Search Results (10)

This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this project is that the use of technological tools, such as mathematical modeling, visualization, automatic reasoning and artificial intelligence, significantly improves the teaching and learning of mathematics, in addition to fostering positive attitudes in students. With this hypothesis in mind, in this article, we describe an investigation that has been developed in initial training courses for mathematics teachers in several universities in Madrid, where students used GeoGebra Discovery automated reasoning tools to explore geometric properties in real objects through mathematical paths. Through these activities, future teachers modeled, conjectured and validated geometric relationships directly on photographs of their environment, with the essential concourse of the automated discovery and verification of geometric properties provided by GeoGebra Discovery. The feedback provided by the students’ answers to a questionnaire concerning this novel approach shows a positive evaluation of the experience, especially in terms of content learning and the practical use of technology. Although technological, pedagogical and disciplinary knowledge is well represented, the full integration of these components (according to the TPACK model) is still incipient. Finally, the formative potential of the approach behind this experience is highlighted in a context where Artificial Intelligence tools have an increasing presence in education, as well as the need to deepen these three kinds of knowledge in similar experiences that articulate them in a more integrated way. Full article

Interdisciplinary teaching enhances student learning but poses challenges in practical implementation. This study examines the co-design of an interdisciplinary MathCityMap trail by mathematics and physics educators, analyzing tensions and synergies through the ROGI framework (Resources, Orientations, Goals, Identity). Using qualitative methods, including reflective journals and co-design, we explore how disciplinary perspectives shape task design. A key constraint was the MathCityMap system’s requirement for verifiable outcomes, limiting open-ended inquiry, particularly in mathematics. While mathematics educators emphasized conceptual understanding, physics educators prioritized hands-on experimentation, leading to tensions in defining inquiry-based learning. Despite these challenges, the collaboration yielded innovative solutions, such as adapting tasks to balance system feasibility with inquiry-driven exploration. The study highlights the need for digital tools that accommodate both procedural and exploratory learning and emphasizes interdisciplinary collaboration as a valuable professional development approach. Future research should focus on enhancing digital platforms to support inquiry-based methodologies in STEM education. Full article

Advances in education are increasingly important, and it is necessary to look for methodological strategies that enhance the value of mathematics in society and promote integrated training that helps students reason critically and rigorously. In this sense, math trails with a focus on STEM and sustainable development are a good resource to connect mathematics with the environment in a transversal way with other disciplines. A total of 35 postgraduate students in secondary education and 30 undergraduate students in primary education participated in this research and received a training course from experts in mathematics teaching. During the experience, the graduate students designed trails that were tested by the undergraduate students after a prior review by three in-service primary teachers. Likert scale questionnaires and open questions were asked of the students to evaluate the training received and the execution of the experience. Likewise, it was also decided to hold a debate with the participants and a guided interview with in-service teachers to assess the possible application of the resource in primary education courses. The results show a very positive assessment of the experience and allow us to support this approach to promote a change in the teaching–learning of mathematics in the last years of primary education. Full article

Objective: The tangram puzzle is a serious math puzzle game used to promote mathematic development in children, which improves visuospatial function and creativity. A game to improve cognitive functions is useful for patients with neurocognitive disorders. This pilot study aimed to determine whether this game could improve cognitive function in patients with neurocognitive disorders. Materials: This study recruited patients with mild Alzheimer’s disease or mild cognitive impairment who were followed longitudinally by the Department of Psychiatry, Juntendo University Hospital, or Juntendo Tokyo Koto Geriatric Medical Center (Tokyo, Japan). Methods: Participants were asked to solve Tangram puzzles 2–3 times weekly, spending 30–40 min/session at home with or without family members for approximately 90 (Study 1) or 180 (Study 2) days. Mini-Mental State Examination (MMSE) in Study 1 as well as a Japanese version of the Montreal Cognitive Assessment and Trail Making Test in Study 2 were performed on the initial and final days. Results: Study 1 comprised eight participants and Study 2 comprised nine participants. Statistically significant improvement was observed in MMSE total score (p = 0.016) and orientation segment (p = 0.026) in Study 1. No statistically significant difference was noted in MMSE total score, orientation segment, or MoCA-J (Japanese version of Montreal Cognitive Assessment) score between the initial and final days in Study 2 (p = 0.764, p = 0.583, and p = 0.401, respectively). Conclusions: Study 1 revealed that Tangram puzzles may ameliorate the progression of cognitive functions in patients with neurocognitive disorders within a short time (3 months); however, Study 2 did not show a consistent result. Thus, randomized controlled trials are warranted to draw a conclusion. Full article

