 25% difficult. The results of the measurement of students' spatial reasoning ability obtained that 25% of students had low spatial reasoning abilities (Plane), 60.71% in the medium category (Fuzzy), and 14.29% in the high category (Spatial)

Identifikasi Tingkat Berpikir Geometri Siswa Berdasarkan Teori Van Hiele

The purpose of this study was to describe and identify students' level of thinking in doing questions based on Van Hiele's theory and to give an idea to teachers to be able to use learning methods in accordance with Van Hiele's level of thinking at IBNU Abbas Tarakan IT Junior High School. The method used in this research is a combination method (qualitative & qualitative) with sequential model. The research instruments used were tests on Van Hiele's geometry levels, and interview guidelines. Based on the results of the study obtained 3 students were in pre visualization or have not reached Van Hiele's thinking level, 6 students are at level 1 (visualization), 9 students are at level 2 (analysis), and 3 students are at level 3 (informal deduction). Based on interviews students still have difficulty in understanding the relationship between wakes as well as elements in geometry such as theorem, axiom, and definition. In conclusion, Van Hiele's geometry thinking level at Ibnu Abbas IT Junior High School is generally at level 2, namely the analysis stage and has not reached level 4 (informal deduction). 
 Keywords: Geometry, Level of thinking, Van Hiele Theory

PENGEMBANGAN INSTRUMEN EKSPLORASI KONSEP GEOMETRI BERSTRUKTUR DARI TEORI VAN HIELE BERBANTUAN SOFTWARE GEOGEBRA

The purpose of this study was to analyze the requirements of instrument, the characteristics of the developed questions prototype, the feasibility of the questions, and the thinking level of students regarding Van Hiele's Theory of geometry concept taught with assistance of Geogebra Software. This study was a Research and Development using Wina Sanjaya's model. The instrument' development procedure consists of four stages, namely: Preliminary Stage, Product Development Stage; Stage of Trial and Product Validation and Dissimination Stage of products. The instrument feasibility is based on the accuracy and practicality test. The subjects of this study were all students of class XI Santu Petrus Pontianak 2016/2017 Academic Year, with a sample of class XI-MIA3 students chosen randomly. The results showed the level of instrument feastibility which expressed through experts' testing and student' opinions, calculation of validity, reliability, distinguishing factors, levels of difficulty, and practicality test results. The instrument obtained an average validity of 0.68 belongs to high category, a reliability of 0.998 belongs to very high category, and a difficulty level of 0.35 belongs to moderate category. The percentage of content validity, construction and language content rated by the experts amounted to 91.16%, which categorized as high. The student response rate was 80.9% which belong to good category.Keywords: Instruments, Van Hiele's theory, Geogebra Software

KEMAMPUAN SPASIAL PERCEPTION DALAM MENYELESAIKAN MASALAH GEOMETRI BERDASARKAN TEORI VAN HIELE DITINJAU DARI KEMAMPUAN MATEMATIKA

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.

Pencapaian Kemampuan Berpikir Geometri Tingkat Rendah Siswa: Analisis Berdasarkan Tipe Pembelajaran Kooperatif

Two important elements in the learning process at school are how students' understanding and learning activities are. On the other hand, most students only memorize algorithmic formulas without understanding the concept in depth. As a result, students' thinking abilities at low levels become dominant in learning operations. This study was conducted with the aim of analyzing the achievement of students' low-level geometry thinking skills between the learning group of think pair share (TPS) and the two stay to stray (TSTS). This quantitative study was conducted on students in one of the junior high schools in the East Jakarta area. Data were obtained using instruments developed based on three initial levels of geometrical thinking according to van Hiele's theory. Data were analyzed with parametric statistics. The results of the data analysis concluded that there were differences in the achievement of the ability to think of low-level geometry students in the TPS and TSTS learning groups. Based on descriptive statistics, the average achievement of TPS group students is more than TSTS. According to the results of this study, learning the geometry of the triangle concept for junior high school students is suggested by learning TPS. There are indications based on the distribution of data that the level of thinking of students in geometry is mostly at the level of analysis.

ANALISIS PEMECAHAN MASALAH GEOMETRI BERDASARKAN TINGKAT BERPIKIR TEORI VAN HIELE DAN GENDER

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.

Pengembangan Perangkat Pembelajaran Kesebangunan Bangun Datar Berbasis Teori Van Hiele Untuk Meningkatkan Kemampuan Berpikir Tingkat Tinggi Siswa

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.

