This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative ...of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the meaning is composed of: (a) conceptual structure, (b) representation systems, and (c) sense and usage. This qualitative, descriptive study analysed the replies of 37 pre-service teachers to questions involving the definition, requirements, and structural concept of derivatives. It also explores the sense and usage attributed by participants to this mathematical concept. At least five profiles of meanings for derivatives could be constructed from the results. The most prominent findings included the prevalence of the geometric interpretation of the concept and participants' failure to mention elements and requisites essential to the definition of derivatives.
Obsesionado con su imagen Paz Rodríguez, Marta María
Pensamiento matemático,
2020, Volume:
10, Issue:
2
Journal Article
Open access
This paper shows one of the tales presented to the contest about tales with mathematical content organized by the Innovation Educative Group “Mathematical Thinking”. Ordinary language and technical ...concepts play together in a poetic story.
En este artículo se muestra uno de los cuentos presentados al concurso de relatos con contenido matemático organizado por el GIE (Grupo de Innovación Educativa) Pensamiento Matemático de la UPM (Universidad Politécnica de Madrid), para alumnos de la ESO, Bachillerato y universitarios. El juego de palabras y los conceptos que en él aparecen son muy bellos. Lenguaje cotidiano y técnico se juntan en un relato casi poético.
This story is intended to begin in an entertaining way and from a didactic point of view the beginning of the study of complex numbers.
Con el presente cuento se pretende iniciar de forma amena y ...desde un punto de vista didáctico el comienzo del estudio de los números complejos.
This issue continues with the publication of the awarded tales in the First
MathematicalShort Tales Contest “π-ensa” organized by the Mathematics Museum
Workshop Classroom “π-ensa” during the ...2015-2016 course. This tale awarded a special
jury award in the highschool and college student category. All information on the contest is
available on the website of the Classroom:
http://innovacioneducativa.upm.es/museomatematicas/
En este número se continúa con la publicación de los relatos premiados en el Primer
Concurso de Relatos Cortos Matemáticos “π-ensa” convocado por el Aula Taller Museo de
las Matemáticas “π-ensa” durante el curso 2015-2016. Este cuento resultó premiado con una
mención especial del jurado en la categoría de estudiantes de bachillerato y universidad.
Toda la información del concurso puede consultarse en la web del Aula:
http://innovacioneducativa.upm.es/museomatematicas/
This issue continues with the publication of the awarded tales in the First Mathematical Short Tales Contest “π-ensa” organized by the Mathematics Museum Workshop Classroom “π-ensa” during the ...2015-2016 course. This tale awarded a special jury award in the high school and college student category. All information on the contest is available on the website of the Classroom: http://innovacioneducativa.upm.es/museomatematicas/.
En este número se continúa con la publicación de los relatos premiados en el Primer Concurso de Relatos Cortos Matemáticos “π-ensa” convocado por el Aula Taller Museo de las Matemáticas “π-ensa” durante el curso 2015-2016. Este cuento resultó premiado con una mención especial del jurado en la categoría de estudiantes de bachillerato y universidad. Toda la información del concurso puede consultarse en la web del Aula: http://innovacioneducativa.upm.es/museomatematicas/.
Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view ...proof and the teaching of proof. The purpose of this survey research was to explore PSMTs' knowledge and beliefs about proof and proof teaching in the context of secondary mathematics teaching and learning. Six cases (PSMTs' survey responses) were purposively selected from an entire data set comprising participants from the United States and Australia. Using a situative learning perspective as the theoretical framework, the authors developed a sensible belief system Leatham, K. R. (2006). Viewing mathematics teachers' beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91-102.
https://doi.org/10.1007/s10857-006-9006-8
for sampled PSMTs and inductively conceptualized how their knowledge of and orientations toward proof acted as a function of their teaching and learning contexts. Furthermore, an analysis of data revealed that PSMTs' knowledge and beliefs about proof are multifaceted, dynamic and evolving as they engage with proof in their various contexts.
The Peasant Education is based on the valorization of the peasant context and consequent defense of the contextualization of the content from local contexts, also defends the teaching of the formal ...knowledge. However, in mathematics teaching problems are perceived to satisfy these conditions, such as relating local contexts to the rigidity of formal mathematical content. In this sense, this article presents reflections from the statements of students of the Peasant Education Course, in the habilitation in Mathematics, about what they think of these contexts (Peasant context and formal mathematics) and the languages practiced in educational activities, such as uses of algorithms and contextualized problems. Wittgenstein's (1999) philosophy of language and the concepts of language games and family resemblances are used to analyze students' speeches. The discourse of the defense of the contextualization from the daily life is shown present in the speeches of the students, as well as defend the importance of the formal content. The students still demonstrate to prefer the use of algorithms to contextualized problems.
The research is relevant as educational computer games are included in students’ mathematical activity and form additional opportunities to improve the quality of teaching mathematics in a digital ...school, to support the formation of the demanded professional competence - computational thinking. To form the appropriate skills that determine the essence of special computational thinking, the authors propose to include game educational spaces based on digital gamification resources into students’ mathematical activities. The research aims to resolve the contradiction between requirements of the modern economy for specialists’ high level of computational thinking and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of this research is to study the features of using gamification technologies in teaching mathematics to form the skills and abilities that make up the essence of computational thinking. The article describes directions of educational and cognitive mathematical activity based on the principles of gamification. The authors clarify the concept of “computational thinking”, which includes a system of actions for activating patterns, connections between them from human memory, and compile an effective algorithm for solving them: to obtain relevant information on advanced technological developments; to state the problem and model; to use a software product with mathematical content.
Understanding trigonometry relational system is a school mathemat-ics demanding topic. The angle, the unit circle and the trigonometric functions are its foundational notions. Trigonometric contents ...mean-ing and their understanding involve these three concepts and their re-lationships. This research aims to deepen in the pre-service teachers’ understanding about the angle, the unit circle and the trigonometric function when converting notions between two trigonometric repre-sentation systems based on the unit circle and the trigonometric func-tions. The results indicate that pre-service mathematics teachers’ pre-sent a lack of connections between the goniometric and the analytical representation system.
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