The second law enunciated by Isaac Newton in the Principia is not equivalent to F = ma, as it is popularly known. The latter was described by Leonhard Euler, in 1752. However, for some historians, this formulation would be implicit in the statement proposed by Newton, and in this way, F = ma is considered by some of them only as a mathematical reformulation of Newton's law. In this paper, initially, the considerations of these historians are used and is it is performed an interpretation in order to establish a connection between the law proposed by Newton and F = ma, using current mathematical language. Based on this interpretation and on a bibliographic research, made from primary and secondary historical sources, reasons for the non-equivalence of these laws are discussed, as well as aspects that lead to this confusion of interpretations; limitations of Newtonian mechanics are discussed too, which are about mathematical method, natural coordinates, and Newton's conceptions of force. Next, the elements not covered by Newton's mechanics are indicated, thus showing that, in fact, F = ma is a much more general law than that proposed by Newton. Finally, it is briefly discussed the importance of using the historical approach in Science Teaching, especially with respect to the episode discussed here.
Context: In general, teachers and students have distorted views about the functioning of a scientific work. This research uses the episode of the historical construction of the Second Law of Movement and seven distorted views on the subject. Objectives: This work aims to exemplify the distorted views students can construct about scientific endeavour if a didactic approach that does not consider the history and philosophy of science is used. Design: Seven distorted views regarding scientific work are explained and, subsequently, exemplified from the episode in question, showing how this history is seen, in general, in textbooks, and by most teachers. Environment and participants: This is a theoretical analysis, not including participants. The materials used were primary and secondary bibliographic sources. Data collection and analysis: Seven distorted views on science, from the episode of the historical construction of the Second Law of Movement, were collected, and a historical-philosophical reflection was carried out on them. Results: Following the presentation of the views and examples, criticism and allusion to how this episode should be treated are offered. Conclusions: Throughout the text, as well as in its final considerations, relevant aspects to be worked on in the classroom are discussed, for a critical view of the construction of scientific knowledge.
O Rolling Playing Game (RPG) deve ser sinalizado como forma como os estudantes podem utilizar o conhecimento para resolver problemas, projetar novas experiências e comunicar o processo de aprendizagem. Neste trabalho é apresentada a adaptação do RPG para o ensino de Ciências, com conteúdos específicos de Física e de Astronomia. Esta adaptação foi realizada em uma escola extracurricular brasileira. Foi feita a análise dos níveis de aprendizagem a partir da taxonomia Structured of Observed Learning Outcomes (SOLO). É apresentado o jogo tradicional de RPG e detalhadamente demonstrado como adaptá-lo ao ensino, fazendo a apresentação da ficha de personagem adaptada ao ensino. É descrita a história “Jornada a Marte”. São apresentados os resultados que indicam indícios de aprendizagem, a partir da taxonomia SOLO, proposta e baseada no alinhamento construtivista, tendo sido obtidos resultados nos dois níveis de aprendizagem máximos da taxonomia SOLO, assim como bom engajamento dos estudantes e o desenvolvimento de pensamento crítico baseado nos conteúdos abordados. A adaptação do RPG e a aventura apresentadas servem de guia a professores que pretendam concretizar o uso de metodologias ativas de ensino, podendo ser adaptada para outros contextos escolares e a outros conteúdos curriculares.
A lei de Newton e F = ma são princípios diferentes. Cerca de sessenta anos de desenvolvimentos conceituais e matemáticos foram necessários para que a Segunda Lei do Movimento fosse elaborada, em 1752-1776, pelas mãos de Leonhard Euler. Neste trabalho, são discutidos os principais desses fatores adjacentes à construção dessa lei, sem os quais não seria possível Euler, e nenhum outro, obter a Segunda Lei do Movimento, como a conhecemos hoje. Será discutido o que estava sendo feito na mecânica no início do século XVIII e que contribuiu para que bases conceituais fossem elaboradas para que então fosse possível a emergência da Segunda Lei do Movimento como um princípio geral da mecânica, como a busca pela generalização de princípios, a introdução da mecânica analítica, com novas técnicas e ferramentais matemáticos, o estudo de determinados tipos de problemas, a unificação de conceitos e a elaboração de bases alternativas para a mecânica, como os princípios variacionais. Essas realizações contribuíram para que a lei proposta por Newton fosse aperfeiçoada e ampliada por Euler para uma classe muito maior de problemas.
