Connecting Spatial Reasoning Process to Geometric Problem

The field of spatial reasoning has seen a lot of research. The process of spatial reasoning, on the other hand, needs to be investigated further. The goal of this study is to capture an elementary school student's spatial reasoning process when solving geometric problems. The spatial skills used in solving geometric problems were also identified in this study. A geometric test was given to seventeen elementary school students. Three participants were chosen as the study's subjects based on their written responses. According to the findings, the subject's spatial reasoning process always begins with the processing of information in mental visualization. Mental visualization is used to help with orientation and selecting the appropriate visual perspective. The spatial skills of spatial visualization and spatial orientation are critical in spatial reasoning. Furthermore, this research initiated the emphasis on the focus of spatial reasoning in the process.

Implementation of the Heinrich Spatial Visualization Test in a Virtual Environment

A virtual environment was developed for PC and Android to be used with a desktop display and the Gear VR, respectively. The goal with it is to measure and enhance the spatial skills of people, because the latter can be achieved by solving simple geometric problems. Originally, this virtual environment consisted only of three such tests, namely the Mental Rotation Test, Mental Cutting Test and Purdue Spatial Visualization Test. Measurements were done in the past with these tests, but now the Heinrich Spatial Visualization Test is also included in the virtual environment. In this paper, its implementation and future measurement plan are presented.

OVERVIEW OF GEOMETRIC REASONING ABILITY OF SIXTH-GRADE STUDENTS IN SOLVING FLAT PLANE GEOMETRIC PROBLEMS AT THE INTEGRATED ISLAMIC ELEMENTARY SCHOOL AL-MAWADDAH SEMARANG IN INDONESIA

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.

Actualization of gifted schoolchildren’s intentional experience in the process of mastering geometric concepts: from support to activity mechanism

People’s intellectual abilities become a powerful civilization resource. Therefore, intellectually gifted schoolchildren’s development should be the focus of the state educational policy. Russian opinion leaders interpret the phenomenon of giftedness as a systemic quality that describes the child’s psyche as a whole. Such an approach turns into a priority to update and enrich the gifted schoolchildren’s intentional experience during geometry teaching. It assumes the development of a particular subjective state of orientation and selectivity of individual cognitive activity in preferences. This unique state becomes a mental activity mechanism, not just an accessory. The statistical data analysis confirms the hypothesis: the efficiency of actualizing gifted schoolchildren’s intentional experience in the form of their individual dispositions, beliefs, and emotional assessments while solving geometric problems during academic competitions is provided by specifically organized educational activities. It positively correlates with the level of mental activity development during mastering the activity methods with geometric concepts.

Combining Methods of Euclidean, Affine, and Projective Geometries in Solving Geometric Problems

The aim of the paper is to demonstrate how the techniques of one of the geometries indicated in the title can be used for solving problems formulated in the framework of one of the other geometries. In particular, it is shown how problems formulated in the framework of affine or projective geometry can be solved with an appropriate choice of Euclidean scalar product.

Solving the Inverse Problem of Recovering the 3D Surface of a Detail According to its 2D Projections in the Modelling of Electroplating Processes

The article considers the influence of the surface geometry of a detail on the deposition of coating thickness in the simulation of electroplating processes. The methods for obtaining sets of points describing the surface of a detail are analyzed. Solving the inverse problem (recovering the 3D surface of a detail according to its 2D drawings) is the most promising method. The inverse problem solution is decomposed into simpler geometric problems: input data processing; obtaining primitives; obtaining the desired surface of a detail by applying logical operations to primitives. Mathematical statements are formulated and solution algorithms are proposed for solving these problems. The inverse problem solution is implemented through software. The distribution of the nickel coating thickness is shown for a detail, the surface of which is obtained by solving the inverse problem.

Developing creative activity abilities of students in higher educational establishments

The article discusses methods for solving geometric problems with the active use of methods such as analysis and synthesis, analogy and generalization, based on theoretical thinking on the principle of ascent from simple to complex in order to develop students' ability to creative activity. The authors have developed systems of problems, focused on the formation of their ability to "make" independent discoveries both in the process of solving a problem and at the stage of researching the result of the solution. The developed system of problems is aimed at finding a way to solve a more complex problem, after a similar method has been used in relation to another simpler or particular problem. The participants in the experiment are future masters of pedagogical education (profile "Mathematical Education") at Togliatti State University. The article shows that the most effective methods of preparing future masters of mathematics education for creative professional activity can be such methods of scientific knowledge as analogy and generalization. It was revealed that in the process of learning to solve geometric problems included in the developed system, students demonstrate higher indicators of the level of formation of creative activity, as a result of the development of the ability of the future master of pedagogical education (profile "Mathematical Education") to analogy and its application in specific situations, his ability to use the established properties, skills and abilities formed, techniques and methods of action in relation to another object in new conditions and for new purposes, the use of mathematical concepts and theorems in more and more diverse specific problems.

Some vector equality and application to the solution of geometric problems

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