Dynamic geometry and square of the circle in Thomas Hobbes

This paper aims to present the reconstruction of the arguments offered by Thomas Hobbes about the classic problem of the squareness of the circle in the seventeenth century, from the perspective of the work: De Corpore of the same author. Where research is based on the support offered by Dynamic Geometry in the 21st century in the classroom with the use of GeoGebra software. This to be able to address and overcome the problems of the history of mathematical science and philosophy. For this it was chosen, by the methodology of a design of a teaching experiment in the classroom carried out with future teachers of the bachelor's degree in mathematics of 8th semester. Among the most important results is the recognition of renowned philosophers in the development of the history of mathematics. This implied that prospective mathematics teachers had to integrate their mathematical knowledge into the construction of the quadrature of the circle, which at the time was a problem for Hobbes, but with the perspective of modelling mathematical concepts in dynamic geometry, today it is done efficiently

Nuances of the philosophy of mathematics

Historically, the term philosophy of mathematical education is associated with the term philosophy of mathematics. However, mathematics as a mathematical education has its own foundations, schools, currents, and authors. Thus, it is possible to visualize from different research that one's own research with foundations in the philosophy of mathematics is stronger than in the philosophy of mathematical education. In order to base the present research on the philosophy of mathematics education, we have made use of a mixed method, which involves a quantitative analysis of the references made in Scopus databases through their search algorithms, in addition to a qualitative design under the contributions of the onto-semiotic approach and the Kantian synthetic analysis. When, trying to particularize the identity of the philosophy of mathematical education as an area of research in development, it is evident among the main approaches: (i) the identity process of the philosophy of mathematical education is still under construction; and, (ii) recognize the decoloniality of mathematical knowledge, imposed for centuries by Western mathematics, and backed by a single philosophy of mathematics

Más allá de Zoom, Teams y Google Meet: en busca de la auténtica educación virtual

Hablar de una búsqueda de la educación virtual auténtica, tiene que ser el derrotero que la comunidad académica de educadores matemáticos o educadores en general se tiene que plantear en esta nueva modalidad virtual suscitada por la crisis sanitaria mundial. La conferencia tratará una serie de reflexiones en torno de la educación presencial y virtual que se están viviendo en medio de la crisis sanitaria que vive Colombia y el mundo. En donde el objetivo principal es analizar ¿qué debería ser la educación virtual en el siglo XXI en medio de la pandemia colombiana?, y cómo implementar el vellocino dorado de la autentica educación virtual; si existe

Filosofia, educação matemática e ciencia

Talking about mathematics education is no longer a novelty when we think about the work of the mathematics educator, and even more so when we analyse thatthis work is as old as educational action, and as old as the teaching of mathematics. What automatically links this concept to the history of mathematics, andconsequently to the epistemological work that philosophy has been developing alongside mathematics. The aim of this paper is to describe how this relationshipis presented in the history of mathematics, philosophy and educational work. In order to develop this idea, we will use a qualitative perspective presented in thehistory of mathematical thought as recorded in the texts, to try to determine what is understood today by mathematics education and how it is treated by the workof the mathematics educator in the triple relationship that we have proposed as a title.Hablar de educación matemática ya no es una novedad en cuanto se piensa en la labor del educador matemático, y más cuando se analiza que este trabajo estan antiguo como la acción educativa, y como la enseñanza de la matemática. Lo que automáticamente liga este concepto a la historia de la matemática, y porconsecuencia a la labor epistemológica que viene desarrollando la filosofía al lado de la matemática. El presente escrito tiene como objetivo describir cómose presenta esa relación en la historia de la matemática, la filosofía y en la labor educativa. Para desarrollar tal idea, nos vamos a valer de una perspectiva cualitativapresentada en la historia del pensamiento matemático consignada en los textos, para intentar determinar qué se entiende hoy por educación matemáticay cómo es tratada esta por la labor del educador matemático en la triple relación que hemos propuesto como título.Parler d’éducation mathématique n’est plus une nouveauté lorsqu’on pense au travail de l’éducateur mathématique, et encore plus lorsqu’on analyse que cetravail est aussi vieux que l’action éducative, et aussi vieux que l’enseignement des mathématiques. Ce qui relie automatiquement ce concept à l’histoire desmathématiques, et par conséquent au travail épistémologique que la philosophie a développé parallèlement aux mathématiques. L’objectif de cet article est dedécrire comment cette relation est présentée dans l’histoire des mathématiques, de la philosophie et du travail pédagogique. Pour développer cette idée, nousallons utiliser une perspective qualitative présentée dans l’histoire de la pensée mathématique dans les textes, pour essayer de déterminer ce que l’on entendaujourd’hui par éducation mathématique et comment elle est traitée par le travail de l’éducateur mathématique dans la triple relation que nous avons proposéecomme titre.Falar de educação matemática já não é uma novidade ao pensar no trabalho do educador matemático, e ainda mais ao analisar que este trabalho é tão antigocomo a acção educativa, e tão antigo como o ensino da matemática. O que liga automaticamente este conceito à história da matemática, e consequentementeao trabalho epistemológico que a filosofia tem vindo a desenvolver a par da matemática. O objectivo deste documento é descrever como esta relação é apresentadana história da matemática, filosofia e trabalho educativo. Para desenvolver esta ideia, vamos utilizar uma perspectiva qualitativa apresentada na históriado pensamento matemático nos textos, para tentar determinar o que se entende hoje por educação matemática e como esta é tratada pelo trabalho do educadormatemático na tripla relação que propusemos como títul

