Cuadernos de Investigación y Formación en Educación Matemática

CARRERA ENSEÑANZA DE LA MATEMÁTICA, SEDE DE OCCIDENTE: ¿QUÉ HA PASADO EN LOS ÚLTIMOS QUINCE AÑOS?

Norman Noguera Salgado, María Fernanda Vargas González, Patricia Maroto Vargas — Tue, 25 Feb 2025 00:00:00 -0600

El propósito de este ensayo es analizar las conclusiones contenidas en la referencia Bachillerato y Licenciatura en Enseñanza de la Matemática con salida lateral al profesorado: pasado y futuro en la Sede de Occidente, de Ulate et. al (2009). En ese trabajo, entre otras cosas, se hizo un recuento histórico de la carrera Enseñanza de la Matemática en la Sede de Occidente de la Universidad de Costa Rica, su impacto en las instituciones de secundaria en la región de Occidente, así como estudio de las principales fortalezas y debilidades de la carrera hasta 2008. En esta nueva entrega, se examinan las conclusiones emitidas entonces, a la luz de los hechos históricos que han marcado a la carrera en los últimos quince años.

MATEMÁTICAS EN CUBA: ENSEÑANZA, INVESTIGACIÓN, AVANCES Y RETOS. Una visión en el contexto de América Latina

Tue, 25 Feb 2025 00:00:00 -0600

This article does not intend to be exhaustive, but to offer and share with readers an overview that reflects what the Teaching of Mathematics in Cuba is like, providing reflections on the context, achievements, obstacles and deficiencies still to be overcome. Not everything has been progress, many challenges still remain, although good results and successes have also been achieved that are shared in this text.

This contribution presents aspects ranging from the training of Mathematics teachers for more than 6 decades, the attention to children with talents, to the multiple actions and achievements in the teaching of Mathematics outside the School, through extra-curricular channels.

Although in Cuba, and it is fair to recognize this, there has been progress in the midst of a complicated context and global and internal crises, there is still much to be done and shared, especially in the Central American and Caribbean regions.

PROFESSIONAL EXPERIENCE: REMEDIAL CLASSES IN SEVENTH GRADE BASED ON PROBLEM SOLVING

Dilan Josué Jiménez Sánchez — Tue, 25 Feb 2025 00:00:00 -0600

In this essay, a professional experience is presented in which the knowledge acquired in the Mathematics Education program at the University of Costa Rica (UCR) was applied. Specifically, the theoretical frameworks on problem-solving proposed by Polya and Schoenfeld were implemented in the planning and development of remedial classes for a seventh-grade course within the Costa Rican educational system.

EXPERIENCIA DE FORMACIÓN: ESTUDIO SOBRE LA RESOLUCIÓN DE PROBLEMAS

David Córdoba Segura, Emmanuel Ramírez Garita, Yendry Quesada Calderón — Tue, 25 Feb 2025 00:00:00 -0600

Relato de la experiencia de formación en la carrera de Educación Matemática sobre una investigación llevada a cabo en uno de los cursos. El tema de la investigación giraba en torno a la resolución de problemas.

PRESENTACIÓN VOLUMEN 18, NÚMERO 1, 2025

William Poveda — Tue, 25 Feb 2025 00:00:00 -0600

On the epistemological interplay among three realities: The Geometric, the Physical and the Algebraic (GPA).

Luis Moreno-Armella, Guershon Harel — Tue, 25 Feb 2025 00:00:00 -0600

Our interests in cognitive and epistemological issues were born from our lived experiences in the classroom

as observers of the student's encounter with mathematics.

We attend to two essential categories of reality: the mathematical reality, this assumed-to-be-shared among the mathematics community at large and the realities inferred from the students’ actions by an observer. We offer a theoretical model accompanied with episodic illustrations of a particular way of thinking, that of the habit of constructing the three mathematical realities, the Geometric, the Physical and the Algebraic. This way of thinking is largely absent from students’ repertoire of reasoning thus presenting an instructional challenge. Even more challenging is the construction of a suitable Semanticreality, that which coordinates the relationship among the three realities.

The environments where these experiential realities can develop and mature are called local organizations, where students can begin to unveil the mathematical meaning of their tasks and gradually refine their understanding.

Local organizations work as early versions of ways of thinking where deduction play a central role. Before concluding the paper, we offer examples from Calculus, cardinality of infinite sets, and linear algebra of the pedagogical manifestations of the GPA model.

