Revista Latinoamericana de Investigación en Matemática Educativa
La Revista Latinoamericana de Investigación en Matemática Educativa (Relime) es una revista científica arbitrada e indizada que busca diseminar conocimiento original resultado de la investigación en Matemática Educativa, y publica manuscritos inéditos en español, portugués, inglés o francés. Se dirige a investigadores, docentes de Matemáticas y Ciencias, estudiantes de licenciatura y posgrado y tomadores de decisiones relacionados con el campo disciplinar. A partir del volumen 28, de 2025, la Relime adopta la modalidad de publicación continua. La Relime es la publicación oficial de investigación del Comité Latinoamericano de Matemática Educativa A. C. (Clame), asociación científica y académica sin fines de lucro. Actualmente, la Relime se edita y publica desde la Ciudad de México, en México, por el Colegio Mexicano de Matemática Educativa A. C. en representación legal del Clame.
Colegio Mexicano de Matemática Educativa A.C.
War, Peacer, Nonviolence, and Matemática Education
In the context of international armed conflicts, a culture of war takes root and permeates society, profoundly affecting human relationships. Against this backdrop, this editorial explores the interconnections between the cultures of war and peace and mathematics education. This discussion is based on documents from international organizations, contemporary research on the subject, and an analysis of three writings by Ubiratan D’Ambrosio addressing the relationship between mathematics, its teaching, and education for peace. In a world where armed conflicts are proliferating, this editorial urges the scientific community to focus its attention, reflection, and action on promoting mathematics education oriented toward peace and nonviolence.
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Manifestation of Costa Rican elementary school students' algebraic thinking: structures and representations of generalization
Qualitative research was carried out with fourth- and sixth-grade students in Costa Rica after the pandemic in the context of a curricular reform incorporating elements of early algebra. The students completed a written questionnaire that included a generalization task based on the functional relationship . The objectives were oriented toward the analysis, description, and comparison (between grade levels) of the generalization representations and the structures of functional relationships patterns exhibited by the students. The findings, from a single work session, reveal that only half of the participants were able to generalize. They employed different forms of representation (predominantly verbal), with notable variations across grade levels. In sixth grade, a greater number of students accurately represented the underlying structure and demonstrated greater consistency in its use. Additional resources were also identified in the expression of generalization, such as generic examples and representations linked to indeterminacy.
Copyright (c) 2025 Revista Latinoamericana de Investigación en Matemática Educativa https://creativecommons.org/licenses/by-nc/4.0
Resignification of school mathematical knowledge in a teacher professional development space
This study analyzes how the resignification of school mathematical knowledge (SMK) is configured among in-service teachers within a professional development program oriented toward teacher empowerment. The program was designed and implemented, and two episodes related to algebraic and geometric thinking were analyzed. Methodologically, indicators were constructed based on the model of problematization of school mathematics in order to identify evidence of confrontation, resignification, and changes in the relationship with SMK. The results show that the resignification of SMK is configured as a cyclical, collective, and progressive process that articulates both epistemic and didactic dimensions across the experiential phase, classroom implementation phase, and reflective practice phase. The epistemic dimension emerges more strongly in the experiential phase, while the didactic dimension becomes consolidated in the subsequent phases. It is concluded that the resignification of SMK is not only a central mechanism for teacher empowerment, but also a constitutive element of the mathematics teaching profession.
Understanding confidence intervals: A characterization of the relationships among the elements of the cognitive Schema
This study characterizes conceptual relationships necessary for understanding confidence intervals through the construct of Schema as proposed in APOS theory. The research is developed through a Theoretical Analysis of the concept, complemented by an empirical exploration based on semi-structured interviews with preservice mathematics teachers who had completed a statistics course at least one year prior. This approach made it possible to identify relationships that persist after formal instruction, as well as those that fail to consolidate. The results reveal difficulties in interpreting the confidence level, in articulating the relationship between the sample mean and the population parameter, and in recognizing the role of sample size in the precision of the interval, suggesting a limited Schema. Based on the identified relationships, the genesis of a Genetic Decomposition of the Schema of the confidence interval is proposed.
