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The purpose of this study is to determine the reasoning ability of sixth-grade students in solving basic geometry problems on a flat plane. The subjects of this study were 6 students from 24 students of the Integrated Islamic Elementary School "Al-Mawaddah", representing the leading public and private elementary schools in the city of Semarang. For research on three intellectual abilities, namely intelligent, moderately intelligent, and less intelligent, two students were obtained for each on the recommendation of the homeroom teacher. The research method used is a mixed method, which is a type of research in which a researcher combines elements of a qualitative and quantitative research approach. The data collection techniques were observation, written test, and interview test. The results showed that the research value exceeded the completeness value (= 70). The validity of the data was carried out by triangulation of different times, and valid data were analyzed to draw conclusions. The following is a profile of students' basic geometric reasoning abilities in solving problems as a form of mathematical ability. The results showed that subjects with high, medium, and low abilities met the indicators of ability and basic geometric reasoning skills, including visual, verbal, drawing, logic, and applied skills.

This study aims to determine students' ability in solving geometric problems through a metacognitive approach to the planning aspect. The approach used is qualitative descriptive type. The subjects of this study consisted of three grade VIII students of SMP Negeri 2 Benjeng Gresik who were included in the medium category. Data collection was carried out by means of instrument testing and interviews. The validity of the instrument in this study was the validity of the items and showed the respective values ​​of 0.74; 0.78; 0.76 which meant that the three items had fulfilled the validity. Whereas for the reliability test the results obtained were 0.76. The results showed that the planning aspects of the students were in the middle category of solving different geometric problems, this was influenced by the abilities of the students and the habitual factors in problem solving activities

It has been suggested that not only domain-specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain-specific factors and of verbal versus visuospatial WM on geometric learning of a new geometrical figure (trapezoid), never presented previously by the teachers participating to the study, after a lecture also involving manipulatives. Results on 105 children in their Year 4 indicated that not only some domain-specific components (geometric declarative knowledge and calculation) but also visuospatial working memory had a significant specific impact on the ability of solving geometric problems requiring to calculate the perimeter and the area of the new figure. On the contrary, verbal WM and geometrical mental imagery did not offer a specific contribution. These findings could have important educational implications, stressing the importance of taking into account the main different aspects supporting the acquisition of geometry.

Automated discovery of geometric theorems has attracted considerable attention from the research community. In this paper, a new method is proposed to discover geometric theorems automatically. This method first generates vector equations based on given geometric relations about a geometric figure and then transforms the vector equations into a system of homogeneous linear equations; after computing the determinants of the coefficient matrices corresponding to the system of equations, the elimination method is applied to obtain a large number of geometric relationships. The test on more than 200 geometric problems shows that the geometric relationships discovered automatically by the proposed method are of obvious geometric meaning.

The article considers the phenomenon of urban geometry and the essence of geometric problems in urban planning. The proposed approach corresponds to the generally accepted understanding of cities through knowledge of the arts, humanities, social sciences and engineering. Geometry expands the understanding of cities and processes in them both in the historical context and in modern realities and conditions. The definiteness of the geometric dimension in the problems of spatial organization and development of urbanized systems is confirmed. Professional consideration and use of geometric indicators and properties is a condition for increasing the validity of architectural and urban planning decisions. The geometry of the functional city was based on ideas and solutions that focused on process control. The geometry of the space of today's city, according to the author, should stimulate its development by analogy with a living organism. Historical analysis expands the idea of the geometry of the city and its spatial implementation. The characteristics of the geometric measurement of different periods allowed us to conclude that the principles of geometry apply to cities of any time and any culture, are associated with the patterns of urban growth. Urban forms change depending on the scale: increasing the scale of the city to hypercomplex urban systems, the organic analogy grows, pure geometric planning is preserved on a local scale. The theoretical provisions of urban geometry, geometric problems and methods of their solution are substantiated. Identified dichotomies are important for understanding, researching and designing the development of urban systems. They are useful for generalizing different worldviews of space, time and urban geometry: the opposition of the concepts of simplicity and complexity; division and integrity; continuous and intermittent; homogeneity and heterogeneity of the system; certainty and uncertainty. New paradigms and thinking of the city as a hypercomplex system of organic complexity are covered. Geometry determines complexity, scale and shape. Views on space and geometry on the scale of human history have been studied. An attempt is made to understand the "reality" of development and spatial organization of cities. Geometry is used to display order and regularity, as well as in solving urban problems of today. The article highlights, structures and reveals the role of geometry and geometric problems in urban systems, their relationship with other dimensions and problems of spatial organization and urban development. In the model of multidimensional urban space "human - functions - conditions - geometry - time", which was substantiated by the author to solve problems of urban planning (spatial organization and development of urban systems) a special role is given to the geometric dimension, which is described in detail in the article. It includes many characteristics and indicators: size, configuration, shape, concentration of elements, as well as properties related to scale, intrasystem connections and location in the environment. The importance of urban geometry is illustrated using the author's model of multidimensional urban space on the example of geometric problems of Lviv, in particular placement, relocation and division. The solution of the communication and transport problem in the city is characterized and substantiated taking into account the requirements of the new geometry.

