O artigo apresenta resultados provenientes de um projeto de pesquisa já finalizado, cujo objetivo foi analisar as docências da área de Matemática engendradas na Educação Básica do Brasil na contemporaneidade. A investigação consistiu em examinar enunciados presentes em revistas pedagógicas destinadas aos educadores brasileiros sobre os modos de ser professor de matemática. As bases teóricas encontram-se no campo dos Estudos Culturais em Educação em seus entrecruzamentos com o pensamento de Michel Foucault. Em termos metodológicos, a investigação é de natureza qualitativa, baseada na perspectiva pós-crítica operando com a análise do discurso de inspiração foucaultiana. Os materiais empíricos consistem nos artigos e reportagens sobre a matemática escolar publicados na Revista do Professor, artefato que circulou no Brasil de 1985 a 2016. O corpus analítico foi constituído por excertos desses materiais que abarcavam o uso de jogos nas aulas de matemática. Os resultados encontrados organizam-se em duas dimensões: a primeira refere-se à construção de uma narrativa vitoriosa sobre o uso dos jogos como metodologia a ser adotada pelos professores para garantir a aprendizagem da Matemática. Essa narrativa encontra sustentação em documentos oficiais brasileiros e em estudos de autores relevantes para a área que destacam as fortes relações entre os jogos escolares e as brincadeiras do contexto social dos alunos. A segunda dimensão diz respeito a um deslocamento nas docências engendradas pela Revista do Professor: nas décadas de 1980 e 1990, os imperativos direcionados aos docentes enfatizavam atitudes de investigação sobre o conhecimento matemático dos alunos. A partir dos anos 2000, o educador assume o papel de coordenador ou gerente do espaço lúdico, em um processo de esmaecimento da docência.
Este estudio analiza la comprensión conceptual de la cinemática y el desarrollo de la alfabetización algorítmica crítica mediante la integración de Arduino e inteligencia artificial generativa en educación media superior. Se adoptó un enfoque cualitativo interpretativo, con un diseño de estudio de caso intrínseco, en un grupo de 13 estudiantes de Física I. La intervención se estructuró mediante el modelo PRIAAA (Predicción, Recolección, Interpretación, Argumentación, Ajuste y Autorreflexión) y el método CPS+ para orientar la interacción con sistemas de inteligencia artificial. Los datos se examinaron mediante análisis temático, con apoyo de NVivo, y la triangulación de bitácoras, registros experimentales, producciones gráficas, código de Arduino, interacciones con inteligencia artificial y entrevistas. Los resultados permitieron identificar que el aprendizaje del movimiento rectilíneo uniforme se configuró como un proceso iterativo de revisión conceptual, mediado por las discrepancias entre los modelos teóricos, los datos experimentales y las respuestas algorítmicas. También se identificaron procesos de modelación científica, validación empírica, pensamiento computacional, autorregulación del aprendizaje y evaluación crítica de la información generada por la inteligencia artificial. La interacción con estas herramientas evolucionó desde un uso instrumental hacia uno reflexivo, basado en la contrastación con la evidencia. Se concluye que la articulación de Arduino e inteligencia artificial mediante un diseño didáctico estructurado propició las condiciones para la construcción de conocimiento científico y el desarrollo de la alfabetización algorítmica crítica. El estudio aporta evidencia empírica situada sobre el potencial de integrar la experimentación, la modelación y el uso crítico de tecnologías emergentes en la enseñanza de la física.
Dialogic teaching, which foregrounds purposeful classroom talk, has the potential to transform secondary mathematics classrooms by supporting reasoning, collaboration, and deeper conceptual understanding. This study examines three case studies across Year 9, Year 11, and Year 12, exploring how dialogue mediates problem-solving in diverse mathematical tasks: lift-capacity modelling, paper-folding, and farm optimisation. Findings show that dialogic teaching surfaces assumptions, promotes multiple solution strategies, develops precise mathematical language, and fosters resilience in the face of uncertainty. Critical reflection highlights the role of teacher facilitation, task design, and classroom culture in shaping the effectiveness of dialogue. The study offers practical insights for curriculum design, assessment, and professional development, demonstrating that mathematics learning can move beyond procedural fluency to become a collaborative, reasoning-rich practice.
