ABSTRAKSI REFLEKTIF SISWA SEKOLAH MENENGAH PERTAMA PADA MATERI SEGIEMPAT DAN SEGITIGA

The purpose of this study is to determine a person's ability to perform mental activities mechanically in associating new information received with previously owned information (reconstruction) which is a reflective abstraction. The process of reconstructing the concepts of quadrilaterals and triangles by students uses the mental mechanism approach of APOS theory (interiorization, encapsulation, de-encapsulation, coordination). The process can be known by observing students and analyzing the results of student work, starting with determining 1 class to be given a mathematical ability test. 29 students were present when the math ability test was given. The results of the mathematical ability test were analyzed and then found 2 students of different sexes with moderate ability. The first student is male and the second student is female, hereinafter referred to as the research subject, then the research subject is given the task of quadrilateral and triangle. The results showed that female students had done all stages of reflective abstraction in APOS theory. So, that these students were at the level of relational understanding. Meanwhile, male students only did several stages in the reflective abstraction stage on the APOS theory so that these students were included in the level of instrumental understanding.

IDENTIFIKASI KEMAMPUAN PENALARAN SISWA KELAS XI DI MAN 4 BANTUL PADA SUHU DAN KALOR

Reasoning skill is essential for students to have to face the challenges of the 21st century. This study aims to determine the percentage of students' reasoning skills based on deductive hypothesis, inductive hypothesis, and reflective abstraction. This research used a descriptive method involving 26 students of Islamic Senior High School 4 Bantul. The data from tests were analyzed quantitatively, while the data from interviews were analyzed qualitatively as supporting data. The results showed that the indicators of deductive hypothesis: Aspects of explaining a fact, there are 62% of students explained the facts correctly but were incomplete and 38% of students explained the facts incorrectly; Aspects of making conclusions deductively, there are 77% of students made correct conclusions but were incomplete and 23% of students made incorrect conclusions. Based on inductive hypothesis indicators: Aspects of making conclusions inductively, all students can make conclusions, but incorrect in associating equations; Aspects of giving reasons, all students gave incorrect reasons. Based on indicators of reflective abstraction: Aspects of developing concepts, there are 50% of students who can connect concepts in a case correctly and 50% of students incorrectly connect concepts in a case. This showed that students' reasoning skill is still low. AbstrakKemampuan penalaran penting dimiliki oleh siswa untuk menghadapi tantangan abad 21. Penelitian ini bertujuan untuk mengetahui persentase kemampuan penalaran siswa berdasarkan hipotesis deduktif, hipotesis induktif dan abstraksi reflektif. Penelitian ini menggunakan metode deskriptif yang melibatkan 26 siswa MAN 4 Bantul. Data dari tes dianalisis secara kuantitatif, sedangkan data dari wawancara dianalisis secara kualitatif sebagai data pendukung. Hasil penelitian menunjukkan bahwa pada indikator hipotesis deduktif: Aspek menjelaskan fakta, terdapat 62% siswa yang menjelaskan fakta secara tepat namun kurang lengkap dan 38% siswa kurang tepat dalam menjelaskan fakta; Aspek membuat kesimpulan secara deduktif, terdapat 77% siswa membuat kesimpulan dengan tepat namun kurang lengkap dan 23% siswa membuat kesimpulan yang kurang tepat. Berdasarkan indikator hipotesis induktif: Aspek membuat kesimpulan secara induktif, semua siswa dapat membuat kesimpulan, namun tidak tepat dalam mengaitkan persamaan; Aspek memberi alasan, semua siswa memberikan alasan yang kurang tepat. Berdasarkan indikator abstraksi reflektif: Aspek pengembangan konsep, sebanyak 50% siswa mampu menghubungkan konsep dalam suatu kasus secara tepat dan 50% siswa kurang tepat dalam menghubungkan konsep pada suatu kasus. Hal ini menunjukkan kemampuan penalaran siswa masih rendah.

