Van Hiele Levels Research Articles

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.

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.

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

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.

Kesulitan Siswa dalam Menyelesaikan Soal Setara PISA konten Shape and Space ditinjau Berdasarkan Level Tingkat Berpikir van Hiele

This study aims to determine students' difficulties in working on PISA-like mathematical problems on shape and space content based on van Hiele's level of thinking. This type of research was descriptive with a qualitative approach. The research subjects comprised 6 class X at High School in Mataram using VHGT instruments and PISA-like problems. The students' answers were thoroughly examined through in-depth interviews. Data analysis was performed using the Miles and Huberman model with data reduction, data display, and conclusion drawing/verification steps. The results showed that students were at the visualization, analysis, and informal deduction levels of thinking. The difficulties experienced by students at the visualization level were the same as students at the analysis level, which is found in several aspects such as language comprehension, visual perception, knowledge transfer, and numeracy. The difficulties of students with informal deduction thinking levels occur in 3 aspects: visual perception, knowledge transfer, and counting ability. Language comprehension includes students' understanding or confusion of the meaning of the problem and students' ability to convert the problem into mathematical form. Difficulties in the visual perception aspect of students relate to students' ability to visualize mathematical concepts in the problem. The knowledge transfer aspect focuses on how students connect existing ideas, and the numeracy aspect is related to students' ability to operate numbers.

The Journey Continues: Mathematics Curriculum Analysis from the Official Curriculum to the Intended Curriculum

In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.

Construct It! Triangle Puzzle Challenges

This article presents an original puzzle that supports students’ development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought.

Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking

Acknowledging the value of understanding defining and classifying special quadrilaterals for prospective mathematics teachers (PMTs), the present study attempts to track this understanding so that the progress of thinking from Van Hiele's level 2 to level 3 could be theorised. Thus, a bounded case study sample of PMTs, who had graduated and joined the mathematics teacher preparation diploma at the Faculty of Education, Tanta University in Egypt, were selected and requested to (a) define trapezoid, parallelogram, rhombus, rectangle, and square, and (b) represent the relationship among these quadrilaterals. The data were collected and analysed in two cycles. During the first cycle, participants' responses were scrutinised upon Prototype 1; it was developed based on the literature review to describe levels of special quadrilaterals understanding as faulty, partitional-uneconomical, partitional-economical, hierarchical-uneconomical, and hierarchical economical. Similarly, the researchers replicated the same analytical process in the second cycle in order to validate the levels suggested in Prototype 1. Also, some clinical interviews were conducted to confirm the participants’ representations of relationships among the defined quadrilaterals. The results enabled advancing the hypothetical Prototype 1 to Prototype 2. Prototype 2 reconceptualised the levels of understanding into faulty, slightly economical, fairly economical, and economical, wherein each level was determined based on (a) the economics of the concept definition and (b) the awareness of relationships among other related definitions to the concept defined (recognising subsets and supersets). These results are prospective for further investigations to sufficiently unpack all sub-levels of geometric thinking embedded in Van Hiele’s fixed levels. It also provides basics on proper pedagogical approaches and corresponding interventions to train PMTs effectively teach geometric thinking.

KEMAMPUAN SPASIAL SISWA DITINJAU DARI TAHAPAN BERPIKIR VAN HIELE DI SMP NEGERI 1 BANDUNG TULUNGAGUNG

The objectives of this study were (1) to describe the spatial abilities of students using the Van Hiele thinking stages, (2) to find out the differences in students' spatial abilities in terms of the Van Hiele thinking stages based on the Van Hiele level groups. The method used is a mixed method type design, sequential explanatory with qualitative research followed by quantitative research first. Qualitative data collection techniques using observation, tests, and interviews with the subject of 6 students. Quantitative data collection technique with a sample obtained of 64 students using a test, by testing the hypothesis using the one way ANOVA test. The results of this study are as follows (1) Students' spatial abilities in terms of the Van Hiele thinking stage level 0 (Visualization) only meet the indicator spatial ability, namely spatial visualization, at the Van Hiele thinking stage level 1 (Analysis) meets the spatial ability indicators, namely spatial visualization and mental rotation. at the Van Hiele thinking stage level level 2 (informal deduction) fulfills all spatial ability indicators, namely spatial visualization, spatial perception and mental rotation, (2) There are differences in students' spatial abilities in terms of Van Hiele thinking stages based on group level 0 (Visualization), level 1 (Analysis), and level 2 (Informal Deduction).

