Camilo Andrés Rodríguez-Nieto

The literature shows that primary, secondary, and higher education students have difficulty solving problems involving arithmetic operations. The research goal was to implement a teaching sequence based on the ethnomathematical connections identified in the marketing of chontaduro in Santander de Quilichao, Cauca, Colombia, to promote the resolution of additive and multiplicative problems in primary school children. The research was based on the extended theory of connections, the typology of additive and multiplicative problems according to semantic structure, and universal activities. This is a qualitative-exploratory research with an ethnographic approach developed in two large stages. In the first, the daily practices of chontaduro marketing were analyzed. The merchant was selected and interviewed, and then the data were analyzed to identify ethnomathematical knowledge. The second stage included three moments: selection of volunteer students from a public institution in Santander de Quilichao; design of a didactic-ethnomathematical sequence based on the practice of chontaduro marketing and additive and multiplicative structures; and development of the seminar-workshop with the students to analyze problem-solving. The results showed that, in the sale of chontaduro in different units (bags, segments, and bundles) and in the counting processes, arithmetic operations with money are fundamental for solving and understanding additive problems (change, combination, comparison, and equalization) and multiplicative problems (multiplying factor, repeated addition, ratio, or proportion). This type of ethnomathematical teaching sequence has allowed students to consistently solve problems that involve everyday practices in their immediate sociocultural context.

In the digital era, statistical reasoning is a key competency required for students to interpret data and make evidence-based decisions. However, many students continue to struggle to progress beyond procedural stages toward deeper conceptual understanding. This study aims to identify the statistical reasoning profiles of eighth-grade students in Indonesia based on four developmental classifications: Idiosyncratic, Transitional, Quantitative, and Analytical. An exploratory case study design was employed with 27 students from a public junior high school in Bandung. Data were collected using the Statistical Reasoning Assessment Tool (SRAT) consisting of open-ended tasks and analyzed with a developmental rubric for statistical reasoning. Coding was conducted independently by two raters with high inter-rater reliability (Cohen’s κ = 0.87). Descriptive statistics, chi-square tests, and qualitative analyses of reasoning patterns and misconceptions were used to address the research questions. The findings revealed that most students were situated at the Quantitative level (63%), followed by Transitional (33%), and Idiosyncratic (4%), with no students reaching the Analytical level. These results indicate that while students were able to recognize and organize statistical information, they had not yet developed higher-order analytical reasoning skills. The implications highlight the need for pedagogical strategies that leverage digital technologies to move students beyond procedural competence toward analytical reasoning, through multi-representational approaches, engagement with authentic datasets, and inquiry-based learning, thereby supporting the development of data literacy as a 21st-century competency.

Geometric learning among coastal elementary students in Indonesia is often constrained by limited access to learning resources and difficulties in visualizing three-dimensional concepts. Grounded in Van Hiele theory and Cognitive Load Theory, this study examined the effectiveness of the Flipped Semi-Concrete Geometry Model (FSC-GM), which integrates flipped learning with locally sourced semi-concrete media from coastal contexts. Using a sequential explanatory mixed-methods design, the study involved 19 fifth-grade students in a coastal elementary school in Cirebon Regency. Quantitative data were analyzed using one-sample t-tests and correlation analysis, followed by qualitative content analysis of student interviews and classroom observations. The results showed that students' geometric thinking scores significantly exceeded the minimum mastery criterion (KKM = 60) following the intervention (t = 3.269, p < 0.05, d = 0.76), indicating a medium-to-large practical effect, while self-efficacy gains were not statistically significant (t = 1.143, p = 0.268) and exhibited a weak correlation with geometric thinking (r = 0.237). Qualitative findings revealed that the use of semi-concrete coastal objects reduced extraneous cognitive load, supported students’ progression across Van Hiele levels, and enabled meaningful connections between geometry and everyday coastal experiences. The findings suggest that cognitive and affective outcomes follow distinct developmental trajectories, highlighting the need for sustained and culturally responsive instructional approaches in coastal and resource-limited contexts.

