Geometry Thinking Research Articles

Spatial Thinking and Movements in Geometry: GeoGebra with a focus on building animated scenarios

Animated Scenarios are constructions created in GeoGebra with mathematical elements and movement, constituting an animated scene. Movement is fundamental to the construction of Animated Sceneries, it is also essential to spatial thinking and spatial abilities. This theoretical essay aims to discuss the potential of building Animated Scenarios in GeoGebra in/for the recognition of flat and spatial geometric objects, articulated with the movements associated with spatial thinking. For this, the House Animated Scenario are considered. Thus, we identified that movements performed during this construction allow rotating and modifying the shape of objects and that these movements are related to spatial abilities. Furthermore, the use of these movements in construction contributes to the recognition of important characteristics that distinguish flat and spatial objects.

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.

Development of Definitory and Classificatory Thinking in Geometry through Storytelling and GBL Activities

Little is discussed regarding the meaning of “definition” in primary school, where children often memorize definitions. In geometry, students frequently confuse “definition” with the “description” of a geometric object. The aim of this study is to verify whether a new hybrid methodology between storytelling and game-based learning called Geometrikoland exercises skills that fall within what we understand as “definitory thinking”, which the set of competencies and meta-competencies is associated with acquiring a true mastery of definitions in geometry. This goal can be achieved because the dynamics of Geometrikoland alter the approach to definitions. The methodology applied is a hybrid of storytelling and adventure game-based learning applied to a “engine” of quadrilateral theory. The experiment took place in a fifth-grade class in an Italian school. The analysis of some data based on the accuracy of geometry actions during workshops and qualitative analysis based on the analysis of oral arguments produced during the labs lead to the conclusion that, on average, children have gained a greater awareness of what it means to define a geometric object and a better understanding of the relationships between various subsets of the set of quadrilaterals, previously seen as separate sets. Further confirmation has been provided by comparing the results of two mini-tests (a placement test and an exit test), which are useful for assessing the skills associated with the criterion of arbitrariness, the criterion of uniqueness, and classificatory thinking.

Cross-cultural insights on computational thinking in geometry: Indonesian and Japanese students’ perspectives

Cross-cultural insights on computational thinking in geometry: Indonesian and Japanese students’ perspectives

Students’ Inconsistency when Solving a Geometry Problem in Three-Dimensional Context

There is an issue regarding students' consistency in completing geometry assignments, as indicated by several research findings and assessments. Diagnosing how students integrate concepts in the conceptual design and understanding the reasons behind their inconsistency in completing assignments are the main focuses of this case study. This research was conducted with 58 high school students in Tanjungpandan, Indonesia. The data were obtained from students' answers to problems of the three initial levels of geometry thinking and retrospective reports about their answers. The data were analyzed based on three phases: the concept-eliciting and integrating phase, the relationship-eliciting phase, and the relationship-integrating phase. The study revealed that students' performance in geometry analysis aligned with the epistemological concept issue. Visual objects garnered the most attention from students, leading to their analysis techniques being primarily object-oriented. Some stages of property analysis were skipped, causing students to make claims about objects of thought when they should have been establishing relationships between properties to classify shapes through rigorous geometry analysis. Numerical computation remains an essential aspect of geometry analysis. The conceptual design has not yet reached the abstraction stage, resulting in experiments to solve problems not always yielding the correct solutions. In education, this highlights the need for a deep understanding of concept epistemology, efficient concept integration, and the cultivation of abstract thinking skills.

The Effectiveness of Using Augmented Reality on the Geometry Thinking Ability of Junior High School Students

This study aimed to test the effectiveness of using augmented reality applications in learning geometry in junior high school students. The method used in this study is the quasi-experiment method. In this study, researchers used learning with augmented reality to find its effect on student learning outcomes in grade 8 junior high school, which has an average age of 13 years. The research design used in this study was a quasi-experimental nonequivalent control group design. This study, 2 sample classes were taken: an experimental class (learning with augmented reality) and a control class (learning without augmented reality). The experimental and control classes have the same characteristics; each has 20 male and 20 female students. The instrument used in this research is a geometric thinking ability test. This study uses a test instrument in the form of essay questions. The instrument was given twice, namely during the pretest and post-test. There are ten essay questions made. After obtaining the data from the pretest and post-test results, the normalized gain score formula (N-Gain) was used to know the increase in geometric thinking skills. The N-Gain result of the experimental class is 78% or 0.78, which is in the high category. Whereas in the control class, it was 50% or 0.58, this result is in the moderate category. The N-gain results show that there is a difference between the experimental class and the control class. In this case, the effectiveness of using augmented reality for learning geometry in junior high school students is higher than those who did not receive augmented reality treatment. From the N-gain value, it proves that learning using augmented reality learning media is effective in increasing the ability to think Geometry. Then the results of observations made during learning activities using augmented reality show that students look active and make students more enthusiastic when learning Geometry. The results of the responses showed that 39 students had become more proactive in learning Geometry by using augmented reality applications.

