Van Hiele Research Articles

Noticing Students’ Geometry Learning Using Van Hiele’s Geometry Thinking Model at the Senior High School level in Builsa South District of Upper East Region

Noticing Students’ Geometry Learning Using Van Hiele’s Geometry Thinking Model at the Senior High School level in Builsa South District of Upper East Region

Effectiveness of Paper Folding and GeoGebra on Students’ Geometric Thinking and Visualization

Finding teaching methods that foster students' development of geometric thinking and visualization skills is still a current challenge. This study analyses the effects of the combined use of paper folding and dynamic geometry on high school students’ geometric thinking and visualization skills. A quasi-experimental study pre-test/post-test design was conducted in distance learning in Italy. The instruments employed were van Hiele Geometry Test (VHGT) and the Visual Test (VT) before and after the treatment. The data were analysed using statistical tests according their nature. The results revealed that both groups have improved in the post-tests compared to their respective pre-tests. However, the students in the experimental group achieved better geometric thinking scores and performed better in three out of four sections of the visual test compared to the students in the control group. Thus, the proposed combination of instruments may be suggested in high school to make geometry teaching more effective, even with distance learning.

Analytical Study on the Impact of Teaching-Learning of ‘Transformation Geometry’ in Secondary Schools in General using Van Hiele’s Model

An analysis of the methods involved in the teaching-learning of the topics related to Transformation Geometry’ is one of the topics in mathematics in which learners have not been performing very well. The purpose of the study is aimed to identify the difficulties of the learners encounter when learning transformation geometry using Van Hiele’s model. Data was analysed through a process of coding, categorizing, clustering and performance indicators corresponding to the Van Hiele’s model were used in the analysis of data. The result of the study indicated that learners, experienced difficulties to solve problems involving enlargement transformation geometry problems. Learners struggle to grasp the fundamental concepts of enlargement, particularly with the concept of the centre and scale factor. The study findings revealed the challenges faced by the students in comprehending geometrical figures that were transformed to a larger dimension. The Learners inability to understand the steps of transformation geometry because they had insufficient background knowledge on the topic is taken to relevance in this paper writing. The study focuses on the limitations, challenges and remedies being intended for better learning prospects.

The influence of the ability to understand mathematics concepts based on van hiele's level of thinking on the learning outcomes of mathematics education students

The influence of the ability to understand mathematics concepts based on van hiele's level of thinking on the learning outcomes of mathematics education students

Contextualization of Augmented Reality Digital Module Instruction: Grounded Theory Study in Examining Van Hiele’s Level of Geometric Thinking

Van Hiele's thinking level has an important role in understanding, interpreting, and determining the geometric thinking ability. However, the lack of technological products that can support Van Hiele's improvement in thinking level is a challenge in itself. One of the tools that can help prospective teacher students to reach Van Hiele's level of thinking is Augmented Reality technology. Therefore, this study aims to investigate Van Hiele's level of thinking through the intervention of Augmented Reality Digital Module Instruction (ADMI) using grounded theory design. The participants involved in this study were one lecturer and ten prospective teacher students who experienced difficulties in improving the level of Van Hiele geometric thinking. The data collected through observation, tests, and interviews are analyzed qualitatively through the stages of open coding, axial coding, and selective coding. These research found that students who had difficulties in carrying out the first level of Van Hiele could use ADMI to overcome these difficulties; students can construct knowledge about 3D geometry; the success of students in completing the geometry test involves reasoning. This study emphasize that ADMI contributes to geometry learning because it can make it easier for students to reach the lowest level of Van Hiele.

The Effects of Augmented Reality Geometry Learning Applications on Spatial Visualization Ability for Primary School Pupils

Geometry is considered a fundamental component to be mastered in the elementary school mathematics curriculum. Lower primary school pupils frequently experience obstacles because of the abstract nature of geometric concepts and the requirement for spatial visualization skills, which are necessary for strengthening their conceptual understanding. Augmented reality (AR) technology offers a promising solution by providing visual representations of geometric shapes. Thus, this study aimed to investigate the effects of AR technology in primary school education on pupils’ spatial visualization abilities in geometry. Employing a quasiexperimental pre- and post-test research design, this study involved 61 second-grade pupils from two Northern Malaysian primary schools. The selection of schools followed cluster sampling techniques, while intact groups were utilized to select samples. Data were collected from two groups: an experimental group that utilized the LearnGeoAR applications and a control group that employed conventional teaching methods to learn geometric shapes. This study used the spatial visualization ability test (SVAT) instrument, grounded in Van Hiele’s theory of geometric thinking. The findings revealed that the experimental group, which utilized AR applications, exhibited a higher mean score in pupils’ spatial visualization ability in geometry compared to the control group. Additionally, the experiment demonstrated a moderate effect on both groups. This finding highlights the potential of AR technology in enhancing pupils’ spatial visualization skills in geometry instruction, providing valuable insights for instructional methodologies.

