scholarly journals Compreensão do conceito de taxa de variação por professores em formação continuada

2018 ◽  
Vol 2 (1) ◽  
pp. 27
Author(s):  
Vanilde Bisognin ◽  
Eleni Bisognin
Keyword(s):  
Teacher Training ◽  
Mathematics Teaching ◽  
Concept Image ◽  
Integral Calculus ◽  
Continuous Formation ◽  
Variation Rate ◽  
Training Concept ◽  
Intuitive Idea ◽  
Definition Of ◽  
Image Definition

Resumo: Neste trabalho, são apresentados resultados de uma pesquisa que tem como objetivo analisar como professores em formação continuada, participantes da disciplina de Fundamentos de Cálculo Diferencial de um curso de Mestrado em Ensino de Matemática, interpretam e relacionam as informações explicitadas pelas diferentes representações do conceito de taxa de variação. Para tanto foi aplicada uma sequência de atividades sobre as diferentes representações do conceito de taxa de variação e as respostas das questões foram analisadas e categorizadas. Os resultados apontam que, apesar de terem trabalhado o conceito de taxa de variação em seus cursos de licenciatura em Matemática, alguns professores ainda apresentam dificuldades para compreender esse conceito e relacionar suas diferentes representações. Pela análise dos dados, considera-se que as atividades propostas proporcionaram a evolução da ideia intuitiva de taxa de variação e favoreceram a compreensão desse conceito pelos participantes da pesquisa.Palavras-chave: Taxa de variação; Formação de professores; Imagem de conceito; Definição de conceito. Comprehension of the variation rate concept by teachers in continued trainingAbstract: In this work, results of a research are presented that aim to analyze how teachers in continuous formation, participants in the discipline of Fundamentals of Differential and Integral Calculus of a Master course in Mathematics Teaching, interpret and relate the information explained by the different representations of the concept of rate of variation. For this, a sequence of activities was applied on the different representations of the concept of rate of variation and the answers of the questions were analyzed and categorized. The results show that, although they have worked on the concept of rate of variation in their undergraduate courses in Mathematics, some teachers still find it difficult to understand this concept and to relate their different representations. By analyzing the data, it is considered that the proposed activities provided the evolution of the intuitive idea of rate of variation and favored the understanding of this concept by the research participants.Keywords: Rate of variation; Teacher training; Concept image; Definition of concept. 

scholarly journals HISTORYOGRAPHY OF THE OF DEVELOPMENT THE CONTINUOUS PRIMARY SCHOOL TEACHER TRAINING TO WORK IN THE INCLUSIVE EDUCATION CONDITIONS IN THE UKRAINE (END OF THE XX – START OF THE XXI CENT.)

2021 ◽  
pp. 86-91
Author(s):  
T. DZHAMAN
Keyword(s):  
Teacher Preparation ◽  
Teacher Training ◽  
Primary School ◽  
Inclusive Education ◽  
School Teacher ◽  
Primary School Teacher ◽  
Scientific Analysis ◽  
History Of ◽  
Chronological Sequence ◽  
Definition Of

The article analyzes the views of scientists on the specified problem of study. It is specified that the problem of continuous primary school teacher training to work in the conditions of inclusive education that we studied is a certain chronological sequence of transformations of different visions and it is relevant to the sphere of scientific and pedagogical search. We made a scientific analysis of the studies and clarified the definition of some concepts. It is specified, that we understand the historiography of development the continuous primary school teacher training to work in a conditions of inclusive education as a totality of research scientific and pedagogical works directed on the study of the specified problem from the time of its actualization due to today and the main its task we see in the objective coverage of the history of the issue of continuous primary school teacher preparation to work in conditions of inclusive education with taking into account the transformation of the ideas and views on the problem, studied by us. We generalized the sources processed by us on the basis of the analysis in the historiographical dimension into the two groups: continuous primary school teacher training from the end of XX cent. due to today; The history of inclusive education in the Ukraine from the end of XX cent. due to today.

scholarly journals HISTORY OF MATHEMATICS EDUCATION IN PRIMARY SCHOOL AND IN TEACHER TRAINING IN BRAZIL

2020 ◽  
Vol 24 ◽  
Author(s):  
Wagner Rodrigues Valente ◽  
Maria Célia Leme da Silva
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Primary School ◽  
Mathematics Teaching ◽  
History Of Mathematics ◽  
Theoretical Hypothesis ◽  
Disciplinary Field ◽  
History Of ◽  
The 19Th Century ◽  
The Relationship