Ways of thinking senior high school student to solve geometri van hiele problem use reversible thinking ability

Background: Reversible thinking is a cognitive strategy that involves tracing the path from an end result back to the starting point. It is particularly useful in problem-solving.Aim: This study aims to describe the thought process of high school students in finding solutions to van hiele geometry problems using reversible thinking ability.Method: A case study approach was employed. The participants were two high school students, and the research tools included written tests and interviews. These instruments were used to delve into the students' written responses.Result: The findings revealed two key aspects: firstly, the students' van Hiele geometry thinking was predominantly at the deduction stage, evidenced by their ability to model geometric shapes based on their characteristics. Secondly, their reversible thinking in geometry was demonstrated through the simplification of fractional operations to obtain whole parts.Conclusion: The study highlights the efficacy of reversible thinking in solving geometric problems and provides insights into the cognitive processes of high school students. The ability to reverse engineer solutions from a known outcome back to the starting conditions is a valuable skill in mathematical problem-solving.

An Analysis of the Transformation Geometry of the Primary School Mathematics Curriculum According to Levels

In this study, it is aimed to examine the Primary Mathematics Curriculum (1-8th grade) according to the transformation geometry levels. In this context, the transformation geometry in primary and secondary school levels or the acquisitions related to this subject were determined. Then, the acquisitions were examined by considering the transformation geometry thinking levels defined by Soon. It has been researched that the achievements in the curriculum are related to which level and whether this level provides the qualifications. As a method, document analysis was carried out. In the research, it was determined that some gains were given in a way that was not very suitable for the hierarchical structure of the Transformation Geometry Levels. The program is examined, it is seen that the most striking shortcomings are that there is no gain at any level regarding the rotational transformation. The fact that there is no rotational transformation outcome in the mathematics curriculum at any level can be a challenging situation for the student in future learning.

Epistemological Obstacle in 3D Geometry Thinking: Representation, Spatial Structuring, and Measurement

Epistemological Obstacle in 3D Geometry Thinking: Representation, Spatial Structuring, and Measurement

Elements of Algorithmic Thinking in the Teaching of School Geometry through the Application of Geometric Problems

Algorithmic thinking and the creation of algorithms have traditionally been associated with mathematics. It is based on the general perception of an algorithm as a logically unambiguous and precise prescription for performing a certain set of operations, through which we reach a result in real time in a finite number of steps. There are well-known examples from history, such as the division algorithm used by ancient Babylonian mathematicians, Eratosthenes algorithm for finding prime numbers, Euclid’s algorithm for finding the greatest common divisor of two numbers, and cryptographic algorithm for coding and breaking, invented by Arabic mathematicians in the 9th century. Although the usage of algorithms and the development of algorithmic thinking currently fall within the domain of computer science, algorithms still play a role in mathematics and its teaching today. Contemporary mathematics, and especially its teaching in schools of all grades, prefers specific algorithms in arithmetic, algebra, and calculus. For example, operations with numbers, modifications of algebraic expressions, and derivation of functions. Teaching geometry in schools involves solving a variety of problems, many of which are presented as word problems. Algorithmization of school geometric tasks is therefore hardly visible and possible at first glance. However, there are ways to solve examples of a certain kind and to establish a characteristic and common algorithmic procedure for them. Algorithmic thinking in geometry and the application of algorithms in the teaching of thematic parts of school geometry are specific issue that we deal with in this study. We will focus on a detailed analysis of the possibilities of developing algorithmic thinking in school geometry and the algorithmization of geometric tasks.

Kinds of Mathematical Thinking Addressed in Geometry Research in Schools: A Systematic Review

Geometry is one of the content of mathematics which in many studies is associated with students' thinking abilities, such as critical thinking and reasoning abilities or others..This study aims to conduct a systematic review of the geometry research in school for identifying the types of mathematical thinking and their interconnections. We searched the Scopus database for articles published from 2003 to 2023 using relevant keywords. We applied the PRISMA method to select and evaluate the studies or articles based on the empirical data. We retrieved and evaluated data from the studies on the various styles of mathematical thinking evolved. Out of 166 titles that were initially obtained, only 10 titles passed the five stages of the systematic review protocol process. We identified 10 types of mathematical thinking that were discussed in the context of learning geometry at school: Creative Mathematical Reasoning (CMR), Computational thinking, Geometric reasoning, Geometric thinking van hiele theory, Geometric thinking (3D geometric thinking with representations), 3D geometry thinking, Visuo spatial reasoning, Geometry Spatial Reasoning, mathematical creative reasoning (MCR), and Inductive reasoning. We also found some connections of literature between these types of mathematical thinking, such as CMR and MCR, Geometric reasoning and Geometric thinking, and Visuo spatial reasoning and Geometry Spatial Reasoning. This systematic review provides an overview of the current state of research on geometry and reasoning in school mathematics and reveals some gaps and directions for future study. It also has implications for teachers who want to enhance their students’ mathematical thinking skills in geometry by exposing them to different types of mathematical thinking and their connections.

