Hiele Geometric Thinking Levels Research Articles

Examination of Seventh Grade Students' Van Hiele Geometric Thinking Levels and Their Mistakes on 'Quadrilaterals'

In this study, it was aimed to examine seventh grade students' Van Hiele geometric thinking levels and their mistakes on 'Quadrilaterals'. The research was conducted with ten seventh grade students and the case study model, one of the qualitative research methods, was used. The Van Hiele geometric thinking levels test developed by Usiskin and the diagnostic test developed by Başısık were rearranged and administered to the students. According to the research findings, seventh grade students have misconceptions about diagonal, height concepts and special quadrilaterals. One of the most important of these is that the square positioned on one corner cannot be recognized by students at the analysis level, but is recognized by students at the visualization level. Students at the analysis and visualization levels have different misconceptions regarding the trapezoid. While there is a misconception that all side lengths must be different from each other as a condition for being a trapezoid, there is also a misconception that having four sides is sufficient. Another one is related to the concept of diagonal. There is a misconception that shapes with equal side lengths also have equal diagonal lengths. While no errors or misconceptions were encountered in students at the informal level, misconceptions were encountered in students at the analysis level, and more errors were encountered in students who were visualization and could not be assigned to any level.

Pre-Service Elementary Mathematics Teachers’ Evaluations of Meetings with Expert and Peer Participation Based on van Hiele Geometric Thinking Levels

In this study, it was aimed to present the pre-service elementary mathematics teachers’ (PEMT) evaluations of meetings with expert and peer participation based on van Hiele geometric thinking levels (vHGTL). The case study method was used and the study group of the research consists of three PEMT who are studying in the third year of a state university. Data were collected with meeting records, reflection reports of the PEMTs, researcher’s field notes and interviews and were analyzed simultaneously by two researchers to ensure coding reliability with content analysis method. As a result of the research, it was seen that there was a positive change in PEMTs’ criteria for determining vHGTL. It was determined that they had difficulties in clearly distinguishing the differences between the levels at the beginning, and that in the last meetings, they insisted on the criteria related to the levels they determined and made more accurate determinations about the levels. As a matter of fact, the teacher candidates also stated that meetings enabled them to determine the achievements’, solved and unsolved problems’ vHGTL better. In addition, they stated that allowing them to freely express their ideas in meetings contributed to their professional development in geometry teaching knowledge. Suggestions regarding experts and peers participatory meetings were presented.

Prospective Mathematics Teachers’van Hiele’s Geometry Thinking and Habits of Mind: A Description of Hard Skill and Soft Skill by Gender

Geometric thinking level and habits of mind were important hard and soft skills required of prospective mathematics teachers. The purpose of this study is to describe the van Hiele geometric thinking level and habits of mind of prospective mathematics teachers. The descriptive quantitative research method was used. There were 31 female and 17 male prospective mathematics teachers in the sample. The research instrument for measuring geometric level was derived from Usikin's (1982) van Hiele geometric thinking test and a habits of mind questionnaire. According to the findings of this study, prospective mathematics teachers' ability to think geometrically has progressed to the stage of analysis and informal deduction. Furthermore, male prospective mathematics teachers achieved the highest level of geometric thinking, known as rigor. Furthermore, both as a whole and in terms of indicators, prospective mathematics teachers' habits of mind fall into the strong category. Male prospective mathematics teachers have more positive habits of mind than female prospective mathematics teachers. The study's findings can help lecturers, particularly those in the mathematics education study program, determine students' hard and soft skills at the end of the year. Prospective mathematics teachers can also be assigned by institutions based on their geometric thinking and habits of mind.