Lesson study as a basis for mathematical practice at the university level

The aim of this paper is to present the importance of the teaching practice of the future professor of mathematics in a Colombian public university, through the application of the Japanese methodology of lesson study. This methodology is proposed as a set of skills and daily practices that the future professor of physics or mathematics must develop for the preparation of the class as proposed in the paper. Among the main results that the research found is the importance of the practice of lesson study for the teaching of science in general, with emphasis on physics and mathematics, although this methodology can also be applied to the human sciences. On the other hand, the research recognizes that the use of this method should be assumed as part of the process of formation of the student of mathematics, physics or any discipline that requires preparation of the classes for the teaching process. It contributes to the professional profile of the future teacher in terms of quality and professionalism of the teaching work. Thus, it can be concluded that, the teaching of mathematics from this approach is a positive resource in the training of the teacher of mathematics, or any discipline such as physics that wants to implement it, because, it is being reflected in the didactic work that mathematics, or any science wants to exercise in the pedagogical and didactic process of the classroom through the teaching practice and, later on, in the professional work of each probationer

Geometry for design: approaches to the study of representation and dimension and their contributions to the modeling of phenomena

The difficulties of representation and understanding of the dimension are evident in the different educational levels. University education is no stranger to this situation. This communication was developed within the framework of the graphic design course. This course was designed under the use of specialized software in geometry, which was freely available and intuitive. It should be remembered that the adequate use of representations and attributes proper to the dimension aids in the representations of movement phenomena, as well as in the representations in force diagrams in the teaching of physics. This qualitative research aims to address aspects of representation and dimensionality from the description of some selected tasks of the group participants, who contrast the first representations, with their final activities. That is, these representations showed their evolution in construction, to the extent that the flat representations of objects in the portfolio were built in real dimensions, keeping the proportional relationship between its parts

