Van Hiele Research Articles

A Comparison of U.S. and Chinese Geometry Standards through the Lens of van Hiele Levels

The present study aims to compare the geometry standards in U.S. Common Core State Standards of Mathematics (CCSSM) and Chinese Compulsory Education Mathematics Curriculum Standards (CMCS) through the lens of van Hiele levels. The study considered a standard unit as one or multiple learning expectation(s) and placed each learning expectation into van Hiele levels. By examining the van Hiele level distributions of the learning expectations and major topics, this study investigated how CCSSM and CMCS propose the students' development of geometric thoughts. The findings reveal different emphases in geometry learning expectations of CCSSM and CMCS. Specifically, (a) Geometry standards in CCSSM are more general, whereas geometry standards in CMCS are more specific; (b) CMCS shows a more consistent progression through grade bands than CCSSM; (c) CCSSM makes more connections between various aspects within a topic and across multiple topics than CMCS; (d) CCSSM highlights Dynamic Geometry Environments (DGEs), whereas CMCS underscores abstract and rigor at the upper level. Implications of this study and suggestions for future revisions for both standards are discussed.

Analisis Berpikir Siswa Level Van Hiele dalam Memecahkan Masalah Segiempat Berdasarkan Langkah Polya

This study aims to describe student’s level thinking of understanding geometry according to van Hiele’s theory (informal deduction, deduction, and rigor) in solving of a quadrilateral problems based on Polya’s steps. The subjects of the study were 3 students Olympiad of SMPN 2 Jember, each of them have the level in informal deduction, deduction, and rigor. These students were given tests of geometry problem test at beginning and then proceeded to interview. The descriptive qualitative research was used in this study. The results showed that the subjects are able to fulfill all of the indicators according to their level in the step of understanding the problem and make arrangements. In part of carry out the plan, a student with informal deduction level is not able to solve the three indicators and a student with deduction levels is not able to solve one of the indicators, whereas the rigor’s student is not to able accomplish two indicators according to the levels. In step of looking back, a student with informal deduction level and a student with deduction level are not capable to solve the whole of indicators, however the rigor’s student is not able to accomplish two indicators according to the levels.

Dynamic Google SketchUp Software and Conventional Teaching Strategy of Students’ Conceptual Knowledge and Procedural Knowledge in Learning Geometry

The purpose of this study is to identify the effect of using dynamic software Google SketchUp (GSU), without software on van Hiele’s theory and conventional teaching strategy of students’ conceptual and procedural knowledge in learning geometry among primary school students. The study was conducted using pre and post-test true experimental methods. This true experimental research involved 96 students from Year Five primary schools in Malaysia. The selection of site or school take into account as convenience and voluntary participation. The study's findings showed significant differences in student's conceptual knowledge and procedural knowledge based on the different types of the strategy group. The post hoc test indicated that using software showed better conceptual and procedural knowledge when compared to without using software on van Hiele’s theory and conventional teaching strategy.

Geometric Thinking of Future Teachers for Primary Education—An Exploratory Study in Slovakia

Various studies show that the level of knowledge achieved by pupils is influenced by the level of knowledge of their teachers. In this article, we focus on geometric thinking and the solutions for geometric tasks through a study of future teachers of primary education. The research sample consisted of 59 master’s students from the Teacher Training for Primary Education (TTPE) program. To determine the level of geometric thinking of TTPE students, the van Hiele geometric test was used. Two geometric multi-item tasks were proposed and the students’ solutions to these tasks were quantitatively and qualitatively evaluated. The main goal was to analyze students’ misconceptions while solving tasks and to compare and reveal the connections between their solutions and their achieved level of geometric thinking. A statistical implicative analysis was used for a deeper analysis, namely the statistical software C.H.I.C. The research findings show that more than 40% of TTPE students in the research sample did not reach the required level of geometric thinking. The achieved level of the geometric thinking of students is also influenced by the type of high school education. We observed problems with understanding the concept of the triangle and square in TTPE students. The connections between the solutions of two geometric tasks and the achieved level of geometric thinking were also revealed.