This article shows the conceptions about the Analytical Geometry held in the textbooks used in Spain during the xix century. These conceptions are extracted from the presentation of the mathematics concepts in these books. Through the content analysis of ten works we have identified four terms to refer to it (Application of Algebra to Geometry, Analytical Geometry, Determinate Analysis and Indeterminate Analysis. And two conceptions: the first one is to consider it as a method for solving geometric problems by means of Algebra, like the method used to solve arithmetic problems, but instead of operating with quantities operating with segments, the second one as a method of solving geometric problems by means of Algebra, using coordinate systems. Este artículo muestra las concepciones acerca de la Geometría Analítica que aparecen en los libros de texto utilizados en España durante el siglo xix y que se extraen de la presentación de los conceptos matemáticos en dichos libros. Mediante el análisis de contenido de diez obras hemos identificado cuatro términos para referirse a ella: Aplicación del Álgebra a la Geometría, Geometría Analítica, Análisis determinada y Análisis indeterminada. Y dos concepciones: la primera de ellas es considerarla como un método de resolución de problemas geométricos por medio del Álgebra, de manera similar a como se utiliza para resolver problemas aritméticos, pero operando con segmentos en vez de operar con cantidades y la segunda, como un método de resolución de problemas geométricos por medio del Álgebra utilizando sistemas de coordenadas.

УДК 517.54 Розглядається відома проблема геометричної теорії функційпро екстремальне розбиття комплексної площини, і в даній проблемі отримано оцінки максимуму добутку внутрішніх радіусів довільних взаємно неперетинних областей відносно довільних точок комплексної площини, одна з яких може бути нескінченно віддаленою.Точні розв'язки цієї проблеми на даний момент відомі тільки для випадків В даній роботі знайдено оцінки, які можуть бути застосовані в різних екстремальних задачах геометричної теоріїфункцій.

La particular obsesión por la formación en el conocimiento matemático puramente aritmético (una deformación particular del sistema español) produce estudiantes con marcadas dificultades en la resolución de problemas geométricos debido, en particular, a su escasa visión espacial. Sin embargo, en el afán de ir más allá en la implementación de estrategias de aprendizaje basado en problemas para la enseñanza de conocimientos relacionados con el ámbito de la geometría, los enfoques para promover el aprendizaje digital se están volviendo cada vez más diversos, difundidos y generalmente bien aceptados. En particular, las estrategias de codiseño de procesos formativos es un campo de investigación que ofrece grandes posibilidades de desarrollo. En esta contribución presentamos los resultados obtenidos al desarrollar un módulo de aprendizaje mixto con actividades codiseñadas para trabajar el desarrollo de competencias ligadas al desarrollo del conocimiento geométrico en estudiantes de maestro. Este estudio se enmarca en un esfuerzo continuado por implementar metodologías de codiseño y aprendizaje mixto, presentando los resultados acumulados tras una experiencia y analizando, en particular, la utilidad de este tipo de estrategias para el estudio de la geometría.