HÁBITOS DE PENSAMIENTO MATEMÁTICO Y EL USO DE GEOGEBRA EN LA RESOLUCIÓN Y FORMULACIÓN DE PROBLEMAS DE OPTIMIZACIÓN

Dra. Martha Leticia García Rodríguez, Juan Gabriel Herrera Alva — Tue, 25 Feb 2025 00:00:00 -0600

The objective of this work was to analyze the mathematical thinking habits that students develop when they work on solving and proposing optimization problems in a dynamic geometry environment. The resolution and formulation of mathematical problems is assumed as a route of thought in which the student shows habits, resources, strategies and a disposition to understand ideas and concepts. Currently, research on problem solving and formulation processes incorporates the use of digital technologies; therefore, it is interesting to know the mathematical activities derived from the use of these technologies. The process of problem solving and formulation carried out by six students enrolled in a calculus course in the first semester of a science degree program was analyzed, considering four phases: orientation, connection, generation and reflection. The data showed the mathematical thinking habits that emerged during problem solving and formulation. semester of a science degree program was analyzed, considering four phases: orientation, connection, generation and reflection. The data showed the mathematical thinking habits that emerged during problem solving and formulation. The principle of problematization contributed to the development of habits such as analyzing a problem from different approaches and formulating conjectures. The evidence collected through the construction protocols in GeoGebra made it possible to identify mathematical activities related to the use of technology, such as discovering relationships, testing and verifying conjectures, replacing extensive calculations with others performed with digital technologies, and confirming results obtained analytically.

Português

Vilmar Fonseca, Matheus Terra — Tue, 25 Feb 2025 00:00:00 -0600

O desenvolvimento do pensamento algébrico é um dos principais objetivos do ensino da álgebra. Este artigo analisa o pensamento algébrico evidenciado por estudantes brasileiros sobre a fatoração algébrica. O estudo teve por base uma experiência de ensino híbrido, utilizando a metodologia de sala de aula invertida, composta por um processo cíclico de atividades instrucionais, exploratórias e avaliativas, integrando tecnologias digitais e um jogo didático. Busca-se, ainda, compreender o impacto da sala de aula invertida no desenvolvimento do pensamento algébrico dos estudantes. A coleta de dados incluiu a gravação em áudio das aulas e as produções escritas e digitais dos estudantes na resolução das tarefas, sendo analisados qualitativamente, considerando dois elementos, referidos na literatura, como vertentes do pensamento algébrico: representar e raciocinar. De modo geral, os estudantes foram capazes de interpretar expressões fatoradas, destacando os fatores comuns ou representando o valor algébrico das raízes quadradas dos termos quadráticos. Além disso, demonstraram a habilidade de mobilizar adequadamente processos de raciocínio matemático, como classificação, comparação e justificação, ao aplicarem as técnicas de fatoração por agrupamento e por diferença de quadrados. Evidenciam-se algumas dificuldades, especialmente na generalização da técnica de fatoração por agrupamento. Ao final, retiramos algumas implicações educacionais desses resultados.

IA EN LA RESOLUCIÓN DE PROBLEMAS MATEMÁTICOS

Alexánder Hernández — Tue, 25 Feb 2025 00:00:00 -0600

This research focuses on analysing the capability of a generative artificial intelligence, named o1, to reflectively analyse mathematical problems within a teacher training scenario that utilizes digital tools in a coordinated manner. Starting from a mathematical problem previously worked on in a teacher seminar, interaction with o1 is conducted to carry out the different phases of problem solving, paying special attention to the dynamic approach with GeoGebra and how o1 performs in this context. The findings indicate that, although o1 can generate structured proposals and promote mathematical reflection, it also makes errors that require critical evaluation by the user. It is concluded that AI can be a useful tool to facilitate problem analysis by teachers, provided that its responses are reflected upon using mathematical knowledge and practical teaching experience.

LA CULTURA COMO OPERADOR EN LAS OPCIONES METODOLÓGICAS EN EDUCACIÓN MATEMÁTICA

Carlos Mometti — Tue, 25 Feb 2025 00:00:00 -0600

This paper aims to present a case study about the influences that culture exerts on the methodological choices of a pedagogue teacher when developing her practice in primary education. For this purpose, we used the teaching practice in primary education as a context, giving special attention to teaching Mathematics in the five early years. To access the methodological choices of the subject teacher of this research, we used a semi-structured interview as a source of information, from which analysis data were generated through ipsis litteris transcription and discursive analysis from the French perspective. As a result of this study, we realized that the cultural operator was present in the methodological choices made by the teacher, mainly associated with her emotions and elements of her story. In addition, emotionality was perceived as an intrinsic element of the emotion/quality of teaching/choice of method triad. The present study opened a door for us to studies related to the methodological choices of pedagogical teachers in the first years of elementary school, as well as to the understanding of the fact that culture can be an essential operator of tension in the teaching process.