Abstract This article discusses results from research developed on the transformations in mathematics teaching in primary school and the mathematics in teacher training from the 19th century to the mid-20th century in Brazil. We have analyzed the understanding of the relationship between the mathematical disciplinary field and pedagogy in order to confirm the theoretical hypothesis that the interactions between the two fields produce mathematics of different natures, which are interconnected.

scholarly journals A inserção da prática como Componente Curricular em um curso de Licenciatura em Matemática: um estudo de caso em cálculo diferencial e integral

2019 ◽  
Vol 41 ◽  
pp. 4
Author(s):  
Paulo Roberto Barbosa ◽  
Livia Carolina Vieira ◽  
Graziela Marchi Tiago
Keyword(s):  
Teacher Training ◽  
Basic Education ◽  
Science And Technology ◽  
Academic Work ◽  
Integral Calculus ◽  
Initial Teacher Training ◽  
Federal Institute ◽  
Reflective Teachers ◽  
Education Science

This work aims to discuss the insertion of the Practice as a Curricular Component (PCC) in a Mathematics Undergraduate course of one Federal Institute of Education, Science and Technology, addressing some works developed and planned more specifically for the discipline of Differential and Integral Calculus. Nowadays, the legislation for initial teacher training at undergraduate courses is established by Resolution no. 2/2015 of the CNE / CP of July 1, 2015, which in article 13, among others, establishes that these courses must have at least 3,200 hours of effective academic work, these being at least 400 hours of PCC. In this way, studies focused on the training practices that are being offered are essential for understanding and improving these PCC applied to undergraduate courses developed at the Federal Institutes. Among the perspectives reached are the possibility of applying these activities in basic education and the training of reflective teachers, concerned with properly aligning practice and theory.

Mathematics and Modern Life

1928 ◽  
Vol 21 (6) ◽  
pp. 350-352
Author(s):  
Harry C. Barber
Keyword(s):  
Secondary School ◽  
Mathematics Teaching ◽  
School Curriculum ◽  
Modern Life ◽  
Mathematics Courses ◽  
The World ◽  
The Subject ◽  
Definition Of

Present day demands that each subject justify its existence in the school curriculum are so well known as to need no review in this paper. The bearing of these demands on mathematics, however, presents an interesting situation when considered in relation to the increasing importance of mathematics in modern civilization. It is a curious phenomenon that mathematics should be challenged just at this time when its value in the world is greater and more apparent than ever before. This challenge docs not so much question the value of mathematics itself as the objl?ctives of ntathematics teaching, the content of mathematics courses, and the methods of presentation. The mathematics of the secondary school may well be criticized as being too mechanical, too much concerned with technique, too little concerned with the true kernel of the subject. The leaders within the field of mathematics teaching are in hearty accord with these criticisms, and they are making a constant battle against (1) too meagre a definition of mathematics and too narrow a concept of its possibilities, (2) the use of obsolescent material, (3) the rote method of presentation.

scholarly journals Brightness and image definition of pictures viewed from between the legs

2010 ◽  
Vol 73 (1) ◽  
pp. 144-159 ◽  
Author(s):  
Atsuki Higashiyama ◽  
Miyuki Toga
Keyword(s):  
Definition Of ◽  
Image Definition

scholarly journals Empleo de simulaciones dinámicas en matlab como parte del proceso de enseñanza-aprendizaje de las matemáticas con aplicación al cálculo diferencial e integral.

2018 ◽  
Vol 5 (1) ◽  
pp. 36-41
Author(s):  
Miguel Lema Carrera
Keyword(s):  
Learning Process ◽  
Definite Integral ◽  
Integral Calculus ◽  
Dynamic Simulations ◽  
Student Community ◽  
Basic Ideas ◽  
Definition Of ◽  
Teaching Learning ◽  
Disk Method ◽  
Geometric Definition

