scholarly journals Iconic and Symbolic Representation in Early Mathematics Teaching

2021 ◽  
Vol 16 (3(61)) ◽  
pp. 11-25
Author(s):  
Joanna Żądło-Treder
Keyword(s):  
Mathematics Teaching ◽  
Symbolic Representation ◽  
Physical Activities ◽  
Pictorial Representation ◽  
Symbolic Language ◽  
Mathematical Concepts ◽  
Early Mathematics ◽  
Careful Preparation ◽  
Graphic Element ◽  
Teaching Of Mathematics

Mathematics is an abstract science, it uses a specific symbolic language, a kind of code that is difficult for children to comprehend. Using operation signs and numbers is not simple and obvious for them. The learning of mathematics by children cannot therefore be based on symbols alone. Action is needed first. However, since there is a large gap between an action and a symbol, it is necessary to support the teaching of mathematics with graphic means. Introducing a graphic element as a kind of methodological aid requires careful preparation, motivation and embedding it in previous physical activities performed by children. Otherwise, such an item, instead of facilitating the understanding of a concept, hinders that understanding and becomes an illusory aid. This paper describes the role and importance of pictorial representation in early mathematics teaching. Based on selected examples of tasks from textbooks, the difficulties of illustrating mathematical concepts are presented, and appropriate methodological solutions in this area are indicated.

scholarly journals O Fractal Árvore Pitagórica e Diferentes Representações: uma Investigação com Alunos do Ensino Médio

2018 ◽  
Vol 11 (2) ◽  
pp. 160
Author(s):  
Veridiana Rezende ◽  
Mariana Moran ◽  
Thais Michele Mártires ◽  
Fabricia Carvalho Paixão
Keyword(s):  
High School ◽  
Public School ◽  
Natural Language ◽  
Mathematics Teaching ◽  
Pythagorean Theorem ◽  
Mathematical Concepts ◽  
Teaching Situation ◽  
Methodological Procedures ◽  
Teaching Of Mathematics

A Geometria dos Fractais em sala de aula propicia diversas possibilidades de estudos de conceitos matemáticos, incentiva o uso de recursos tecnológicos, proporciona surpresas pela beleza e complexidade dos fractais. Apresentamos neste texto uma investigação acerca das possibilidades do uso de diferentes registros de representação semiótica aliado à Geometria dos Fractais, no que concerne ao ensino de matemática. E, para exemplificar estas possibilidades em sala de aula, relatamos uma situação de ensino, que foi implementada com quinze (15) alunos do 3º ano do Ensino Médio de uma escola pública do interior do Paraná, relacionada à construção do fractal Árvore Pitagórica. Como procedimentos metodológicos elaboramos cinco tarefas associadas ao fractal Árvore Pitagórica que tiveram por finalidade explorar diversos conceitos matemáticos emergidos no processo de construção deste fractal, nas quais foram contempladas as representações figural, numérica, algébrica e linguagem natural. As análises dos registros mostram que a implementação das tarefas possibilitou aos alunos: o estudo de diversos elementos matemáticos tais como: áreas e perímetros de quadrados e triângulos, teorema de Pitágoras, ângulos, congruência de triângulos, frações, potências, números decimais entre outros; as construções figurais da Árvore Pitagórica por meio de diferentes representações e a visualização das principais características de um fractal, bem como a compreensão de seu processo de construção.Palavras-chave: Ensino de Matemática. Representação Semiótica. Geometria dos Fractais.AbstractThe geometry of the fractures in the classroom provides several possibilities for studying mathematical concepts, encourages the use of technological resources, provides surprises for the beauty and complexity of the fractals. We present in this text an investigation about the possibilities of the use of different registers of semiotic representation allied to the Geometry of the Fractais, in what concerns the teaching of mathematics. And, to exemplify these possibilities in the classroom, we report a teaching situation, which was implemented with fifteen (15) students of the 3rd year of High School in a public school in the interior of Paraná, related to the construction of the Pythagorean Tree fractal. As methodological procedures we elaborated five tasks associated to the fractal Pythagorean Tree that had as purpose to explore several mathematical concepts emerged in the process of construction of this fractal, in which figural, numerical, algebraic and natural language representations were contemplated. The analysis of the registers shows that the implementation of the tasks enabled the students to study several mathematical elements such as: areas and perimeters of squares and triangles, Pythagorean theorem, angles, congruence of triangles, fractions, powers, decimals, among others; the figurative constructions of the Pythagorean Tree by means of different representations and the visualization of the main characteristics of a fractal, as well as the understanding of its process of construction.Keywords: Mathematics Teaching. Semiotic Representation. Geometry of Fractions.

