PENGEMBANGAN KEMAMPUAN PEMECAHAN MASALAH MATEMATIS SISWA SD DENGAN DIDACTICAL ENGINEERING

ABSTRAK Berbagai penelitian, baik di tingkat internasional maupun nasional, mengungkapkan kemampuan pemecahan masalah siswa sekolah dasar masih sangat rendah. Padahal, kemampuan memecahkan masalah merupakan bagian dari kodrat manusia yang diciptakan oleh nalar, karena pada prinsipnya tidak ada manusia yang tidak berpikir. Potensi siswa sangat mungkin berkembang pada diri siswa jika guru sebagai jembatan pengetahuan benar-benar menguasai metode pembelajaran dan mengenali karakter siswa dalam pembelajaran matematika dengan baik. Oleh karena itu, dalam penelitian ini mencoba menerapkan strategi pembelajaran menggunakan Didactical Engineerering (DE), sebagai dasar untuk mengembangkan kemampuan pemecahan masalah siswa SD. Harapannya, pembelajaran menggunakan DE dapat berimplikasi pada pengembangan ilmu pedagogik yang sangat dibutuhkan oleh para guru, khususnya guru sekolah dasar.

Pengaruh Problem Based Learning Disertai Didactical Engineering Terhadap Literasi Matematis Siswa

Tujuan penelitian ini adalah untuk mendeskripsikan secara komprehensif tentang pengaruh problem based learning (PBL) disertai didactical engineering (DE) terhadap kemampuan literasi matematis siswa. Metode penelitian yang digunakan adalah kuasi eksperimen, dengan desain penelitiaan Posttest-Only Design with Nonequivalent Groups. Populasi dalam penelitian ini seluruh siswa kelas VIII pada salah satu SMP Negeri di Kabupaten Subang dengan melibatkan sampel sebanyak 62 siswa yang tersebar dalam dua kelas, yakni kelas eksperimen dan kontrol. Instrumen yang digunakan dalam penelitian ini meliputi butir tes kemampuan literasi matematis dan pedoman observasi kegiatan guru dan siswa. Analisis data dilakukan secara kuantitatif dan uji statistik yang digunakan adalah uji t, uji Mann-Whitney, anova dua jalur. Berdasarkan hasil analisis data dapat disimpulkan bahwa faktor pembelajaran berpengaruh terhadap kemampuan literasi matematis siswa dan tidak terdapat interaksi antara model pembelajaran dan kategori KAM.

Lesson study with didactical engineering for student teachers in Brazil

Purpose The purpose of this paper is to experiment with ideas from didactical engineering (DE) in student teachers’ first experience with lesson study (LS). Design/methodology/approach This is a case study. Findings LS in pre-service education can be enhanced by elements from DE. Originality/value The idea indicated in the purpose is new and holds strong potential for the use of LS in teacher education.

Engenharia Didática de Formação (EDF): sobre o ensino dos Números (Generalizados) de Catalan (NGC)Didactical Engineering: about the teaching of generalized Catalan numbers