Teaching of informal statistical inference in teacher training. A systematic review
This systematic review examines the teaching of informal statistical inference in teacher education. Studies published between 2010 and 2024 in four academic databases were analyzed, resulting in 16 articles. The aim was to identify reports on the use of tasks for teaching informal inference and their connection to learning formal inference. The analysis was organized around three dimensions: content knowledge, technological knowledge, and knowledge related to teaching practice. The results show a growing interest in this topic. The reported tasks generally promote the components of content knowledge, although different levels of complexity were found. The use of technology as a tool to reorganize inferential thinking remains limited. Although several studies link the informal approach to formal methods, there is no empirical evidence presented on its impact on learning formal statistical inference.
The teaching of Combinatorics and its reason for being: trajectories in mathematics teacher education
This study seeks to (re)define the teaching of combinatorics, mobilizing its rationale in a study process supported by a teaching device, and articulating these elements with teacher training, integrating mathematical and didactic knowledge in this field. The theoretical and methodological framework of this study is based on the Anthropological Theory of Didactics and is methodologically guided by the principles of Didactic Engineering, which encompassed its four phases: preliminary analysis, a priori analysis, in vivo analysis, and a posteriori analysis. A Study and Research Path was developed with a group of mathematics teachers as part of a training process. The results indicate that the SRP went beyond the limits of combinatorics and mathematics itself, taking on an interdisciplinary character and enabling the coordinated study of different counting problems, in contrast to traditional segmented teaching. In addition, the study highlighted the need for and importance of experiencing this SRP in high school classes.
Updating the editorial processes of Relime and the ongoing training of its community
Artificial Intelligence and Mathematical Learning: Evidence and Impacts
This study investigates the use of Artificial Intelligence (AI) as a tool for learning Mathematics in high school through a systematic literature review conducted in accordance with PRISMA guidelines. The selected studies were organized into three main areas: (i) methodologies integrating AI into mathematics teaching; (ii) the impact of AI on mathematical thinking and problem- solving; and (iii) AI-based technologies applied to education, including intelligent tutoring systems, adaptive platforms, and simulation environments. Findings indicate that AI supports personalized instruction, enhances logical-mathematical reasoning, and fosters algorithmic thinking, contributing to improved performance in algebra, trigonometry, and geometry. Nevertheless, challenges remain, such as the limited adoption of these technologies, the risk of automated use without critical reflection, and students’ difficulties in adapting to AI-mediated learning. The review also highlights gaps in assessing long-term effects, particularly regarding reliable metrics to validate AI-supported learning outcomes.
Measuring instruments for mathematical self-efficacy in Primary Education: a systematic literature review
The number of studies analyzing mathematical self-efficacy has increased in recent years, highlighting its correlation with academic performance and other constructs within the affective domain. Given the diversity of instruments used to assess this construct—an issue noted by several authors—and with the aim of understanding how and with which tools mathematical self-efficacy has been measured among primary education students, a systematic review of the scientific literature was conducted following the PRISMA 2020 protocol, with special attention to the instruments described for this purpose. The results reveal a wide variety of tools, many of which were not developed with sufficient attention to domain specificity, appropriateness for the target population, or item wording, which in some cases may reflect constructs related to but distinct from self-efficacy. It is concluded that the concerns raised in the literature remain unresolved, and the identification of valid and reliable instruments is proposed to support future research and improve educational practice.
Epistemology of graph use in parametric contexts through trajectory modeling
This study examines how university students use graphs to model trajectories when working with parametric functions without analytic expressions. Drawing on Socioepistemology, and particularly on the Functionings–Forms (Fu–Fo) model, the analysis focuses on students’ progression through the three moments of graph use. The study adopts a qualitative approach and is based on the analysis of graphical productions and discourse generated by eight students in two parallel modelling activities. Results show that students: (1) construct initial representations through spatial segmentations and numerizations; (2) justify transformations of the graph, horizontal stretches due to changes in speed and constant segments due to stops, by articulating graphical features with the phenomenon; and (3) generalize criteria constructed for one component function to adjust the other without rebuilding the reasoning from scratch. Based on this evidence, an extension of the Fu–Fo model is proposed for parametric contexts.