     La matemática en todos los tiempos ha tenido como principal fuente de inspiración la visualización, jugando un papel importante en el desarrollo de conceptos, nociones e ideas básicas del cálculo diferencial e integral. El presente trabajo proporciona herramientas y métodos básicos de uso relativamente sencillo, desarrollados en el paquete computacional MATLAB, trabajando temas como la definición geométrica de derivada, la integral definida y cálculo de volúmenes de revolución utilizando el método de discos, que permite obtener resultados muy poderosos en simulaciones dinámicas “animadas” que sirvan de soporte y recurso didáctico facilitador en el proceso de enseñanza-aprendizaje del cálculo. Modificando y renovando en una primera instancia la forma tradicional de enseñanza de esta asignatura en los primeros años del ciclo básico universitario en esta institución y porque no del país, además, se espera que este trabajo, permita desterrar el paradigma entorno a la comunidad estudiantil, que ha relacionado al cálculo matemático con una idea pura y completamente algebraizada, estática y memorística. ABSTRACT The mathematics of all time has had as the main source of inspiration the visualization, playing an important role in the development of concepts, notions and basic ideas of the differential and integral calculus. The present work provides tools and basic methods of use relatively simple, developed in the computational package Matlab, working topics such as the geometric definition of derivative, the definite integral and calculation of volumes of revolution using the disk method, which allows to obtain very powerful results in "animated" dynamic simulations that serve as support and facilitating didactic resource in the teaching-learning process of calculus. Modifying and renewing in the first instance the traditional way of teaching this subject in the first years of the basic university cycle in this institution and why not in the country, in addition, it is expected that this work, to banish the paradigm around the student community, that has related to the calculus with a pure and completely algebraic, static and rote idea.

scholarly journals La danza en el ámbito de educativo (Dance in the Educational Context)

Retos ◽  
2015 ◽  
pp. 42-45
Author(s):  
Gregorio Vicente Nicolás ◽  
Nuria Ureña Ortín ◽  
Manuel Gómez López ◽  
Jesús Carrillo Vigueras
Keyword(s):  
Teacher Training ◽  
Gender Discrimination ◽  
Emotional Development ◽  
Dance Education ◽  
Educational Context ◽  
Human Beings ◽  
Education Movement ◽  
And Gender ◽  
Definition Of

El presente trabajo ofrece una visión general del fenómeno de la danza en el ámbito de la educación. En un primer momento se realiza una exposición de los diferentes componentes o aspectos del ser humano sobre los que la danza incide de forma más evidente. Posteriormente se presenta una revisión de las definiciones propuestas por diferentes autores que consideramos más relevantes y se incluye una definición propia del concepto. También se destacan las aportaciones de la danza a la educación desde el punto de vista social, físico, intelectual y afectivo y se señalan los mayores problemas que esta disciplina ha tenido para ser incluida como una materia más: falta de formación del profesorado, falta de recursos y espacios adecuados y discriminación de género. Finalmente, se concluye con una reflexión sobre las formas de danzas más adecuadas en el ámbito educativo.Palabra clave: danza, baile, educación, movimiento, expresión corporal.Abstract: This paper provides an overview of the phenomenon of dance in the field of education. At first, it is made a presentation of the different components or aspects of human beings on that dance impacts in a more obvious way. Subsequently, we present a review of the definitions proposed by different authors that we consider most relevant and it is included a personal definition of the concept. It also highlights the contributions of dance to education in terms of social, physical, intellectual and emotional development and identifies the major problems that this discipline has had to be included as a subject: lack of teacher training, lack of adequate space and resources and gender discrimination. Finally, it concludes with a reflection on the most appropriate forms of dance in the educational context.Key words: dance, education, movement, corporal expressión.

scholarly journals Forms of applıcatıon of algorıthms ın school mathematıcs teachıng

2021 ◽  
Vol 2021 (2 (135)) ◽  
pp. 7-12
Author(s):  
Kamala Yunis
Keyword(s):  
Problem Solving ◽  
Computer Technology ◽  
Mathematics Teaching ◽  
Numerical Data ◽  
Point Of View ◽  
The Third ◽  
Theoretical Structure ◽  
Definition Of ◽  
Integrated Mathematics