Analysis Of Students 'Ability To Complete The Problem Of Geometry And Building Side Rooms Based On Van Hiele Geometry Thoughts On Class IX Students Of SMP PGRI Poncokusumo Malang

The purpose of this study was to describe the ability of students' level of thinking insolving geometry problems with curved side spaces based on Van Hiele's level ofgeometry thinking in class IX students of SMP PGRI Poncokusumo Malang.This research method is descriptive qualitative research. In this case the analysis of the description of the level of thinking of students in solving geometry problems arising from the curved side space based on Van Hiele's theory. The research subjects taken were grade IX students of Poncokusumo Middle School, totaling 11 students. The instruments used were test, interview and documentation instruments.The results of the geometry problem analysis test show that the curvature shows that students have improved from previous studies where at level 0 and 1 all students have been able to achieve it, for level 2 there are 2 students who have not been able and level 3 there are 3 people who did not reach this level while for level 4 there are 5 students who are unable to achieve it. Researchers hope that the teacher who will teach the material to build curved side spaces to pay attention to methods that are suitable for students so that the student learning process does not experience complexity and pay attention to the process of working on problems and drawing conclusions. To increase the level of thinking students on geometry material, build curved side spaces can use teaching aids so that students easily understand.

The Influence of Cooperative Learning Based on The Van Hiele Theory Toward Problem Solving Ability on Geometry of Mathematics Education Students

One of the mathematical problems whose solution requires the problem solving ability is geometry. Van Hiele's Theory is a learning solution that can be applied to practice the problem solving ability of geometry. Van Hiele states that the 5 levels of geometry thinking are the stages of introduction, analysis, sequencing, deduction and accuracy. The purpose of this study was to determine whether or not the influence of Van Hiele's theory-based cooperative learning on the geometrical problem solving abilities of students of Mathematics Education at Pasir Pengaraian University on space geometry. This study uses a quasi-experimental method with the design of Two Group Posttest Only. The population in this study were students of mathematics education at the Pasir Pengaraian University. The technique used for sampling is saturated samples, namely fifth semester students taking three-dimentional geometry. The instrument used was a test of problem solving ability. Data analysis using t-test. The results showed that the acquisition value of sig 0.001 <0.05. Thus it can be concluded that there is an influence of Van Hiele's theory-based cooperative learning on the ability of problem solving geometry of students of Mathematics Education at Pasir Pengaraian University on space geometry.

Analysis of the Difficulty of Mathematical Education Students in Completing the Geometric Running Problem Based on Van Hiele Theory in Geometry Transformation

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.

Analisis Proses Abstraksi Matematika dalam Memahami Konsep dan Prinsip Geometri Ditinjau dari Teori Van Hiele

This study aims (1) to analyze the process of abstraction of class XI IPA 2 of Lubuklinggau State 6 High School in understanding the concept of geometry overviewed from Van Hiele theory; (2) to analyze the process of abstraction of students of class XI IPA 2 in Lubuklinggau State Senior High School 6 in understanding the principles of geometry overviewed from Van Hiele theory. The method used in the study was a qualitative method. The results of data analysis obtained from five thinking stages based on Van Hiele's theory that theoretical of grade XI science 2 students of State Senior High School 6 Lubuklinggau only at stage 0 to stage 2, meanwhile at stage 3 and stage 4 the level of thinking of students of class XI 2 Science 2 State Senior High School 6 Lubuklinggau was still having difficulties in drawing conclusions from general matters towards specific matters and at this stage it is also a stage of thinking that is high, complicated and complex. Therefore, it can be concluded that the level of thinking of XI IPA 2 students at State Senior High School 6 Lubuklinggau is still low.&#x0D; Keywords: abstraction process, geometry concept, Van Hiele theory

Preschool Students' Understanding of a Geometric Shape, the Square

Abstract The purpose of this study was to explore preschool children's conceptual understanding of geometric shapes, the square in particular. There were a total of 115 children, 61 girls and 54 boys, from state preschool education programs, who participated in the study. The data were collected in two semesters through interviews in a one-on-one setting, where the researchers administered a paper-pencil test to the participants. The test included six questions. One question asked children to draw a square, one question asked to select the square among three other geometric shapes, three questions asked to differentiate the square among five to seven geometric shapes which were printed in rotated directions and in various fonts and sizes and one question asked to identify a picture of a square-like real life object among a selection of pictures. The findings showed that 65% of children were able to draw a square accurately, and 77% of children were able to identify a picture of a square-like object. Approximately 69% were able to differentiate three squares in different sizes among five geometric shapes, while 27% of the remaining were not able to identify the square in smaller sizes. Approximately 79% in one task and 56% in another task were unsuccessful in identifying squares in rotated directions. Moreover, there was no gender difference in the test between boys and girls. Findings were interpreted linking to Duval's theory, van Hiele's theory, Prototype theory and Simon's task design model.