Using the Van Hiele Theory to Explain Pre-Service Teachers’ Understanding of Similarity in Euclidean Geometry

Helping learners to develop a solid grasp of geometric concepts poses a challenge for teachers. Therefore, it is important that teachers have a sound understanding of the geometry they teach. The aim of this qualitative study was to explore pre-service teachers’ (PST’s) understanding of the concept of similarity in Euclidean geometry and to use van Hiele’s theory to explain misconceptions evidenced by the PSTs. Data in this study were collected from 34 first-year PSTs studying for a Bachelor of Education degree in high school mathematics. The authors analysed the written responses to a 13-item worksheet and also conducted interviews with seven of the participants. The analysis of the data was guided by van Hiele’s theory which was used to identify misconceptions amongst PST’s who had not yet developed the appropriate reasoning skills linked to particular van Hiele levels of geometric thought. It was found that these students used reasoning that is characteristic of the elementary levels to make judgments. Many PST’s faced challenges with similarity notation and the process of proving the similarity between two figures. This study recommends that PST’s should be given more opportunities to connect visual and analytic representations of similarity.

Relationship between Mathematics Teachers’ van Hiele Levels and Students’ Achievement in Geometry

Using non-experimental quantitative correlational design, the van Hiele levels of thirty grade 9 mathematics teachers, as well as the achievement of 1489 students in geometry were investigated in this study. Results showed a significant difference with a substantial effect size of .64 between the achievement of students whose teachers are operating at level 5 in the van Hiele Levels of Geometric Thinking and those of students whose teachers are operating at level 2. This study underscored the importance to leverage on teachers’ van Hiele level of geometric thinking as it is highly correlated to student achievement. Developing teachers’ geometric thinking ability at the expected levels in order to improve students’ achievement may require trainings, further studies, or curriculum improvement for pre-service teachers. Moreover, a deeper study focusing on other content areas and skills in mathematics may be done to further assess their interrelationships with teachers’ van Hiele levels and student achievement. In addition, it would be of interest to investigate the grade level where student mathematics achievement starts to decline.

Experimentation of Transformative Learning and Realistic Mathematic Education Learning Models on Mathematics Learning Achievement

The research aims to investigate and evaluate the efficacy of different learning models on mathematics learning outcomes, specifically focusing on the students' van Hiele geometric reasoning capacity. The study employed a quasi-experimental design. The practice is carried out in Public Junior High Schools in Sukoharjo Regency, part of the Central Java Province in Indonesia. The utilized learning models were transformative learning, actual mathematics education, and direct instruction. The study encompassed a total of 281 individuals, who were selected from 9 classes across three distinct institutions. Data analysis is conducted with a two-way analysis of variance (ANOVA) approach. The research findings indicate that (1) the learning model has a positive and significant impact on mathematics learning outcomes; (2) the van Hiele level of geometric thinking ability has a positive and significant influence on mathematics learning outcomes; (3) there is a positive and significant interaction between learning models and van Hiele level of geometric thinking ability on mathematics learning outcomes; and (4) among the transformative learning, Real Mathematics Education, and Direct Instruction models, the transformative learning model yields the best mathematics learning outcomes.

Analysis of Changes in Robot Activity Levels in Mathematics Classes Based on Van Hiele Theory

This study designed robot programming classes toward mathematical concepts and curriculum to introduce robotics, a representative technology of the Fourth Industrial Revolution era, into the mathematics classroom, and analyzed the changes in students’ van Hiele levels. This study presented the robot activity levels (RLs) per the van Hiele levels of geometric thinking (VLs), and applied each RL to the class’s design, including tasks. The students’ learning process and class results were analyzed to ascertain whether their VL increased. The class was conducted with gifted middle school students, and utilized LEGO Mindstorms EV3, an extensively used educational robot. While performing RL based tasks, students sequentially completed tasks RL1~RL4. This study focused on the task performance process of VL3 students to investigate how they transition to a RL beyond their VL. As students performed the five tasks designed to help them transition from VL3 to VL4, reflecting the rise in the van Hiele levels of geometric thinking, they gradually progressed through the active inquiry and finally reached VL4 by completing RL4 tasks.

