Swafoto Kelompok Sebagai Task Design Permutasi pada Pembelajaran Jarak Jauh

Task design atau desain tugas merupakan komponen penting dalam mendorong terjadinya proses belajar matematika. Tujuan penelitian ini adalah untuk menyusun task design pembelajaran topik permutasi. Penelitian ini melibatkan 80 siswa Sekolah Menengah Atas di Ngabang, Kalimantan Barat pada tanggal 1 Januari sampai 5 Maret 2021. Penelitian ini menggunakan metodologi didactic engineering yang terdiri dari empat tahap yaitu 1) preliminary analysis, (2) design and a priori analysis, (3) implementation, observation, and data collection, dan (4) a posteriori analysis. Task design disusun dengan menggunakan kerangka Teori Situasi Didaktis. Pada setiap tahap, khususnya tahap keempat, data dianalisis secara deskriptif. Hasil penelitian menunjukkan bahwa untuk materi permutasi dapat dibuat task design berupa swafoto kelompok. Swafoto kelompok merupakan fundamental situation dalam task design yang dikonstruksi dengan kerangka Teori Situasi Didaktis dan sesuai dengan konteks siswa. Task design ini juga mampu mendorong siswa mengkonstruksi pengetahuannya melalui permasalahan swafoto kelompok. Dalam konteks pembelajaran jarak jauh, pada masa pandemi ini, swafoto kelompok merupakan bentuk task design yang kontekstual dan mendorong siswa terlibat aktif karena sifatnya personal. Hasil penelitian ini juga menunjukkan potensi dan penggunaan Teori Situasi Didaktis sebagai kerangka task design pada topik permutasi di Sekolah Menengah Atas.

Development of a Learning Model of Quadric Surfaces With Augmented Reality and Didactic Engineering

<p class="0abstract">Augmented reality (AR) is an emerging technology that has permeated different spheres of life, one of them is education, and specifically the teaching-learning process at different educational levels and objects of study. For this reason, this paper presents the development of a learning model of quadric surfaces mediated by a mobile AR application and based on didactic engineering. The model was applied to a group of environmental engineering students of the Catholic University of Manizales. To obtain information on the use of the application and the learning results obtained, some intervention instruments were developed. The students stated that the use of AR allowed them to better understand the concepts of quadric surfaces, even more so in a time of pandemic by COVID-19, where education was highly measured by ICTs.</p>

Didactic Engineering as a research method in physics teaching

Several mathematical concepts have application in physics; this paper reports the results of a pedagogical investigation based on the methodology known as didactic engineering, which has been proposed with the aim of improving the skills exhibited by a group of eleventh grade students from a private institution in the interpretation of kinematic graphs. The concept of the slope of the straight line and how this mathematical concept can represent velocity or acceleration according to the variables considered in the kinematics graph provided was enhanced in the pedagogical intervention. This methodology offers a process of internal validation, after comparing the results obtained in a knowledge test at two different points in time (pre-test and post-test). The results allowed us to identify improvements in all students in terms of basic kinematics graph interpretation skills, and a group of students stood out by advancing in more complex reasoning and interpretation processes. These results contribute to the improvement of the pedagogical practices of Physics teachers at secondary and middle school levels, making them more competent when they enter higher education.

Didactic Sequence for Teaching Exponential Function

This paper presents a methodological proposal for the teaching of exponential function, resulting from the application of a didactic sequence involving exponential function, where evidence of learning and the consolidation and application of mathematical concepts in problem solving were identified and analyzed. The Didactic Engineering of Michèle Artigue (1988) was used as a research methodology. As theoretical contributions that guided and enabled the development of the research, we chose the use of Mathematical Investigation in the classroom; Didactic Sequence in the conception of Zabala (1999); the Articulated Units of Conceptual Reconstruction proposed by Cabral (2017) and assumptions of Vygotsky's theory. A didactic sequence composed of five UARC's was elaborated to work the exponential function, with a view to minimizing the difficulties naturally imposed by the content to be explained. Microgenetic analysis of verbal interactions between teacher and students was used to analyze the results of the application. The results show that the students participating in the experiment showed evidence of learning, recorded during the process, and began to have a good understanding of the concepts and properties related to the topic, in addition to a good performance in carrying out the activities, facts that corroborate the potential of the didactic sequence proposed herein.

