Van Hiele Research Articles

Analysis of students’ anxiety based on Van Hiele’s levels in solving geometry problems

[English]: Mathematics anxiety emerges due to discomfort when dealing with mathematical problems, including problems in geometry. This qualitative research aims to analyze how students' anxiety in solving the problems referring to Van Hiele’s levels. The participants were sixty grade 7 students. Data was collected through a test, questionnaire, observations, and semi-structured interviews. It was then analyzed following the stages of condensation, presentation, and drawing and verifying conclusions. The research found that students at the visualization level have moderate anxiety and panic levels, students at the analysis level have moderate anxiety, and students with informal deduction levels have low anxiety. The high level of students' geometric thinking does not necessarily result in lower anxiety or vice versa. Math anxiety is able to encourage students, but at a certain level, it could be detrimental to students. [Bahasa]: Kecemasan matematika timbul salah satunya karena rasa tidak nyaman ketika berhadapan dengan masalah matematika termasuk dalam menyelesaikan masalah geometri. Penelitian kualitatif ini bertujuan untuk menganalisis kecemasan siswa dalam menyelesaikan soal geometri ditinjau dari level Van Hiele. Enam puluh siswa SMP kelas 7 dilibatkan dalam penelitian. Data penelitian dikumpulkan melalui tes, angket, observasi, dan wawancara semi terstruktur. Analisis data dilakukan melalui tiga tahap yaitu kondensasi data, penyajian data, serta penarikan dan verifikasi kesimpulan. Hasil penelitian menunjukkan bahwa siswa yang berada di level visualisasi memiliki tingkat kecemasan sedang dan panik, siswa pada level analisis memiliki kecemasan sedang, dan siswa pada level deduksi informal memiliki kecemasan rendah. Tingginya tingkat berpikir geometris siswa belum tentu mengakibatkan kecemasan yang rendah atau sebaliknya. Kecemasan matematika dapat mendukung siswa, akan tetapi pada tingkat kecemasan tertentu, dapat merugikan siswa.

STUDENTS' GEOMETRY THINKING ON CIRCLE MATERIAL BASED ON VAN HIELE'S THEORY

The purpose of this study was to describe students' geometric thinking skills on circle material based on Van Hiele's theory (Visualization, Analysis, Informal Deduction, Deduction, Rigor). The subjects of this study were 3 students of class IX-A SMP Hang Tuah 4 Surabaya based on their initial mathematical abilities (high, medium, and low). The initial mathematical ability data was obtained from data on report cards for the even semester of the 2021-2022 academic year and based on the considerations of the mathematics teacher for class IX-A. This type of research is descriptive qualitative research. Collecting data in this study used tests and interviews. The test instrument used in this study was a circular geometry test in the form of mathematical questions with circle material arranged based on the Van Hiele indicator without stage 4 (Rigor) with the consideration that the research was conducted in class IX SMP so students have not been able to understand the material at stage 4 (rigor). Student with high initial mathematical abilities, geometric thinking abilities is already at stage 2 (informal deduction). Student with medium mathematical abilities, geometric thinking skills is at stage 2 (informal deduction). Student with low mathematical abilities, geometric thinking skills is at stage 0 (visualization).

Passing the exam and not mastering the material in geometry

It is a common assumption that taking a mathematics course and passing the exam means that one has mastered the course requirements and gained a sufficiently deep understanding of the course material. According to the communication part of the Van Hiele Theory, if someone does not reach the expected entry-level, they won’t be able to develop during the course. In our research, we investigated this contradiction in the field of geometry. We examined this phenomenon with mathematics major and pre-service mathematics teacher students during their first geometry course.

A theoretical analysis of the validity of the Van Hiele levels of reasoning in graph theory

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of reasoning whose descriptors need to be validated according to the structure of this model. In this paper, the validity of these descriptors has been approached with a theoretical analysis that is organized by means of the so-called processes of reasoning, which are different mathematics abilities that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. The analysis gives support to the internal validity of the levels of reasoning in graph theory as the properties of the Van Hiele levels have been verified: fixed sequence, adjacency, distinction, and separation. Moreover, the external validity of the levels has been supported by providing evidence of their coherence with the levels of geometrical reasoning from which they originally emerge. The results thus point to the suitability of applying the Van Hiele model in the teaching and learning of graph theory.