Learning Trajectories of Mathematics Teacher Educators for Integrating Digital Technology in Initial Teacher Education in Chile
Given their high level of responsibility and autonomy, it is essential to understand how teacher educators prepare to support future teachers in integrating technology. This study characterizes the learning trajectories of ten mathematics teacher educators in the use of digital technology in Chile, within the framework of new initial teacher education standards. The findings, analyzed using Kennedy’s (2014) framework of Continuous Professional Development and the strategies of Goos and Beswick (2021), suggest that learning mechanisms are heterogeneous, not institutionally mediated, and primarily informal “bottom-up” processes led by trainers with shared interests in technology integration who organize themselves to develop joint solutions. Four balanced categories are identified: transmissive, malleable, transformative, and self-directed learning models.
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The algebraic thinking of the deaf in pan-school times: challenges and possibilities
This research aimed to investigate the algebraic thinking of deaf students in the context of a pan-school that is emerging and undergoing a process of change, which is still uncertain. The research was characterized as a qualitative case study and, in order to investigate algebraic thinking, the students’ productions and the dialogues constructed during the meetings were analyzed based on proposals created based on a digital game and investigative tasks. The results found showed challenges and possibilities when seeking to develop and understand the algebraic thinking of deaf students in a remote teaching proposal. It was concluded that there is a possibility of developing the algebraic thinking of deaf students in the context of a pan-school, but that the creation of materials and tasks alone is not enough, and collective work, dialogue and synchronous moments were the basis for this to occur.
Effective mathematics teaching: a systematic review of the literature
This systematic review has two objectives: to determine the factors of effective mathematics teaching that inf luence the development of cognitive achievements in students and to conceptualize the term effective mathematics teaching. A protocol was followed that allowed filtering and analyzing 31 articles that reveal the multidimensionality and close relationship that is interwoven between the identified factors, which were grouped into 3 categories: factors associated with characteristics of the teacher as a professional, the general dimension of teaching and the specific dimension of mathematics teaching. Also notable among the results is the scarcity of studies in the Spanish language and the need to implement a mixed methodology in studies on this topic.
The approach to the decimal number system in textbooks and in first grade primary school classrooms
A didactic research study with an ethnographic approach was conducted to analyze how the content of the decimal numeration system is addressed by two first-grade primary school teachers. They used lessons on this topic from the Free Textbook Mathematics First Grade (LTG-M1°). The study was based on the notion of Didactic Transposition and some constructs from the Didactic Situations Theory. The teachers’ management was conceptualized as didactic transpositions concerning the textbook and revealed some difficulties mainly related to the problem-solving expectations for children as presented in the textbook activities. For this reason, an analysis of the didactic suggestions in the LTG-M1° was carried out. The study concludes that maintaining coherent approaches in the development of curricular proposals is essential. It was also found that the rules of the decimal numeration system continue to pose a challenge for designing activities and for first-grade children’s learning.
Transparency and accountability in the use of artificial intelligence in research.Continuous updating of the Relime editorial policy
Accumulation of Degree-hours and category of modelling. A resignification of the definite integral with mathematics teachers
This research analyzed the resignification of the definite integral by mathematics teachers in a situation of change, argued by accumulation. To this end, an instrumental case study was conducted with four teachers in Chile, who developed a classroom-based learning activity using GeoGebra. Framed within the socioepistemological program Forgotten Subject and Transversality of Knowledge, the data were analyzed using constructs from the category of modelling and document analysis techniques. The results revealed a resignification in which quantities of continuous variation functioned as the instrument, comparisons of states as the procedure, and areas between curves and accumulations of degree-hours as the meanings. The discussions proposed modeling phases from an educational perspective to identify situated resignifications of mathematical knowledge. In conclusion, this study is expected to contribute to the design and implementation of school situations to analyze the students’ resignifications through the different phases of this model.
Ethnomathematics as a research and teaching method and decolonial thinking: a possibility of a teaching proposal for Higher Education
This work presents a problematization of the teaching of subjects linked to Mathematics in Higher Education. It aims to point out ways that enable student-centered teaching so that they can glimpse the applicability of mathematical concepts in their future profession. To this end, a theoretical framework is used based on Foucault's concepts of power and counter-conduct, the Decolonial movement and Ethnomathematics from the perspective of D’Ambrosio and Lara. In the end, it seeks confluences between these theories to point out possible paths for teaching committed to equity and quality training in Higher Education.