A construção do conhecimento matemático na teoria APOS

ResumoEste artigo é um recorte de uma tese de doutorado em andamento, desenvolvida pela primeira autora e orientada pela segunda, cujo objetivo principal é investigar a concepção, na acepção de Dubinsky, de professores do ensino público paulista sobre o Teorema Fundamental da Aritmética. O objetivo deste artigo é trazer a ideia de como ocorre a construção do conhecimento matemático segundo a teoria APOS de Ed Dubinsky, apoiado nas ideias de Jean Piaget com a Epistemologia Genética. São apresentados o conceito de abstração reflexiva, considerado o mecanismo mental mais importante no desenvolvimento do pensamento, as definições dos elementos mentais Ação, Processo e Objeto e como interagem entre si para a construção do conhecimento matemático. Palavras-chave: Construção do conhecimento matemático; Teoria APOS; abstração reflexiva; ciclo ACE.AbstractThis article is an excerpt from an ongoing doctoral thesis, developed by the first author and guided by the second, whose main objective is to investigate the conception, in Dubinsky's sense, of São Paulo public school teachers about the Fundamental Theorem of Arithmetic. The purpose of this article is to bring the idea as is the construction of mathematical knowledge according to APOS theory of Ed Dubinsky, supported by the Jean Piaget's ideas with the Genetic Epistemology. The concept of reflective abstraction is presented, considered the most important mental mechanism in the development of thought, the definitions of the mental elements Action, Process and Object and how they interact with each other for the construction of mathematical knowledge.Keywords: Construction of mathematical knowledge; APOS theory; reflective abstraction; ACE cycle.

STUDENTS’ REFLECTIVE ABSTRACTION ABILITY ON LINEAR ALGEBRA PROBLEM SOLVING AND RELATIONSHIP WITH PREREQUISITE KNOWLEDGE

This study aims to describe the achievement of the ability of students' reflective abstraction in solving Linear Algebra problems and the relationship with prerequisite knowledge. The important of this research because the characteristic of Linear Algebra requiring reflectif abstraction skill that must be support by the prerequisite knowledge. The reflective abstraction abilities studied in this study are level, i.e.1) recognition,2) representation, 3) structural abstraction, and 4) structural awareness. These stages are adjusted to Polya's problem solving stages, namely: understanding the problem, devising a plan, carrying out the plan, and looking back. This type of research is descriptive-quantitative. The subjects of this study were students of the Mathematics Education Study Program, Faculty of Tarbiyah and Teacher Training of UIN Sunan Gunung Djati Bandung Indonesia. Collecting data through tests and interviews, data were analyzed with percentage and the pearson product-moment correlation.The results showed that the achievement level consisiting of ) recognition,2) representation, 3) structural abstraction, and 4) structural awareness of the students’ reflective abstraction abilities on linear algebra problem solving are very good, this can be seen from the percentage achieved at stages of the recognition,the representation,the structural abstraction, and the structural awareness which is associated with Polya problem solving measures above an average of 73,31% (moderat category); there are relationship between students' reflective abstraction abilities and their prerequisite knowledge; and prerequisite knowledge influences the students’reflective abstraction abilities

Abstraction reflective student in problem solving of Mathematics based cognitive style

The student's reflective abstraction ability in solving problems is necessary because the result of a person's reflective abstraction is a scheme used to understand something, finding solutions or solving problems. Besides, reflective abstractions are essential to higher mathematical, logical thinking as they occur in logical thinking in children. Therefore, to develop a reflective abstraction notion of high-level mathematical thinking, it is necessary to separate what is an essential feature of reflective abstraction, reflect its rules on higher mathematics, recognize and reconstruct it so that a similar theory of knowledge Mathematics and its instructions. While research that will researchers do is to know how the process of reflective abstraction of students in solving problems in terms of cognitive style. This is because the cognitive style is closely related to how to receive and process all information, especially in learning. The various trends in their learning can be identified and then classified whether the child belongs to an independent field cognitive style (thinking tends to have the independence of views) or field dependent.