Uma análise semiótica e cognitiva na aprendizagem de áreas de triângulos e quadriláterosA semiotic and cognitive analysis of the learning of triangle and quadrilateral areas

ResumoEste artigo analisa mudanças de representação e de registro no cálculo de áreas de triângulos e quadriláteros. As atividades descritas foram realizadas por alunos do quinto e do sexto ano do ensino fundamental de uma escola privada de Campo Grande, MS. Este estudo fundamenta-se na teoria de registros de representação semiótica, de Duval, e em dois de seus elementos teóricos que tratam dos olhares e apreensões para a aprendizagem em geometria. Adotou-se como metodologia a engenharia didática, de Artigue. Constatou-se que solucionar as atividades por meio da exploração heurística das figuras, da desconstrução dimensional e do olhar não icônico, transitando em diferentes representações, permitiu aprendizagens sobre o cálculo de áreas. A diversidade de registros e estratégias nesses cálculos, nessas perspectivas, favoreceu soluções distintas, contribuindo para a superação de dificuldades e o desenvolvimento de autonomia em geometria, oportunizando um novo modo de aprender, de raciocinar e principalmente de olhar para uma figura geométrica.Palavras-chave: Geometria, Apreensões, Olhares, Ensino fundamental.AbstractIn this article, representation and register changes in the calculation of triangle and quadrilateral areas were analysed. The activities described were performed by 5th- and 6th-grade students attending a private school in Campo Grande, Mato Grosso do Sul, Midwest Brazil. This study drew on Duval’s theory of registers of semiotic representation and on two of its theoretical elements addressing ways of visualising and apprehending in geometry learning. Artigue’s didactic engineering method was adopted. Solving activities by heuristic exploration of figures, dimensional deconstruction, and use of non-iconic visualisation, while transiting across different representations, promoted learning of area calculation. The diversity of registers and strategies involved in the calculations furthered the emergence of a range of solutions, helping learners to overcome difficulties, gain autonomy in dealing with geometry, and experience new ways of learning, reasoning, and, most notably, of visualising geometric figures.Keywords: geometry, apprehension, visualisation, primary school.ResumenEste artículo analiza cambios de representaciones y de registro en cálculo de áreas de triángulos y cuadriláteros. Las actividades descritas fueron realizadas por alumnos del quinto y sexto grados de la enseñanza básica de una escuela privada en Campo Grande, Mato Grosso do Sul, Brasil. Este estudio se fundamenta en la teoría de registros de representación semiótica, de Duval, y en dos de sus elementos teóricos que tratan de entendimiento y visión para aprendizaje en geometría. Se adoptó como metodología la ingeniería didáctica, descrita por Michèle Artigue. Se verificó que resolver actividades mediante la exploración heurística de figuras, la deconstrucción dimensional y el uso de visualización no icónica, mientras se transita por diferentes representaciones, promovió el aprendizaje del cálculo de áreas. La diversidad de registros y estrategias en esos cálculos, en esas perspectivas, favoreció soluciones distintas, contribuyendo para la superación de las dificultades y el desarrollo de autonomía en geometría, creando la oportunidad de un nuevo modo de aprender, de raciocinar y principalmente de mirar una figura geométrica.Palabras clave: Geometría, Aprehensiones, Miradas, Enseñanza fundamental.

Méthodologies de recherche en didactique des mathématiques : Où en sommes-nous ? Research Methodologies in didactic of mathematics: Where Are We?