Including the Brügner Tangram in an Undergraduate Mathematics Education Course: Systematic Search for Solutions and Graphs

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the implementation of a sequence of activities designed to convey to future teachers the importance of systematically solving problems that involve searching for or constructing different cases. Specifically, participants are provided with the three pieces of the Brügner’s tangram and assigned the task of identifying all possible convex polygons that can be constructed. Moreover, they are required to elucidate the methodological approach underpinning their exploratory process, with an emphasis on establishing relationships between the polygons. Graphs are introduced as one of the possible approaches for modelling the problem, offering a graphical representation that aids in the systematic search for solutions. This paper describes different activities involving the Brügner’s tangram which has demonstrated its adaptability as an instructional resource. The teaching sequence adheres to the five-phase structure proposed within the framework of the van Hiele model, which is also part of the course.

Mapping Geometric Minds: Exploring 3D Thinking Skills of Elementary School Students Using the Van Hiele Model

Mapping Geometric Minds: Exploring 3D Thinking Skills of Elementary School Students Using the Van Hiele Model

Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

The use of Van Hiele’s geometric thinking model to interpret Grade 12 learners’ learning difficulties in Euclidean Geometry

The 21st-century mathematics classrooms should equip learners with well-grounded knowledge and thinking skills pertaining to geometry. However, Euclidean geometry remains one of the challenging, if not the most difficult topic for many learners. As a result, the purpose of this article is to interpret Grade 12 learners’ learning difficulties in Euclidean geometry. We use Van Hiele’s geometric thinking model and Hoffer’s skills to argue an interpretation of learning difficulties in Euclidean geometry as a focal point towards creating effective teaching and learning of this important topic. This explanatory sequential mixed-methods approach involved 60 Grade 12 learners who wrote a geometry test and completed a questionnaire based on Van Hiele’s geometric thinking levels. In addition, semistructured interviews were conducted with a sample of 12 learners and four educators to investigate their views about geometry learning difficulties. The findings of the study revealed that learners had poor conceptualisation of properties of shapes, visualisation skills, circle theorems and geometry terminology, resulting in them experiencing learning difficulties. The recommendations are that, during instruction learners should be given the opportunity to manipulate real geometric objects to enhance their visualisation and visual thinking skills. In addition, we recommend that educators should teach level-specific geometry vocabulary to enable learners to understand concepts at different Van Hiele’s levels. Furthermore, we recommend that educators should use constructivist teaching approaches that encourage learners’ conceptual understanding instead of traditional methods that promote rote memorisation of geometric facts. Educators should develop learners’ broad knowledge of geometry to overcome geometry-related errors and misconceptions.

An Investigation into the Challenges and Strategies of Secondary Students' Geometric Thought Processes through the Lens of Van Hiele's Theory

An Investigation into the Challenges and Strategies of Secondary Students' Geometric Thought Processes through the Lens of Van Hiele's Theory

Geometry ability in Senior High School Students: Based on Learning Style

Geometry becomes an important component in mathematics which is learned by students at every stage. Learning style is one of the factors that influence students' geometry abilities. Therefore, it is important to describe how students' geometry abilities are viewed from learning styles. This research is quantitative descriptive research. The instruments used were a learning style questionnaire and a van hiele thinking test (VHGT). The data analysis technique used is descriptive statistical techniques with percentages, namely data from geometry tests that are successfully collected and then analyzed using a category assessment scale. The instruments used were the learning style questionnaire and the Van Hiele thinking test (VHGT). The research subjects were 276 high school students from eleven different schools in West Sumatra with the dominant learning style being visual as many as 104 students, followed by auditory as many as 98 and kinesthetic as many as 74. The results showed that the average students' geometric ability was 47.4 (on a scale of 0-100). In addition, students with a visual learning style have a higher average geometric ability compared to other learning styles. Therefore, it is hoped that teachers can consider using learning models that apply the Van Hiele level of thinking and the dominant learning style in geometry classes, for example by integrating technology.