This research was conducted at SMP Negeri 2 Ende in the 2018/2019 school year. The purpose of this study was to describe: the ability to think in solving geometry problems in class VIII students using Bloom's taxonomy in the cognitive domain, the ability to think in solving geometric problems in class VIII students using Bloom's taxonomy in the affective domain, the ability to think in solving geometric problems in class VIII students using Bloom's taxonomy. psychomotor realm. This type of research is a descriptive study using qualitative methods. Data collection techniques using written tests, interviews, observation, and documentation. The subjects in this study were six students who were selected based on 3 groups of ability, namely high, medium, and low. The selection of research subjects was based on written test results. The results showed that based on Bloom's taxonomy, the thinking abilities of class VIII A students of SMP Negeri 2 Ende in solving geometry problems were as follows: in the higher thinking group the ability to think was at the level of analysis. Students in the medium ability group are at the application level and students in the low ability group are at the knowledge level.

Reasoning that is constructed from remembering is imitative reasoning, while the opposite is creative reasoning. This study aims to explore creative mathematical reasoning in solving geometric problems. Mathematical creative reasoning is reasoning that contains elements of novelty, plausibility, and mathematical foundation. This type of research is descriptive qualitative, which is explorative. The research subjects were the first-semester student in the mathematics education study program with 32 students. The results showed that from 32 students, there was only one student identified as having creative mathematical reasoning in solving geometry problems. Creative mathematical reasoning can be identified when the subject is able to reason algorithmically but is aware of problems so they cannot be resolved algorithmically so that they must form new reasoning, which consists of novelty, plausibility, and mathematical foundation. Creative mathematical reasoning arises after students make an algorithmic reasoning process, but find no solution. Novelty is the weakest indicator of creative mathematical reasoning, so it requires scaffolding to bring it up.

The nilpotent Filippov algebra of class two plays an essential role in some geometric problems, and the classification of nilpotent Lie algebras of class two is one of the most important issues in Lie algebras. In this paper, we classify 9-dimensional nilpotent 3-ary algebras of class two over an arbitrary field.

Geometry is a very interesting, applicable and beautiful part of mathematics. However, geometry is often difficult for students to understand and demanding for teachers to teach [1]. Constructing proofs in geometric problems turns out to be particularly difficult, even for high attaining students [2]. Sometimes, students do not even know where to start when trying to solve these [3].

espanolEste articulo presenta una contribucion a la historia de la ensenanza del algebra, el estudio del metodo cartesiano de resolucion de problemas geometricos en las diferentes ediciones del libro Les Elemens de Geometrie (Lamy, 1685). Este libro de texto circulo en Francia durante casi un siglo, se uso en los colegios de la congregacion de los oratorianos y establecio un modelo de ensenanza de la geometria que desarrollo el analisis propuesto en la Geometrie (Descartes, 1637). Al analizar la seccion sobre el metodo en las ediciones del libro desde 1685 hasta 1756 se evidencio que la ensenanza se focalizo en desarrollar una tecnica por medio de reglas para usar el analisis. En cada edicion la importancia de los diagramas en la aplicacion del metodo fue disminuyendo y la construccion de la solucion de ecuaciones de primer y segundo grado fue perdiendo importancia. Como cartesiano Lamy recurrio al principio de simplicidad de esta filosofia y del metodo, por lo tanto, uso relaciones entre lineas descritas por medio de la proporcionalidad y la semejanza de triangulos como medio para organizar sus justificaciones. EnglishThis article presents a contribution to the history of the teaching of algebra, the study of the Cartesian method of solving geometric problems in the different editions of the book Les Elemens de Geometrie (Lamy, 1685). This textbook circulated in France for almost a century, was used in colleges of the congregation of the Oratorians and established a teaching model of geometry that developed the analysis proposed in the Geometrie (Descartes, 1637). When analyzing the section on the method in the editions of the book from 1685 to 1756 it was evident that the teaching focused on developing a technique by means of rules to use the analysis. In each edition the importance of the diagrams in the application of the method was decreasing and the construction of the solution of equations of first and second degree was losing importance. As a Cartesian, Lamy resorted to the simplicity principle of this philosophy and method, therefore, he used relationships between lines described by means of proportionality and the similarity of triangles as a means to organize their justifications.

This study aims to describe the mathematical representation of students solving geometric problems based on sex differences. Both subjects have equivalent mathematical abilities based on the results of the math ability test. The results showed that the subject used mathematical representation in expressing his idea to solve geometry problems by using Polya's problem solving steps: (a) understanding the problem (b) devising the plan (c) carrying out the plan, and (d) looking back. The mathematical representations of female subjects in solving geometric problems are: understanding information and what is asked verbally and symbolically, carrying the plans visually in the form of geometric formulas and mathematics, carrying out planning by drawing, and manipulating mathematical models, at the stage of looking back the subject performed symbolic recalculation. While mathematical representations of male subjects in express their ideas to solve geometric problems by: understanding information and what is asked verbally, devising the plans in visual form in the form of images and then making mathematical formulas, carrying out the plans by manipulating mathematical models that has been made and looking back by doing recalculation and writing conclusions.