MEDIATION AND ECOLOGICAL SUITABILITY OF DIDACTIC-MATHEMATICAL AND TECHNOLOGICAL KNOWLEDGE OF TEACHERS IN THE MATHEMATICS EDUCATION PROGRAM AT THE UNIVERSIDAD DE COSTA RICA

José David Vargas Gamboa — Tue, 25 Feb 2025 00:00:00 -0600

The purpose of this article is to communicate the analysis of the mediational and ecological facets of didactic-mathematical knowledge among faculty members in the Mathematics Education program at the Universidad de Costa Rica (UCR). This analysis was conducted by the author as part of their master's research. The study employed a qualitative descriptive approach, examining these facets and exploring the various ways digital resources and technological tools are utilized. One of the key findings is the significant potential for improvement in integrating technology into the educational process, particularly in areas related to resource design and communication. Future research within the same population is recommended to explore additional dimensions of didactic-mathematical knowledge, providing a more comprehensive understanding of faculty characteristics.

ANÁLISIS FACTORIAL EXPLORATORIO DE LAS EXPECTATIVAS DE EFICACIA Y LOS VALORES DE LAS TAREAS EN MATEMÁTICA, UN ANÁLISIS REALIZADO EN PERSONAS ESTUDIANTES DE INGENIERÍA Y CIENCIAS.

Adolfo Rojas Cruz — Tue, 25 Feb 2025 00:00:00 -0600

The research explored efficacy expectations and task value in engineering and science college students, focusing on motivation towards mathematics. Efficacy expectations, achievement value, intrinsic value, utility and cost of tasks were assessed using a scale adapted from Safavian (2019). Achievement motivation in mathematics was analyzed from a quantitative correlational perspective. The research design is ex post facto, meaning that the variables have already been manifested and are not directly manipulated. Cognitive interviews were conducted with 10 calculus students at the University of Costa Rica to validate the scale, verifying the understanding of the items. Exploratory factor analysis (EFA) revealed four main factors: efficacy expectations, intrinsic value, utility and cost. Promax rotation allowed analyzing the factor loadings. The study identified that achievement value is closely related to utility value, suggesting that a high utility value positively influences academic achievement. Some questions from the scale were removed to improve the accuracy of the results. Finally, the analysis showed that intrinsic value, utility and cost factors are the key components for measuring motivation in mathematics students, highlighting the importance of these factors in their academic performance.

COMPRENSIÓN DEL APRENDIZAJE DE LA ARITMÉTICA DESDE LA DIVERSIDAD COGNITIVA: HACIA LA ACCESIBILIDAD

Elba Azucena Martínez Cárdenas — Tue, 25 Feb 2025 00:00:00 -0600

The presence of intellectual disability and dyscalculia in regular school classrooms poses a challenge for teachers, particularly due to the low comprehension of mathematics learning from a cognitive diversity perspective. This literature review article highlights the emergence of research in mathematics education aimed at enhancing didactic reflection on understanding the learning processes of students with neurodevelopmental disorders, to promote the design of arithmetic learning environments that are accessible. Cognitive, semiotic, and affective aspects are related to understand cognitive diversity as inherent to every learning environment, and to establish hypothetical learning trajectories, specifically of arithmetic patterns mediated by mathematically structured games. Game-based learning is introduced as a didactic device, related to problem-solving practice, in which heuristics are developed, state changes occur, and affective connections are generated, achieving progression in the learning of arithmetic patterns, in the construction and development of representations from interaction with the other and with others. Finally, the possibility of using electroencephalography in tracking arithmetic learning is considered, in order to demonstrate connections between the aforementioned aspects and the biological response of brain electrical activity during gaming practices.

