In the context of mathematics education, the integration of artificial intelligence (AI) in teaching calculus is revolutionizing instructional methodologies and enhancing learning experiences both inside and outside the classroom. This study explores the use of specific AI tools, including ChatGPT, MathGPT, Gemini, and Wolfram Alpha, to deepen students’ understanding of key mathematical concepts such as derivatives and rates of change through continuous interaction with a virtual tutor. By employing well-designed prompts, these tools facilitated problem-solving exercises that were verified and refined by AI, fostering both precision in calculations and conceptual clarity. Observations from the classroom implementation reveal that students not only improved their accuracy in performing derivative calculations but also developed a clear understanding of the distinctions between average and instantaneous rates of change. The AI tools created a dynamic, adaptive learning environment, providing immediate feedback and simulations that significantly boosted student engagement and motivation. These findings underscore the potential of AI to transform mathematics education by making learning more personalized and accessible, ultimately enhancing educational outcomes and preparing students for future academic and professional challenges. Furthermore, this study introduces an innovative approach to refining AI prompts and interactions, highlighting the importance of iterative improvement to enhance the quality of AI feedback. This approach is crucial for developing better problem-solving skills and ensuring a comprehensive understanding of mathematical concepts.

This study introduces a comprehensive educational intervention designed to strengthen numerical thinking in third-grade mathematics education through problem-solving. Anchored in Pólya’s problem-solving framework, this research employs a qualitative, descriptive methodology to design and assess a didactic unit. The intervention comprises six structured activities aimed at evaluating and enhancing students’ competencies in numerical thinking and problem-solving. This study’s findings reveal a marked improvement in students’ mathematical abilities, particularly in applying problem-solving techniques to various mathematical contexts. This progress highlights the intervention’s effectiveness in fostering critical thinking and boosting educational outcomes in mathematics. The proposed model demonstrates versatility, offering a scalable approach for enhancing mathematical competencies in diverse educational environments. By integrating Pólya’s systematic steps into instructional practices, this research contributes significantly to pedagogical strategies in mathematics. The innovative use of problem-solving as a learning and evaluation tool not only bridges theoretical and practical knowledge, but also provides a replicable framework for advancing numerical thinking. The methodological approach, which combines qualitative analysis with tangible classroom applications, underscores the potential for transforming mathematics education and improving students’ engagement and proficiency in the subject.

This study examines the outcomes of implementing a teaching unit that integrates problem-solving with the history of mathematics to improve fifth-grade students' understanding of fractions at an educational institution in Yopal, Colombia. Utilizing an educational action research methodology, the study commenced with a diagnostic assessment to identify learning gaps, followed by the design and implementation of a didactic unit. This unit comprised three activities embedded in historical contexts to facilitate the learning of fractions, with its effectiveness assessed through an exit test. Conducted with 32 fifth-grade students, the research employed diagnostic and exit tests to evaluate student performance before and after the activities. The results demonstrated that the teaching unit significantly enhanced students' abilities to understand and apply fractions, as evidenced by their improved performance in the activities within the didactic unit.

The study presents an integrated stochastic modeling framework that combines Markov chains and queuing theory to optimize production efficiency in a metallurgical machining process. The model captures the dynamic behavior of key manufacturing stages, milling, drilling, reaming, and packing, by representing rework, inspection, and waste as distinct probabilistic states. Effective arrival rates and service rates are computed to evaluate machine utilization, total processing time, and throughput. The proposed approach was applied to an industrial case study, where the results showed that reprocessing activities increased the total cost per conforming unit by approximately 0.3% and affected overall system performance. By adjusting machine allocation and minimizing rework probabilities, the model demonstrated measurable improvements in cycle time and cost efficiency. This integrated methodology provides a practical decision-support tool for optimizing production flow, balancing resource utilization, and reducing the financial impact of nonconformity in continuous manufacturing environments.

This study addresses the critical issue of mathematical underperformance among preschoolers in Yopal Casanare, Colombia, through the perspective of an action research project. It focuses on the design and implementation of a didactic unit aimed at promoting numerical thinking, specifically seriation and structured counting, in preschool students. The methodology centers on qualitative action research, combining problem-solving approaches to comprehensively examine and transform educational practices. The intervention was designed to address identified weaknesses in mathematical competencies. To assess the initial state of mathematical competence, the Utrecht Early Mathematical Education Test was administered to 25 transition-grade children, revealing significant deficiencies in seriation and structured counting. The didactic unit included three activities focused on pattern identification, structured counting, and comparison of collections. Post-intervention assessments demonstrated notable improvements in these areas, though the emphasis remains on qualitative insights rather than statistical significance. This study contributes valuable insights into early childhood mathematics education, highlighting the potential of problem-solving-based interventions to enhance foundational mathematical competencies and emphasizing the importance of early diagnostic assessment and targeted educational strategies.

Purpose: This study aims to enhance production quality by applying Quality Control (QC) principles through acceptance sampling, specifically analyzing the efficacy of attribute acceptance sampling plans in final lot receptions.Design/methodology/approach: Through a comprehensive review and critical evaluation of various sampling methodologies found in literature, this paper assesses their efficiency under distinct administrative and operational conditions. It emphasizes the comparison of different attribute acceptance sampling plans by examining variations in parameters and key performance indicators, such as Average Outgoing Quality (AOQ) and inspection time allocation percentage. Furthermore, it proposes a model for Continuous Sampling Plans (CSP) to evaluate these plans' performance in response to operational characteristic variations.Findings: The analysis reveals that the selected methodologies significantly aid in decision-making processes for lot acceptance, utilizing non-conforming rates depicted by the Average Quality Level (AQL). This provides a robust framework for improving Quality Control strategies, demonstrating the potential of these methodologies to optimize production quality through strategic lot acceptance.Practical implications: This paper outlines a practical approach for industry practitioners to enhance decision-making in lot acceptance, offering a method to balance quality control with operational efficiency effectively.Originality/value: By comparing a wide range of attribute acceptance sampling plans and introducing a novel CSP model, this research contributes valuable insights into the optimization of QC strategies. It offers a unique perspective on enhancing production quality, marking a significant advancement in the field of Quality Control and management.