Analisis Kecerdasan Spasial Siswa dalam Menyelesaikan Soal-Soal Geometri Berdasarkan Tingkat Berpikir Van Hiele

The purpose of this research is to describe, identify and analyze students' spatial intelligence in working on geometry problems according to Van Hiele's theory. The method used in this research is descriptive research with a qualitative approach. This research was conducted at SMP Negeri 2 Tarakan. The research instrument used was the Van Hiele geometric thinking level test and spatial ability test, interview guides and documentation. Prior to use, the test, an interview guide, was first validated. The data analysis technique will be used in 4 stages, namely collecting, reducing, presenting, and concluding all the data obtained. The results of this study are that students with high spatial intelligence (KST) are at the level of informal deductive thinking (level 3) where at this ability students are able to know the relationship between shapes. While students with moderate spatial intelligence (SCC) are at the level of analytical thinking (level 2), namely the ability to know and mention the properties of flat shapes. Students with low spatial intelligence (KSR) are at the level of visualization thinking (level 1). In conclusion, it is important for teachers to know students' abilities in learning geometry by paying attention to the level of geometric thinking, being able to use the Van Hiele Geometry learning model, increasing spatial intelligence and van Hiele levels can be done through training involving geometric media or software (geogebra).
 
 Keywords: spatial intelligence, geometry, level of thinking, Van Hiele

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

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

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

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

Investigating the Effect of Using GeoGebra as an Instructional Tool on van Hiele’s Geometric Thinking Levels of Senior High Technical School Students’

The study utilized mixed method approach involving one group pretest-posttest pre-experimental design to explore the effect of using GeoGebra on 80 second year Senoir High school students’ effectiveness of the use of GeoGebra on their van Hiele level of geometric thinking. Inferential statistics of one-way ANOVA and paired sample T-test were used to test the hypotheses. Findings revealed that the use of GeoGebra on students van Hiele level of geometric thinking was effective because majority of the students obtained more than half of the marks allotted to the test. The hypotheses concluded that there was a statistically significant difference in students van Hiele geometric thinking levels (VHGTL) after GeoGebra instruction and also in their pre-VHGTL and post-VHGTL scores. Heads of senior high schools and other educational stakeholders’ should organise in- service training for mathematics teachers to equip them with the required skills on how to utilise GeoGebra for effective teaching and learning of geometry and other lessons in mathematics.

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.

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.

İşitme Yetersizliği Olan Öğrencilerin van Hiele Geometrik Düşünme Düzeyleri

Hearing loss is undoubtedly affecting students' learning processes. It is important to identify the current learning situations of students with hearing impairment in order to design appropriate learning environments. Therefore, the purpose of this study is to determine how the hearing impaired students perceive geometry according to the van Hiele geometric thinking model which has an important place in geometry teaching. For this purpose, geometric thinking levels of middle school hearing impaired students are described. The model of this study is a cross-sectional survey. The sample of the study consisted of 126 students attending hearing impaired middle school in Ankara, Kirikkale, Nigde and Konya. The van Hiele geometric thinking levels test was used to determine the geometric thinking levels of hearing impaired students. Findings are presented by cross-table only by interpreting the frequencies and percentages. As a result of the research, 92 (73%) of 126 hearing impaired students were at the pre-recognition level, 31 (24.6%) at the visualization level and only 3 (2.4%) students were at the level of analysis. In the light of the findings, it was proposed to design the learning environments by using language and materials appropriate to their current learning situations in the process of teaching geometry to hearing impaired students.

فاعلية وحدة فى الهندسة قائمة على نظرية التعلم المستند للدماغ لتنمية مستويات التفکير الهندسي لفان هايل لطلاب المرحلة الإعدادية