PROJECT BASED LEARNING (PBL) TO STRENGTHEN MATHEMATICAL COMPETENCIES IN SECONDARY SCHOOL

Laura Yanneth Cañas Mendoza, Emil Hernández Arroyo — Tue, 25 Feb 2025 00:00:00 -0600

The mathematical skills developed in primary school impact the child's interest in this area of knowledge, as well as the student's academic performance. The evidence of gaps in this regard and accentuated in less favored socioeconomic contexts, motivated this research that provides a proposal for project-based learning based on the premises of active teaching methodologies. With the objective of contributing to the strengthening of these competencies in sixth grade students, school project xxx is presented, which is framed in the Boss and Larmer model for gold standard projects. Going through the holistic spiral of evaluative research, when designing the strategy, we go through the exploratory, descriptive, comparative, analytical, explanatory, predictive, projective, interactive, confirmatory and evaluative stages. With a quasi-experimental design, the results of pre- and post-evaluative tests were statistically analyzed, applied to two groups of students: One control and one experimental (n=32), verifying the validity of the methodological proposal, replicable in other school contexts.

LAS EMOCIONES EN LOS LIBROS DE TEXTO DE LA NUEVA ESCUELA MEXICANA

Tue, 25 Feb 2025 00:00:00 -0600

Currently, the Mexican Educational System (SEM) is experiencing relevant and necessary changes, one of the issues that has emerged with great force is related to the role that educational institutions play in emotional training, although it is not a new term, its Incorporation as an educational innovation in the education curriculum is recent and responds to different social needs. The New Mexican School (NEM) has implemented actions to address this situation, among them is the development of plans and programs, as well as the creation of free textbooks (LTG), which contribute to the training of the student. Therefore, the objectives of this partial qualitative research report are: 1. to analyze the emotional contents in mathematics in the primary and secondary level LTG and 2. To identify in the plans and programs of the Benemérita Escuela Nacional de Maestros (BENM) and the Escuela Normal Superior de México (ENSM) these aspects, through a qualitative documentary methodology. Among the findings, it is noted that primary and secondary LTG consider greater sections for teaching emotions than mathematics and that the BENM and ENSM programs deal with emotions in two curricular spaces. It is concluded that the efforts on the part of the SEM or the NEM have not been sufficient for the emotional approach, however it is a beginning that should be the watershed of many proposals for students.

CONOCIMIENTO ESPECIALIZADO DE UNA PROFESORA DE MATEMÁTICA EN LA EJEMPLIFICACIÓN DE LA ECUACIÓN CUADRÁTICA. EL CASO DE LA DESCOMPOSICIÓN DE RADICALES

Tue, 25 Feb 2025 00:00:00 -0600

Uno de los factores más relevantes que incide en el aprendizaje matemático de los estudiantes es el profesor de matemáticas, específicamente, el repertorio de conocimiento que le permite gestionar la enseñanza y el aprendizaje de manera coherente con los objetivos de enseñanza. Así, el diseño de la enseñanza incluye diversos elementos que interactúan, como recursos, estrategias, curriculum, ejemplos, etc., los cuales tienen sentido en el conocimiento del profesor. En este contexto, los ejemplos son un elemento relevante en el aprendizaje de las matemáticas, debido a su versatilidad en la enseñanza de procedimientos, conceptos, demostraciones y estrategias. Sin embargo, las secuencias de ejemplos intencionadas movilizan de mejor manera aspectos relevantes de un objeto matemático, resaltando los aspectos críticos y no críticos. De esta manera, el objetivo de este trabajo es explorar el conocimiento especializado del profesor de matemáticas en la ejemplificación en la ecuación cuadrática, específicamente en la descomposición de radicales. Para ello usamos un estudio de caso instrumental con análisis basados en observaciones de aula y entrevistas semiestructuradas. Los resultados muestran que la selección de ejemplos y secuencias de ejemplos intencionados permite que afloren aspectos críticos de los ejemplos, movilizando específicamente, conocimiento didáctico del contenido en diferentes subdominios, en relación con la enseñanza, las características del aprendizaje y del curriculum escolar; en relación con el conocimiento matemático, se evidencia conocimiento de los temas relacionados con los procedimientos y los registros de representación.

ANÁLISIS DE LA RELACIÓN ENTRE LA ACTITUD HACIA LA ESTADÍSTICA, EL PENSAMIENTO CRÍTICO Y EL RENDIMIENTO ACADÉMICO

Tue, 25 Feb 2025 00:00:00 -0600

This article examines the relationship between attitudes toward statistics, critical thinking, and academic performance, using students' overall GPA and their grades in statistics. A non-experimental quantitative study with a cross-sectional design was conducted, involving 629 university students from various undergraduate programs. The Attitudes Toward Statistics Questionnaire (CAHE) was used to measure attitudes, while critical thinking was assessed using the Critical Thinking Questionnaire (CPC 2). Results showed a significant correlation between critical thinking and academic performance. Additionally, students with a positive attitude toward statistics were more likely to develop strong critical thinking skills, which in turn improved their performance in the subject. Although no direct relationship was found between attitudes toward statistics and academic performance, critical thinking emerged as a key mediator. These findings highlight the importance of fostering critical thinking skills and promoting positive attitudes toward statistics in educational settings.

