scholarly journals ON THE NATURE AND ORIGIN OF ALGEBRAIC SYMBOLISM

2008 ◽  
Author(s):  
ALBRECHT HEEFFER
Keyword(s):  
Algebraic Symbolism

scholarly journals Meanings given to algebraic symbolism in problem-posing

2018 ◽  
Vol 98 (1) ◽  
pp. 19-37 ◽  
Author(s):  
María C. Cañadas ◽  
Marta Molina ◽  
Aurora del Río
Keyword(s):  
Problem Posing ◽  
Algebraic Symbolism

Historically Speaking,— On The Practicality of The Rule of False Position

1958 ◽  
Vol 51 (8) ◽  
pp. 606-608
Author(s):  
Howard Eves
Keyword(s):  
False Position ◽  
Algebraic Symbolism

In the Rhind (or Ahmes) papyrus, which dates back to at least 1650 B.c., we find the following problem : “A quantity, its 2/3, its 1/2, and its 1/7, added together, become 33. What is the quantity?” Today, with our algebraic symbolism, we would probably solve this problem by letting x denote the sought quantity

Using Spreadsheets to Promote Algebraic Thinking

1998 ◽  
Vol 4 (8) ◽  
pp. 470-478
Author(s):  
Michael T. Battista ◽  
Caroline Van Auken Borrow
Keyword(s):  
Real World ◽  
Algebraic Thinking ◽  
Algebraic Reasoning ◽  
Elementary Grades ◽  
Division Algorithm ◽  
Arithmetic Operations ◽  
Algebraic Symbolism ◽  
Real World Problems

For students to find algebra conceptually meaningful, as well as useful in modeling and analyzing real-world problems, they must be able to reflect on, make sense of, and communicate about general numerical procedures (Kieran 1992). Such procedures consist of set sequences of arithmetic operations performed on numbers. Examples include computing an average and performing the standard division algorithm. Thinking about numerical procedures starts in the elementary grades and continues in successive grades until students can eventually express and reflect on the procedures using algebraic symbolism. This article outlines how such thinking can progress to algebraic reasoning and illustrates how computers used to promote this progression.

scholarly journals On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought

2015 ◽  
pp. 7 ◽  
Author(s):  
Sören Stenlund
Keyword(s):  
Sixteenth Century ◽  
Decimal Place ◽  
Place Value ◽  
Late Nineteenth Century ◽  
Value System ◽  
Early Modernity ◽  
Modern Physics ◽  
Ontological Sense ◽  
Modern Mathematics ◽  
Algebraic Symbolism

The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity.

Changing Objectives in the Teaching of Algebra and Trigonometry in the Senior High School

1946 ◽  
Vol 39 (7) ◽  
pp. 314-319
Author(s):  
Benjamin Braverman
Keyword(s):  
High School ◽  
Foreign Language ◽  
Instructional Material ◽  
Secondary Mathematics ◽  
Senior High School ◽  
Point Of View ◽  
Elementary Algebra ◽  
Language Teacher ◽  
Recent Origin ◽  
Algebraic Symbolism

That considerable changes have taken place in the point of view governing the teaching of secondary mathematics, as well as in the content of the instructional material and its pedagogic presentation is quite obvious to any one who takes the trouble to compare a text in secondary mathematics published, let us say, in 1915 with one of more recent origin. It was forcibly brought home to me at the beginning of the present semester when I offered our department lesson-by-lesson syllabus in elementary algebra to a foreign language teacher who had been assigned to teach that subject in my department. He studied the first few pages with considerable surprise. These pages of the syllabus deal with algebraic symbolism and the formula. “What,” he exclaimed, “no x's, y's, and z's.” He felt a little relieved when I assured him that a little of that would come later, but in a much more modified form than he had been exposed to.