As for the qualitative definition of the theoretical structure of the concept of algorithm, obtained by building a system of its study on the basis of component analysis in the article, it should be completed by studying the types of algorithmic processes. Three common types of such processes (linear, branching and recursive) play a slightly different role here. The first two types are somewhat simple, as we tried to show in Example 1, it would be natural to use them in the study of the components of the algorithm. Recursive processes can be applied to the play of already separated concepts. There are plenty of examples in various sections of Algebra, such as the "sequences" section, in particular. Finding the approximate value of an expression using the Heron formula can be a good example of recursive processes. The purpose of the research is to develop a methodological system that identifies opportunities to improve the quality of integrated mathematics teaching in V-IX grades and connect it with computer technology as well as identifies ways to apply it in the learning process. Textbooks often show the performance of a particular action on a few specific examples. We come across different situations here. Sometimes the rule is stated after the solution of the work, and sometimes the work is considered after the expression of the rule. The third case is possible, there is no definition of the rule in the textbook, but specific examples of the application of the formed algorithm are considered. This is quite common in school textbooks, especially when considering complex algorithms. In such cases, it is accepted to call the solutions of the studies as examples. The sample solution must meet certain requirements. Let's separate some of them from the point of view of the formed algorithm: the most characteristic cases of the considered type of problem should be considered; numerical data should be selected in such a way that the necessary calculations can be performed orally in order to draw students' attention to the sequence of elementary operations that make up the steps of the formed algorithm. If the problem-solving example meets these requirements, then the type of problem assigned to it can be considered as an algorithm for solving the problem. If, depending on the initial data, there are several fundamentally different cases of problem solving, it is necessary to consider examples of problem solving for each such case.

scholarly journals Review of Suppes 1957 Proposals For Division by Zero

2021 ◽  
Author(s):  
James Anderson ◽  
Jan Bergstra
Keyword(s):  
Real Numbers ◽  
Integral Calculus ◽  
Arithmetical Functions ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Definition Of ◽  
Type 3 ◽  
Order Predicate Calculus

We review the exposition of division by zero and the definition of total arithmetical functions in ``Introduction to Logic" by Patrick Suppes, 1957, and provide a hyperlink to the archived text. This book is a pedagogical introduction to first-order predicate calculus with logical, mathematical, physical and philosophical examples, some presented in exercises. It is notable for (i) presenting division by zero as a problem worthy of contemplation, (ii) considering five totalisations of real arithmetic, and (iii) making the observation that each of these solutions to ``the problem of division by zero" has both advantages and disadvantages -- none of the proposals being fully satisfactory. We classify totalisations by the number of non-real symbols they introduce, called their Extension Type. We compare Suppes' proposals for division by zero to more recent proposals. We find that all totalisations of Extension Type 0 are arbitrary, hence all non-arbitrary totalisations are of Extension Type at least 1. Totalisations of the differential and integral calculus have Extension Type at least 2. In particular, Meadows have Extension Type 1, Wheels have Extension Type 2, and Transreal numbers have Extension Type 3. It appears that Suppes was the modern originator of the idea that all real numbers divided by zero are equal to zero. This has Extension Type 0 and is, therefore, arbitrary.

Computability and λ-definability

1937 ◽  
Vol 2 (4) ◽  
pp. 153-163 ◽  
Author(s):  
A. M. Turing
Keyword(s):  
Computable Function ◽  
General Recursive Function ◽  
Technical Details ◽  
Intuitive Idea ◽  
Short Space ◽  
Definition Of ◽  
Definable Functions ◽  
Positive Integers ◽  
Computable Functions ◽  
Definable Function

Several definitions have been given to express an exact meaning corresponding to the intuitive idea of ‘effective calculability’ as applied for instance to functions of positive integers. The purpose of the present paper is to show that the computable functions introduced by the author are identical with the λ-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene. It is shown that every λ-definable function is computable and that every computable function is general recursive. There is a modified form of λ-definability, known as λ-K-definability, and it turns out to be natural to put the proof that every λ-definable function is computable in the form of a proof that every λ-K-definable function is computable; that every λ-definable function is λ-K-definable is trivial. If these results are taken in conjunction with an already available proof that every general recursive function is λ-definable we shall have the required equivalence of computability with λ-definability and incidentally a new proof of the equivalence of λ-definability and λ-K-definability.A definition of what is meant by a computable function cannot be given satisfactorily in a short space. I therefore refer the reader to Computable pp. 230–235 and p. 254. The proof that computability implies recursiveness requires no more knowledge of computable functions than the ideas underlying the definition: the technical details are recalled in §5.

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