RésuméDans cet article s’interrogeant sur les méthodologies de recherche en didactique, après une introduction resituant ce questionnement dans l’histoire de ce champ de recherche, et les méthodologies au sein des praxéologies de recherche, je m’intéresse dans un premier temps à l’ingénierie didactique, une méthodologie emblématique de la volonté des didacticiens d’élaborer des méthodes de recherche répondant à leurs besoins spécifiques. Je rappelle ses caractéristiques et montre aussi son évolution au contact de différentes théories. Dans un second temps, j’examine les relations entre ingénierie didactique et design-based research, en incluant le cas de l’ingénierie didactique coopérative. J’envisage ensuite diverses évolutions méthodologiques liées à l’évolution des problématiques et théories didactiques et à celle des moyens technologiques de la recherche, avant d’aborder dans une dernière section ces questions méthodologiques sous l’angle des rapports entre recherche et action didactique. Mots clefs : Didactique des mathématiques, Méthodologie de recherche, Praxéologie de recherche, Ingénierie didactique, Design-based research, Ingénierie didactique coopérative.AbstractIn this article questioning research methodologies in mathematics education, after an introduction that situates this questioning in the history of this field of research, and the methodologies within research praxeologies, I first consider didactic engineering, a methodology that is emblematic of the willingness of didacticians to develop research methods meeting their specific needs. I recall its characteristics and also show its evolution in the contact with different theories. Secondly, I examine the relationship between didactic engineering and design-based research, including the case of cooperative didactic engineering. I then consider various methodological evolutions linked to the evolution of research problematics and theories and to the evolution of technological means of research, before addressing, in a last section, these methodological questions from the point of view of the relationship between research and didactic action.Key words: Didactics of mathematics, Mathematics education, Research methodology, Research praxeology, Didactic engineering, Design-based research, Cooperative didactic engineering.ResumenEn este artículo cuestionando las metodologías de investigación en didáctica de las matemáticas, después de una introducción que resitúa este cuestionamiento en la historia de este campo de investigación, y las metodologías dentro de las praxeologías de investigación, me intereso en primer lugar a la ingeniería didáctica, una metodología emblemática de la voluntad de los didactas de desarrollar métodos de investigación que respondan a sus necesidades específicas. Recuerdo sus características y también muestro su evolución en el contacto con diferentes teorías. En segundo lugar, examino la relación entre la ingeniería didáctica y la investigación basada en el diseño, incluyendo el caso de la ingeniería didáctica cooperativa. A continuación, considero diversas evoluciones metodológicas vinculadas a la evolución de las problemáticas y teorías didácticas y a la evolución de los medios tecnológicos de investigación, antes de abordar en una última sección estas cuestiones metodológicas desde la perspectiva de la relación entre la investigación y la acción didáctica. Palabras claves: Didáctica de las matemáticas, Metodología de investigación, Praxeología de investigación, Ingeniería didáctica, Investigación basada en el diseño, Ingeniería didáctica cooperativa.

Engenharia Didática como metodologia de pesquisa e dispositivo metodológico para a sala de aulaDidactic Engineering as a research methodology and methodological procedure for the classroom

ResumoEste trabalho é o resultado dos estudos de um grupo de investigação que trabalha com Engenharia Didática como metodologia de pesquisa; é oriundo de duas pesquisas e tem como objetivo expor uma defesa desta metodologia em trabalhos que focam, sobretudo, nos eventos que ocorrem na sala de aula. Essa pertinência de “como” realizar a pesquisa se justifica, por um lado, pelo fato de sistematizar a tarefa do pesquisador, mantendo foco e disciplina. Por outro, por permitir internalizar os efeitos da observação, desde o modo pelo qual os alunos realizam as atividades propostas até todo aparato que está no entorno físico e cognitivo em questão, servido também como procedimento metodológico às atividades de ensino. Diante disso, a questão que norteia este artigo é “quais as potencialidades e limitações que a Engenharia Didática como procedimento metodológico ofereceu durante a realização da pesquisa?” Para responder esta questão, optou-se por analisar os resultados obtidos por uma aluna que participou de todas as fases da Engenharia Didática, como procedimento metodológico, durante abordagem de ideias que circundam os primeiros contatos com o conceito de probabilidade. Diante disso, apuramos que as potencialidades podem ser descritas como a possibilidade de verificar os conhecimentos prévios dessa aluna; a valorização do contexto em que a aluna se encontra inserida; a participação da aluna ativamente no processo; os momentos de discussão e a voz da aluna, carregada de crenças, enquanto as limitações nos fizeram enxergar a dependência dos alunos na figura do professor, visto como detentor do saber.Palavras-chave: Engenharia Didática, Metodologia de pesquisa, Procedimento metodológico, estatística e Probabilidade.AbstractThis work is the result of the studies of a research group that works with Didactic Engineering as a research methodology; it comes from two researches and aims to expose in defense of this methodology in works that focus, above all, on events that occur in the classroom. This relevance of “how” to conduct a research is justified, on the one hand, by the fact of systematizing the researcher's task, maintaining focus and discipline. On the other hand, because it allows internalizing the effects of observation, from the way in which students carry out the proposed activities to any apparatus that is in the physical and cognitive environment in question, also served as a methodological procedure. Therefore, the question that guides this article is: What are the potentials and limitations that Didactic Engineering as a methodological procedure offered during the research? To answer this question, it was decided to analyze the results obtained by a student who participated in all phases of Didactic Engineering, as a methodological procedure, during the approach of ideas that surround the first contacts with the concept of probability. In view of this, we have found that the potentialities can be described as the possibility of checking the students' previous knowledge; valuing the context in which the student is inserted; the student’s active participation in the process; the moments of discussion and the student's voice, full of beliefs, while the limitations have led us to see the students' dependence on the figure of the teacher, as the holder of knowledge.Keywords: Didactic Engineering, Research Methodology, Methodological procedure, Statistics and Probability.ResumenEste trabajo es el resultado de los estudios de un grupo de investigación que trabaja con la Ingeniería Didáctica como método de investigación; proviene de dos investigaciones y pretende exponer en defensa de esta metodología en un trabajo que se centra, sobre todo, en las ocurrencias que ocurren en clase. Esta pertinencia del “cómo” realizar la investigación se justifica, por un lado, por la necesidad de sistematizar la tarea del investigador, manteniendo el enfoque y la disciplina. Por otro lado, porque permite internalizar los efectos de la observación, en la forma en que los Estudiantes realizan las actividades propuestas con todos aparatos que se ubique en el entorno físico y cognitivo del campo, sirviendo también como dispositivo metodológico. Por tanto, la pregunta que guía este artículo es: ¿cuáles son las potencialidades y limitaciones ofrece Ingeniería Didáctica como procedimiento metodológico durante la investigación? Para responder a esta pregunta, se decidían alisarlos resultados obtenidos por un estudiante que participo en todas las fases de la Ingeniería Didáctica, como procedimiento metodológico, durante el abordaje de ideas que hizolos primeros contactos con el concepto de probabilidad. Por tanto, encontramos que el potencial podría describirse como la posibilidad de verificar el conocimiento previo de este alumno; valorar el contexto en el que se inserta el alumno; participación del alumno en el proceso; momentos de discusión y la voz del alumno, cargado de creencias, mientras las limitaciones nos hacían ver la dependencia de los alumnos de la figura del profesor, entendido como poseedor de conocimientos.Palabras clave: Ingeniería Didáctica, Metodología de la Investigación, procedimiento Metodológico, Estadística y Probabilidad.