Política e religião em Thomas Hobbes

Orientador: Yara Adario FrateschiTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: O objetivo deste trabalho é a caracterização da questão religiosa nos escritos políticos de Thomas Hobbes. Pretende-se reconstruir os argumentos que o autor utilizou para aprensentar como a religião em Hobbes é um instrumento da política tanto do soberano civil quanto da Igreja, ao considerar que a religião, como a principal virtude do estado, não é contraditória ao governo civil. No entanto, o filósofo de Malmesbury entende que a Igreja faz uso da religião mediante uma série de falsas práticas religiosas para manter o poder e conservar os beneficios que isso implica. Isto é, precisa disseminar e alimentar o medo nas pessoas, o qual impede a obediência absoluta ao soberano civil, como representante do poder de Deus na Terra. Com essas idéias, Hobbes retomará a história cristã e às Sagradas Escrituras, explicando de que maneira a Igreja, seus representantes e a Sagrada Escritura constituem um impedimento para obediência do povo ao Príncipe e suas leis. Com tudo, estes argumentos são refutados em De Cive e no Leviatã, onde o autor demonstra amplamente que, por iure divino, o soberano é o intérprete legítimo da tradição e das escrituras, em quem se deve obediência absoluta tanto quanto a DeusAbstract: The objective of this work is the characterization of the religious question in the political writings of Thomas Hobbes. It is intended to reconstruct the arguments that the author used to show how the religion in Hobbes is a political instrument, both the civil sovereign and the Church, considering that religion, as the main virtue of the State, is not contradictory to civil government. However, the philosopher of Malmesbury understands that the Church uses religion through a series of false religious practices to stay in power and preserve the benefits that this implies. In other words, it needs to sow and nurture the fear in the people, which becomes an impediment to absolute obedience to the civil sovereign, as a representative of God's power on earth. With these ideas, Hobbes will return to Christian history and the Holy Scriptures, to explain in what ways the Church, its representatives and the Holy Scriptures constitute an impediment to the obedience of the people to the Prince and its laws. On the other hand, these arguments are refuted in De Cive and Leviathan, where the author amply demonstrates that, by divine jure, the sovereign is the legitimate interpreter of the tradition and of the scriptures on earth, to whom absolute obedience is due, as much as GodDoutoradoFilosofiaDoutor em Filosofi

Brousseau y los retos de la didáctica matemática en educación

El presente escrito tiene como objetivo responder a la pregunta de cuáles son los retos para la educación matemática desde la educación hoy. Esto a partir de una perspectiva de la filosofía de la educación matemática encarnada en la propuesta de Brousseau. Sin embargo, lo que se pretende es mirar esos hilos de sororidad entre las matemáticas, la pedagogía y otras ciencias auxiliares que colaboran en la actualidad a una ciencia que por antonomasia se cree pura, pero que en la realidad para ser enseñada en el siglo XXI precisa de otras ciencias que tienen eco en la educación

Geometría dinámica y la cuadratura del círculo en Hobbes

La cuadratura del círculo ha sido estudiada desde diferentes perspectivas. La historia de la matemática, hasta ahora, no ha reconocido el aporte hecho por el filósofo Thomas Hobbes [3]. Este escrito pretende presentar la reconstrucción de las argumentaciones por él realizadas en aquella época, pero con el apoyo de la geometría dinámica. Esto es, se realizará una integración de aquí concepto históricamente abordado, pero con el objeto matemático a través de la Geometría Dinámica-GD. Esta investigación es de tipo cualitativa, la cual se desarrolla usando el experimento de enseñanza con la participación de futuros profesores dentro del curso de didáctica de la Geometría. Este abordaje permite identificar los aprendizajes teniendo por base la modelación matemática, bajo la construcción de applets en GeoGebra. Finalmente, esta investigación en desarrollo pretende dar respuesta a la pregunta: ¿cómo los argumentos usados en la demostración de la cuadratura del círculo en Hobbes pueden contribuir para la enseñanza de conceptos propios de la didáctica de la geometría en licenciados en matemáticas? El uso de GD, en particular la modelación, permitirá a los licenciados llegar a las argumentaciones y conclusiones que el propio Hobbes no llegó en aquella época, por la falta de instrumentos que dieran sustento a sus propuestas de demostración. Esto es, la propuesta que era irresoluble según Lindemann en 1882 para resolver con regla y compás, la cual sólo fue validada por eminentes matemáticos de la época, como John Wallis de la Royal Society

Matemáticas, tecnología y formación STEM

Esta propuesta pretende identificar indicadores de conocimiento especializado del profesor de Matemáticas bajo una propuesta STEM, del inglés, ciencias, tecnología, ingeniería y matemáticas. Esta investigación es cualitativa. Los resultados iniciales muestran algunos elementos teóricos frente a una propuesta de formación inicial de profesores de matemáticas, bajo una perspectiva interdisciplinar