The critical thinking abilities of female students at the level of Van Hiele abstraction

Critical thinking abilities are very important to improve the quality of thinking and make students better understand the content that has been studied. But in reality, students' critical thinking skills are still very low. So it is necessary to have a study that describes the critical thinking skills of these students . The purpose of this study is to describe students' critical thinking skills at the abstraction level in solving space construction problems. This research is a qualitative descriptive type because it describes in detail the critical thinking ability of Van Hiele's abstraction level in solving space construction problems. The instruments of this research are the van Hiele geometry test, the space construction problem solving test, and the interview guide. The research subjects consisted of one student of class VIII of SMP Negeri 2 Pamekasan at the Van Hiele level of Abstraction. The selection of female subjects in this study was due to the fact that female subjects were more communicative in expressing what was in their minds making it easier for researchers to uncover critical thinking of students at the level of Van Hiele abstraction. The results showed that the subject solved the space construction problem according to the critical thinking indicator stage but was not perfect because the subject made an error when solving the problem (indicator evaluation), so that the final answer obtained was not correct. This affects the conclusions obtained (inference indicators) namely the subject draws conclusions but the answers are not correct.

Need for cognitive closure predicts stress and anxiety of college students during COVID-19 pandemic

The COVID-19 pandemic has taken a massive toll on mental well-being. The unprecedented level of uncertainty associated with the pandemic may be a contributing factor to stress and anxiety, especially among individuals with high intolerance to uncertainty (Rettie & Daniels, 2021). Individual differences in need for cognitive closure have also been linked to mental distress during unpredictable situations (Berenbaum et al., 2008). The present study tested the hypothesis that individuals with a high need for cognitive closure would experience relatively higher stress and anxiety during the COVID-19 pandemic. College students (N = 400) completed an abbreviated Need for Closure Scale (Roets & Van Hiel, 2011), the Generalized Anxiety Disorder Scale (Spitzer et al., 2006), and the short-version of the Perceived Stress Scale (Cohen & Williamson, 1988). Results supported the hypothesized relationship between high need for cognitive closure and higher levels of stress and anxiety. Findings have relevance to college students who are experiencing heightened psychological stress during the COVID-19 pandemic.

Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.

Analysis of students' thinking level in solving Pythagoras' theorem problems based on Van hiele's theory

The aims of this analysis are to explain the level of thinking of grade VIII students at SMP Negeri 1 Talang Ubi in solving Pythagorean Theorem questions based on Van Hiele's theory. The research approach used in this analysis is descriptive qualitative case study research. The subjects of this research were three students of grade VIII of SMP Negeri 1 Talang Ubi, South Sumatera Indonesia. The three students were chosen based on their test answers on the Pythagorean Theorem material, with one being a high-ability student, one being a medium-ability student, and one being a low-ability student. The study's data collection techniques included assessments, interviews, and documentation. Techniques for data processing include data reduction, data presentation, and conclusion. The findings revealed that high-ability students could complete all four stages of Van Hiele's thinking: imagination, interpretation, informal deduction, and deduction. Moderate students achieved three levels of Van Hiele's thinking, including visualization, analysis, and informal deduction, while low-ability students achieved only one level of Van Hiele's thinking, visualization.

Assessing van Hiele’s geometric thinking levels among elementary pre-service mathematics teachers