Macrodidactic analysis based on linear algebra and analytic geometry syllabi: evolution of knowledge in engineering education in Argentina
We analyze 504 curricula of engineering degrees in Argentina and 125 syllabuses of the courses of Linear Algebra (LA) and Analytic Geometry (AG) in the period 1810-2021. We aim to investigate the transformations of such knowledge to be taught from four stages defined in the research. Yves Chevallard's Anthropological Theory of Didactics is adopted as a theoretical reference. The results show the changes in the LA and AG knowledge necessary for the formation of engineers in each stage and the reasons for these transformations are analyzed.
Dialogue between the community and the school: the corn tortilla cooking as a learning situation
This paper presents a situation designed within the framework of variational thinking to foster a dialogue between school mathematics and community knowledge. This dialogue is builtthrough the articulation of school concepts of the mathematics of change and variation with community knowledge linked to the corn tortilla cooking process. In this proposal, the context of meaning is the basis for the intentional development of practices of variational thinking such as serialization, comparison and prediction. In particular, evidence is presented of the use of graphics referring to the cooking process of a well-made tortilla; its different forms and functions act as a bridge between the school and the community, demonstrating a meaningful dialogue between the two.
CONCEPCIONES DE LOS ALUMNOS DE BACHILLERATO Y CURSO DE ORIENTACIÓN UNIVERSITARIA SOBRE LÍMITE FUNCIONAL Y CONTINUIDAD
To establish the conceptions of the students of Bachillerato and Curso de Orientación Universitaria about functional limit and continuity, it has been analized and categorized the answers employed by 145 pupils when they answered a questionaire with problems about this two topics. It has been proved that some conceptions were linked with the ones that has been appeared along the history of mathematics, and the others, were induced by the teach-ing received.
Copyright (c) 2000 Revista Latinoamericana de Investigación en Matemática Educativa https://creativecommons.org/licenses/by-nc/4.0/
DE LA INVESTIGACIÓN EN MATEMÁTICA TEÓRICA A LA INVESTIGACIÓN EN MATEMÁTICA EDUCATIVA: UN VIAJE PERSONAL
The main goal of this essay is to understand why and how a mathematican, very much dedi-cated to research in theoretical mathematics might change his field to research in mathema-tics education. In order to understand a change, it is necesary to probe a little deeply into how it was before and also after the change; how I came to the point of changing, how I made the transformation and where I went with my new professional life. To do all this, I intend to ex-plore my own experiences in the hopes that through the introspection of an individual we might learn something about the situation for everyone.
SOBRE LA PREPARACIÓN TEÓRICA DE LOS MAESTROS DE MATEMÁTICAS
On the basis of various experiences in this area, the authors present in this article some re-flections on the training of teachers of mathematics. After taking certain general positions on some "controversial" issues in the current international debate, the authors focus their attention on the study of language, seen from various perspectives, and on the difference between the positions of Piaget and Vygotski with regard to this topic, proposing that arguments of this type should be part of the expertise of future lecturers, given that didactics makes up a part of the larger field of communication.
LA CREACIÓN DE EXPONENTES CONTINUOS: UN ESTUDIO SOBRE LOS MÉTODOS Y LA EPISTEMOLOGÍA DE JOHN WALLIS
The following is a work of historical investigation that focuses on specific mathematical mo-ments where methods, concepts, and definitions underwent profound changes. There are two main goals. First to sketch the history of the development of a continuous concept of expo-nents, and second to examine carefully he epistemological setting in which these develop-ments took place. Put more simply, what was it that convinced certain mathematicians that their concepts were viable. It is not intended to be a complete historical discussion, but rather a series of illuminating snapshots. The mathematical details of these moments are provided to the extent necessary for an understanding of the epistemology.