“Technology of leading questions” as a teaching method is considered in the article. Substantial features of learning technology are disclosed. Pedagogical approaches to learning technology are considered. The components of learning technology as elements of the content structure are considered. The concepts: “leading question” and “technology leading questions” are defined. An example of the application of “technology leading questions” is proposed. The relevance of learning technology for the formation of skills to solve geometric problems on the proof is explained.

Solving geometric problems of special importance is the transformation of a plane called inversion. When solving geometric problems, the transformation of the plane called inversion is of special importance. An inversion is a mapping of a plane that a set of directions and a circle maps to the same set, and in doing so it can map a line either to a line or to a circle, and it can also map a circle to either a line or a circle.

Integrated teaching is a modern, learner-centered trend. Today, Vietnam is strongly innovating from teaching academic knowledge to integrated teaching. Integrated teaching helps learners to develop their competencies. This method makes students to be active and creative. Students have more motivation in learning. Integrated teaching means helps us to find the relationship between these knowledge, methods and other ones. The above things are illustrated by teaching geometric extremes. This is a practical problem in Hau Giang, Vietnam. Teacher gives questions and students answer them. These questions are pedagogic. In addition, the article gives some results of empirical investigation confirming the superiority of integrated teaching compared to traditional teaching. The article proposes a number of research results on the concept of integration and features of integration. Some features of integration are subjective, association, useful combination, expression of introvert and extrovert orientation, creating a unified block, in a certain context. https://doi.org/10.26803/ijlter.18.8.11

In recent years, construction of databases from digitized documents of Japanese mathematics (wasan) has been progressing. We can search documents individually by keywords such as titles and authors in these databases. On the other hand, it is unable to cross-search them from contents such as problems in the documents. To realize this cross-searching based on problems, the authors propose a system to tag images of geometric problems in wasan automatically. In addition, the authors consider generating vector based on tags to evaluate the similarity of geometric problems., "The study of the history of mathematics 2018". September 18-21, 2018. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

We study the symmetry of solutions to a class of Monge-Ampere type equations from a few geometric problems. We use a new transform to analyze the asymptotic behavior of the solutions near the infinity. By this and a moving plane method, we prove the radially symmetry of the solutions.

This is qualitative research with a descriptive-explorative approach that aims to determine students' mathematical representation skills in solving Geometry problems. The population is all students in the mathematics education department who study Basic Geometry. The main subject was chosen by stratified technique and purposive sampling. The instruments are placement tests, diagnostic tests, and guided interviews. Data collection uses a triangulation method that aims to examine legitimate data. The results showed that 1) subjects with high skills always present visual representations and mathematical expressions, 2) subjects with intermediate skills present visual representations and mathematical expressions, and verbal but less representative representations, 3) subjects with low skills don’t present visual representations and mathematical expressions and verbal representations of problem-solving steps; and 4) there are several factors that influence the ability of mathematical representation to solve geometric problems, among others, subjects are less able to present problems in geometric patterns, because the subject does not understand the problem.

Computational complexity and exact polynomial algorithms are reported for the problem of stabbing a set of straight line segments with a least cardinality set of disks of fixed radii r > 0, where the set of segments forms a straight line drawing G = (V,E) of a plane graph without edge crossings. Similar geometric problems arise in network security applications (Agarwal et al., 2013). We establish the strong NP-hardness of the problem for edge sets of Delaunay triangulations, Gabriel graphs, and other subgraphs (which are often used in network design) for r ∈ [dmin, ηdmax] and some constant η, where dmax and dmin are the Euclidean lengths of the longest and shortest graph edges, respectively.