Se presenta el proceso de estructuración y validación de un instrumento orientado a recopilar, identificar y representar el Conocimiento Didáctico del Contenido (CDC) de los profesores de Educación Básica Primaria (EBP) sobre la geometría del triángulo. La revisión de la literatura permitió identificar antecedentes enmarcados en el CDC, el MKT y el MKTS y las Representaciones del Contenido (ReCo) y reconocer teóricamente los avances y vigencia del CDC en la enseñanza de las ciencias. Partiendo de estos hallazgos, se retomaron las ReCo, se adaptaron los ocho ítems allí planteados a tres dimensiones reformuladas desde los tres subdominios del dominio del Conocimiento Pedagógico del contenido del modelo MKTS, pero dirigido hacia la enseñanza de la geometría del triángulo. Se pidió a un grupo de profesores que evaluaran la validez del nuevo instrumento desde criterios específicos, la validación de contenido se realizó mediante el estadístico de Lawshe y la confiabilidad mediante el Alpha de Cronbach.
Este artigo discute como a negociação de significados sobre interpretações de respostas de estudantes do Ensino Médio que mobilizam a ideia de infinitésimo, em uma comunidade de prática constituída numa disciplina de Análise Real, oportuniza aprendizagens profissionais sobre a relação entre a Análise Real e a Matemática do Ensino Médio. Adotamos uma abordagem qualitativa interpretativa, ancorada na pesquisa baseada em design, conduzida em três microciclos correspondentes a três Tarefas de Aprendizagem Profissional elaboradas a partir de registros autênticos de estudantes do Ensino Médio. Participaram 14 futuros professores no sétimo semestre em um curso de Licenciatura em Matemática no Brasil. A análise temática, orientada pelo construto das Práticas Matemáticas Pedagógicas (PMP) e articulada à perspectiva da aprendizagem como participação em comunidades de prática, identificou seis PMPs mobilizadas pelos futuros professores ao interpretarem o pensamento dos estudantes. Os resultados sugerem que objetos situados na fronteira entre a intuição escolar e o formalismo acadêmico, como os infinitésimos, são particularmente produtivos para essa mobilização e oferecem condições para que futuros professores construam, eles próprios, pontes entre a Análise Real e a Matemática Escolar.
This article proposes a problematization of the History of Mathematics through the lens of what we call a Critical History of Mathematics. Taking the so-called Pascal’s Triangle as a pivot, we examine how historiographical practices have contributed to epistemic erasures by associating mathematical concepts with singular origins, thereby reinforcing asymmetries of power in the production and transmission of knowledge. While the arithmetic triangle is commonly attributed to Blaise Pascal, historical evidence reveals prior developments in Chinese, Persian, and Maghrebi contexts. However, even when these contributions are acknowledged, their cultural motivations and epistemic conditions are often neglected. Drawing on Chimamanda Ngozi Adichie’s notion of the “single story,” Vandana Shiva’s critique of the universalization of Western knowledge, and Ole Skovsmose’s framework of Critical Mathematics Education, we argue that the History of Mathematics operates not merely as a descriptive field but as a mechanism of legitimation that formats epistemic authority. A Critical History of Mathematics, therefore, must function as an epistemic, socio-political, and dialogical enterprise: questioning classificatory regimes, interrogating the historical construction of mathematical legitimacy, and remaining open to plural narratives. Rather than replacing one canonical origin with another, such an approach seeks to destabilize the logic of singularity and to foreground mathematics as a culturally situated, collectively constructed human endeavor.
This article presents the results of a qualitative systematic review the Professional Noticing in relation to equity in the teaching practices in-service primary school teachers. 50 studies published between 2020 and 2025 were reviewed and identified through a structured search Spanish and English. The methodology adopted a qualitative approach, and concept-guided analysis allowed for characterizing how recent erature conceptualizes the dimensions of attending, interpreting, and deciding in relation to equity. The findings show a reconfiguration of field toward sociocultural and sociopolitical approaches that conceptualize professional noticing as a reflective, ethical, and situated skill, although cognitive contributions remain relevant. Furthermore, a limited body of research focused on primary education is evident, revealing a search gap at this educational level. The study contributes to consolidating a broader and critical understanding of the construct and highlights the need to strengthen research that articulates equity, teacher training, and contextualized classroom practices.
