Adalira Sáenz-Ludlow

University of North Carolina at Charlotte | UNC Charlotte · Department of Mathematics & Statistics

The focus of this chapter is twofold. The first is a semiotic description of the nature of diagrams. The second is a description of the type of reasoning that the transformation of diagrams facilitates in the construction of mathematical meanings. I am guided by the Peircean definition of diagrams as icons of possible relations and his conceptualiz...

Cuando el DIE (Doctorado Interinstitucional en Educación) de la Universidad Distrital Francisco José de Caldas le propuso a nuestro énfasis de Educación Matemática publicar un libro que concentrara lo más relevante de las investigaciones en nuestro campo, los docentes del doctorado elegimos sin dudarlo a los mismos, como autores de la primera publi...

Proving an existence theorem is less intuitive than proving other theorems. This article presents a semiotic analysis of significant fragments of classroom meaning-making which took place during the class-session in which the existence of the midpoint of a line-segment was proven. The purpose of the analysis is twofold. First follow the evolution o...

Using a semiotic perspective based on Peirce’s triadic sign theory, we try to capture part of the complexity that teacher and students encounter during the transition from an empiric procedure used to solve a geometric problem to a mathematical procedure needed to validate the construction, within a theoretic system for Euclidean geometry.

During the last two decades, semiotics has been attaining an important explanatory role within mathematics education. This is partly due to its wide range of applicability. In particular, the success of semiotics in mathematics education may be also a consequence of the iconicity and indexicality embedded in symbols, in general, and mathematical sy...

Semiotic reality is a fundamental part of our common reality. Where we stand in this chapter looks upon the teaching-learning of mathematics as a double semiotic process of interpretation. It takes place within the socio-mathematical semiotic reality that teachers and students inherit and jointly activate in the classroom.

This chapter is framed both within the Kantean notions of sensible and intellectual intuitions and within the Peircean notion of collateral knowledge and classification of inferential reasoning into abductive, inductive, and deductive. An overview of the Peircean notion of abduction is followed by a sub-classification of abductions according to Tha...

Semiotics as a Tool for Learning Mathematics is a collection of ten theoretical and empirical chapters, from researchers all over the world, who are interested in semiotic notions and their practical uses in mathematics classrooms. Collectively, they present a semiotic contribution to enhance pedagogical aspects both for the teaching of school math...

The meaning of a geometric object is consolidated through the use of its definition and of the statements that establish its properties; also in the use of the object itself as a tool. So, understanding a geometric object involves, among other things, operationalizing its definition. That is, the learner should be able to pertinently use the defini...

El énfasis de Educación Matemática del Doctorado Interinstitucional en Educación de las Universidades Distrital Francisco José de Caldas, del Valle y Pedagógica Nacional, presenta a la comunidad de profesores e investigadores esta obra como un aporte a la discusión de los desarrollos de este campo intelectual. La obra compila resultados de investig...

Historically the words representation and symbol have had overlapping meanings, meanings that usually disregard the role played by the interpreter. Peirce’s theory of signs accounts for these meanings and also for the role of the interpreter. His theory draws attention to the static and dynamic nature of signs. Sign interpretation can be viewed as...

Usando la teoría de signos de Charles Sanders Peirce, este artículo introduce la noción de riqueza matemática. La primera sección argumenta la relación intrínseca entre las matemáticas, los aprendices de matemáticas y los signos matemáticos. La segunda, argumenta la relación triangular entre interpretación, objetivación y generalización. La tercera...

Classroom communication has been recognized as a process in which ideas become objects of reflection, discussion, and amendments affording the construction of private mathematical meanings that in the process become public and exposed to justification and validation. This paper describes an explanatory model named “interpreting games”, based on the...

Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of...

Fourth graders who participated in a yearlong teaching experiment constructed their own bridge between natural number knowledge and initial conceptualizations of fractions in discrete wholes. This bridge was established by a chain of signs individually and collectively generated. Students came to re-conceptualize natural number as “manifold of unit...

This paper analyzes the interpretations of equality and the equal symbol of the third-grade children who participated in a year long whole-class socio constructivist teaching experiment. These children initially interpreted the equal symbol as a command to perform an arithmetical operation; it was less natural to them to interpret it as a relationa...

A longitudinal constructivist teaching experiment that lasted approximately one academic year was conducted with six third graders. The purpose of the teaching experiment was to analyze the itinerary of children's ways of operating while solving fraction tasks. Ann was one of the third graders who participated in the teaching experiment, and her ca...

In this classroom a child introduced the word "split" when he was asked to describe his mental activity in performing the addition of two numbers; the teacher initiated a spatial representation using a broken line. Subsequently, the children used their own pictorial representations. The paper presents an analysis of the numerical diagrams used by t...

A longitudinal teaching experiment was conducted with six third graders to analyze the itinerary of their ways of operating while solving fraction tasks. These children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. They solved fraction tasks in similar ways, though with different degrees of...

Documents from different educational organizations had long advocated a synergistic method for the teaching and learning of mathematics (Everybody Counts, NRC, 1989; Professional Standards for School Mathematics, NCTM, 1991; A Call for Change, MAA, 1991; Principles and Standards for School Mathematics, NCTM, 2000). This method advocates a conceptua...

A four-month pilot teaching-experiment on the learning of geometry was conducted with two pre-service teachers and two in-service teachers. The purpose of the pilot teaching-experiment was to understand how learners, who already have some knowledge of geometric objects, are able to reorganize this knowledge and broaden it in order to develop a bett...

The paper analyzes the method of a third-grade teacher to elicit the generation of story-problems on the part of the students throughout the school year. The teacher triggered the students' creativity and encouraged them to use their personal experiences and their imagination to make stories and to take into account numerical relations to ask numer...

Since antiquity perception and imagination have been relegated to a necessary but secondary place. Philosophers before Kant did not embrace sense experience and imagination in the process of knowing but they were unable to divorce themselves from it. Aristotle, for example said, "The soul never thinks without an image" (Aristotle, Posterior Analyti...