Fostering a Student’s Abstraction of the Relationship Between Parallelogram and Trapezoid Within Quadrilateral Hierarchy

ABSTRACT This article provides an analysis of a data set coming from a two-phase qualitative study that focused on fostering primary students’ abstraction of interrelations among quadrilaterals (squares, rectangles, parallelograms, rhombuses, trapezoids). The pilot study consisted of work with eight primary students operating at van Hiele level 2 (e.g., understanding quadrilaterals without interrelations). We benefitted from the teaching experiment methodology to develop a task sequence applied in a dynamic geometry environment and a paper-pencil environment to help each participant develop quadrilateral hierarchy at van Hiele level 3 (e.g., understanding quadrilaterals with their interrelations). The main study used a case study approach to investigate two primary students’ progress (Efe and Ayla, age 10). After the pre-interviews, each participant was taught the developed task sequence individually during seven up-to-one-hour teaching sessions, followed by a post-interview. This article only details Efe’s case as he worked on developing the relationship between parallelogram and trapezoid. We analyzed Efe’s data (from the pre-interview, Teaching Session-7, and the post-interview) to describe how the different parts of the task sequence fostered his abstraction of the interrelation between parallelogram and trapezoid as he moved from van Hiele Level 2 to 3. This article provides initial evidence for the classification process.

Geometric Thinking: Reflections Manifested by Preservice Mathematics Teachers in van Hiele Model Studies

Background: The study of geometric thinking in the preservice education of mathematics teachers is an emerging theme that can reverberate in the teaching of geometry in basic education. Objectives: To analyse reflections manifested by prospective mathematics teachers (PMTs), working with tasks supported by van Hiele theoretical model to develop geometric thinking. Design: The nature of this study is qualitative and interpretative. Setting and participants: Twenty-four PMTs members of a geometry teaching subject were investigated in a mathematics degree course at a public university in Paraná - Brazil. Data collection and analysis: The data was collected from the video-recorded training sessions, the written production of the PMTs promoted by the tasks and the registers kept on the field diary. The analysis focused on the reflections expressed by PMTs regarding the work with tasks involving geometric thinking, considering the levels of reflection proposed by Muir and Beswick (2007). Results: The results show descriptive, deliberate, and critical reflections, with different levels of incidence, associated with (I) the levels of thought proposed in the van Hiele model; (II) the teacher’s role in classroom practice; and (III) the geometric concepts and properties of flat figures. Conclusions: The promotion of formative actions that privilege discussions and reflections on geometric thinking can allow PMTs to seek connections between knowledge of geometry, geometric thinking, and their future teaching practice.

Rethinking strategy on developing students’ levels of geometric thinking in Sokoto state, Nigeria

<span lang="EN-US">Geometric thinking skills remained a topical issue in mathematics education. The purpose of this research is to investigate the van Hiele levels of geometric thinking skills of the students in Sokoto state to provide a clear picture of the students’ levels for the appropriate development of learning activities, and better understanding. The study involves three mathematics teachers and 200 students (100 students each of basic and senior secondary school students). The samples of the teachers were purposely selected and students were randomly selected. There were two instruments used in the study; interviews for the mathematics teachers while a van Hiele test for geometric thinking was adopted to collect data for the students’ van Hiele levels of thinking. Thematic analysis (for teachers’ interview), descriptive, and Mann-Whitney U test for the analysis of students’ van Hiele levels of thinking was used. The result shows that all the teachers indicate that the traditional approach is the dominant method used in teaching and learning and that students in the state lack basic skills in school geometry. Also, the result indicated that the majority of students sample among Basic and Senior secondary schools in Sokoto state were operating at level 0 respectively. Furthermore, a significant difference between the two independent groups was found in favor of senior secondary school students. It is hoped that in the future, educational institutions could use the present research as a guide for the development and design of modules, learning activities based on the van Hiele levels to bridge the gap in the state.</span>