Subtractive counting, though rarely examined as a distinct object of research, offers significant promise for advancing ethnomathematical and sociocultural perspectives in mathematics education. This short communication argues that subtractive counting foregrounds mathematics as a culturally mediated practice, embedded in historically developed linguistic and social routines rather than a neutral system of abstract symbols. Despite its pervasiveness in everyday activities involving quantity, time, and ordering, subtractive counting remains largely invisible in formal mathematical discourse, illustrating how deeply naturalised cultural assumptions often escape notice. Drawing on insights from cultural theory, this paper suggests that subtractive counting exemplifies mathematical practices that are hidden in plain sight, shaping cognition and communication without being explicitly recognised as mathematical. Recognising subtractive counting as legitimate mathematical knowledge invites a reconceptualisation of where mathematics resides and how it is enacted. Such recognition has the potential to make mathematics education more reflexive, inclusive, and responsive to learners' lived cultural experiences, while opening new directions for ethnomathematical research.
This article aims to explore how neoliberal governmentality on public higher education in Colombia can have harmful effects for doctoral students' personal and professional development. Neoliberal governmentality is understood as a set of policies-which have resulted in the defunding of universities, leading to a lack of scholarships and high tuition fees-but also, as a rationality that fosters an individualistic and uncareful ethos, can have harmful effects on the personal and professional development of those studying for a doctorate. The empirical data for this article, based on an exploratory narrative approach, were collected through five in-depth interviews with individuals enrolled in doctoral programmes with a transdisciplinary emphasis in the social sciences. The information was subjected to thematic analysis and revealed that, for these people, precariousness, forsaking and pragmatism are harmful effects of neoliberal governmentality in doctoral training. This underlines the urgent need to transform universities into more responsible and caring places.
The Porcipolis video game was examined as an ICT-based didactic tool aimed to foster awareness of Animal Welfare (AW) among students in the early semesters of Veterinary Medicine (VM) and Veterinary Medicine and Zootechnics (VMZ). Using a quasi-experimental design, changes in empathy, compassion, and knowledge related to animal welfare were analyzed. Participants were assigned to a control group (without exposure to the video game) and an experimental group (exposed to the video game). Data were collected through a pretest and a posttest using questionnaires with Likert-scale items and openended questions to assess user experience, empathy, compassion toward animals, and knowledge of animal welfare. Total scores were calculated for the questionnaires, and the data were analyzed through statistical comparisons. The results revealed positive evaluations of User Experience (UX), particularly in the dimensions of usability and learning experience, highlighting the pedagogical potential of the video game. However, the findings also indicate the need to strengthen the educational process through teacher-guided feedback strategies. Porcipolis emerges as an effective didactic resource for the teaching of animal welfare, whose effectiveness can be expended through educational environments that promote critical reflection on decision-making within the virtual environment.
The increasing and complex influence of regulative discourse has an effect of controlling power over the instructional discourse that focuses on geographic knowledge. The author analyzes the conditions that motivate the influence of regulative discourse by public authorities, private agents, and social actors. Given the view of such influences of regulative discourse, the author proposes strategies to recontextualize the geographic knowledge in the classroom. These strategies would allow the creation of an efficient link between instructional and regulative discourses.
Mi objetivo en este artículo es mostrar cómo la gubernamentalidad neoliberal en la educación superior pública en Colombia, entendida como un conjunto de políticas —que ha tenido como consecuencia el desfinanciamiento de las universidades, que se traduce en falta de becas y cobro de elevadas matrículas—, pero también como una racionalidad que se caracteriza por promover un ethos individualista y descuidado, puede tener efectos perniciosos para el desarrollo personal y profesional de quienes estudian un doctorado. Los datos empíricos de este artículo, basado en un enfoque narrativo exploratorio, se obtuvieron a partir de cinco entrevistas en profundidad con personas pertenecientes a programas doctorales con énfasis transdisciplinarios en áreas de las Ciencias Sociales. La información fue sometida a un análisis temático y develó que, para dichas personas, la precarización, el desamparo y el pragmatismo son efectos perniciosos de la gubernamentalidad neoliberal en la formación doctoral. Esto subraya la urgente necesidad de transformar las universidades en lugares más responsables y cuidadosos.