The Attitudes of Students to the Geometry and Their Concepts about Square

One of the reason that influences the studentś achievements at school is connected with their inner motivation. The attitudes of a students to the individual school subjects can be built or changed through the influence of the interaction with their own experiences. There are a lot of different factors, external or internal, but one of the main is the impact of a teachers at school. Geometry and geometrical thinking is strong connected with the educational process and according to Van Hiele (1999) is not age-dependent in the way of Piaget described development. In our investigation we focused to the students conceptions about a square in accordance with their ability to solve the tasks that are assigned to the different levels of geometrical thinking. We investigated also connectionsbetween their results in the pre-test and the post-test to their attitudes to the geometry. We used the attitude questionnaire and the typical geometrical tasks for the detection of the level of geometrical thinking according to van Hiele's theory. Our sample consists of pre-service teachers of pre-primary and primary education. For evaluating the results, the implicative analysis with statistical software C.H.I.C.(Classification Hiérarchique Implicative etCohésitiv) has been used.

The Development of Spatial Skills through Discovering in the Geometrical Education at Primary School

There is a strong connection between 3-D and 2-D visualization of the geometrical shapes and solids. For better understanding of 3-D solids properties, it is important to have enough opportunities for manipulation with their 2-D representations, such are solid nets. According to the van Hiele's theory, the development of geometrical thinking depends on the educational process, especially at school. We focused on the discovery activities with the 3rd and 7nd grade pupils at primary school. We chose the cube and its nets as the most familiar 3-D solid in this age. We preferred IBL pedagogies and manipulation with the Polydron as the geometric construction product. We present some analysis of pupilś work and their results when they were finding, sorting and repairing the cube nets. Through presented activities, spatial skills and geometrical conceptions of pupils are developed.

From geometrical figures to definitional Rigour: Teachers’ analysis of teaching units mediated through van Hiele's theory

Abstract: The present study reports on curriculum design implemented in eight parallel classes of high school, with students aged 14–15, by means of work‐sheets dealing with properties of the principal plane geometric figures. Van Hiele's theory was used to facilitate teachers’ discussion of student performances on work‐sheets in order to enhance their didactical awareness. We hypothesize that van Hiele's theory is a proper means to provide encouragement and support for teachers in rethinking their teaching goals and practices. This environment enables teachers to manage their students’ transition from the perception of a figure to its definition. In this paper, we will recount a teachers’ discussion as it unfolded in a school‐university work group. The analysis of students’ work on work‐sheets interweaves with an analysis of the teaching actions that foster the process of understanding definitions.

Developing geometry thinking through multimedia learning activities

In this study, a multimedia learning software program named GeoCAL is described. It is based on van Hiele's geometric thinking level theory, which consists of four levels: recognition, visual association, description/analysis, and abstraction/relation. In addition to presenting the software design, this study also explores the learning effects of GeoCAL on each of the geometric thinking levels and on overall geometric thinking. The subjects of this study are second-grade elementary school students of an average age of eight who have not previously had formal lessons in geometry. The experimental results indicate that, with the exception of recognition ability, GeoCAL produces significant learning effects on visual association, description/analysis and abstraction/relation as well as overall geometric thinking.

Connecting arguments to actions— Dynamic geometry as means for the attainment of higher van Hiele levels

New technology requires as well as supports the necessity to raise the level of geometric thinking. Freudenthals view of van Hiele's theory corroborates a dynamic multi-level curriculum that offers material support for higher levels. For levels higher than 2, the dynamic locus capability of Dynamic Geometry software is crucial, e.g. in the study of loci of orthocentres and incentres. Discrepancies between their algebraic and geometric descriptions can motivate a deeper involvement with basic curve theory on the side of the teacher, who thereby can predict in which cases the students may succeed in restructuring the construction to overcome the discordance.

Techniques for stimulating reflection in teacher education seminars

The article describes four techniques which can be used in teacher education seminars in order to stimulate student teachers to reflect on their teaching practice and to promote cognitive change. The techniques are based on Schön's notion of reframing and Van Hiele's theory on levels in thinking. The effects of the techniques were investigated in a group of 18 student teachers at a Dutch university. Some favourable effects were demonstrated, although cognitions of prospective teachers about educational goals seem to be rather resistant to change.

Van Hiele Levels of Geometric Thought Revisited

The purpose of this article is to reexamine the van Hiele theory of levels of geometric thinking and to compare this theory with the geometry curriculum recommended by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). Examples of activities for students are included to illustrate the ways in which van Hiele's theory can be translated into classroom practice.