هدف البحث إلى: التعرف على مدى فاعلية وحدتي (المساحات والتشابه وعکس فيثاغورث وإقليدس) قائمتين على نظرية التعلم المستند للدماغ فى تنمية مستويات التفکير الهندسي عند فان هايل لدى تلاميذ الصف الثانى الإعدادى للعام الدراسى 2019/2020. ولتحقيق هدف البحث تم استخدام المنهج شبه التجريبي، وتکونت عينة البحث من مجموعة تجريبية عددها (30) تلميذا وتلميذة، ومجموعة ضابطة عددها (30) تلميذا وتلميذة من مدرسة الشهيد محمد الشاذلى التابعة لإدارة کفر الزيات التعليمية، ولجمع بيانات البحث تم إعداد بيانات ومواد البحث کما يلى: بطاقة تحليل لمحتوى وحدتي(المساحات والتشابه وعکس نظرية فيثاغورث ونظرية إقليدس)، بطاقة تحليل مضمون وحدتي(المساحات والتشابه وعکس نظرية فيثاغورث ونظرية إقليدس)، اختبار التفکير الهندسي قائم على مستويات فان هايل، دليل المعلم لوحدتى(المساحات والتشابه وعکس نظرية فيثاغورث ونظرية إقليدس)، کتاب التلميذ، وتوصل البحث إلى النتائج التالية: وجود فرق دال إحصائيا بين متوسطى درجات المجموعتين (التجريبية، والضابطة) فى التطبيق البعدى لإختبار التفکير الهندسي القائم على المستويات الأربعة الأولى من مستويات فان هايل (البصرى – التحليلى – الاستدلالى غير الشکلى – الاستدلالى الشکلى ) ککل وعند کل مستوى على حدة لصالح المجموعة التجريبية، وقد أثبت البحث أن الوحدتين القائمتين على نظرية التعلم المستند للدماغ على على درجة کبيرة من الفاعلية فى تنمية مستويات التفکير الهندسي عند فان هايل لدى تلاميذ الصف الثانى الإعدادى بوحدتى (المساحات والتشابه وعکس نظرية فيثاغورث ونظرية إقليدس).وفى ضوء ذلک وقدم البحث توصيات تتعلق بضرورة زيادة وعى أطراف عمليات تعليم وتعلم الرياضيات بمستويات التفکير الهندسي لفان هايل فى الهندسة بطرق متنوعة واقترحت بعض الدراسات المستقبلية المتعلقة بمتغيرات البحث الحالى وتطويرها. Abstract Of The Research The Research aimed to identify the effectiveness of the two units (areas and similarities and the opposite of Pythagoras and Euclid) based on the theory of brain-based learning in developingVan Hiele's Geometric Thinking Levels Among second-grade students of The Preparatory Stage Pupils' for the academic year 2019/2020. To achieve the goal of the research, the semi-experimental curriculum was used.The research sample consisted of an experimental group of (30) students, and a control group of (30) students from the Shaheed Muhammad al-Shazly preparatory School in Kafr al-Zayat center, gharbia governorate. To collect Research data, tools and materials were prepared as follows: - Card analysis of the content of units (areas, similarities, The opposite of the Pythagorean theorem and Euclid). - Card analysis of the content of units (areas, similarities, The opposite of the Pythagorean theorem and Euclid) according to Behavioral Objectives . - geometric thinking test based on first four Van Hiele's levels. - Teacher's guide for the areas, similarities, The opposite of the Pythagorean theorem and Euclid and activity booklets. The Research reached the following results: There is a statistically significant difference between the mean scores of the two groups (experimental, and control) in the post- application of the geometric thinking test based on the first four levels of Van Hile's levels (visual - analytical - Informal deduction - Formal deduction) as a whole and at each level separately in favor of the experimental group, The research has proven that the two units based on the theory of brain-based learning are highly effective in developing geometric thinking of Van Hiele's levels among second-grade preparatory school students. In light of this, the research made recommendations related to the necessity of increasing awareness of the parties to the processes of teaching and learning mathematics of the van hiele's geometric thinking levels in a variety of ways and suggested some future studies related to the variables of the current research and their development.

Effects of Dynamic Geometry Activities on Seventh Graders' Achievement in Area of Quadrilaterals

The aim of the study was to investigate the effects of mathematics instruction supported by dynamic geometry activities on seventh grade students' achievements in area of quadrilaterals, based on their van Hiele geometric thinking levels. The study was designed as a nonrandomized control group pretest and posttest research design. Participants of the study were 76 seventh grade students. Students in experimental group worked with dynamic geometry learning environment while other students worked in their conventional settings. The results of the study indicated that there is a significant interaction between the effects of method of teaching and van Hiele geometric thinking levels on students' achievement levels in area of quadrilaterals. In addition, mathematics instruction supported by dynamic geometry activities has significant effects on seventh grade students' achievement on area of quadrilaterals. Moreover, the results revealed that students in dynamic geometry supported instruction group received significantly higher scores in area of quadrilaterals than students in traditional instruction group when students are at second level of van Hiele geometric thinking.