The article explores the mathematical connections activated by Colombian university students when solving a problem involving the construction of frequency distribution tables. This study arose because the literature and teaching experience reveal difficulties in statistics in finding the range and determining the number and size of classes, which are essential aspects for creating frequency tables with grouped data. Grounded in the networking between the extended theory of connections, the onto-semiotic approach, and levels of table reading, A qualitative methodology was implemented with 28 students who completed the task and actively participated in the class. The findings reveal that students activated mainly procedural, part-whole, implication, and different representation connections to construct grouped frequency tables, progressing from data organization to statistical interpretation. These connections supported the articulation of mathematical practices, primary objects, and semiotic functions, evidencing a structured but predominantly procedural understanding. However, students’ comprehension was largely situated at level 1 and level 2 (reading the data and reading within the data), with limited evidence of higher-order reasoning such as inference or critical analysis. Only a small proportion of responses reached level 3, and no evidence of level 4 was identified. These results indicate that, although students successfully complete statistical procedures, their understanding remains incipient. This highlights the need for instructional approaches that foster deeper reasoning and critical statistical literacy through the activation of meaningful mathematical connections.

This study examines the ethnomathematical connections activated by artisans who employ crochet techniques in the production of bucket bags. The research responds to the need to recognize and valorize everyday mathematical practices that contribute to the productive, economic, and cultural sustainability of communities, yet have historically remained marginalized within science education, particularly in school mathematics. Adopting a qualitative approach grounded in an ethnographic perspective, the study was conducted in three phases: (1) the selection of artisan weavers from Barranquilla, Colombia; (2) data generation through semi-structured interviews and direct observation of the weaving process; and (3) thematic analysis aimed at identifying and interpreting ethnomathematical connections embedded in artisanal practice. The findings reveal multiple relationships between every day, and institutionalized mathematical knowledge manifested in the construction of bucket bags. These include the use of numerical sequences, counting strategies, arithmetic operations such as addition and multiplication, proportional reasoning, and geometric concepts including circumference, symmetry, and pattern formation. Furthermore, the study identifies non-conventional measurement procedures and intuitive forms of mathematical modeling employed by artisans during production. These ethnomathematical connections demonstrate how culturally situated practices can serve as meaningful contexts for the construction of mathematical understanding, contributing to the re-signification of mathematical knowledge and highlighting the pedagogical potential of artisanal activities for the teaching and learning of arithmetic and geometry.

The low numeracy skills of students in Indonesia remains a major challenge in many schools, including Junior high school students in the border area of the Republic of Indonesia and the Democratic Republic of Timor Leste. The purpose of this study is to describe the level of students’ numeracy skills, identify aspects that still need improvement, explore the factors affecting students’ numeracy skills, and examine the efforts made to support numeracy development among junior high school students. This study employs a qualitative research design with a case study approach, conducted at one Junior High School in Kefamenanu City, Indonesia, during the odd semester of the 2024/2025 academic year. The participants were 21 eighth-grade students who completed a written test, followed by interviews with six students, their parents, and the mathematics teacher. Test items and interview guidelines were used to collect data. Results indicate that students’ numeracy skills are still relatively low, as reflected in the low average test scores. The numeracy aspects that require the most improvement are application and reasoning. Factors influencing numeracy skills include internal factors-such as interest, motivation, understanding, and attitude-and external factors, including the learning environment, facilities and infrastructure, parental involvement, and teaching strategies. Efforts to enhance numeracy skills include increasing students’ interest and motivation, strengthening conceptual understanding, developing application and reasoning skills, and implementing context-based learning strategies

This paper develops a systematic articulation between two theoretical approaches in mathematics education—ethnomathematical connections and STEAM education—in order to contribute to the advancement of the Sustainable Development Goals (SDGs). To achieve this objective, a networking-of-theories framework is operationalized through four interrelated phases: (1) in-depth examination of each theoretical perspective; (2) critical comparison of their guiding questions, principles, and methodological orientations; (3) coordination and synthesis of complementary elements; and (4) local integration into a situated and context-sensitive pedagogical proposal. The empirical analysis focuses on the everyday practices of a recycler in the Colombian Caribbean, whose work involves collecting valves, aluminum cans, and wire. From an ethnomathematical perspective, these practices reveal the use of contextually grounded mathematical reasoning embedded in routine activities. Specifically, the study identifies the emergence of internal and meaning-oriented ethnomathematical connections, including proportional reasoning, the use of empirical measurement units (e.g., “lines”), counting strategies, and informal economic calculations. These findings highlight the presence of sophisticated, experience-based quantitative reasoning within informal labor contexts. The STEAM perspective, in turn, renders visible the interdisciplinary nature of these practices by elucidating the dynamic interplay among science, technology, engineering, art, and mathematics. Within this framework, recycling is conceptualized as a socio-mathematical practice that integrates material knowledge, technical decision-making, and context-sensitive quantitative analysis. This articulation further demonstrates how such practices align with and promote multiple SDGs, including no poverty, good health and well-being, decent work and economic growth, responsible consumption and production, and climate action. The study contributes to the field by proposing a coherent and transferable networking-of-theories model that bridges ethnomathematical connections and STEAM education. This integrative approach illustrates how culturally situated practices can serve as a pedagogical conduit linking informal knowledge systems, interdisciplinary inquiry, and formal school mathematics, thereby supporting educational processes oriented toward sustainability.