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.

A Bibliometric Analysis of Geometry Education Research Based on Web of Science Core Collection Database

Geometry has an important place in mathematics education because it forms the basis of mathematical thinking and allows us to see the emergence of logical theory. As in all fields, academic journals, which are among the official communication languages of science, play an important role in the construction, dissemination and use of scientific knowledge in the field of geometry teaching. With reference to this fact, the aim of the study was to examine articles published in the field of geometry teaching and indexed in SSCI (1975-2020) and ESCI (2015-2020) in the Web of Science Core Collection database by bibliometric analysis method. 109 articles related to geometry teaching (72 within the scope of SSCI and 37 within the scope of ESCI) were reached for the given periods. According to the findings of the research, while there has been a recent interest in geometry education within the scope of SSCI and ESCI, the number of articles still published is limited. Therefore, in mathematics teaching, geometry teaching lags behind areas such as arithmetic and algebra. Especially in recent years, it is noted that the keyword “Van Hiele Levels” and the keywords of innovations that technology brings to geometry education such as “Dynamic Geometry”, “Virtual Reality”, “Geogebra” and “Geometry Thinking” are frequently used in articles in the field of geometry teaching. It is observed that, while quantitative research methods are widely preferred in studies within the scope of SSCI in the field of geometry teaching, qualitative research methods are preferred within the scope of ESCI.

Analysis of Student's Geometry Thinking Ability Based on Van Hiele's Theory

<p>The purpose of this study was to analyze students' geometric thinking skills in solving geometric problems based on Van Hiele's thinking stages. This research is a qualitative research. The subjects of this study were students of class XII MIPA 2 SMA Negeri Tomo, totaling 29 students. With purposive sampling obtained 6 research subjects representing the stages of thinking Van Hiele, data collection methods with test questions and interviews. Analysis of research data is data collection, data reduction, data presentation, and drawing conclusions. The results of the study are: no student can reach the rigor stage</p>

The Elements of Computational Thinking in Learning Geometry by Using Augmented Reality Application

Augmented Reality (AR) technology has now become a growing trend within the education field. It has the capability to combine both digital and reality world that subsequently leads to the emergence of new possibilities in im-proving the quality of teaching and learning activities. The objective of this research is mainly to analyse the Computational thinking elements in solving Geometry topic after the intervention of AR application. Qualitative data analysis was employed as the research methodology of this study that in-volved interview protocol with 10 pupils enrolled in Form 1 Mathematics class at one of the selected schools in Johor Bahru, Malaysia. Content analy-sis was then administered using the ATLAS.Ti Version 8 software to identify the codes, themes, and meaning conveyed by the pupils’ answers in the Computational thinking test. Based on the interview and Computational thinking assessment show the pupils’ ability to solve Geometrical problems using Computational thinking elements. The researcher found that Computa-tional thinking elements do exist in problem solving pertaining to the topic of Geometry. However, the order of usage of these Computational thinking el-ements differs among the pupils. This leads to the conclusion that pupils who utilise the AR application with Computational thinking successfully solve Geometrical problems through the help of the Geometrical thinking process that comprises the elements of Abstraction, Generalisation, Decomposition, Algorithmic, and Debugging.

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.

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.

Rooting the concept and skills of engineering sense in Egyptian and Arabic research and studies

Geometric sense is one of the types of mathematical sense in its general concept and there is a difference between researchers in Egypt and the Arab countries about the concept of geometric sense and its main and sub-skills and there is also a confusion among researchers between geometric sense measurement tests and achievement tests in geometry. The aim of the research is to accurately define the concept of geometric sense that eliminates differences between researchers, to refute the geometric skills identified by researchers within Egypt and the Arab countries for geometric sense, which confuses geometric sense, geometric thinking, geometric proof and achievement in geometry, to identify key and sub-skills for geometric sense according to the writings of the American Council of Mathematicians NTCM so that researchers can commit to them in future research.

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

PROFIL BERPIKIR KREATIF SISWA SD DALAM MENYELESAIKAN MASALAH PERSEGI MENGGUNAKAN TANGRAM BERDASARKAN LEVEL BERPIKIR VAN HIELE

Creative thinking capability is a capability to deliver a new idea by varied means in solving problem. This research aims to describe creative thinking capability in solving square and rectangle problem reviewed by van Hiele’s thinking level of 4 th grade students of SDN Kejayan 1 Bondowoso. This research type is descriptive research with qualitative approach. Data collecting method using test and interview. The used test is van Hiele’s geometry thinking test and creative thinking capability test related to square and rectangle. Research output shows that student at pre-visualization phase has less creative and sufficient creative thinking capability. Student at visualization phase, has sufficient creative and less creative thinking capability. Student at analysis level has sufficient creative thinking capability . Keywords: creative thinking; van Hiele’s geometry level; square and rectangle