An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape

A major concern in South Africa is the poor performance of learners in mathematics, particularly in geometry. This paper therefore sought to explore the learners’ understanding of Euclidean geometric concepts. The Van Hiele model was a useful framework for understanding the reasoning and challenges that students encounter with geometry. This study focused on 15 participants from rural South African schools, including 5 grade 10 mathematics learners in each of the three secondary schools and three teachers who are teaching mathematics in grade 10, in three secondary schools. Through face-to-face interviews, learners’ comprehension of geometry was qualitatively assessed. Pedagogical and methodological difficulties, lack of learners’ interest and comprehension of numerous geometrical concepts, as well as the absence of technology use, were found to contribute to the challenges in learning and teaching Euclidean geometry. The recommendations suggest that teachers should plan and prepare their geometry classes with the students’ understanding in mind that Euclidean geometry has been a cornerstone of mathematical education for centuries, teaching students critical thinking, problem-solving, and logical reasoning skills. This study adds to the existing literature on introducing new concepts in mathematics into the educational system of South Africa. Keywords: Geometry, Students’ Interest, Self-efficacy, Understanding, Three-Dimensional Shape

Studi Pustaka Kemampuan Menganalisis pada Pembelajaran Geometri dengan Menerapkan Teori Van Hiele terhadap Peserta Didik Kelas V SD

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.

Analysis of Students' Geometrical Thinking from Geometry Task Related to HOTS from PISA

This study intends to analyze geometry tasks related to Higher Order Thinking Skills (HOTS) through geometrical thinking level by Van Hiele which consists of visualization, analysis, abstraction, deduction, and rigor. This study only focuses on visualization, analysis, and abstraction levels. The stages in this study are divided into three steps. Chronologically, the first stage begins with the process of compiling PISA tasks related to geometry and HOTS, especially for examining the students’ spatial abilities. From all the tasks obtained, three tasks match the criteria that were most relevant to Van Hiele’s geometrical thinking level. The second stage was continued by testing the instrument test to 23 students from one of the schools in Tangerang Regency as respondents. In the last stage, analyze the students’ answers based on the steps of their work and compare them with the theory of geometrical thinking from Van Hiele. The results of this study indicate that there are differences between the steps of the students’ answers and theoretical answer steps that are expected in this study. The conclusion that can be drawn is that the students’ learning experiences in understanding geometrical concepts are not theoretically compatible with the principles of spatial ability, especially in completing geometry tasks related to HOTS. Keywords: Students’ Geometrical Thinking, Geometry Task, PISA

Can Induced Awe Reduce Anti-Gay Prejudice in Heterosexual Adults and Does the Need for Closure Moderate this Effect?

With sexual prejudice continuing to be widely prevalent and seriously harmful, there is a need to find ways to reduce anti-gay prejudice (AGP). This online experimental study examined if a novel intervention, induced awe, can reduce AGP; if those high in need for closure (NFC) show higher AGP; and if NFC moderates the effect of awe on AGP. In total, 154 heterosexual adults completed the Need for Closure Scale (Roets & Van Hiel, 2011) before being randomly assigned to one of three emotion inducement interventions – 1) watching a 4.43 min long video of the target emotion, awe, 2) watching the comparison emotion, amusement, or 3) watching a neutral emotion as a control. Post intervention, the participants completed the explicit measures Homosexuality Attitudes Scale (HAS; Kite & Deaux, 1986). Data were analysed using a 2 (NFC) x 3 (emotion type) independent factorial ANOVA. None of the three hypotheses were supported since there were no main effects of awe or NFC on AGP, and no interaction effect of awe and NFC on AGP. Key implications of these results were 1) awe inducement does not change prejudicial attitudes at an explicit level (Dale et al., 2020), 2) factors beyond NFC, like Right Wing Authoritarianism (RWA) and Social Dominance Orientation (SDO), may influence the effectiveness of awe in reducing prejudice, and 3) questions were raised about certain boundaries for awe’s effectiveness. Methodological modifications suggested for future research include using implicit measures or veiled elicitation methods for authentic measurement of AGP, employing more potent awe elicitors, and assessing the mediating role of RWA and SDO on the effect of NFC on AGP.