This work is based on the statement that maintains that any analysis that involves the use of the substantive 'inclusion' must guarantee a framework of interpretation to understand how certain individuals and groups are subordinated within different specific systems of power. Inclusive education as a knowledge project in resistance recovers some of the most far-reaching premises of various intellectual projects that emerge through the Western theoretical-critical tradition. Its focus positions the gaze around the type of arguments and premises that assemble its construction, cautioning that certain ideas and conceptual bodies that appeal to social justice avoid incurring in the proliferation of new forms of inequality. The purpose of this work is to explore some of the defining elements that participate in the construction of the cognitive architecture of inclusive education. Inclusive education is born from a field of multiple theoretical and epistemological roots in resistance. Although they are heirs of certain points of analysis typical of Western critical and social theory, their aims and purposes differ in terms of their languages, objects theorists and propositions. It is the type of gestures, especially minor ones, that begin to deterritorialize their axes of work. The method used is critical documentary review. Among its main conclusions: a) Both radical contextualism and external relations become essential constructs to understand the construction of knowledge of inclusive education and b) the theory of inclusive education consolidates an open knowledge structure, a horizon in permanent reconstruction, allowing its subjects to locate and reposition themselves in a completely different way. Inclusive education is an open horizon. His paradigmatic thinking is his opening point in the construction of his theory and epistemology.
Las constantes transformaciones sociales, económicas, laborales y ambientales exigen que las instituciones educativas realicen reformas profundas en sus modelos educativos. El propósito del presente estudio fue analizar la percepción de los y las estudiantes sobre el grado de avance del modelo educativo institucional en torno a los retos de la sociedad del conocimiento. Para ello, se aplicó un instrumento a 200 estudiantes de dos universidades públicas del norte de México. Inicialmente, se analizaron las propiedades de validez de constructo y confiabilidad del instrumento, posteriormente, se procedió con un diagnóstico mediante un análisis inter-ítems (identificación de ítems atípicos) y análisis intra-ítems (frecuencia de respuesta por nivel para cada ítem). El instrumento mostró que posee validez de constructo y adecuada confiabilidad. De acuerdo con los y las estudiantes, la formación para el emprendimiento fue el aspecto que presentó una menor evaluación, mientras que el desarrollo del pensamiento sistémico y el uso de las tecnologías digitales fueron los mejor evaluados. Para potencializar la formación para el emprendimiento y mejorar todos los aspectos evaluados se sugiere la aplicación del enfoque socioformativo, particularmente, los procesos de emprendimiento creativo y el Proyecto Ético de Vida.
Los desarrollos investigativos en evaluación y modelación matemática en el ámbito educativo constituyen un tema de interés en las últimas décadas. Existen estudios que se han preocupado por la evaluación de la competencia de modelación, los instrumentos y sus alcances, pero sigue vigente la necesidad de informar los conocimientos evaluados y su articulación con los intereses y desarrollo profesional de los estudiantes. Este artículo se propone identificar los propósitos, fases, estrategias e intereses de formación en los que se enfocan las investigaciones sobre evaluación en modelación matemática. Para ello, se realizó una revisión crítica de literatura, se establecieron procedimientos de búsqueda de los documentos y criterios de inclusión, exclusión y análisis. Se encontró un panorama amplio en cuanto a concepciones y focos de atención de la evaluación. La revisión evidenció que la evaluación en modelación matemática no solo centra la atención en los conocimientos y procesos matemáticos, sino en los elementos propios de la modelación. Esta revisión aporta dos consideraciones importantes, la primera de ellas en relación con los propósitos e instrumentos de evaluación y, la segunda, en coherencia con las fases y procesos de modelación que se evalúan.