This article discusses three basic relationships and shows them when applied to solving geometric problems. However, teaching students how to use vectors to solve problems in a limited curriculum is difficult. To overcome these difficulties, you need a well-thought-out exercise system. The proposed article describes the experience in solving this issue

We give a complete solution to the extremal topological combinatorial problem of finding the minimum number of tiles needed to construct a polyomino with $h$ holes. We denote this number by $g(h)$ and we analyze structural properties of polyominoes with $h$ holes and $g(h)$ tiles, characterizing their efficiency by a topological isoperimetric inequality that relates minimum perimeter, the area of the holes, and the structure of the dual graph of a polyomino. For $h\leqslant 8$ the values of $g(h)$ were originally computed by Tomas Olivera e Silva in 2015, and for the sequence $h_l=(2^{2l}-1)/3$ by Kahle and Róldan-Roa in 2019, who also showed that asymptotically $g(h) \approx 2h$. Here we also prove that the sequence of polyominoes constructed by Kahle and Róldan-Roa that have $h_l=(2^{2l}-1)/3$ holes and $g(h_l)$ tiles, are in fact unique up to isometry with respect to attaining these extremal topological properties; that is, having the minimal number of tiles for $h_l$ holes.

En este artículo se presentan los resultados académicos obtenidos a raíz de la implantación de una experiencia docente en la utilización de herramientas informáticas de diseño asistido por ordenador para la enseñanza de la Geometría Descriptiva en el Doble Grado en Edificación y Dirección y Administración de Empresas de la Universidad Politécnica de Madrid. Se expone la nueva metodología utilizada, el programa académico desarrollado, incluidas algunas de las construcciones más interesantes en la resolución de problemas geométricos estudiados, y los resultados académicos obtenidos. El seguimiento se realizó a través de una encuesta anónima dirigida a todos los alumnos matriculados. De acuerdo al análisis de los resultados obtenidos, la utilización de TIC’s ha permitido aumentar la estimulación y el interés de los alumnos hacia la asignatura de geometría descriptiva, mejorando su comprensión espacial y aumentando sus conocimientos. Las calificaciones finales han sido cualitativamente mejores y el número de alumnos aprobados en relación a los del curso anterior, ha crecido cerca de un 10%. Además, la impresión subjetiva del profesorado es que lo aprendido por el alumno dejará un mayor poso que el derivado de otros procedimientos de enseñanza tradicional. Por añadidura a lo anteriormente mencionado, el grado de absentismo cosechado fue inferior al de cursos pasados.AbstractThis article presents the academic results obtained due to the implementation of a teaching experience in the use of computer aided design tools for the teaching of Descriptive Geometry in the Double Degree in Building and Management and Business Administration of the Universidad Politécnica de Madrid. It presents the new methodology used, the academic program developed including some of the most interesting examples in the resolution of geometric problems, and the learning outcomes obtained. The monitoring of the experience was done through an anonymous survey addressed to all students enrolled in the subject. According to the analysis of the results achieved, the use of ICTs has allowed to increase the stimulation and the interest of the students towards the subject, improving their spatial understanding and increasing their knowledge of geometry. The final grades have been qualitatively better and the number of passing students compared to those in the previous year has grown by about 10%. In addition, the teaching staff has the feeling of having achieved a “better learning” than that derived from other methods. On top of that, the rate of absenteeism was lower than in previous courses.

The paper describes an ontology-controlled geometric solver. The solver functions as a part of an integrated problem-solving system with a natural language interface. It is implemented in a prototype version of the system for the “school geometry” subject area. We described the solver interaction with the system linguistic processor, ontology, and the graphic component. We provided examples demonstrating automated solving non-trivial geometric problems formulated in a natural language. We suggested using cognitive structures in the dialogue for an effective linguistic analysis and building up a correct drawing.

In the recent years, increasing attention has been drawn toward adaptive e-learning, which is a learning method that uses educational big data to flexibly change the learning content according to the proficiency of a learner. In this study, we proposed an overview of an adaptive e-learning system that focuses on the solution procedure, which comprises the knowledges and operations used by a learner to solve a problem. Using the example of elementary geometric problems, we develop a prototype of our proposal in which the situations of learning are formalized on the basis of an adaptive e-learning context model, which is represented using a meta-network. This prototype comprises three subsystems. One is an expert system that automatically generates various solution procedures for a given problem. The other two are an inference system that identifies the procedures that a learner is using by calculating their similarity with the procedures generated by an expert system and a classification system of given problems by calculating the similarity of the procedures of each problem; the similarity is calculated using both the Levenshtein distance and Needleman–Wunsch algorithm, respectively. Compared with conventional methods, the proposed system might provide more detailed support for learners.