Teachers’ geometric thinking is crucial to teaching efficacy in geometry since teacher knowledge or thinking serves as a basis for the quality of instruction provided for students’ learning. Teachers’ thinking about geometry has attracted much attention among mathematics education researchers. This study therefore aimed at assessing elementary pre-service teachers’ geometric thinking within the first three levels of van Hiele’s model. The study was guided by three objectives. The objectives were to (1) assess the distribution of van Hiele’s geometric thinking among the study participants, (2) determine if the participating pre-service teachers’ geometric thinking is significant for teaching geometry, and (3) find out if any difference in geometric thinking of the pre-service teachers existed with regard to gender. The study used the descriptive survey design. The study participants were prospective mathematics teachers drawn from four Colleges of Education in the Bono Region and Ashanti Region of Ghana. The Colleges were randomly selected for the study. The study participants comprised 217 pre-service teachers. The van Hiele’s test instrument was adapted and pilot tested to assess the internal consistency of the items in the various levels. The calculated reliability coefficient of the instrument ranged from 0.71 to 0.74. The instrument was administered to the study participants on the scheduled date. Data generated from the participants were analysed based on the study objectives. Findings from the analyses show that pre-service teachers have limited geometric thinking within the first three levels. However, their geometric thinking of the levels assessed was found to be significant which could have some impact on teaching geometry. Findings also reveal gender differences in pre-service mathematics geometric thinking. It is recommended that conscious effort must be made by mathematics teacher educators in the Colleges of Education to deepen the pre-service mathematics teachers’ geometric thinking.

Raising the Van Hiele Level of College Students

ABSTRACT This article describes the application of technology to the van Hiele Model for Geometric Thought to increase the van Hiele levels in an undergraduate Euclidean geometry course. Following the model with activities and phase-based instruction, students showed significant gains in the van Hiele levels in five different sections over the course of five semesters. By including the use of the CanFigureIt website, a Desmos activity, the Geometer’s Sketchpad and WebSketchpad during the fifth semester, students showed the largest gains in levels as measured by the van Hiele test.

BERPIKIR GEOMETRI LEVEL VISUALISASI SISWA SEKOLAH MENENGAH PERTAMA MELALUI TOPIK SEGIEMPAT MENURUT TEORI VAN HIELE

This research aims to describe the level of geometric thinking and geometric thinking processes of Junior High School students according to van Hiele's level of thinking on the topic of quadrilaterals. The qualitative approach is the research method used in this study through a case study method by testing the Van Hiele Geometry Test (VHGT) which was adapted from Usiskin's CDASSG and conducting interviews about the thinking process in the form of identifying, defining, and classifying which was adapted from the interview guide of Burger and Shaughnessy (1986). The subjects of this study were 297 grade VII and VIII students from two schools located in the Lembang sub-district. The results of the VHGT test showed that there were 81 students counting level 0 (visualization). The results showed that the students of class VII and VIII level 0 were as follows: 1) students were able to recognize the types of quadrangle but still affected by the prototype, 2) students were not able to classify quadrilaterals, and 3) overall description of the geometric thinking process level 0 in the form of identifying, defining, and classifying aspects according to van Hiele's thinking characteristics in general.

Examination of 4th Grade Students' Definitions for Square, Rectangle and Triangle Geometric Shapes

The aim of this study is to obtain information about students' definitions, mistakes, misconceptions, and van Hiele geometry thinking levels by using the definitions of 4th grade students for geometric shapes of rectangle, square, isosceles triangle, equilateral triangle, and scalene triangle. The study was carried out with 156 primary school 4th grade students. In the study, the case design, one of the qualitative methods, was used. Students were asked to describe geometric shapes. It was observed that most of the 4th grade students participating in the study were in the visualization stage of van Hiele. There are very few definitions of the hierarchical structure in the study. Most correct definitions are in the partitional form. In the study, misconceptions were detected in some of the students.

Mapping pre-service teachers’ faulty reasoning in geometric translations to the design of Van Hiele phase-based instruction

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs’ faulty reasoning displayed in errors they make.Aim: The aim of this study was to explore the use of Bachelor of Education (BEd) students’ faulty reasoning in geometric translations, in designing a Van Hiele phase-based instructional programme that could address such faulty reasoning.Setting: The setting for the study was a newly established rural university in South Africa.Methods: Tests on geometric translations were administered to BEd Foundation Phase students, followed up by interviews to explore errors made when responding to the test items. The errors were then mapped to the design of a Van Hiele phase-based instructional programme.Results: The results revealed that the students had several misconceptions with geometric translations. The misconceptions were delineated into the errors that the students displayed and these were classified under two themes. The first theme was incorrect properties of transformation and under this theme, the errors were coded as confusing translation with rotation, wrong translation method, incorrect interpretation of coordinates and confusing the x and y axis. The second theme was errors involving basic mathematics operations including wrong diagrammatic representation of coordinates and incorrect calculations.Conclusion: The study showed that if the students’ misconceptions and the resulting errors are mapped to specific instructional approaches, their faulty reasoning in geometric transformations is addressed and effective learning is enhanced.