UMA PROPOSTA DE INVESTIGAÇÃO HISTÓRICO-EPISTEMOLÓGICA SOBRE SEQUÊNCIAS RECORRENTES DE 2ª ORDEM

A formação de professores no Brasil não pode prescindir de um componente histórico-matemático e evolutivo. Nesse sentido, se torna imprescindível ao professor compreender a natureza intrinseca sobre o conhecimento matemático e seus processos ou itinerários de evolução e de irrefreável generalização. Dessa forma, o presente trabalho apresenta os dados preliminares de uma investigação amaparada pelos pressupostos de uma Engenharia Didática de Formação, em desenvolvimento no Brasil. O trabalho revela a uma importante cooperação científica envolvendo pesquisadores portugueses, sobre o asssunto de sequências recorrentes de 2ª ordem e aponta a contribuição de pesquisas desenvolvidas no período de 2015 – 2020, no Programa de Pós-graduação em Ensino de Ciências e Matemátca, do Instituto Federal de Educação, Ciências e Tecnologia do Estado do Ceará – IFCE. Por fim, o trabalho apresenta algns indicadores que devem demarcar um importante cenário para a formação (inicial e continuada) de professores no Brasil.Palavras-chave: História e Epistemologia da Matemática; Sequências recorrentes; Formação de Profesores de Matemática; Engenharia Didática de Formação.A PROPOSAL FOR HISTORICAL-EPISTEMOLOGICAL RESEARCH ON THE 2ND ORDER SEQUENCESAbstract. Teacher training in Brazil cannot do without a historical-mathematical and evolutionary component. In this sense, it is essential for the teacher to understand the intrinsic nature of mathematical knowledge and its processes or itineraries of evolution and irrepressible generalization. Thus, the present work presents the preliminary data of an investigation supported by the assumptions of Didactic Engineering of Training, under development in Brazil. The work reveals an important scientific cooperation involving Portuguese researchers, on the subject of recurrent 2nd order sequences and points out the contribution of research developed in the period 2015 - 2020, in the Postgraduate Program in Science Teaching and Mathematics, of the Institute Federal Institute of Education, Science and Technology of the State of Ceará - IFCE. Finally, the work presents some indicators that should outline an important scenario for the training (initial and continuing) of teachers in Brazil.Keywords: History and Epistemology of Mathematics; Recurring strings; Mathematics Teacher Training; Didactic Engineering Training.