Geometric Thinking Profile in Problem Solving Based on SOLO Plus Taxonomy

The purpose of this study is to describe geometric thinking based on the SOLO Plus taxonomy. This research used qualitative method which involved 34 students of the mathematics education study program. Data collection is done by tests and interviews. Data analysis is done by triangulation which, includes data reduction, data presentation, and conclusion drawing. The results showed that subjects with high and moderate mathematical abilities were included in the Van Hiele category of geometric thinking analytically by connecting components and geometric properties that were interconnected. This analytical ability is categorized as multistructural by identifying information that is considered useful and has a relationship with the problem solving process. In ordering-multistructural geometric thinking, it is done by sorting and connecting properties accompanied by informal arguments. Deduction-semirelational geometric thinking is done by analyzing and explaining the relationships between shapes and being able to prove theorems deductively, giving reasons with formal proof but not reaching the truth. Meanwhile, subjects with a low ability to think are said to think analytically geometrically by connecting components and geometric properties and in problem solving have multistructural responses. In ordering thinking, it is done by sorting and connecting the properties found previously and providing informal arguments. In the problem solving process included in the pre-structural category, they do not understand the problem and the information provided and do something that has nothing to do with the problem that is given.

Math Learning in a Science Museum—Proposal for a Workshop Design Based on STEAM Strategy to Learn Mathematics. The Case of the Cryptography Workshop

In mathematics teaching, great efforts are made, and diverse teaching strategies are employed in order to facilitate students’ learning process. Informal environments have proven to be conducive and motivating spaces for science learning. In particular, science museums can be used as a complement and collaborate in order to leverage each of their strengths to motivate mathematics learning. Educational models give a global explanation to the learning process. Taking into account all these aspects and considering van Hiele’s model as didactic reference, we propose the design of a general workshop that has among its objectives the learning of mathematics. To do this, we start from the three main elements and processes set forth in van Hiele’s model: insight, reasoning levels and learning phases. The insight or student’s competence are formulated through Hoffer’s abilities, and for the development of the activities of the learning phases, the STEAM (science, technology, engineering, art and maths) strategy. Once the general proposal has been made, we use it to design a scientific workshop for learning mathematics about cryptography. Our greatest challenge was in generating activities adapted to the established requirements. It would be interesting, for future works, to design research to evaluate the effectiveness of the proposal presented. Moreover, it would be interesting to develop a proposal for assessing student learning.

Effects of Dynamic Geometry Software on Students’ Geometric Thinking Regarding Probability of Giftedness in Mathematics

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an opportunity to provide differentiated activities. Therefore, the aim of this study is to explore effects of mathematics lessons integrated with dynamic geometry activities on students' van Hiele geometric thinking levels controlling their probability for mathematical giftedness. Participants of the study were fifty-three fifth graders from a private school in Marmaris, Turkey. These students were grouped in terms of their probability of mathematical giftedness. Seven dynamic geometry activities about properties of line segments, triangles and quadrilaterals were developed and implemented in classrooms with tablets. Van Hiele geometric thinking level test was administered to the participants as pre-test and post-test. Results showed that dynamic geometry activities help students to move from geometric thinking level about recognizing shapes with visual clues to higher level about geometrical properties of shapes, namely relationship among shapes and their properties. Moreover, interaction between their probability for mathematical giftedness and improvements in geometric thinking levels were found. This study may contribute both to the gifted education and mathematics education fields by exploring the improvements in geometric thinking level and differentiated opportunities for gifted students. As a suggestion, a more comprehensive experimental study with larger samples so as to obtain generalize the findings could be conducted as a further study.