In this work, an information booklet on the topic of Stellar Evolution was prepared, based on a bibliographic review of the literature in the field, aiming to create subsidies for the development of this science at different levels of knowledge. The booklet, which is intended to be used by teachers and students of Basic Education, was designed as a way of contributing to the shortage of teaching materials in this field. Here, it is presented the main scientific concepts worked on the booklet to support teachers and students, as well as comments on the experience with the presentations of lectures and workshops based on the booklet, in educational environments, in the Brazilian city of Marabá, in the state of Pará, as a way of disseminating and encouraging Astronomy in the region. It was noticed that the school community, in general, has a great interest in the learning of Astronomy, which contrasts with the scarcity of didactic materials and knowledge opportunities in the field. It is expected that more proposals for teaching materials, as well as applications of activities in Astronomy, will be developed, in order to disseminate such science in the school environment, and also in the general community.
A busca por métodos alternativos de ensino e aprendizagem em Matemática, que substituam as aulas tradicionalmente expositivas e conteudistas, tem sido um desafio para o professor, atualmente. Com o intuito de oferecer alternativas nesse sentido, este estudo apresenta metodologias ativas de ensino e aprendizagem que são adequadas ao Ensino de Matemática na Educação Básica. A fim de contribuir no âmbito da atuação docente, foi realizada uma revisão na literatura, na busca da caracterização e da definição de propostas pedagógicas de metodologias ativas para o Ensino de Matemática. Dessa forma, neste trabalho, são destacadas as metodologias Sala de Aula Invertida, a Instrução por Colegas e o Júri Simulado. São apresentados uma breve descrição de cada metodologia, os procedimentos para sua utilização, bem como sua relação com o Ensino de Matemática. O trabalho mostra a relevância, assim como incentiva o uso de metodologias ativas de ensino e aprendizagem no Ensino de Matemática.
The present article uses the description of the "circulatory system" (sensu Latour) oftechno-science around COVID-19 - in particular regarding the development ofvaccines and scientific evidence on the treatment of symptoms - as a didacticproposition for Science Teaching, showing how current events can and should alsobe mobilized as substrate for the critical understanding of the Nature of Science inthe classroom. From the description of the various actors involved in the COVID-19event, we discuss how it is possible to articulate scientific knowledge and criticaldiscussions about the Nature of Science to mobilize scientific literacy - that is, themastery and internalization of a properly scientific way of looking at the natural andsocial worlds, while at the same time rejecting negationism and absolutism about asupposedly univocal and linear science. The COVID-19 event allows us tounderstand the role of supposedly "alien" actors to technosciences as part of thewhole "circulatory system", combining Latour's stance with feminist perspectives,such as Helen Longino's, on objectivity and inter-subjectivity, and how theseelements can be articulated to promote scientific literacy.
Background: The F = ma principle was produced by Euler, between 1752 and 1776, and not by Newton in 1687, as is usually brought up in the physics manuals. It took over sixty years of conceptual and mathematical developments to develop this fundamental principle of mechanics. Still, after all this time, the principle continues to be called “Newton’s law”. Objectives: This paper seeks to discuss the possible reasons that led to the omission of Euler’s contributions to the elaboration of the fundamental principle of mechanics. Design: The study fits as documentary analysis, followed by a philosophical analysis of the researched material. Data collection and analysis: Historical research was carried out, using primary and secondary sources, regarding the reasons that led to such omission. After that, four main hypotheses were listed. Thomas Kuhn’s philosophical structure was applied to these hypotheses to support the explanation of the historical omission. Results: From the Kuhnian analysis, the Newtonian paradigm was presented and discussed, of which the principle formulated by Euler is part. Conclusions: The principle remains “Newton’s,” due to being within the Newtonian paradigm; and the conclusion that the principle ought to remain Newtonian matches the image of science within the baselines of the field of science teaching.
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