scholarly journals Algebraic Symbolism

1909 ◽  
Vol 68 (1752supp) ◽  
pp. 78-79
Author(s):  
Susan R. Benedict
Keyword(s):  
Algebraic Symbolism

scholarly journals A Organização do Ensino de Álgebra: Contribuições da Atividade Orientadora de Ensino

2021 ◽  
Vol 22 (4) ◽  
pp. 499-509
Author(s):  
Mara Viviane da Silva Pelegrinello Camargo ◽  
Anderson Minosso ◽  
Maria Lucia Panossian ◽  
Luciana Schreiner de Oliveira
Keyword(s):  
Sao Paulo ◽  
Department Of Education ◽  
São Paulo ◽  
Research Groups ◽  
Learning Spaces ◽  
History Of ◽  
And Mathematics ◽  
Theoretical Thinking ◽  
The University ◽  
Algebraic Symbolism

ResumoAs constantes dificuldades manifestadas por estudantes em relação à aprendizagem do conhecimento algébrico têm provocado a necessidade de repensar o processo de organização do ensino deste conteúdo. Nesse sentido, grupos de pesquisas vinculados às Instituições de Ensino Superior se debruçaram nesta temática e aqui serão destacadas as pesquisas de membros do Grupo de Estudos e Pesquisa sobre a Atividade Pedagógica (GEPAPe), coordenado pelo professor Dr. Manoel Oriosvaldo de Moura, junto ao departamento de Educação da Universidade de São Paulo (USP). Assim, neste artigo serão analisadas as contribuições da Atividade Orientadora de Ensino para a organização do ensino de álgebra, a partir das produções do GEPAPe. Para o cumprimento deste objetivo foram buscados textos na forma de artigos, de livros, de capítulos de livros e anais de eventos que foram selecionados a partir da plataforma lattes de cada um dos pesquisadores deste grupo. Como resultado foi possível reconhecer que as produções revelam a compreensão sobre a álgebra e seu ensino sustentadas pelo estudo do movimento dialético histórico e lógico visando o desenvolvimento dos nexos conceituais do conhecimento algébrico e o desenvolvimento do pensamento teórico dos estudantes, superando o reconhecimento empírico e aparente do simbolismo algébrico. Tal compreensão sobre a organização do ensino de álgebra se materializa por meio das Situações Desencadeadoras de Aprendizagem (Situação Emergente do Cotidiano; Jogo; História Virtual do Conceito), que são desenvolvidas em espaços de aprendizagem como Clubes de Matemática e Oficinas Pedagógicas de Matemática em diferentes instituições brasileiras. Palavras-chave: AOE. GEPAPe. Situação Desencadeadora de Aprendizagem. AbstractThe constant difficulties expressed by students regarding learning algebraic knowledge have led to the need to rethink the teaching organizing process of this content. Thus, research groups linked to Higher Education Institutions, focused on this theme and the research will be highlighted of the Study and Research Group on Pedagogical Activity members (GEPAPe), coordinated by Professor Dr. Manoel Oriosvaldo de Moura, with the Department of Education at the University of São Paulo (USP). Thus, in this article, the Teaching Guidance Activity contributions to the algebra teaching organization will be analyzed, based on the GEPAPe productions. To fulfill this objective, texts were sought in the form of articles, books, book chapters and event proceedings that were selected from the lattes platform of each of the researchers in this group. As a result, it was possible to recognize that the productions reveal the understanding of algebra and its teaching supported by the study of the historical and logical dialectical movement aiming at the development of the conceptual nexus of algebraic knowledge and the students' theoretical thinking development, surpassing the empirical and apparent recognition of algebraic symbolism. This understanding of the algebra teaching organization is materialized through the Learning Trigger Situations (Emerging Situation of Everyday Life; Game; Virtual History of the Concept), which are developed in learning spaces such as Math Clubs and Mathematics Pedagogical Workshops in different institutions Brazilian companies. Keywords: AOE. GEPAPe. Learning Triggering Situation.

Sign in / Sign up

Export Citation Format

Share Document