Van Hiele Geometric Thinking Levels of Junior High School Students of Atebubu Municipality in Ghana

This study was to measure the Van Hiele’s levels of geometric thinking attained by Ghanaian Junior High School Form 3 (JHS 3) students before writing the BECE. A quantitative research approach was employed in the study and a sample of 105 students randomly selected from the four schools. The results showed that 22 students (20.95%) of the students could not attain any VHG level at all, that means they were in level 0. 65 students (61.91%) of the students attained Van Hiele’s level 1, 17 (16.19%) reached level 2, and only 1 (0.95%) reached level 3. An independent t-test yielded no statistically significant difference between public and private school students in their geometric thinking levels t(103) = 0.926, p > 0.05. The findings indicated that most of the Ghanaian JHS graduates do not attain satisfactory levels of VHGT. Recommendations are made for improving the teaching of geometry.

Analysis of the Relationship between Quadrilaterals Achievement Levels and Van Hiele Geometric Thinking Levels of the Seventh Grade Students

In this study, it was aimed to examine the relation between seventh-grade students' quadrilaterals achievement levels and Van Hiele geometric thinking levels. Survey method was used. The sample of the study was 160 students from the three different districts of Kayseri, as Melikgazi, İncesu, and Tomarza. Van Hiele geometric thinking test and quadrilaterals achievement test, which was developed by the first researcher, were used to collect the data. Descriptive statistics such as mean, frequency, and standard deviation and percentage tables Pearson correlation analysis which was applied to analyze the relationship between the quadrilaterals achievement test and Van Hiele geometry thinking test scores of the seventh-grade students and independent samples t-test was used to for analysis. The results of the study indicated that Van Hiele geometric thinking levels of the seventh school students were lower than expected levels. A high level of correlation was found between quadrilaterals achievement levels and their Van Hiele geometric thinking levels of the seventh-grade students. As a result of the study, quadrilaterals achievement test and Van Hiele geometric thinking test were measuring the students’ geometric abilities in the same direction.

Analysis on geometry skills of junior high school students on the concept congruence based on Van Hiele’s geometric thinking level

Analysis of geometry skills using Van Hiele's geometric thinking level is an attempt to overcome students' difficulties in studying geometry especially the topic of similarity. The purpose of this study is to describe the geometry skills of junior high school students on the concept of similarity based on the level of thinking geometry of Van Hiele. The research method is qualitative descriptive with the subject of research is the students of SMP Negeri 2 Pontianak class IX as many as six people. The data collection instrument is a geometry skill test. The results of the analysis show that students at level one, two, and three from Van Hiele's geometric thinking level have all the skill such as visual, verbal, drawing, logic, and applied but different in characteristics for each level.

The effect of creative problem-solving learning model using geometry transformation book based on Al-Qur’an on students’ van Hiele thinking level and learning outcome

This study aimed at analyzing the differences between Creative Problem Solving and conventional learning model to students’ van Hiele geometric thinking level and learning outcome. This study used quasi-experimental design, and this paper focused on the implementation phase of design research. Research subjects were determined by random sampling technique, i.e., an experimental class of 12 students and a control class of 11 students. The Geometry Transformation book was developed based on Al-Quran and includes a discussion on the relationship between geometry concepts and Al-Qur’an. The results of this study showed that the level of geometric thinking ability of 33.33% of the students in the experiment class is at level 4, while only 9.09% of the control class is at the same level. The ANAKOVA test showed that there was a significant difference (P = 0.041 <α = 0.0050) in cognitive learning result between the experimental class (63.08) and the control class (59.27).