The integration of science, technology, engineering, and mathematics (STEM) into educational systems has grown rapidly in international research. The literature reports on policies, experiences, and programs focused on interdisciplinary STEM integration around the world, as well as the challenges that the approach represents for the integration processes that teachers may undertake. Teachers, then, play a key role in the implementation of STEM Education in the school system. This systematic literature review analyzed the strategies for STEM Education of future mathematics and science teachers and the purposes for which they have been incorporated in both research and teacher education. The review considered peer-reviewed studies published in the period 2012-2021 written in Spanish, English, and Portuguese. The review followed a three-step process: planning, conducting and reporting the review. The results show the roles that STEM Education has played in teacher education, both in research and the design of preparation programs. The methodological strategies for preparing future teachers are also reported. Finally, the review provides evidence of the opportunities offered by including STEM Education approaches in early teacher education, regarding the impact on their perceptions, conceptual knowledge, self-efficacy, and future practices.
Teacher learning on mathematical modelling is a significant goal of mathematics education. This article presents the results of a study conducted within a course designed for prospective teachers. Rooted in the principles of authentic learning, authentic tasks were designed to promote the prospective teacher's learning of mathematical modelling and its teaching. Data were collected from 18 prospective teachers across two groups of a mathematical modelling course at a public University. Analysis of documents, videos, and interviews evidenced the learning achieved by prospective teachers about learning environment configuration, use of context, and modelling project development. The results of this study provide empirical evidence regarding characteristics and components that configure authentic tasks that contribute to mathematical modelling learning and its teaching. Some implications regarding the way to integrate authenticity in mathematical modelling emerged from this study.
Constant economic, labor, and social transformations require educational institutions to carry out far-reaching reforms in their educational models. The purpose of this study was to analyze the student perception about the level of progress of the institutional educational model regarding the challenges of the knowledge society. Therefore, an instrument was applied to 200 students from public universities in Chihuahua, Mexico. At first, the construct validity and reliability properties of the instrument were analyzed, then, a diagnosis was made through an inter-item analysis (identifying atypical items) and intra-item analysis (response frequency per level for each item). The instrument showed to have construct validity and good reliability. According to the students, training for entrepreneurship was the aspect that presented the lowest evaluation, while developing systemic thinking and using digital technologies were the best evaluated. To potentiate training for entrepreneurship and improve all the aspects evaluated, apply the socioformative approach is suggested, particularly, processes of creative entrepreneurship and Life Ethical Project.
This paper presents the results of a research that estimated the effect of a university entrance preparation program conducted by a public university in Colombia. Specifically, it highlights the relationship between personal, socioeconomic, and academic characteristics to the participants, the actions of the program in which they participated, and their chances of entering higher education. Through an observational analysis of secondary information sources, a sample of 20,708 program participants, who enrolled at the university between 2015 and 2019, was structured and standardized. The variables of interest were measured only once. The results derived from a frequency analysis of variables determined during the research and from the establishment of possible associations between the outcome variables with the independent ones. The results revealed that the characteristics of the participants, except for the geographical location of the educational institution, have a statistically significant association with the passing of the admission exam. Being male, under 18 years of age, coming from urban areas of stratum three and four, having studied in academic institutions, and taking independent courses in literacy, mathematics, and physics, improve the possibility of entering university. Finally, the text discusses the contribution of the student characterization component in university preparation programs aimed at promoting equitable access to university education and proposes to understand them as continuous and multidimensional processes, from which training actions must be adapted and improved.
The objective of this study, developed from 2016 to 2019, is to show the evolution of teaching practice through the Action-Research Program (ARP). Active learning environments were promoted and developed by applying teaching-learning strategies to improve the interaction between teacher-student-teaching material. This research was qualitative to get information from the teacher through analytical programs and the self-reports of teaching inventories; also, it was descriptive to analyze the information collected from the students on their academic performance and the better activities for learning. With the ARP teaching-learning methodology, during the study period, the average approval rate increased from 51% to 64%. It is due to an interaction between peers and teaching material which promoted an effective learning in such a way that students became more reflective. Regarding the teacher-student interaction, the teacher came closer to the student through the supervision of the group work in class and through conversations with the students about their academic performance. This study has shown that the teacher, when using the action-research method, has become the action-reflection process a habit of continuous improvement in each academic period being more aware of his teaching practice and its evolution and influencing the student academic performance.
