Proportional reasoning is considered a key element in probabilistic reasoning. Various studies have suggested that insufficient proportional reasoning may be the cause of many errors made by students when dealing with probability problems. [Objective] The aim of this study is to identify the proportional reasoning used by sixth grade students (11-12 years old) when solving sample space quantification and probability comparison tasks. [Methodology] Through an exploratory qualitative approach, the responses of 47 Spanish students from a public school were analyzed in relation to two problems: one focused on comparing probabilities (ratio comparison), and the other on determining the composition of a box to generate equal probabilities (proportional distribution). The analysis of the solutions using semiotic functions allows identification of relationships between objects involved in the tasks and the characteristic elements of proportional reasoning, facilitating interpretation of students’ errors. [Results] The results show that the students struggled to select the box with the highest probability of success, which indicates insufficient proportional reasoning. However, most students were able to correctly determine the composition of a box needed to maintain a given probability, whereas few could justify their reasoning based on probability or proportionality. [Conclusions] The results contrast with previous research findings and show previously unidentified difficulties in solving proportional distribution problems in a probabilistic or arithmetic context.

[Objective] The objective of this research is to identify the mental structures and mechanisms used by a group of Business Administration students to understand the solution set of a system of linear inequalities in two variables (SSSLI), as they establish Cartesian Connections. The theoretical foundations used are the APOS theory articulated with the concept of Cartesian Connection. [Methodology] This study is qualitative. For the design of the instrument, a preliminary genetic decomposition (PGD) was developed, and based on the PGD three tasks were designed. For data collection, these tasks were applied to a group of 19 students (between 18 and 22 years old). Later, the three participants who provided the most detailed answers were selected to conduct a semi-structured interview. [Results] The results showed that participants constructed the SSSLI Process by coordinating the solution set Process of the linear inequality in two variables (SSLI) with the set intersection Process. It was observed that participants associated the SSSLI with a polygon and did not consider it to be an empty, convex or bounded set. [Conclusions] It was concluded that those participants who constructed the action structure or a SSLI process showed the same type of structure in relation to SSSLI. New research is suggested that delves deeper into the mechanisms and mental structures described in this study, as well as into the design of teaching proposals that contribute to improving SSSLI learning.

[Objective] The main objective of this research was to measure the impact on academic performance of a teaching proposal for mathematical modeling of functions using Brousseau’s theory of didactic situations. [Methodology] A quantitative study with a pre-experimental design was conducted with a sample of 22 high school students belonging to the Remigio Crespo Toral Educational Unit (Ecuador). Previously, the participants followed a conventional study routine on the topics of function modeling. A pretest was then administered to evaluate the group’s academic performance. Subsequently, eight work sessions were conducted during which the didactic situations were implemented. Finally, a posttest was administered to evaluate the results after the intervention. [Results] The results of a descriptive analysis of the grades showed an 87% improvement in posttest scores, and the results of a student’s t-test analysis showed a significant difference between the pretest and posttest scores (p-value < 0.05). Furthermore, it was confirmed that the theory of didactic situations is compatible with the modeling cycle by strengthening various modeling competencies, such as the use of graphs and algebraic language. [Conclusions] It was shown that mathematical modelling using didactic situations significantly improved academic performance.

[Objetive] The objective was to characterize different sperm subpopulations based on morphometric parameters of frozen-thawed semen in two bovine subspecies using a CASA system. [Methodology] The experiment was carried out at the Costa Rica Institute of Technology from May to December 2023. Spermatozoa from 10 bulls (five animals of each subspecies, Bos taurus and Bos indicus) were evaluated after thawing of the semen doses by an ISAS®v1, Computer-Assisted Sperm Analysis (CASA)-Morph system. Sub-populations of head morphometric spermatozoa were characterized using multivariate procedures such as principal components (PCs) analysis and clustering methods (k-means model) [Results] The ejaculate of male exhibits significant heterogeneity and comprises diverse sperm subpopulations with differing morphometric patterns. Three different sperm subpopulations were identified from three PCs: head size, head shape, and symmetry of the sperm head and the degree to which it was pyriform. The proportions of the different sperm subpopulations varied in the two-bovine subspecies; Bos taurus and Bos indicus. Results indicated that subpopulations SP1, SP2, and SP3 were different for PC criteria and these differences were relevant. The variability in sperm morphometry assessments underscores the need to standardize semen evaluation protocols [Conclusions] These findings highlight the importance of knowing the diversity in sperm morphometry between subspecies to both improve in vitro evaluation tests and to distinguish subspecies.

In this text, four examples of gestures produced and arising from an investigation with mathematics undergraduate students are presented. Gesticulations were used to convey the concepts of point, line, and plane in conversations about the spatial geometry of position. [Objective] Thus, we aim to share an analysis of the gestures produced by prospective mathematics teachers to indicate the primitive entities of geometry. [Methodology] The data come from a research study involving students aged between 19 and 23 years as participants at a public university in the state of São Paulo, Brazil. This research is qualitative. The analysis of the gestures, as well as their possible meanings, was conducted through an attentive and detailed examination of the video recordings of the two meetings held for each of the six pairs of undergraduates, facilitated by teaching experiments. [Results] As a result, we noticed that the same geometric notion was communicated through identical gestures at different times. It was also found, in line with the assumed theoretical framework, that gestures are an integral part of the discourse. Finally, we verified the presence of three gestures produced sequentially, one after the other, to indicate notions of point, line, and plane. [Conclusions] These considerations are relevant and show the power of gestures in the sense that they can provide clues to how students are expressing and/or learning concepts of greater complexity.

