ESTETIKA MATEMATIS MOTIF SONGKET PADA ANYAMAN MENDONG TASIKMALAYA

Mathematics is an enigmatic and captivating idea. Mathematics can also be defined in the context of patterns. This is because mathematics contains patterns, structures, and depictions of an object that grows and is rooted in real life. The structure or pattern that is arranged systematically will produce work, objects, and even an agreement. Life mathematics and mathematics in school learning can be combined with aesthetic studies to achieve contextual learning. This study uses qualitative research with an ethnographic approach. The purpose of this study was to reveal the aesthetic value and mathematical concepts of the mendong woven pattern with the songket motif. The location of this research is Babakan Cikawung Village, Margabakti Village, Cibeureum Awipari District, Tasikmalaya Regency. This study involved 3 subjects. Data collection techniques were carried out through unstructured interviews, observation, documentation, and literature review. Unstructured interviews were used to ask about the craft of mendong and the process of making mending weave with songket motifs. Observations or observations are made to find mathematical concepts and mathematical aesthetic values by studying the aesthetics of Thomas Aquinas' theory. The results of the research are mathematical aesthetics by examining the theory of Thomas Aquinas. Mathematical concepts such as repeating patterns 1-2-3-4 and 4-3-2-1, geometric concepts such as parallel lines, reflection, congruence, and rhombus flat shapes.

Inflection Points in Cubic Structures

In this paper, we introduce and study new geometric concepts in a general cubic structure. We define the concept of the inflection point in a general cubic structure and investigate relationships between inflection points and associated and corresponding points in a general cubic structure.

Identifying Concepts Created for Geometric Objects: Mind Map

The purpose of this research is to determine the knowledge, perceptions and misconceptions of preservice primary school teachers about geometric objects through mind maps. For this purpose, the research was designed with a case study, one of the qualitative research methods. The study group of the research consists of 52 pre-service primary school teachers studying at a state university in the Aegean Region of Turkey. After giving information about mind maps to pre-service primary school teachers, they were asked to create mind maps about the concept of “Geometric Objects”. The created mind maps were subjected to content analysis and codes and categories were created. The mind maps of pre-service primary school teachers were analysed one by one, starting from the centre towards the outer branches and separated as related and unrelated concepts. As a result of the research, it was revealed that most of the pre-service primary school teachers who participated in the study used the concepts of geometric objects and geometric shapes interchangeably. In addition, as a result of the analysis of the first branches of mind maps, it was determined that unrelated concepts were more than related concepts. Very few of them have reached the fourth branch in the mind maps created by pre-service primary school teachers, and they had difficulty explaining the concept. In line with the results obtained from the research, the concepts related to geometric objects should be taught in the undergraduate education of pre-service primary school teachers to provide meaningful learning about geometric concepts in pre-service primary school teachers.

Global Dimensional Mathematics

Here we build the fundamentals of global dimensional mathematics in order to build the new basis of the new theoretical scientific paradigm. Research on the foundations of mathematics covering the definition of fundamental mathematical concepts such as point, line, direction, dimension, addition, multiplication, division, zeros, infinities, limits, factorization, integers and prime numbers, were carried out and further still the resolution of the Goldbach conjecture is now effective. New original fundamental mathematical notions are established building the core of global dimensional mathematics based on the decomposition of integers into an addition of prime numbers terms and on fundamental geometric concepts such as the concept dimension based on the notion of direction and point, as well as research on set theory and work on the notion of limits and infinity. The termization as a decomposition of integers into an addition of prime number terms by a python program, breaks the unique factorization theorem, the fundamental theorem of arithmetic while the geometric notions developed break Euclidean geometry leading to a new mathematical framework, geometry, topology and metrics leading to a total change of theoretical scientific paradigm. Global dimensional mathematics forms the basis for the construction of the new scientific paradigm of the 21st century and beyond, opening up a still unknown perspective on the world of science in general.

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.

Problem-Based Geometry in Seventh Grade: Examining the Effect of Path-Based Vs. Conventional Instruction on Learning Outcomes

This experimental study examined the impact of learning and teaching ge-ometry in seventh-grade geometry education comparing learning-path and conventional instruction. According to constructivism, a learning path with the use of learning objects should enhance learner autonomy and self-directedness by providing differentiated instruction. We designed a model of path-based geometry learning in a learning management system–based learning environment with the use of dynamic geometry programs and applets, which fosters visualisation and the exploration of geometric concepts through the manipulation of interactive virtual representations. The results show that the experimental group (EG) achieved higher scores on all levels of knowledge and statistically significantly better results in taxonomy level-III tasks (problem-solving knowledge) and overall score than the control group (CG). There was initial equivalence between the EG and CG in prior knowledge. The authors concluded that path-based geometry learning empirically develops knowledge at higher cognitive levels.