Construction with ruler and compass, van Hiele model for geometry thinking and Project-based learning

We describe how problems of geometric construction using straightedge and compass can be introduced to students through project-based learning. We discuss how these problems can be extended to the upper half-plane model. Furthermore, we discuss the use of these problems to assess advanced levels in van Hiele model for geometry thinking.

STUDENTS’ GEOMETRIC THINKING ON TRIANGLES: MUCH IMPROVEMENT IS NEEDED

A look into students’ misconceptions help explain the very low geometric thinking and may assist teachers in correcting errors to aid students in reaching a higher van Hiele geometric thinking level. In this study, students’ geometric thinking was described using the van Hiele levels and misconceptions on triangles. Participants (N=30) were Grade 9 students in the Philippines. More than half of the participants were in the van Hiele’s visualization level. Most students had imprecise use of terminologies. A few had misconceptions on class inclusion, especially when considering isosceles right triangles and obtuse triangles. Very few students correctly recognized the famous Pythagorean Theorem. Implications for more effective geometry teaching are considered.

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.

Analisis Berpikir Siswa dalam Memecahkan Masalah Dimensi Tiga Berdasarkan Van Hiele

In learning mathematics, innovation is still needed to make mathematics more easily understood by students, especially in the field of geometry. This becomes interesting when examined and is associated with van Hiele's level of geometrical thinking which is modified by Polya's problem solving steps. This study aims to determine the thought process of vocational students majoring in Modeling Design Engineering and Building Information in solving three dimensional problems. This type of research is a qualitative descriptive study. The research subjects are students of pre-visualization, visualization, analysis, and informal deduction level. The research subjects worked on the three dimensional problem test and were interviewed. The results obtained are pre-visualization level students fulfilling several indicators at the visualization level, students at the visualization and analysis level meet all indicators at their respective levels, while informal deduction level students are unable to meet one indicator when implementing a plan that is having another way of solving problems. This can be seen from the results of problem solving given and interviews conducted on research subjects.
 Kata kunci: Berpikir, Pemecahan Masalah, Dimensi Tiga, Van Hiele

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)

The Effectiveness of Infusion of Metacognition in van Hiele Model on Secondary School Students’ Geometry Thinking Level

The Effectiveness of Infusion of Metacognition in van Hiele Model on Secondary School Students’ Geometry Thinking Level

Impulsing the Development of Students' Competency Related to Mathematical Thinking and Reasoning through Teaching Straight-Line Equations

The research was carried out to develop students' ability to think and reason mathematically by teaching straight-line equations in a plane. Accordingly, teaching activities were designed according to five learning stages, which were integrated with mathematical thinking levels according to Van Hiele's model. Simultaneously, the learners' mathematical thinking and reasoning competencies were assessed according to the competency requirements specified in the Mathematics General Education Program and the levels of Van Hiele's model, the above three aspects of knowledge, skills and attitudes. The experiment involved 84 students in class 10, 44 of whom were in the experimental group, and 40 were in the control group. The research results showed that students in the experimental group achieved higher mathematical thinking and reasoning skills. Specifically, the two groups had equivalent results for the level of visualization and analysis. However, at the informal deduction and formal deduction and rigor levels, the ranking results of the two groups had a clear difference. The study group observations and students' opinion surveys also revealed that learning stages were designed according to Van Hiele's model and thought-provoking measures and visual images and language contributed to students' interest in learning and positive thinking.