MATHEMATICS PROJECTS WITH ATTENTION TO SCHOOL-RELATED PROBLEMS

Jesús Antonio Larios Trejo — Tue, 25 Feb 2025 00:00:00 -0600

This work consisted of the compilation and implementation of school projects at the secondary level, aligned with the principles of the New Mexican School. This educational reform emphasizes placing students and their communities at the center of teaching, promoting a more contextualized and relevant educational approach. Therefore, it is essential to address the issues that students identify in their immediate environment. In response to this need, this document presents two innovative project proposals that address real issues in the State of Colima. These projects aim to link mathematics with other subjects such as sciences (physics, chemistry, and biology) and social sciences (civic and ethics education), without neglecting the student’s integral development, which includes the arts. Both proposals were implemented in two secondary schools, achieving favorable results in the development of mathematical and transversal skills. The integration of various disciplines allowed students not only to acquire academic competencies but also to develop a greater awareness of their social and natural environment. Thus, these initiatives are framed within the vision of forming critical and engaged citizens, while reinforcing fundamental mathematical skills essential for their education and daily lives.

DISEÑO DE UNA TAREA FENOMENOLÓGICA PARA LA EXPLORACIÓN DEDUCTIVA DE LA REGLA DE LA CADENA EN VARIAS VARIABLES

Tue, 25 Feb 2025 00:00:00 -0600

In this document a route for the design of a mathematical phenomenological task is presented. For exemplify, we make an analysis of its implementation, in the context of the course MA-1022 Cálculo para Ciencias Económicas II focused on the chain rule in several variables. Our theoretical background is the Design Thinking methodology, considering the theory of Carroll's Learning Scenarios and based on Matos's Design Principles. With the design of the problem proposed in the task, we sought to achieve a better understanding of hierarchy and the relationships between the variables involved, which favored the consolidation of the procept associated with the chain rule theorem in several variables according to Tall. As the task provided a context close to the disciplinary area, it allowed students to identify the composition of functions in several variables and to make sense of the tree diagram of dependencies between variables, useful in the application of the theorem.

LAS FRACCIONES EN LA RECTA NUMÉRICA. UN EXPERIMENTO DE DISEÑO BASADO EN MODELOS DE LONGITUD

Tue, 25 Feb 2025 00:00:00 -0600

This study investigated the feasibility of a Design Experiment framed in Realistic Mathematics Education with the aim of recognizing the mental objects that students develop when working with fractions in the context of length, specifically on the number line. The analysis presented here is the result of a Hypothetical Learning Path, applied to fifth grade students in a school in Mexico City, which shows favorable results for students to modify their fraction schemes towards multiplicative fractional thinking, which is developed by iterating unit fractions so that they can recognize when a fraction is less than, equal to or greater than the unit of reference. The findings suggest that working with fraction comparison in a measurement context, specifically length, is a viable entry point for work with rational numbers and subsequent more complex mathematical knowledge, e.g. algebra.

ANÁLISIS DE LA IDONEIDAD DIDÁCTICA EN LA ENSEÑANZA DE LA FUNCIÓN LOGÍSTICA: UN ESTUDIO DE CASO EN LA ESCUELA SECUNDARIA

Claudio Rodríguez, Ricardo Fabián Espinoza — Tue, 25 Feb 2025 00:00:00 -0600

This study investigates the didactic suitability in mathematics teaching through the use of the logistic function to model population growth among secondary school students. It is based on the Ontological and Semiotic Approach to Mathematical Knowledge and Instruction (EOS), using tools from this framework to assess students' practices and mathematical understanding. A qualitative methodology was employed, involving the design and validation of an inquiry instrument, implemented with fifth-year secondary school students. The results indicate that the logistic function provides a more comprehensive and realistic understanding of population growth phenomena, enabling students to develop critical and analytical competencies in mathematics. The importance of integrating Logistic Function into the Secondary school curriculum is highlighted to promote meaningful and contextualized learning.