This paper deals with a didactic experience gained in courses that are part of the first year of studies for the Schools of Architecture and Design at Politecnico di Milano. One of the themes of these courses concerns geometric problems, in order to introduce students to 3D space. The peculiarity of the didactic method used is, first of all, to induce the student to observe the real object by identifying its geometric characteristics (symmetries, proportions, contours, and surfaces enveloping it).

We prove that if the Hausdorff dimension of $E\subset\mathbb{R}^d$, $d\geq 2$ is greater than $\frac{d}{2}+\frac{1}{3}$, the set of gaps of $2$-chains inside $E$, $$\Delta_2(E)=\{(|x-y|, |y-z|): x, y, z\in E \}\subset\mathbb{R}^2$$ has positive Lebesgue measure. It generalizes Wolff-Erdogan's result on distances and improves a result of Bennett, Iosevich and Taylor on finite chains. We also consider the similarity class of $2$-chains, $$S_2(E)=\left\{\frac{t_1}{t_2}:(t_1,t_2)\in\Delta_2(E)\right\}=\left\{\frac{|x-y|}{|y-z|}: x, y, z\in E \right\}\subset\mathbb{R},$$ and show that $|S_2(E)|>0$ whenever $\dim_{\mathcal{H}}(E)>\frac{d}{2}+\frac{1}{7}$., Comment: Compared with the last version, we rewrite the proof in terms of weighted spherical averaging operators. Also we delete the discussion about product of distances since it is not very close to the main topic of this paper

We consider two apparently unrelated classes of combinatorial and geometric optimization problems. First, we give compact extended formulations, i.e., polynomial-size linear programming formulations with integer optima, for optimum path problems with turn restrictions satisfying a nested compatibility condition in acyclic digraphs. We then apply these results to optimum convex polygon problems in the plane, by interpreting certain dynamic programming algorithms as sequences of optimum turn-restricted path problems with nested compatibility in acyclic digraphs. As a result, we derive compact extended formulations for these geometric problems as well.

Simulation of manned and unmanned vehicles has become more and more important in the last decades. High-performance real-time DIL (Driver-In-The-Loop) and HIL (Hardware-In-The-Loop) simulators require efficient, accurate, and fast algorithms to properly model how a vehicle moves in a virtual environment. Most of the time, the virtual world is made from a multitude of basic geometric entities that can collide and modify accordingly. The ability to quickly resolve basic geometric problems is one of the most important roles in this kind of simulation. Acme library is built to efficiently perform simple operations on a large number of basic geometric entities. In particular, the library is designed to address specific hard real-time tire–road contact geometry analysis. In this paper, we discuss the details about the Acme library implementation, data types, features, and an example application to demonstrate the capabilities of this newly born software.

Dynamic geometry environments can support learning of geometry through mediating learners’ activity. To understand how dynamic geometry environments mediate the activity of mathematics teachers, we used Rabardel’s categories of tool mediations in an instrument-mediated activity. We analyzed the discursive and inscriptive interactions of 4 mathematics teachers who worked for 15 weeks as a team to construct geometric figures and solve open-ended geometric problems in a collaborative, dynamic geometry environment. Teachers’ specialized content knowledge was evident when they used the environment epistemically. In addition to Rabardel’s epistemic and pragmatic mediations, we found and coined a third mediation—pedagogic mediation—by which teachers use the environment to help other team members understand particular geometric objects and relations among them. Understanding how teachers use technological tools can inform the design of professional development programs that engage them with such tools to extend their specialized content knowledge.

The three books reviewed in this column are about central ideas in algorithms, complexity, and geometry. The third one brings together topics from the first two by applying techniques of both property testing (the subject of the first book) and parameterized complexity (including its more focused incarnation studied in the second book, kernelization) to geometric problems.

In recent years, construction of databases from digitized documents of Japanese mathematics (wasan) has been progressing. We can search documents individually by keywords such as titles and authors in these databases. On the other hand, it is unable to cross-search them from contents such as problems in the documents. To realize this cross-searching based on problems, the authors propose a system to tag images of geometric problems in wasan automatically. In addition, the authors consider generating vector based on tags to evaluate the similarity of geometric problems.

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.