Analysis of Student's Geometry Thinking Ability Based on Van Hiele's Theory

<p>The purpose of this study was to analyze students' geometric thinking skills in solving geometric problems based on Van Hiele's thinking stages. This research is a qualitative research. The subjects of this study were students of class XII MIPA 2 SMA Negeri Tomo, totaling 29 students. With purposive sampling obtained 6 research subjects representing the stages of thinking Van Hiele, data collection methods with test questions and interviews. Analysis of research data is data collection, data reduction, data presentation, and drawing conclusions. The results of the study are: no student can reach the rigor stage</p>

The use of Multimedia of geometry Based on Van Hiele Thinking Theory: An Alternative to Improve Critical Thinking Skill of Elementary School Students

This research was aimed to explore the learning process and the perception of student toward multimedia of geometric based on Van Hiele’s thinking theory and to inspect the effectiveness of multimedia of geometry based on Van Hiele’s thinking theory used in the process of mathematics learning. This research was implemented in SDN Mojoroto 6 Kediri City, Indonesia in 2021/2022 academic year. The samples were 33 at the age of 11-12 years old. This study was designed with mixed research. The data were collected through the instruments of observation, interview, and critical thinking sheets. The results of this research have indicated that the implementation of multimedia of geometry based on Van Hiele’s thinking theory was running properly. Multimedia of geometry based on Van Hiele’s thinking theory can be received in the mathematics learning process. The students became more motivated in learning, the learning process was more interesting and meaningful, while the results of the critical thinking skill of students have indicated significant improvement after the implementation of multimedia of geometry based on Van Hiele’s thinking theory compared to the prior condition.

Proof levels of graph theory students under the lens of the Van Hiele model

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with graphs. We have thus analysed them adapting the methodology for computing the degrees of acquisition of the Van Hiele levels. Our analysis leads to different proof profiles of Graph Theory students whose characteristics provide empirical support to consider proof levels in Graph Theory from the perspective of the Van Hiele model.

Examination of the Relation between Science High School Students’Geometry Success and Van Hiele Geometric Thinking Levels

The aim of this study is to detect the relation between Science High School students' success in geometry lesson and Van Hiele geometric thinking levels according to the datum results of geometry success test (GST) and Van Hiele geometric thinking level test (VHGTLT). The survey model, which is one of the quantitative research methods, was used in the study. The study group consists of 244 students selected by purposive sampling method, studying at three Science High Schools in Diyarbakır city center in the first term of the 2020-2021 academic year. The datum in the research were obtained by using the 25 questions of the VHGTLT suitable for the grade level of the students and the GST consisting of 25 questions prepared by the researchers. The datum were calculated by calculating descriptive statistics and the relation between the point of the students in the VHGTLT and the GST was analyzed with Pearson correlation the SPSS package program. Moreover, one-factor analysis of variance technique was applied to detect whether there was a meaningful difference between Science High Schools according to both tests. The results of the study are as follows: It was observed that the most of the students (63.6%) who participated in the study were at or above Level 3 (Informal Inference) Van Hiele geometric thinking level. A middle correlation was found between the students' point obtained from both test results. In addition, as a result of the point obtained from both tests, a meaningful difference was found between the Science High School, which received the highest point in the province according to the high school entrance exam point, and the other two Science High Schools.

Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians

ABSTRACT Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and early years teachers collaborated on a child-led exploration of ‘patterns in nature.’ The early years teachers ran the project within the setting, meeting regularly with the mathematicians to discuss potential areas of interest, and to highlight the children’s mathematical thinking. We found that, with the appropriate environment and guidance, the children naturally displayed deep levels of geometrical thinking and found enjoyment and satisfaction in the exploration of mathematical ideas. We define what we mean by the term ‘deep geometrical thinking’ and demonstrate this by looking at three excerpts through the lens of the van Hiele levels of geometric thought, finding that the children are capable of exhibiting thought at level 3 (abstraction), more advanced than previously thought of children of this age. Using a second taxonomy we also assess the range of skills across which they are demonstrating such geometric thought.

Worked-examples instruction versus Van Hiele teaching phases: A demonstration of students’ procedural and conceptual understanding

This study explores the worked-example instruction (WEI) and the van Hiele teaching phases (VHTP) pedagogies to advance students’ acquisition of procedural and conceptual understanding of solving simultaneous equations. The quasi-experimental study involved two groups of high school students (age=15): 157 students in total with 72 in one group and 85 in the other. The study followed a pre-, post- and delay tests design. This study adapted two conceptual frameworks, the structure of the observed learning outcomes (SOLO) model and the Rasch model, and employed Rasch analysis and Statistical Package for Social Sciences (SPSS) as data analysis tools. The results indicated that both WEI and VHTP improved students’ procedural and conceptual understanding of solving simultaneous equations at the post-test; however, the WEI effects (on both procedural and conceptual understanding) were not sustained after the post-test while the VHTP had a lasting effect on only conceptual understanding. Furthermore, the VHTP group significantly outperformed the WEI group at the post-test and delay test in both conceptual and procedural understanding. These results indicated that the WEI is only beneficial at the initial stage of knowledge acquisition and VHTP is better at the initial and long-term. Practical implications of these results were discussed.