Supporting Young Children’s Development of Executive Function Through Early Mathematics

2021 ◽  
Vol 8 (2) ◽  
pp. 192-199
Author(s):  
Christina Mulcahy ◽  
Crystal A. Day Hess ◽  
Douglas H. Clements ◽  
Jasmine R. Ernst ◽  
Sarah E. Pan ◽  
...  
Keyword(s):  
Executive Function ◽  
Mathematics Achievement ◽  
Mathematics Teaching ◽  
Early Childhood Teachers ◽  
Academic Skills ◽  
High Quality ◽  
Alternative Strategies ◽  
Early Mathematics ◽  
General Skills ◽  
And Behavior

Early childhood teachers face competing instructional priorities to support specific academic skills and general skills that underlie learning, such as executive function (EF) skills that allow children to control their own thinking and behavior. As the evidence shows, EF skills predict later mathematics achievement, and early mathematics predicts later EF. These relations between mathematics and EF suggest high-quality mathematics teaching has a dual benefit: Teachers can promote children’s math and EF competencies by embedding support for EF in high-quality mathematics activities. Children benefit when guided to reflect on solutions and alternative strategies, and teachers benefit from guidance on how to support both math and EF. Finally, research on teachers developing both domains can inform educational policy.

scholarly journals COMPLEMENTARY EDUCATION SPACES OF VENEZUELAN MATHEMATICS EDUCATORS. CASE: VENEZUELAN SCHOOL FOR THE TEACHING OF MATHEMATICS - EVEM

2020 ◽  
Vol 24 ◽  
Author(s):  
Cinthia del Carmen Humbría Burgos ◽  
Fredy Enrique González
Keyword(s):  
Mathematics Education ◽  
Qualitative Study ◽  
Social History ◽  
Mathematics Teaching ◽  
Scientific Field ◽  
Epistemology Of Science ◽  
Complementary Education ◽  
Mathematics Educators ◽  
Teaching Of Mathematics ◽  
Teaching Learning

ABSTRACT Qualitative study on mathematical educators complementary education spaces, considering the Venezuelan School for Mathematics Teaching. Referents: Social history (Bernal); Epistemology of Science (Toulmin); Scientific Field (Bourdieu); Systemic vision of Mathematics Education in Venezuela (Beyer). Finding: EFC-EMVs are dialogic, interdisciplinary, generate knowledge about teaching-learning of mathematics, for the Venezuelan educational reality.

scholarly journals Um cenário de estudos envolvendo o ensino de Matemática através da Resolução de Problemas em periódicosA study scenario involving the teaching of mathematics through problem solving in journals

2020 ◽  
Vol 22 (2) ◽  
pp. 252-280
Author(s):  
Kaique Nascimento Martins ◽  
Jamille Vilas Bôas
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
The State ◽  
University Education ◽  
Teaching Mathematics ◽  
Mathematics Teaching And Learning ◽  
Teaching Of Mathematics

ResumoO presente estudo é uma pesquisa bibliográfica inspirada no Estado do Conhecimento, tendo como objetivo compreender focos temáticos nas produções acadêmicas que utilizam/abordam o ensino de matemática através da resolução de problemas. Para tanto, realizou-se um mapeamento das produções acadêmicas publicadas nos periódicos: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista e Educação Matemática Pesquisa, entre janeiro de 2011 e junho de 2019. De um modo geral, percebemos uma variedade de estudos contendo diferentes perspectivas discutidas e abordadas tanto na educação básica quanto no ensino superior.  A partir deste trabalho, é possível ampliar o entendimento sobre a temática, fortalecendo a ideia de que esta pode potencializar o processo de ensino e aprendizagem de matemática.Palavras-chave: Resolução de problemas, Mapeamento, Educação matemática.AbstractThe present study is a bibliographic research inspired by the state of knowledge, aiming to understand thematic focuses on academic productions that use/approach teaching mathematics through problem-solving. For this purpose, we mapped the academic productions published in journals: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista, and Educação Matemática Pesquisa, published between January 2011 and June 2019. We noticed a variety of studies containing different perspectives discussed and addressed both in basic and university education. From this work, it is possible to broaden the understanding of the theme, strengthening the idea that it can enhance the mathematics teaching and learning process.Keywords: Problem solving, Mapping, Mathematics education. ResumenEl presente estudio es una investigación bibliográfica inspirada en el estado del conocimiento, con el objetivo de comprender enfoques temáticos sobre producciones académicas que utilizan/abordan la enseñanza de las matemáticas a través de la resolución de problemas. Para ello, mapeamos las producciones académicas publicadas en las revistas: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista y Educação Matemática Pesquisa, publicadas entre enero de 2011 y junio de 2019. Notamos una variedad de estudios que contienen diferentes perspectivas discutidas y abordadas tanto en educación básica como en educación universitaria. A partir de este trabajo, es posible ampliar la comprensión del tema, fortaleciendo la idea de que puede potenciar el proceso de enseñanza y aprendizaje de las matemáticas.Palabras clave: Resolución de problemas, Mapeo, Educación matemática.

