Van Hiele Levels Research Articles

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.

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.

Characterizing Levels of Reasoning in Graph Theory

This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We thus obtain four levels of reasoning: an initial level of visual character in which students perceive graphs as a whole; a second level, analytical in nature in which students distinguish parts and properties of graphs; a pre-formal level in which students can interrelate properties; and a formal level in which graphs are handled as abstract mathematical objects. Our results, which are supported by a review of the literature on the teaching and learning of graph theory, might be very helpful to design efficient data collection instruments for empirical studies aiming to analyze students’ thinking in this field of mathematics.

Reviewing the Van Hiele model and the application of metacognition on geometric thinking

<span lang="EN-US">Metacognition, or the ability to think about thinking, is essential in the development of geometric thinking. However, studies on the Van Hiele model and the application of metacognition on geometric thinking are still under-researched. This study aimed to provide a review of the Van Hiele model and the application of metacognition on geometric thinking. A total of 844 articles were retrieved through internet search engines from 1995 to 2020 and manually selected and reviewed systematically. The keywords used related to the Van Hiele model, metacognition, and geometric thinking. The findings that emerged from the review were categorized into two main themes which were the effectiveness of the Van Hiele model towards geometric thinking and the effectiveness of the application of metacognition on geometric thinking. Most articles revealed the positive indication of the geometric thinking development through the Van Hiele model intervention. It also seems that the potential of the application of metacognition in the Van Hiele model can strengthen geometric thinking development. Researchers and educators may find this knowledge useful in conducting empirical studies and developing learning instructions based on the application of metacognition in the development of geometric thinking.</span>

Van Hiele Levels: Errors in Solving Geometry Problems from Mathematical Disposition

The purpose of this study is to analyze student errors based on van Hiele’s level of understanding in solving geometric problems in terms of mathematical dispositions. This research is considered important as it can reveal mistakes often made by students based on van hiele levels. There are 5 levels contained in van hiele levels, namely level I-visualization, level II-analysis, level III-ordering, level IV-deduction, and level V-rigor. This research is a qualitative descriptive study. Subjects in this study were selected based on high, medium, low mathematical disposition abilities. This research shows that students with high mathematical disposition in solving geometric problems reach level IV-deduction. Students with moderate dispositions are able to reach level II-analysis and make mistakes at level III-ordering. Furthermore, students with low mathematical disposition only reach level I-visualization and make errors at level II-analysis.

Assessing Analytic Geometry Understanding: Van Hiele, SOLO, and Beyond

In the context of analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999; Biggs & Collis, 1982); syntactic and semantic elaborations (Kaput, 1987a, 1987b, 1989); and isomorphic, transcendent, and mixed connections (Adu-Gyamfi, Bossé, & Lynch-Davis, 2019). Along with producing a fuller analysis of student work and communication, the study found that for only the students with the lowest and highest scores regarding either their understanding or actions on the analytic geometry task might there be a predictive association between knowledge and action levels. For other students, a predictive association could not be determined. This may mean that the level of understanding a student possesses regarding a particular mathematical concept may not parallel the level of actions they use when working with an associated task.

The Impact of Using the Van Hiele Model in Developing Geometric Thinking Levels among Tenth Grade Students in Jordan.

This study aimed to investigate the impact of the usage of the Van Hiele model in the development of geometric thinking levels among tenth grade students in Jordan. The sample of the study was selected from tenth grade basic students in Amman schools. Two hundred and forty students studying the mathematics course in the circle unit were divided into two groups: experimental (using the Van Hiele model) and the control (using the traditional approach of teaching).To achieve the objectives of the study, a test of geometric thinking in the unit of the circle was developed. Validity and reliability of the test was verified. The instructional material was also prepared in the circle unit for the students of the tenth grade using the Van Hiele model of geometric thinking. Four mathematics teachers were trained on the model, and the content validity of the training material was verified. The results of the study showed a statistically significant difference (α=0.01) between the two arithmetic means of the experimental and control agencies in favor of the experimental group that used the Van Hiele model in geometric thinking in general, and in sub-levels (visual, descriptive, logical), and the study showed no statistical significance difference (α=0.01) between the arithmetic means of male and female in geometric thinking, also the study showed an interaction between the model variable and gender variable in geometric thinking.

Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices

This study aimed to establish the relationship between pre-service elementary mathematics teachers’ (PEMTs) van Hiele geometric thinking levels and their constructivist-based teaching practices. In order to address the research questions framing this study, data related to the PEMTs’ van Hiele geometry reasoning stages were gathered through the van Hiele Geometry Test (VHGT). In addition, constructivist-based teaching practice was examined by conducting the observation protocol named as Reformed Teaching Observation Protocol (RTOP) to the 108 PEMTs. Moreover, interviews were conducted to 15 Turkish PEMTs in order to obtain detailed information about the research question. The results of the data analysis represented that there was a statistically significant positive correlation between the PEMTs’ constructivist-based teaching practice and their van Hiele geometry reasoning levels. As a conclusion, the PEMTs having high level of van Hiele geometry thinking were likely to enact their teaching practices more appropriately to the constructivist approach.

Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book

In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students.

Representasi Matematis Siswa Bina Prestasi MTsN 1 Jember dalam Menyelesaikan Masalah Segiempat Ditinjau dari Level van Hiele

This study aims to determine mathematical representation of Students’ Ability in Solving Quadrilateral Problems Based on Van Hiele’s Levels at an Enrichment Program in MTsN 1 Jember.. This research is a descriptive qualitative research. The subjects of this study were 17 students of class IXA at ​​MTsN 1 Jember. The data collection method on this research are using test and interview methods. The test instrument on this research were a test of ability to think geometry and a test of mathematical representation on rectangular material. The results of data analysis were carried out by comparing the results of the mathematical representation test with interviews, then categorized based on Van Hiele's level of thinking from the results of the geometric thinking ability test. The results showed that students with a visual thinking level had a tendency to use symbolic and verbal representations in solving problems. Students with the analytical thinking level tend to use verbal, visual, and symbolic representations in solving problems. 
 Keyword: Mathematical Representation, Quadrilateral, High Achiever Student, Van Hiele levels

The development of tangram-based geometry test to measure the creative thinking ability of junior high school students in solving two-dimentional figure problems

Geometry is a branch of mathematics that demands creative thinking. Teachers need a geometry instrument that is fun, simple, and meaningful to measure the creative thinking ability of junior high school students. This developmental research used a 4-D model consisting of defining, designing, developing, and disseminating the tangram-based geometry test. This research was intended to describe the process of developing a tangram-based geometry test. Tangram-based geometry test development included validation by experts. The product has passed the validation stage and obtained a score of 4,47 (scale 1-5), so it was feasible to use. Research try out subjects were 3 out of 30 students who were VIII grader at junior high school that was chosen due to van Hiele levels. Data on students’ creative thinking profile acquired through tests and interviews. Fluency, originality, flexibility, and elaboration are the aspects of creative thinking ability. The results showed that in solving tangram-based geometry tests, a student at the creative level (level 3) satisfied all aspects of creative thinking, a quite creative student (level 2) satisfied fluency and flexibility aspects, and almost uncreative student (level 1) satisfied fluency aspect only. According to the results, this developed tangram-based geometry test was valid, feasible, and effective to measure junior high school students’ creative thinking ability.

PROFIL KEMAMPUAN KOMUNIKASI MATEMATIS SISWA DALAM MENYELESAIKAN MASALAH GEOMETRI DITINJAU DARI LEVEL VAN HIELE

Mathematical communication skills are needed to express ideas, messages, and ideas through written or oral. The research subjects were five students of class XII SMAN Ambulu who were categorized in van Hiele level. The results of the data analysis obtained were students with informal deduction had the ability to express mathematical ideas through written or oral, the ability to understand mathematical ideas both orally and in writing and the ability to use terms and notations to present data, and had the ability to present ideas. mathematics in solving or describing models of mathematical problems. Students of analysis have the ability to express mathematical ideas through oral, the ability to understand and evaluate mathematical ideas both orally and in writing, and are able to use mathematical terms and notations in presenting mathematical ideas. Visualization students are able to explain how to describe geometric transformations orally and are able to use notations and terms in presenting data.