This article analyzes the mathematical activity of students entering a university mathematics course for the first time, based on their completion of a diagnostic questionnaire consisting of five problems in elementary arithmetic and algebra. The study is developed from an onto-semiotic approach, integrating the analysis of mathematical practices, cognitive configurations of primary objects, and the types of mathematical connections established by the students while solving the tasks. The methodology was qualitative, based on a content analysis of the mathematical activity of students in logical-mathematical reasoning. The results show that the first problems primarily activate procedural and instructional connections, associated with prior school knowledge, which is reflected in high success rates. However, as the onto-semiotic complexity of the tasks increases, especially in the linear function modeling problem, a significant decrease in performance is observed. This decrease is explained by the need to simultaneously coordinate multiple mathematical connections, particularly those related to the articulation of representations, the construction of meaning, and the activation of procedures. It is concluded that the difficulties identified do not stem from a lack of mathematical knowledge, but rather from a breakdown in the connections necessary to reinterpret school content within university contexts. These findings provide relevant elements for the design of teaching strategies aimed at facilitating the transition from school to university level.

In recent years, there has been a growing emphasis on incorporating innovative resources into the teaching of physics and mathematics to enhance student engagement and understanding. Among these, cinema stands out as a powerful didactic medium capable of fostering motivation, critical thinking, and the construction of scientific knowledge. This study investigates the mathematical connections that emerge from analyzing scenes in films and television series, proposing their use as pedagogical strategies to bridge abstract concepts with real-world contexts. Grounded in the extended theory of connections, the research highlights how cinematic narratives can activate diverse types of mathematical connections such as modeling, representations, and meaning making scientific content more accessible and meaningful. The study also presents findings from a workshop with secondary-level physics and mathematics teachers, revealing that the integration of cinema not only stimulates inquiry and problem-solving but also enhances reflective teaching practices and interdisciplinary thinking among educators and students.

This quasi-experimental study investigated the effectiveness of ChatGPT-integrated discovery learning on high school students' mathematical literacy in three-variable linear equation systems, while examining the moderating role of self-efficacy. Eighty tenth-grade students from a public high school in Indonesia were assigned to either an experimental group receiving ChatGPT-supported discovery learning instruction or a control group receiving conventional instruction, with mathematical literacy assessed through problem-solving tests and self-efficacy measured using validated questionnaires. Statistical analyses using non-parametric tests, including Wilcoxon Signed Rank Test, Mann-Whitney U Test, and Rank-Based ANCOVA, revealed that the experimental group achieved significantly higher post-test scores (M=79.25, SD=8.42) compared to the control group (M=65.30, SD=9.18), yielding a large effect size (d=1.24, p<.001) that substantially exceeded typical outcomes reported in meta-analyses of computer-assisted mathematics instruction. Contrary to established theoretical frameworks positing strong relationships between self-efficacy and mathematics achievement, this study found that self-efficacy neither significantly predicted mathematical literacy (F=3.171, p=.083, η²=.077) nor interacted with the learning model, suggesting that ChatGPT's pedagogical benefits operated uniformly across students with varying confidence levels. These findings suggest that ChatGPT functioned as adaptive conversational scaffolding that provided immediate formative feedback, facilitated metacognitive engagement through dialogic prompting, and generated multiple mathematical representations to support conceptual understanding. The null self-efficacy effect may indicate that robust AI scaffolding serves as an external compensatory mechanism that equalizes learning opportunities by reducing students' dependence on internal confidence judgments, thereby contributing novel theoretical insights into the conditional nature of motivational constructs in AI-mediated learning environments and offering practical implications for implementing conversational AI in mathematics education.