The Van Hiele Model in Teaching Geometry

The primary purpose of this study was to determine the effectiveness of the Van Hiele model in teaching Geometry to Grade 8 students as the basis for designing instructional materials using the Van Hiele model. This study used the quasi-experimental group design to assess whether there was a significant difference between the pretest performance to the posttest performance of the control and experimental groups. The results revealed that both groups had established a significant mean gain difference from Pretest to Posttest, although the experimental group, taught using the Van Hiele model, performed better than the control group. The teacher and the students encountered many challenges in each phase, but undeniably, the students enjoyed the activities. The majority of the students found that it is interesting to learn Geometry using the phases of the model. The instruction using the Van Hiele model is thus considered an effective way of teaching Geometry and an alternative teaching strategy to the traditional method. Therefore, this method is proper when teaching Geometry, especially to students with different learning needs, because of the presence of various geometric experiences.

Analysis of mathematics problem-solving ability on plane figure subject based on van hieles theory at Junior High School

This study aims to describe the ability to solve mathematical problems in Plane Figure Subject based on van Hiele's theory in class VIII students of SMP Negeri 1 Mataram in the academic year 2021/2022. The type of research used is descriptive qualitative, which produces data in the form of written or spoken words from people and observed behavior. The subjects in this study were students in class VIII-E at SMP Negeri 1 Mataram, totaling 36 students. The method of taking the subject in this study used purposive sampling, which was selected based on the objectives to be achieved. The data collection methods used are the van Hiele test and the flat wake problem-solving ability test, interviews, and documentation. The thinking level of students in taking the van Hiele test was: 20 students at level 0 (visualization) with a percentage of 55.56%, 13 students at level 1 (analysis) with a percentage of 36.11%, and 3 students at level 2 (informal deduction) with a percentage of 8.33%. Furthermore, students at each level of van Hiele's thinking were taken as representatives of each of the 2 subjects to carry out a problem-solving ability test. Based on the results of the research on the problem-solving abilities of students based on the Polya problem-solving stage, students who are at level 0 can understand the problem but have not been able to carry out the other Polya-solving stages. Students at level 1 can understand the problem and develop a settlement plan but have not been able to carry out the other stages of Polya solving. Students at the level can understand the problem, develop a settlement plan, and carry out a settlement plan but have not been able to re-examine. It shows that the higher the van Hiele thinking level of the students, the better their problem-solving abilities will be.

KEMAMPUAN SISWA DALAM PROSES PEMECAHAN MASALAH BANGUN DATAR SEGI EMPAT BERDASARKAN TAHAPAN VAN HIELE

This study aims to determine and describe problem solving abilities based on the stages of thinking about rectangular flat shapes. The technique utilized is expressive subjective. The subjects in this study were seventeen students selected at random with the highest scores being selected by three grade VII understudies of SMP Negeri 2 Pemangkat. The data collection technique used is a test that will be given to the selected subject based on problem solving based on Van Hiele's thinking. The results of describing the data show that there are three subjects who are in the Visualization stage, they know the name of the rectangular shape from the visual form without knowing the nature and conditions of the shape, for the analysis stage the three subjects have not reached, students cannot explain and determine the nature of the requested shape and for the stage of abstraction there are no students who reach this stage, judging by the results of their answers that students have not been able to define a rectangular shape in indonesian itself and have not been ready to decide similar properties between one shape and another.

PROBLEM SOLVING FOR FIFTH GRADE IN QUADRILATERAL LEARNING USING VAN HIELE THEORY AND CONTEXTUAL APPROACH

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.

Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education

This article is an advanced theoretical study as a result of a chapter from the first author’s PhD study. The aim of the article is to discuss the relationship between commognition and the Van Hiele theory for studying discourse during Euclidean geometry problem-solving. Commognition is a theoretical framework that can be used in mathematics education to explain mathematical thinking through one’s discourse during problem-solving. Commognition uses four elements that characterise mathematical discourse and the difference between ritualistic and explorative discourses to explain how one displays mastery of mathematical problem-solving. On the other hand, the Van Hiele theory characterises five levels of geometrical thinking during one’s geometry learning and development. These five levels are fixed and mastery of one level leads to the next, and there is no success in the next level without mastering the previous level. However, for the purpose of the Curriculum and Assessment Policy Statement (CAPS) we only focused on the first four Van Hiele levels. Findings from this theoretical review revealed that progress in the Van Hiele levels of geometrical thinking depends mainly on the discourse participation of the preservice teachers when solving geometry problems. In particular, an explorative discourse is required for the development in these four levels of geometrical thinking as compared to a ritualistic discourse participation.

Basic Mathematical Literacy Skills Ability by Van Hiele Project Based Learning Theory

Mathematical literacy is a person's ability to formulate, apply, and interpret mathematics. The fact that Mathematical Literacy Skills is the main challenge in learning basic mathematics and can also be used as a key to explore mathematics learning. This article aims to analyze basic mathematical skills related to Van Hiele's project-based learning theory. The following type of research is qualitative research. The subjects of this research are fourth grade students at SDN 2 Korowelanganyar Cepiring Kendal. The instruments used in the study were tests and interviews. The results of the following research show that SDN 2 Korowelanganyar improves students' geometric reasoning abilities and the characteristics of fourth grade geometric reasoning by learning basic mathematical knowledge related to Van Hiele's theory. This shows that learning basic mathematical knowledge by van Hiele's project-based learning theory can improve students' ability to solve geometry problems. Literasi matematik ialah kemampuan seseorang untuk merumuskan, menerapkan, serta menafsirkan matematika. Fakta bahwa literasi matematika adalah tantangan utama dalam pembelajaran matematika dasar serta juga bisa digunakan sebagai kunci untuk mengeksplorasi pembelajaran matematika. Artikel ini bertujuan untuk menganalisis keterampilan matematika dasar yang terkait dengan teori pembelajaran berbasis proyek Van Hiele. Jenis riset berikut ialah penelitian kualitatif. Subyek riset berikut ialah peserta didik kelas IV SDN 2 Korowelanganyar Cepiring Kendal. Instrumen yang digunakan dalam penelitian ialah tes serta wawancara. Hasil riset berikut menunjukkan bahwa SDN 2 Korowelanganyar meningkatkan kemampuan penalaran geometrik peserta didik serta karakteristik penalaran geometrik kelas IV dengan mempelajari pengetahuan matematika dasar yang berkaitan dengan teori Van Hiele. Ini menunjukkan bahwa dengan mempelajari pengetahuan matematika dasar oleh teori pembelajaran berbasis proyek van Hiele mampu meningkatkan kememampuan peserta didik dalam menyelesaikan soal geometri.

A Systematic Review on Geometric Thinking: A Review Research Between 2017-2021

<p style="text-align: justify;">Geometric thinking affects success in learning geometry. Geometry is studied from elementary school to university level. Therefore, in higher education and basic education, it is necessary to carry out a systematic review in order to obtain tips for improving geometric thinking skills. A systematic review of geometric thinking was done in this study. In this study from 2017 to 2021, geometric thinking was investigated in the form of a synthesis review of the effect size of the given treatment. This is a comprehensive discussion of theories, models, and frameworks on the topic of geometric thinking from 36 articles. The research findings revealed that the interventions used were predominantly effective, with effect sizes ranging from "small" to "very large," with the "very large" effect obtained in the intervention of van Hiele's learning phase and various technology-based-media and concrete manipulative media. The research trend was reflected through twelve clusters of interrelated keywords. The results of this literature review suggested that it is necessary to carry out a specific study on how to achieve the highest level of geometric thinking, a more detailed form of scaffolding, and concrete manipulative media and technology that can be explored for a certain level of the participants’ geometric thinking.</p>