In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a…

The aim of this research is to study how students recognise the concept of gradient of a function of two variables in its different representations and how they make conversions between these representations. Three groups of university students with different profiles took part in this research, and Duval's theory of semiotic representations was…

The study reported in this paper contributes to the literature on prospective teachers' decision making, specifically regarding how they analyze and make informed decisions about the use of their textbooks. We designed a training intervention with 28 future Costa Rican teachers, in which they had to identify and manage semiotic conflicts that can…

Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models.…

The aims of this article are to document the types of signs that young children make to represent their mathematical thinking, and to determine the extent to which features of usage-based language acquisition are evident in children's early graphical communications made in mathematical contexts. Studies of young children's symbolic principles in…

This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

In the context of early algebra research and as part of a classroom teaching experiment (CTE), we investigated fourth grade (9- to 10-year-old) students' justifications of how they performed tasks involving the functional relationship y = 2x. We related their written justifications (part of the task) to the task characteristics, which included…

In this paper, we take a semiotic/dialogic approach to investigate how a group of UK 12-13-year-old students work with hierarchical defining and classifying quadrilaterals. Through qualitatively analysing students' decision-making processes, we found that the students' decision-making processes are interpreted as transforming their…

While many semiotic and cognitive studies on learning mathematics have focused primarily on students, this study focuses mainly on teachers, by seeking to bring to light their awareness of the semiotic and cognitive aspects of learning mathematics. The aim is to highlight the degree of awareness that teachers show about: (1) the distinction…

This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the point of view of OSA. Results of this study show…

In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…

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…

The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in R[superscript 3]. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The…

The literature on gestures describes how they often comprise iconic, deictic and metaphoric dimensions, but the interplay between these dimensions can be very subtle and nuanced. Due to the abstract nature of the subject, the use of gestures in the learning of mathematics means that the metaphoric dimension is often prominent. However, iconic and…

Researchers have increasingly focused on how gestures in mathematics aid in thinking and communication. This paper builds on Arzarello's (2006) idea of a "semiotic bundle" and several frameworks for describing individual gestures and applies these ideas to a case study of an instructor's gestures in an undergraduate abstract algebra…