EXPLORING IN-SERVICE TEACHERS’ DEFINITION MAKING OF CERTAIN CLASSES OF GEOMETRICAL SHAPES WITHIN A VAN HIELE FRAMEWORK

Ponte Academic JournalJul 2017, Volume 73, Issue 7 EXPLORING IN-SERVICE TEACHERS’ DEFINITION MAKING OF CERTAIN CLASSES OF GEOMETRICAL SHAPES WITHIN A VAN HIELE FRAMEWORK Author(s): Deonarain BrijlallJ. Ponte - Jul 2017 - Volume 73 - Issue 7 doi: 10.21506/j.ponte.2017.7.54 Abstract:The purpose of this paper is to report on classroom-tested geometry activities based on the van Hiele geometric thinking levels in a study which investigated fourth-year students� understanding in definition making of polygons, polyhedra, prisms, pyramids and cylinders. Research was carried out at a South African university. These concepts were taught to preservice teachers (n=85) wishing to specialise in the teaching of mathematics in the GET school curriculum (primary school). Activity sheets based on an examples and non-examples approach was designed to foster collaborative learning. A collaborative approach to learning involved a group of students who participated in the project. This paper, specifically, reports on the investigation of preservice teachers� written and verbal responses based on a learning theory within the context of the van Hiele levels and makes a contribution to an understanding of how these students constructed these concepts in a collaborative way. Download full text:Check if you have access through your login credentials or your institution Username Password

The Effect of Designed Geometry Teaching Lesson to the Candidate Teachers’ Van Hiele Geometric Thinking Level

The aim of this study is to find out how designed Geometry Teaching Lesson affects candidate teachers’ Van Hiele Geometric Thinking Levels. For that purpose, 14 weeks long study was performed with 44 candidate teachers who were university students in Turkey. Van Hiele Geometric Thinking Test was applied to candidate teachers before and after Geometry Teaching Lesson. Percentage, frequency and t-test were used for analyzing the data. When the data was investigated, it is seen that before Geometry Teaching Lesson, candidate teachers’ geometric thinking levels and t- test points were really low, after lesson both their levels and t-test points made a considerable amount of progress. In this context, it can be said that designed geometry teaching lesson has an affect on upgrading candidate teachers’ geometric thinking levels.

Development of Pre-Service Elementary Mathematics Teachers' Geometric Thinking Levels Through an Undergraduate Geometry Course

In this study, it is investigated that development of pre-service elementary mathematics teachers' geometric thinking levels through an undergraduate course. Elementary mathematics teachers' geometric thinking levels are important for people whose particular interest area is preparing mathematics teachers. Participants of this study are 26 pre-service elementary mathematics teachers who attended an undergraduate geometry course. Geometric thinking levels of participants probed by framework of van Hiele geometric thinking levels. Pre-test was administered before starting the course. An undergraduate geometry course in which contains definitions, proofs and examples of fundamental geometric concepts. After this course, a post-test implemented to assess development of participants' geometric thinking levels. The results of this study reveal the need of assessment about development pre-service elementary mathematics teachers through their geometric thinking levels. Also according to findings it is suggested that mathematics teacher educators should revise their geometry courses to encourage growth in their students' geometric thinking levels.

The effect of constructivist learning environment on the academic achievement and van Hiele Geometry Thinking Level of elementary school teaching department students in basic mathematics course

This study was done to find out the effect of the geometry teaching based on constructivist approach on geometric achievement and Van Hiele geometric thinking levels of elementary school teaching department students. The research was designed according to quasiexperimental research design with a pre-test and post-test control group. The population of the study consisted of students at Çukurova University, Faculty of Education; the sample of the study consisted of 70 first grade students at the elementary school teaching department of the same faculty. "Geometry Achievement Test", "Van Hiele Geometry Thinking Test" and "Portfolio" were used as data collection tools. The data were analyzed through descriptive statistics and independent groups' t test. It was concluded that there was not any statistical difference between the academic achievements of experimental group and control group; however, there was a significant difference in favour of the experimental group in terms of Van Hiele geometry thinking levels.