[Objective] Currently, individuals must understand statistical data to form critical opinions and make informed decisions. For this reason, various organizations and authors have pointed out the need to begin to develop gradually, from an early age, data reading skills and their graphic representation, an aspect that has been progressively incorporated into the mathematics curricula of various countries. In this context, this study aims to conduct a systematic review of research articles published over the last decade (2014-2023) that have analyzed the knowledge of statistical graphics among infant and primary school students (4 to 12 years old). [Methodology] Based on the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) statement, after applying the exclusion criteria, 12 articles published in the Web of Science, Scopus, and SciELO databases were analyzed. [Results] The main findings show: a) a low number of articles related to students in the first years of school, predominantly research focused on primary education; b) the most researched topic is reading and interpretation of graphs. [Conclusions] New studies should be promoted to more precisely identify the different types of knowledge regarding statistical graphics that students can acquire according to their age (4-12 years). This will help in designing and implementing teaching practices aimed at fostering optimal graphic comprehension.

[Objective]: This research aimed to identify and analyze topics in the scientific literature related to dengue, with a focus on diagnosis, signs, and symptoms using the Latent Dirichlet Assignment (LDA) model. [Methodology]: Articles were collected from various databases, including VHL, Web of Science, Ovid, Scopus, PubMed, Health & Medical, ScienceDirect, and Google Scholar, covering 2000-2024. The search equation was designed using key terms such as “dengue,” “signs,” “symptoms,” and “diagnosis,” along with MeSH terms to ensure the inclusion of relevant articles. The LDA model was then implemented to analyze the collected articles. [Results]: The implementation of the LDA model identified four main themes: 1) Dengue diagnosis and clinical presentation, 2) Research and control interventions, 3) Severe dengue and its clinical manifestations, and 4) Virus detection, including dengue, zika, and chikungunya. This thematic analysis facilitated the organization and understanding of literature, providing an overview of the predominant themes in dengue research. [Conclusions]: The study’s approach not only enhanced the organization and understanding of the articles found but also provided insights into the predominant themes in dengue literature, which may guide future research and improve diagnostic and treatment strategies.

[Objective] The field of computer vision has seen remarkable progress, largely due to the advancements in deep learning. These developments have revolutionized image recognition, interpretation, and application across numerous domains. This paper introduces a new framework designed to expand the potential of computer vision systems by harnessing the power of deep learning techniques. Deep neural networks are at the core of this new system, providing exceptional accuracy and reliability in tasks such as object recognition, image segmentation, and scene understanding. [Methodology] Furthermore, this framework offers a versatile platform for real-time image processing, paving the way for numerous applications in areas like industrial automation, medical diagnostics, and autonomous vehicles. This study comprehensively explores the architectural elements and methodologies that drive this innovative framework. It emphasizes the framework's technological capabilities, scalability, adaptability, and potential for broad adoption across industries seeking advanced computer vision solutions. [Results] The proposed model, Convolutional Neural Network-Feature Pyramid Network (CNN-FPN), demonstrates superior performance across all evaluated metrics for object detection compared to existing models. Specifically, it achieves the highest scores in Accuracy (57.2%), Recall (60.4%), Precision (94.1%), F1-Score (73.5%), and AUC (0.983). These results indicate that the proposed model offers superior performance and reliability in object detection tasks, demonstrating its potential for high-precision computer vision applications. [Conclusions] In conclusion, this innovative architecture represents a significant advancement in computer vision, enabled by the capabilities of deep learning. Our test findings demonstrate that compared to conventional algorithms, the enhanced CNN-FPN produced more accurate results.

[Objective] The objective of the research was to determine the mathematical modeling competencies shown by a group of prospective teachers in Mathematics Teaching, in their fourth year of studies at the Universidad Nacional. [Methodology] For this purpose, a qualitative research was conducted with 20 prospective mathematics teachers during the first half of 2022, when they were required to solve a series of problems as part of a training program in mathematical modeling. The work done by the participants on two specific problems is presented. [Results] The participating prospective teachers demonstrated competencies in solving mathematical modeling problems when the situation presented has the necessary data and its solution requires a specific procedure. In situations that involved conducting research to gather additional information or data, and making assumptions, among other things, which could imply different solutions, the participants had difficulties in solving the problems. [Conclusions] The participants demonstrated their ability to handle and make sense of relevant data for solving mathematical modeling problems. However, when they needed to conduct research to gather additional information or data, they were unable to identify which data should be included in the problem-solving process. Their ability to search for information, connect a mathematical model with another problem situation or a known model, or validate the solution obtained for a problem, was limited. The results obtained could indicate that it is necessary to emphasize these types of activities in the teacher training programs, for their use as a teaching strategy in their professional practice.

[Objective] The objective was to estimate the carbon stock and its spatial distribution in soils of the Zanja Honda micro-watershed (Ibagué, Colombia). [Methodology] Hydrological Response Units were delineated, considering land cover, soil units, and the range of slopes. Based on the representativeness of these hydrological units, 46 sampling sites were identified. After locating sampling sites in the field, the following parameters were determined at each site: thickness of horizons, bulk density (core method), rock fragment content by weight and volume, and organic carbon concentration using the wet oxidation method. [Results] The most significant magnitudes in organic carbon content and soil organic carbon stock generally occur in the lower part of the micro-watershed (0.05 Mg ha-1); while the high slope areas in the middle-upper part present lower magnitudes of these variables (0.002 Mg ha-1). The soils studied store a total of 6736.3 Mg of organic carbon, which is generally stored in the first 0.3 m of the soil profile. [Conclusions] Micro-watershed soils exhibited lower organic carbon stocks compared to other studies conducted in the area, with carbon stocks primarily occurring in low areas with lower inclinations. This suggests that topographic variables play a significant role in determining carbon stocks in these soils.