A Teoria da Aprendizagem Significativa: uma Abordagem na Educação Matemática

ResumoNeste artigo se questiona: como a Teoria da Aprendizagem Significativa se apresenta em situações de ensino e de aprendizagem? Trata-se de um recorte compreensivo de um estudo mais amplo, de mestrado, do qual destaca-se a o ensino de matemática visado da perspectiva desta teoria. Ela foi realizada com alunos do curso de Licenciatura em Matemática da Universidade Federal de Juiz de Fora. Nela foi desenvolvida uma proposta que além de ser metodologia da pesquisa, constituiu-se como proposta pedagógica para a futura atuação docente dos sujeitos. Foi promovido um diálogo acerca de temas da Educação Matemática e foram propostas atividades classificadas como exploratórias e investigativas a serem desenvolvidas de modo colaborativo. Os diálogos e o desenvolvimento das atividades foram transcritos. Assumindo uma postura fenomenológica, o pesquisador buscou, junto às transcrições, convergências que pudessem, quando articuladas, trazer compreensões sobre o fenômeno interrogado. Nesse movimento, foram constituídas unidades nucleares, das quais destaca-se para este estudo, a unidade: a presença da Teoria da Aprendizagem Significativa no desenvolvimento das atividades e na aprendizagem de conceitos geométricos. Ao descrever uma síntese reflexiva dessa unidade, articulando compreensões trazidas do presente estudo, explicitando a presença da teoria em todo o processo de aprendizagem, desde o planejamento do professor ao desenvolvimento dado pelos alunos às atividades planejadas, entende-se estar expressando uma compreensão do que interroga a pergunta norteadora deste estudo. Palavras-chave: Teoria da Aprendizagem Significativa. Educação Matemática. Atividades Investigativas. ResumoThis article asks: how the Meaningful Learning Theory presents itself in teaching and learning situations? It is a comprehensive cut from a broader study, from master's degree, from which the teaching of mathematics stands out based on this theory. It was carried out with students of the Mathematics course at the Federal University of Juiz de Fora. In it, a proposal was developed that, in addition to the research method, constituted itself as a pedagogical proposal for the future teaching performance of individuals. A dialogue on Mathematics Education themes was promoted and activities, classified as exploratory and investigative, were proposed to be developed in a collaborative way. The dialogues and the development of the activities were transcribed, and assuming a phenomenological stance, the researcher sought, along with the transcriptions, convergences that could, when articulated, bring understandings about the questioned phenomenon. In this movement, nuclear units were formed, of which stands out in this study: the presence of the Meaningful Learning Theory in the development of activities and in the learning of geometric concepts. By describing a reflexive synthesis of this unit, articulating understandings brought by the present study, explaining the presence of theory in the entire learning process, from the teacher's planning to the development given by the students to the planned activities, it is understood to be expressing an understanding of what asks the guiding question of this study. Keywords: Theory of Meaningful Learning. Mathematical Education. Investigative Activities

Content Of Pedagogical-Corrective Work On Interdiscipline Formation Of Geometric Concepts For Students With Limited Disabilities

The scientific-theoretical bases of interdisciplinary formation of geometric concepts for students with intellectual disabilities are analyzed. The content of pedagogical-corrective work on interdisciplinary formation of geometric concepts for students with intellectual disabilities is covered.

Uma Revisão Sistemática Abordando o Tangram, o GeoGebra e as Opções de Isometria do Plano