Registramos uma considerável atenção dedicada por parte dos autores de livros de História da Matemática (HM) concernentemente aos clássicos fundamentos do Cálculo Diferencial e Integral. Por outro lado, se mostra imprescindível ao entendimento do professor de Matemática uma compreensão sobre um irrefreável processo matemático e epistemológico evolutivo dos objetos matemáticos, desde seu estádio de nascedouro até o momento atual. Assim, o presente trabalho relata uma Engenharia Didática de Formação (EDF) desenvolvida com a participação de cinco professores em formação inicial, no Instituto Federal de Educação, Ciência e Tecnologia – IFCE, no ano de 2017. O tema abordado envolveu a noção de Números Generalizados de Catalan (NGC) que representa uma contribuição de vários matemáticos e a pesquisa atual sobre inúmeros problemas derivados confirmam seu processo de generalização ininterrupto. O estudo envolveu cinco tarefas e duas situações estruturadas de ensino, com o aporte da Teoria das Situações Didáticas (TSD). Os dados coligidos evidenciam várias propriedades e, sobretudo, teoremas e definições matemáticas descobertas e formuladas pelos sujeitos participantes da investigação o que concorreu para o incremento de suas habilidades profissionais e um conhecimento histórico, epistêmico e pragmático sobre a noção. We have recorded considerable attention on the part of the authors of Mathematical History (MH) books concerning the classical fundamentals of Differential and Integral Calculus. On the other hand, it is essential to the understanding of the Mathematics teacher an understanding about an unstoppable mathematical and evolutionary epistemological process of the mathematical objects, from its nascent stage to the present moment. Thus, the present work reports a Training Didactic Engineering (EDF) developed with the participation of five teachers in initial formation, in the Federal Institute of Education, Science and Technology - IFCE, in the year 2017. The topic covered involved the notion of Numbers Generalized Catalan (NGC) that represents a contribution of several mathematicians and the current research on numerous derived problems confirm its process of uninterrupted generalization. The study involved five tasks and two structured teaching situations, with the contribution of the Theory of Educational Situations (TSD). The collected data show several properties and, above all, the theorems and mathematical definitions discovered and formulated by the subjects participating in the research, which contributed to the increase of their professional skills and a historical, epistemic and pragmatic knowledge about the notion.

Engenharia Didática para o Teorema de Binet, ou Lamé, ou de De Moivre: Análises Preliminares e a Priori

Este trabalho apresenta uma proposta de Engenharia Didática - ED que descreve, apenas, as etapas de análises preliminares, análise a priori (e a concepção de duas situações didáticas), que correspondem aos dois primeiros momentos previstos, de modo sistemático, pela ED no campo da Didática da Matemática. O tema envolve uma das formas ou possibilidades de generalização do modelo secular, que prevê a reprodução de casais de coelhos, nomeado por Sequência de Fibonacci – SF. Diante do rico e variado percurso de evolução e sistematização do referido modelo, opta pela generalização de uma fórmula, cuja autoria, envolve informações conflitantes, embora seja mais conhecida, de acordo com os autores de livros de História da Matemática, como fórmula de Binnet ou Teorema de Binnet. A descrição de duas etapas iniciais de uma ED, envolvem elementos que detêm a possibilidade de explorar novas concepções dos estudantes acerca da SF, inclusive, tendo em vista o uso do CAS Maple, num contexto de investigação histórica, assumindo uma perspectiva de ensino afetada pela Teoria das Situações Didáticas – TSD.AbstractThis work presents a proposal of Didactical Engineering – DE, describing just the preliminarly analyzes and a priori analysis (and the didactical conception´s situations) which correspond to the first two levels in accordance to ED, in the Didactics of Mathematics. The theme involves one way of possibilities to obtain a kind of generalization relative to a secular model, which provides the couples of rabbits reproduction, namely by Fibonacci Sequence – FS. Before the rich and varied path of evolution and its systematization of this model, it is opted for the formula generalization, whose authorship involves a conflicting information, however, it is known, according to the authors of Mathematical History, as a Binnet´s formula or the Binnet´s theorem. The description of the two initial research steps involves some elements that have the potencial to explore new conceptions of the students about the FS, even considering the use of CAS Maple, in a historical research context, supported by the Theory of Didactical Situations – TDS.Keywords: Fibonacci Sequence. Model Generalization. Didactical Engineering. Teaching and Technology.

ENGENHARIA DIDÁTICA: IMPLICAÇÕES PARA A PESQUISA NO ÂMBITO DO ENSINO EM ANÁLISE COMPLEXA - AC

This article discusses and describes the two initial phases provided by a nominated research design of Didactical Engineering – DE. Thus, in view of an interest declared by the teachhing of Complex Analysis – CA, the work emphasizes the elements that hold the potential to constitute the two initial stages of an DE, nomitaded by preliminary and a priori analysis, with emphasis on description and conception of only two problems situations. So, in view of the long heritage of the French tradition in Didactics of Mathematics, also elects the Theory of Didactical Situations – TSD, in complementary character in other to ensure the reasonable control of the didactic mediation, as well as the predictive character of a theorical and conceptual framework for the research, structured for teaching of CA, reproductible and repeatable in any empirical situation of application in academic locus.