CONSTRUCCIÓN DE GRÁFICOS DE FUNCIONES: “CONTINUIDAD Y PROTOTIPOS”
In the frame work of Advanced Mathematical Thinking and related to Functions and Graphics topic, we are developing different focused on secondary students (16-18 years) ideas and performance. The main goal of our work is to improve knowledge about students reasoning and strategies used on solving tasks related with graph construction. We analyze 250 students' answers, in two instants (beginning and middle of a course), at a same task of graph construction of a function given by verbal conditions representing a non contextualized situation. We look especially for the use of continuos graphs (versus non continuos ones), for the use of prototypes like straight lines and parabolic and hyperbolic lines. We look also for the changes (evolution) on those uses.
INFLUENCIA DE UN MODELO DIDÁCTICO EN LA OPINIÓN/ACTITUD DE LOS ALUMNOS HACIA LAS MATEMÁTICAS
During the 1994-1995 and 1995-1996 school years, a research-action was done with First Year “Bachillerato Unificado Polivalente” (BUP) students who were attending night school. One of the objectives was to study the influence on the students’ attitudes and opinions towards Mathematics using A. de La Garanderie’s didactic model of knowledge acquisition. Our work is based on the theory that learning is done by experimenting with concepts in certain social contexts and situations, such as those found in the classroom. This article first explains a part of a wider research that we have carried out in the University of Valladolid, and motivated by its relevance, here we only attend the -positive- influence that the model has on the opinion/attitude of the students towards mathematics. This change has encouraged the improvement of the students' work, by committing themselves to participation in learning tasks.
PERFECCIONAMIENTO DE LA ENSEÑANZA-APRENDIZAJE DEL TEMA LÍMITE DE FUNCIONES CON EL USO DE UN ASISTENTE MATEMÁTICO.
This study proposes a didactic system to impart the theme: limit of a function of a variable with the use of a mathematical assistant in Mathematics I, in the Career of Engineering in Telecommunications in Cuba. The possibilities of using mathematical assistants were explored and, considering the material basis of the study currently available in the "José A. Echevarría" Higher Polytechnic Institute (ISPJAE*), and based on its potential, DERIVE is selected as the most ideal. The proposal solves problems detected in the diagnosis test, introducing data processing in the teaching-learning process of the theme, it is based on the theory of the formation of mental action in stages and its structure contains the three models that permit such action to develop. The thesis includes the proposal of how to validate the didactic system suggested in order to corroborate the methodology advantage it provides.
Copyright (c) 2000 Revista Latinoamericana de Investigación en Matemática Educativa https://creativecommons.org/licenses/by-nc/4.0
ELEMENTOS DE ENLACE ENTRE LO CONCEPTUAL Y LO ALGORÍTMICO EN EL CÁLCULO INTEGRA
A problem in teaching where students of Integral Calculus are immersed consists in the separation between what is conceptual and what is algoríthmic. To propitiate the linkage we theoretically identífíed a necessary condition that refers to the existence of problem situations based on which notions and procedures are fonned, closely related and associ· ated to Integral Calculus. To the extent possible we determined this type of problems by analyzing changes in the epistemological framework (Piaget y García, 1994). In a certain manner we justified the reason why we selec1ed Newton's epistemological framework based on which we build a conceptual field of Calculus, where the notions, prediction, accumulation and constancy 01 what is variable (Cantoral, 1990; Cordero, 1994) are inherent. We performed the aboye based on the genetic epistemology in the theory oC conceptual fields (Vergnaud, 1990a) and considering epistemological aspects of Integral Calculus marked by the perspective oí the redesign 01 school mathematical discourse.
SISTEMA ENTRENADOR INTELIGENTE CON TECNOLOGÍA MULTIMEDIA. ÓPTIMAGEOMETRÍA
The revolution of Computer Assisted Instruction (CAI) began in 1976 with the introduction of the new generation of machines in education, microcomputers. Continuous technological changes have brought a notable evolution in CAI until our days. Intelligent Tutor Systems try to provide the data processing environment with the elements that a professor has at hand to perform his work, considering him an expert where knowledge interacts over domain as an adequate pedagogical strategy and a model focused on the student. Using computers in teaching is very useful, even more with the development of Artificial Intelligence, the use of new data and communication technologies that give it flexibility, personalization, inter-activity and quality in the applications.