ResumoEste artigo apresenta os resultados de parte uma pesquisa de mestrado, e tem como objetivo mapear e analisar pesquisas publicadas de 2015 até 2020, realizadas em nível de ensino básico sobre a utilização do Tangram, GeoGebra e opções de isometria do plano no ensino da matemática. A metodologia utilizada foi a revisão sistemática de literatura, e partiu de buscas de artigos e dissertações realizadas nos periódicos da Biblioteca Digital Brasileira de Teses e Dissertações (BDTD), no Banco de Teses e Dissertações da CAPES e no Google Acadêmico. Usamos as duplas de descritores GeoGebra/Tangram, Tangram/Matemática e GeoGebra/Isometrias e localizamos 293 pesquisas. Após a seleção, guiada fielmente pelo protocolo estabelecido na revisão sistemática, consideramos dez estudos como amostra final da revisão. Concluímos que os trabalhos analisados apontam para a importância da variação de metodologias e utilização de recursos como GeoGebra e Tangram para potencializar o ensino de matemática. A pesquisa evidenciou a significativa contribuição do GeoGebra como incentivador do interesse dos alunos pelo estudo das isometrias do plano. Além disso, constatamos a importância do Tangram utilizado conjuntamente com o GeoGebra como facilitador da apropriação dos conceitos geométricos, instigador da curiosidade, propulsor da criatividade e mediador da percepção espacial. Todavia, percebemos a existência de uma lacuna nesse rol de estudos. Não encontramos estudos que utilizassem simultaneamente estes três elementos: GeoGebra, Simetria e Tangram. E é nessa nova perspectiva, a partir dessa lacuna, que estamos organizando esta pesquisa, ou seja, à luz da teoria da atividade, queremos investigar as estratégias matemáticas dos alunos envolvidos nessas construções de isometrias, durante a formação das figuras do Tangram no ambiente do GeoGebra.Palavras-chave: GeoGebra, Ensino básico, Tangram.AbstractThis article presents the results of part of a master’s research and aims to map and analyse research published from 2015 through 2020 at basic education level on the use of Tangram, GeoGebra and options of isometry of the plane in mathematics teaching. The methodology used was the systematic literature review and started from searches for articles and theses carried out in the journals of the Biblioteca Digital Brasileira de Teses e Dissertações/Brazilian Digital Library of Theses and Dissertations (BDTD), CAPES Banco de Teses e Dissertações/Thesis and Dissertations Bank, and Google Acadêmico/ Google Scholar. We used the pairs of descriptors GeoGebra/Tangram, Tangram/Mathematics and GeoGebra/Isometries and found 293 studies. After the selection, guided faithfully by the protocol established in the systematic review, we considered ten studies as the final sample of the review. We concluded that the works analysed point to the importance of varying methodologies and using resources such as GeoGebra and Tangram to enhance mathematics teaching. The research showed the significant contribution of GeoGebra as an incentive for the student's interest in studying the isometries of the plane. In addition, we note the importance of the Tangram used together with GeoGebra as a facilitator of the appropriation of geometric concepts, an instigator of curiosity, a propeller of creativity, and a mediator of spatial perception. However, we perceived a gap in this list of studies. We did not find studies that used these three elements simultaneously: GeoGebra, Simetria, and Tangram. It is from this new perspective, from this gap, that we are organising this research, i.e., in the light of the theory of activity, we want to investigate the mathematical strategies of the students involved in those isometric constructions, during the formation of the Tangram figures in the environment of the GeoGebra.Keywords: GeoGebra, Basic education, Tangram.ResumenEste artículo presenta los resultados de parte de una investigación de maestría y tiene como objetivo mapear y analizar investigaciones publicadas desde 2015 hasta 2020 en nivel de educación básica sobre el uso de Tangram, GeoGebra y opciones de isometría del plano en la enseñanza de las matemáticas. La metodología utilizada fue la revisión sistemática de la literatura y partió de búsquedas de artículos y tesis realizadas en las revistas de la Biblioteca Digital Brasileira de Teses e Dissertações (BDTD), Banco de Teses e Dissertações de CAPES y Google Académico. Utilizamos los pares de descriptores GeoGebra/Tangram, Tangram/Matemáticas y GeoGebra/Isometrías y encontramos 293 estudios. Tras la selección, guiados fielmente por el protocolo establecido en la revisión sistemática, consideramos diez estudios como muestra final de la revisión. Concluimos que los trabajos analizados apuntan a la importancia de variar metodologías y utilizar recursos como GeoGebra y Tangram para potenciar la enseñanza de las matemáticas. La investigación mostró la importante contribución de GeoGebra como incentivo al interés del estudiante por estudiar las isometrías del plano. Además, notamos la importancia del Tangram utilizado junto con GeoGebra como facilitador de la apropiación de conceptos geométricos, instigador de la curiosidad, propulsor de la creatividad y mediador de la percepción espacial. Sin embargo, percibimos una brecha en esta lista de estudios. No encontramos estudios que utilizaran estos tres elementos simultáneamente: GeoGebra, Simetria y Tangram. Es desde esta nueva perspectiva, desde esta brecha, que estamos organizando esta investigación, es decir, a la luz de la teoría de la actividad, queremos investigar las estrategias matemáticas de los estudiantes involucrados en esas construcciones isométricas, durante la formación de las figuras de Tangram en el entorno de GeoGebra.Palabras clave: GeoGebra, Educación básica, Tangram