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The objective of this study was to assess the current state of research on the use of various semiotic representations in the teaching and learning of school algebra from 2013 to 2022. Given their nature, students can access mathematical objects only through representations that involve signs and symbols. The predominantly symbolic nature of modern mathematics raises important questions about how students acquire and internalize mathematical knowledge. To evaluate the use of semiotic representations in school algebra among secondary education students, a systematic review was conducted following the PRISMA guidelines. This review involved analyzing the themes and theoretical frameworks presented in the selected studies. The findings highlighted a diversity of representations and theoretical principles, yet also revealed a scarcity of research during the 2013-2022 period, a limited number of studies from Latin America, notable variety in the semiotic registers used in study designs, and a strong preference for sociocultural theories. [ABSTRACT FROM AUTHOR]

This article presents the results of a research project whose aim is to characterize manifestations of the use and refinement of semiotic representations in the institutionalizations process of students becoming mathematics teachers, when they formulate and prove conjectures associated with natural numbers. For this, a theoretical network is constructed that allows for coherent connections relating Problem Solving as a methodology, Theory Didactic Situations, the elements of the institutionalization process, as well as the language as part of the cognitive configuration according to the Onto semiotic Approach and the semiotic representation systems of Duval (2004). Regarding the methodology, action research was adopted, analyzing the resolution process of a group of students during four sessions in which the researcher was their teacher. The results show a proposal based on Problem Solving that permits an approximation to the cultural knowledge from the knowledge developed by the students in the resolution process, in which it intervenes the use and refinement of semiotic representations. [ABSTRACT FROM AUTHOR]

In Physics Education Research, it is important to study the difficulties in understanding abstract concepts. To develop the understanding of electromagnetism, it is fundamental that students understand the field concept. The study aims to contribute a methodology that combines phenomenography and the theory of registers of semiotic representations to analyze students' difficulties understanding the electric field concept in relation to the conversion between representations. We conducted a study with 64 university students using questionnaires with conversion tasks between three electric field representations: the algebraic notation, the vector field plot, and the electric field lines diagram. We analyzed students' explanations with a phenomenographic approach and the theory of registers of semiotic representations to create the categories. We found that the difficulties of recognition are associated with the magnitude of the electric field, more than its direction. There is good recognition in the conversions between the vector field plot and the algebraic notation. In the conversions that involve electric field lines, there were difficulties of recognition and conversion. As a result of this study, we recommend that the teaching of the electric field concept should focus on the recognition of the electric field characteristics in each representation and the conversion between representations. [ABSTRACT FROM AUTHOR]

This article is a report of a broader investigation, whose objective is to evaluate the changes or modifications in the students' ability to articulate various records of semiotic representation with respect to the notion of function in students enrolled in the Differential Calculus course of two engineering programs in a public university. The research takes as frame of reference the articulation the work of several researchers, especially Duval and Hitt's. The methodology used is both quantitative and descriptive. Data were collected through an eight-items test, using different records of representation regarding the concept of function. The test was applied at the beginning of the experiment; then, a pedagogical intervention was performed, in relation to the concept of function based on the articulation of several records of semiotic representation, after which a new application of the test was implemented. The results show the detected conceptions between students at two different times of the semester, by comparing the data obtained in the pretest and post-test. The student's notion of function does not correspond to a formal definition; instead, they show a series of conceptual variations that, in some cases, are closer to an intuitive notion. [ABSTRACT FROM AUTHOR]

This study aims to assess the understanding of the notion of function and the ability to articulate different semiotic registers for representation by new students in the university in Colombia. Immediate context is taken as the Faculty of Engineering at a public university. Epistemologically the study is based on symbolic interaction by analyzing the meanings that students attributed to this mathematical concept when addressing problem solving. The methodology, therefore, is qualitatively and use of theoretical coding is done. For analysis of the results it has been applied grounded theory with a structured approach. The information generated by this study corresponds to a test that showed students two graphic representations with the intent to identify which of them was a function, besides which should argue their response. Altogether 86 arguments around the concept are analyzed. Data analysis was done through atlas.ti 7.0 software. The system allows a glimpse of emerging categories the following findings: conceptual deficiencies, diversity in conceptual approaches, conceptual referents, semiotic representations, and finally highlight the various conceptual variations. [ABSTRACT FROM AUTHOR]