PROCESSOS DE ABSTRAÇÃO E AS NOÇÕES SOCIAIS DE GUERRA E PAZ: um estudo com jovens estudantes brasileiros

Tomando por referência os resultados dos principais estudos a respeito da construção do conhecimento social realizados no Brasil e no exterior, o artigo apresenta uma pesquisa que investigou a evolução na construção desse tipo de conhecimento e no desenvolvimento cognitivo em participantes brasileiros. Trata-se de um estudo descritivo, de abordagem qualitativa e quantitativa, pautado no método clínico-crítico piagetiano. Foram participantes 30 sujeitos de 15, 18 e 21 anos de escolas da rede pública estadual e de uma Universidade Pública do interior do estado de São Paulo, matriculados em cursos da área de Humanas. A compreensão sobre guerra e paz foi a noção social investigada, cotejada com a prova do mecanismo da abstração reflexionante, avaliado por meio da construção de relações espaciais. Os resultados indicaram um atraso nas respostas dos participantes em relação aos encontrados em pesquisas internacionais, bem como a dificuldade existente na elaboração de um raciocínio menos aparente e mais contextualizado e argumentativo. As correlações entre a construção do conhecimento social e a abstração reflexionante foram positivas, indicando a necessidade de desenvolvimento cognitivo para se atingir níveis mais elaborados de compreensão do mundo social.PROCESSES OF ABSTRACTION AND THE SOCIAL NOTIONS OF WAR AND PEACE: a study with young brazilian studentsABSTRACTTaking as a reference the results of the main studies carried out in Brazil and abroad on the construction of social knowledge, this article presents a research that investigated the evolution in the construction of this type of knowledge and in the cognitive development in Brazilian participants. Integrating quantitative and qualitative approaches, this is a descriptive study based on the Piagetian clinical-critical method, in which participated 30 students among 15, 18 and 21 years old from state public schools as well as from a Public University, enrolled in courses in Humanities, both from the interior of the state of São Paulo. The understanding of war and peace was the investigated social notion in comparison with the construction of reflective abstraction, which is an essential mechanism for cognitive development, through the application of surfaces and perimeters’ proof. The results indicated a delay in the responses of our participants in relation to those found in international researches, as well as the difficulty in developing a less apparent and more contextualized and argumentative reasoning. Likewise, the correlations between the construction of social knowledge and the reflective abstraction were positive, indicating the need for cognitive development to more elaborated levels of understanding of the social world.Keywords: Reflective abstraction. Cognitive Development. Social knowledge. Piagetian theory.PROCESOS DE ABSTRACCIÓN Y LAS NOCIONES SOCIALES DE GUERRA Y PAZ: un estudio con jóvenes estudiantes brasileñosRESUMENTomando por referencia los resultados de los principales estudios sobre la construcción del conocimiento social llevados a cabo no sólo en Brasil, sino también en el exterior, el artículo presenta una investigación sobre la evolución de la construcción de este tipo de conocimiento y sobre el desarrollo cognitivo en participantes brasileños. Se trata de un estudio descriptivo, con un enfoque cualitativo y cuantitativo, basado en el método clínico-crítico piagetiano con la participación de 30 sujetos entre 15, 18 y 21 años que asisten a escuelas públicas de la red del estado y que cursan carreras en el área de humanidades en una Universidad Pública del interior del estado de São Paulo. La comprensión sobre la guerra y la paz fue la noción social investigada, cotejada con la construcción de la abstracción reflexionante, mecanismo clave del desarrollo cognitivo, mediante la aplicación de la prueba de las superficies y perímetros. Los resultados indicaran un retraso con respecto a las respuestas de nuestros participantes si los comparamos con investigaciones internacionales. bien como la dificultad existente en a la elaboración de un raciocinio menos evidente y más centrado en el contexto y en la argumentación. Las correlaciones entre construcción del conocimiento social y la abstracción reflexionante han sido positivas y indicando la necesidad del desarrollo cognitivo para niveles más complejos de comprensión del mundo social.Palabras Clave: Abstracción reflexionante. Desarrollo Cognitivo. Conocimiento social. Teoria piagetiana.