IDENTIFIKASI KETERAMPILAN GEOMETRI SISWA LAKI-LAKI DAN PEREMPUAN SMP BERDASARKAN TINGKATAN VAN HIELE DALAM MENYELESAIKAN SOAL BANGUN DATAR

This qualitative descriptive study aims to identify the geometry skills of both male and female secondary school (SMP) students based on Van Hiele level in solving a flat wake up problem. The selection of the subject using purposive sampling technique consisting of 2 students (1 male and 1 female) of 35 students in class VIII A SMP Negeri 2 Sumowono who have been working on a test adapted from the project CDASSG Usiskin ie VHGT test and the result has a level of geometry thinking van Hiele. This study will identify differences in geometry skills that exist in female and male students who have geometric thought levels of van Hiele. Data collection techniques using test methods, interviews and documentation. The results showed that both subjects had a level of geometric thinking van Hiele and both had visual, verbal, drawing, logic and applied skills differentiating in solving the problem.

The Difficulty Analysis of Students Spatial Ability Based on Level Van Hiele in Problem Based Learning

This study aims to (1) determine the level of students' spatial ability at Van Hiele's level in problem-based learning. (2) to find out the location of the students' difficulties in solving spatial power problems with the Van Hiele level. This research is a qualitative descriptive study. The subjects of this study were students of class XII SMK Bima Utomo Batang Kuis. The object of this research is the spatial ability based on Van Hiele's level in Problem Based Learning. The results of this study indicate that the level of spatial ability in the low category reaches 51.4%, while the medium category reaches 34.3%, and the high category reaches 14.3%. Subjects in the low category experienced skill difficultiesSubject S.01 (low spatial ability), at Level 1 experienced skill difficulties (question number 1) and concept difficulty (question number 4), at Level 2 experienced skill difficulties, at Level 3 and Level 4 experienced difficulty in principle. Subject S.02 (low spatial ability), has difficulty skills at Level 2 and has difficulty in principle at Level 3 and Level 4. Subject S.03 (moderate spatial ability), has difficulty in principle at Level 3 and Level 4. Subject S. 04 (moderate spatial ability), has difficulty skills at Level 3 and has difficulty in principle at Level 4. Subject S.05 (high spatial ability), has difficulty in principle at Level 4. Subject S.06 (high spatial ability), has difficulty principles at Level 4.Based on the results of this study, it is expected to be an inspiration for users.

Developing instrument to increase students' geometry ability based on Van Hiele level integrated with Riau Malay culture

The purpose of this research is to develop Geometry teaching materials and geometry instruments that can be used to improve the ability of Geometry based on Van Hiele's cognitive level integrated with Malay Culture. The research design used in this research was Research and Development (R&D) which consists of several stages, namely: potential and problems, material collection, product design, product validity, product trials, product revisions, and mass products. The subjects of this study were students of mathematics education department in the first semester consisting of 65 students. The Validity of Teaching Materials inform students work sheet was analyzed using the validation sheets of teaching materials proposed by Akbar (2013) and Practical Analysis was analyzed using the formula proposed by Riduan (2016). The test instrument was analyzed using Aiken's validity and interrater reliability. The questionnaire instrument was analyzed using Aiken's validity and interrater reliability. Data analysis shows that teaching materials are in the form of student worksheets in the valid and practical categories. The test instrument was developed in valid and reliable categories. The developed questionnaire instrument in the form of essays in a valid and reliable category. Teaching materials and instruments in the form of questionnaires and essays according to experts can be used to obtain relevant data and improve the ability of geometry based on the level of Van Hiele integrated with Malay Culture.

Identifikasi Tingkat Berpikir Geometri Siswa Berdasarkan Teori Van Hiele

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