Resume: Cette recherche examine l’approche adoptée pour enseigner la dynamique relativiste sur différents sites web éducatifs destinés aux niveaux secondaire et universitaire. Les sites web sont analysés au moyen d’une catégorisation inductive, qui présente des variables relativement similaires à celles résultant d’une analyse des manuels scolaires utilisés pour enseigner la TER (González et al., 2022). Le travail montre que les sites web développés par des institutions d’éducation formelle telles que les ministères de l’éducation ou les universités ont une approche similaire à celle des manuels, c’est-à-dire qu’ils transfèrent les connaissances des livres vers le web. D’autre part, sur les sites web orientés vers l’enseignement secondaire, la principale approche de la dynamique relativiste est le concept de masse et d’énergie, en remettant en question les lois de Newton, tandis que sur les sites web universitaires, on part du concept de quantité de mouvement et des lois de conservation. Le travail formule quelques considérations didactiques concernant l’enseignement de la dynamique relativiste à l’école.

Resumen Esta investigación realiza una revisión del enfoque adoptado para enseñar la dinámica relativista por distintos sitios y páginas webs educativas orientadas al nivel secundario y universitario. Las webs se analizan por medio de una categorización inductiva, que tiene variables relativamente similares a las que resultan de un análisis de los libros escolares utilizados para enseñar la TER (González, et. al., 2022). El trabajo evidencia que las webs desarrolladas por instituciones de educación formal tales como ministerios de educación o universidades, poseen un enfoque similar a los libros de texto, es decir que trasladan el saber de los libros hacia las webs. Por otro lado, en los sitios web orientados a la enseñanza secundaria, la vía principal a la dinámica relativista es el concepto de masa y energía, partiendo de cuestionar las leyes de Newton, mientras que en las webs universitarias se parte del concepto de momentum y de las leyes de conservación. El trabajo formula algunas consideraciones didácticas sobre la enseñanza de la dinámica relativista en la escuela.

Abstract This research reviews the approach adopted to teach relativistic dynamics by different educational websites aimed at secondary and university levels. The websites are analyzed through an inductive categorization, which has variables relatively similar to those resulting from an analysis of the school textbooks used to teach TER (González et al., 2022). This research shows that websites developed by formal education institutions such as ministries of education or universities have a similar focus to textbooks, meaning they transfer knowledge from books to the web. On the other hand, in websites oriented toward secondary education, the primary way to relativistic dynamics is the concept of mass and energy, starting by questioning Newton’s laws, while university websites begin with the concept of momentum and conservation laws. This research formulates some didactic considerations regarding the teaching of relativistic dynamics in schools.

In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.

Neste trabalho planejamos, implementamos e avaliamos uma sequência didática para ensinar aspectos básicos da teoria especial da relatividade (TER) no Ensino Médio. A sequência propõe um conjunto de situações especialmente planejadas para que os aspectos centrais da TER possam emergir. O processo de conceitualização é analisado segundo o ponto de vista da teoria dos campos conceituais de Vergnaud. Por meio de uma cuidadosa análise das produções dos estudantes durante as aulas, detectamos teoremas em ação e conceitos em ação, de natureza pre galileana. Isso nos conduziu à reformular a sequência para promover a conceitualização da relatividade galileana e os postulados da relatividade especia, antes de considerar aspectos mais complexos.

In this work, we design, implement and analyze a didactic sequence for the teaching of the basic topics of special relativity theory in high school. The sequence proposes a series of situations, specially designed to allow the emergence of the central aspects of special relativity. The conceptualization process is investigated from the point of view of the theory of conceptual fields of Vergnaud. By means of a careful analysis of classroom student productions we detect the key theorems-in-action they use, evidencing that most of conceptual errors are of pre-relativistic nature. This leads us to a reformulation of the sequence, which promotes the conceptualization of Galilean relativity and the principles of the special relativity. This previous step aims at bringing to students a firm basis to address the more complex aspects of the subject.

Este trabalho apresenta uma análise da experiência de fenda dupla com luz, utilizando conceitos do método de "Soma de vários caminhos" da formulação de Feynman da mecânica quântica. São analisadas as vantagens desta formulação para o ensino no nível médio de aspectos básicos da mecânica quântica.

This paper presents an analysis of the double slit experience with light, by using concepts of the Feynman method of "sum of multiple paths" in quantum mechanics. The advantages of this formulation for the teaching of basic aspects of quantum mechanics in the high-school level are analyzed.

This paper describes the process of development of a didactical sequence to teach basic concepts of quantum mechanics in secondary school. Basically, the didactical framework adopted is described. The different conceptual structures that have to be developed to approach the problem of how to teach basic concepts of quantum mechanics starting from the student's knowledge, respecting the student's place (freedom) and inviting him to take his own responsibility, this implies creating an emotional dynamic of acceptance into the classroom. The Conceptual Structure of Reference that must be defined by the researcher is described. The researcher analyzes the conceptual relationships existing in the scientific community where knowledge is generated and that he will adopt as his frame of reference, also, he must take into account the community where that knowledge will be reconstructed and the knowledge transformations that will be necessary for teaching. Briefly, the Conceptual Structure Proposed to Teach is described and some results obtained during the scholar implementation of the CSPT, related to the conceptualization and viability of the sequence, are discussed in general.

En este trabajo se describe el proceso de desarrollo de una secuencia didáctica para enseñar conceptos fundamentales de Mecánica Cuántica en la Secundaria. Fundamentalmente se describe el referencial didáctico que se asume. Se definen las distintas estructuras conceptuales que es necesario reconstruir para abordar el problema de cómo enseñar nociones cuánticas partiendo de la situación del alumno, respetando su lugar e invitándolo a que asuma su responsabilidad, es decir, generando una dinámica emocional de aceptación. Se describe la Estructura Conceptual de Referencia que es definida por el investigador. El analiza las relaciones conceptuales que viven en la Comunidad Científica que genera el conocimiento y que tomará como referencia, y a la vez, la comunidad en la que ese saber va a ser reconstruido y las transformaciones que serán necesarias para enseñarlo. Se describe brevemente la Estructura Conceptual propuesta para enseñar y se discuten de manera general algunos resultados obtenidos en la implementación escolar de la ECPE con relación a la conceptualización y a la viabilidad de la secuencia.

We analyze the possibilities of introducing the basic ideas of quantum mechanics into secondary school, by adapting the path integral formulation's concepts for the students. This work focuses on this proposal's theoretical basis and what aspects of the formalism should be adapted in order to be implemented in the last year's course.

Analizamos las posibilidades de introducir las ideas básicas de la mecánica cuántica en la escuela secundaria, adaptando los conceptos de la formulación de integrales de camino (path integrals) para los estudiantes. Este trabajo focaliza en el fundamento teórico de la propuesta y en las adaptaciones necesarias para una posible implementación de esta en un curso del último año.