Dynamical Mathematical Software

2013 ◽  
pp. 70-88
Author(s):  
Samer Habre
Keyword(s):  
Learning Environment ◽  
Difference Equations ◽  
Mathematical Software ◽  
Mathematical Concepts ◽  
Visual Component ◽  
Innovative Methods ◽  
Modern Learning ◽  
Teaching Of Mathematics ◽  
User Friendly ◽  
The Way

Understanding mathematical concepts is many-folded. Traditional mathematics mostly emphasizes the algebraic/analytical aspect of a problem with minimal reference to its graphical aspect and/or numerical one. In a modern learning environment, however, multiple representations of concepts are proving to be essential for the teaching of mathematics. The availability of user-friendly dynamical software programs has paved the way for a radical yet smooth way for changing the way mathematical concepts are perceived. This chapter presents some of the author’s attempts for employing innovative methods in teaching topics in calculus, in differential and difference equations. The focus is on the use of dynamical programs that boost the visual component of the topics being investigated, hence contributing to a more complete understanding of these topics.

scholarly journals Doing, Teaching, Learning and Thinking About Mathematics – On Becoming a Transformative Teacher

2018 ◽  
Vol 7 (1) ◽  
pp. 11-24
Author(s):  
Binod Prasad Pant
Keyword(s):  
Mathematics Teacher ◽  
Mathematics Teaching ◽  
Teaching Mathematics ◽  
Algorithmic Problem ◽  
Academic Problems ◽  
Mathematical Concepts ◽  
Teaching Career ◽  
Beliefs And Practices ◽  
Mathematical Problems ◽  
Teaching Learning

I solved many mathematical problems till today - countless academic problems inside the classroom, and a few pragmatic problems outside. At the beginning of my teaching career, I spent significant time convincing my students that mathematics teaching is an algorithmic problem solving of routine mathematical items to get the correct answers. Afterwards, I slowly took a shift from doing mathematics to teaching mathematics, identifying lots of tricks, tips and techniques. I spent more than a decade to train myself with better techniques to become a better mathematics teacher seeking better achievements of students in written tests. Later on, I engaged myself as a math learner and sought the significance of the methods I employed to teach the mathematical concepts, relation, and logics. I am now at the crossroads of searching better alternatives that help students learn mathematics in a meaningful way. I frequently ask myself why I am teaching mathematics. What does a good mathematics teacher mean? What we do is largely guided by what we believe. Questioning on the widely accepted assumptions, examining the deep-rooted beliefs for the positive shift, and highlighting the epiphanies of my professional life could be very essential on becoming a transformative teacher. In this paper, I portray my narratives as a student and as a mathematics teacher to explain my shift towards becoming a transformative teacher. Through my verisimilitude narratives, I invite readers to examine their beliefs and practices on teaching mathematics, and envisage for better alternatives being aware of their limitations and contexts.

Teaching machines or what?

1962 ◽  
Vol 55 (5) ◽  
pp. 351-355
Author(s):  
Margaret S. Matchett
Keyword(s):  
Mathematics Teaching ◽  
Programmed Learning ◽  
Teaching Of Mathematics ◽  
Points Of View ◽  
Traditional Patterns ◽  
State Of Affairs ◽  
Teaching Machines ◽  
Wrong Sort

The widespread concern with the teaching of mathematics is coupled, as perhaps such concern is bound to be, with criticisms of present practices from numerous points of view. It is variously held that the wrong mathematics is being taught in the wrong way by the wrong teachers to classes of the wrong sort. Proposals for altering this state of affairs are as diverse as the criticisms. Among those who would radically change the traditional patterns of mathematics teaching are the advocates of some form of programmed learning.

The three faces of (—)

1962 ◽  
Vol 55 (8) ◽  
pp. 668-669
Author(s):  
Kenneth C. Williams
Keyword(s):  
Significant Role ◽  
Mathematics Teaching ◽  
Elementary Algebra ◽  
Mathematical Concepts ◽  
Good Mathematics Teaching

Being able to present concepts clearly is of prime importance in good mathematics teaching. To this end, precise terminology plays a significant role. Whenever the terminology becomes ambiguous, there is the danger of misinterpretation. This is true especially for students of elementary algebra, where many important mathematical concepts are introduced.

A Problem is Something You Don't Want to Have: Problem Solving by Kindergartners

2005 ◽  
Vol 12 (3) ◽  
pp. 146-154
Author(s):  
Lynne Outhred ◽  
Sarah Sardelich
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Social Process ◽  
Mathematical Concepts ◽  
Mathematics Teaching And Learning ◽  
Mental Actions

Although Adrian, when asked by his teacher what a problem is, was adamant that problems are to be avoided, educators believe problem solving is central to mathematics teaching and learning (NCTM 2000). Problem solving supports students as they apply their skills and their knowledge of mathematical concepts and processes to a range of different contexts and as they construct knowledge by reflecting on their own physical and mental actions. When children solve problems together, learning is a social process in which they learn not only from the teacher but also by discussing, arguing, and negotiating with their peers.

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