Using GeoGebra with Van Hiele’s Model in Geometry Classroom: An Experience with Prospective Teacher

Various advances in technology, communication, and information have provided great benefits to all users around the world, especially in digital communication and learning mathematics in the classroom. However, without a systematic and clear model, the use of technology becomes vague and ineffective in cultivating students' interest and understanding in the field of Science, Technology, Engineering, and Mathematics (STEM). This study aimed to explore prospective teachers’ (PT) understanding and experience using GeoGebra with van Hiele’s model in the geometry classroom. The research employed a qualitative approach, specifically a case study design, which included semi-structured one-on-one interviews and classroom observations. Additionally, dynamic GeoGebra task completion, digital objects, tests, and electronic surveys were also administered. The bottom-up data analysis process was conducted inductively by reading the collected data and forming segments, determining the codes, and filtering overlapping codes until themes were identified. The results showed PTs' sequential understanding using GeoGebra occurred enthusiastically in a supportive environment. This understanding was evidenced when students engaged in activities such as examining, analysing, doing, comparing, identifying, explaining, recognising, distinguishing, and solving tasks. Furthermore, the experience of PTs using GeoGebra involved a collaborative environment, motivation to learn, awareness of various technologies, and independent learning. In conclusion, the transformation of PT’s comprehension using GeoGebra in Mathematics is actively demanded with the use of a guidance process such as van Hiele’s model. It provides greater chances for students’ engagement while delivering more appropriate and meaningful learning.

The effect of using teaching plans according to the Van Hiele method in learning the dribbling skill in basketball for students

The study aimed to prepare teaching plans according to the Van Hiele method in learning the basketball dribbling skill, and to identify its effectiveness for intermediate school students. The researchers assumed that there is an effectiveness for the Van Hiele method in performing the basketball dribbling skill for second intermediate school students, and there are statistical differences in favor of the experimental group. The researchers used an experimental approach in the style of two equal groups. The researchers defined their research population as students from Al-Intisar Intermediate School for the academic year (2023-2024), who numbered (564) students. The study sample was deliberately determined to be represented by second-year students, whose number was (90) students, and their percentage was (15.95%). from the research community, and the research sample (45) students, representing (50%) of the total second-year students, was selected in an intentional manner. They were divided into two experimental and control groups, represented by (20) students each, and (5) students were selected for the exploratory experiment. The researchers prepared teaching plans for eight weeks on Monday, 16/10/2023, and the last lesson was on December 4, 2023. As for the control group, the teacher used his usual method, after which a pre-test was conducted for the sample, then the teaching plans were implemented on Sample on Monday 16/10/2023, and the last lesson was on 25/12/2023. As for the control group, the teacher used his usual research method. After that, the two researchers analyzed the results statistically, and by analyzing the data for the test results, it was found that the values of the means The arithmetic mean, the standard deviations, the calculated (t) value, and the error rate for the post-test for the experimental and control groups for the low dribbling skill in basketball, where the arithmetic mean value for the low dribbling skill in the post-test for the experimental group reached (20,594) with a standard deviation of (1,889), while for the control group the arithmetic mean reached (22,447). with a standard deviation of (1.834) and the calculated (t), value was (3.672), while the standard error percentage was (0.01). Since the value of the standard error percentage is smaller than the significance level at (0.05), this indicates the presence of significant differences in the test. Dimension between the experimental and control groups and in favor of the experimental group. The researchers concluded, with the results of the research, that using the Van Hiele method is effective in learning the skill of dribbling in basketball. The researchers came out with several recommendations, including the necessity of using a modern method in physical education lessons and moving away from the traditional methods followed

Effect of the Use of Virtual Reality (VR)-nased Geometry Virtual Lab Media with the Van Hiele Theory Approach to Student Learning Achievement at IVET University Semarang

Effect of the Use of Virtual Reality (VR)-nased Geometry Virtual Lab Media with the Van Hiele Theory Approach to Student Learning Achievement at IVET University Semarang

Junior High School Students’ Geometry Ability Based on Van Hiele Level’s Thinking

The ability to solve problems and logical thinking of students can be grown by studying Geometry. However, the reality in the field and some research in Indonesia shows that the geometric thinking ability of junior high school students is still relatively low. This study aims to examine the geometric thinking ability of junior high school students according to Van Hiele Theory. This research is a qualitative study with a descriptive approach, which was conducted in one of the junior high schools in Pringsewu Regency involving 28 students of class VIII. One student was selected to represent levels 1, 2, 3, and 4 Van Hiele as the research subject. Data collection was carried out using multiple choice tests and interviews. Data analysis techniques were conducted with data reduction, data presentation, and conclusion drawing stages. The data originality technique was carried out by triangulation, in which the researcher compared the test data with the results of student interviews. The results showed that level 1 students (28.57%) could recognize and name geometric shapes visually; level 2 students (14.28%) could study geometric shapes by observing and mentioning the properties of the shapes; level 3 students (7.14%) could make connections between various geometric shapes and detect general properties of certain geometry; level 4 students (3.57%) could distinguish and make simple conclusions about the shapes and properties of shapes.
 Kata kunci: berpikir geometri, level van hiele, siswa SMP.