Math trail is a type of outdoor activity conducted in groups. Group members work together, communicate, and find common and best strategies for solving problems. Thus, it combines the use of mathematics in real life with a pleasant walk. Pupils have the opportunity to explore mathematics linked to real objects, solving standard and non-standard problems. Teachers, in turn, can use mathematics in this way as a tool to connect it to other STEM disciplines. This article first describes the results of research aimed at assessing spatial ability and mental rotation in students at technical vocational schools in Slovakia. A stereometry test was solved by 455 students. We then created a mathematical walk aimed at developing students’ spatial ability. The experiences presented in the article may be helpful as other mathematics’ popularization stimuli. We believe that when students are engaged in problem-based learning activities that are related to STEM disciplines, in particular, by connecting with the subjects in the problem context of the real world, STEM disciplines may become more important for students. Interdisciplinary STEM learning imitates authentic real-world problem-solving. Full article

Whereas researchers regard high school math and science coursework as the best indicator of college readiness for students in the United States, computer science coursework and its relationship to college attendance, particularly for minoritized students, have not received due attention despite its root in the mathematical and scientific reasoning ability. We examined students’ high school course completion patterns across subjects and grade levels with a special focus on elective computer science courses and whether the coursework pattern transitions worked differently for minoritized students in Texas, USA. Latent profile analysis and latent transition analysis revealed multiple patterns of coursework, including Regular, Trailing, and Computer Science-Intensive. However, high school students seemed to attempt computer science courses with an experimental attitude. High school girls, low-income, and Latinx and African American students were less likely to complete computer science courses, despite demonstrating a similar coursework pattern in the previous year. Similarly, students with limited English proficiency, those eligible for free- or reduced-price lunch programs, and Native American students systematically have a lower chance to attend college, despite sufficient academic preparation in high school. Findings highlight the challenges minoritized students face and how students approach elective computer science courses in high school. Full article

This study presents an experience that combines problem-posing and Math Trails in the context of future teachers’ instruction. Pre-service teachers in the third year of their studies were faced with the design of tasks to be included in Math Trails for primary school students. The study analyzes, from a quantitative approach, 117 tasks contained in 11 Math Trails. The analysis was performed on the basis of classification variables (grade, mathematical content and object or real element involved in every task) and research variables which provide information about the nature of the tasks (procedural vs. problem-solving, level of cognitive demand, degree of contextualization, openness and creativity). Additionally, relationships between the different categories of analysis have been studied. The results reveal certain biases in the tasks in relation to the contents addressed (an abundance of tasks with a geometric component and a scarcity of tasks involving algebra or probability concepts). Most of the tasks are presented in a real context. However, a higher percentage of procedural tasks than problem-solving tasks is observed, with a predominance of low openness, creativity and cognitive demand. These results provide useful lines of work to address difficulties faced by future teachers in the STEAM field. Full article

Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context, known to promote positive attitudes and additional engagement for the learning of mathematics, confronting students with a sequence of real-life tasks, related to a particular mathematical theme. Recently, mobile devices and apps, i.e., MathCityMap, have been recognized as an important resource to facilitate the extension of the classroom to the outdoors. The study reported in this paper intends to identify the principles of design for mobile theme-based math trails (TBT) that result in rich learning experiences in early algebraic thinking. A designed-based research is used, through a qualitative approach, to develop and refine design principles for TBT about Sequences and Patterns. The iterative approach is described by cycles with the intervention of the researchers, pre-service and in-service teachers and students of the targeted school levels. The results are discussed taking into account previous research and data collected along the cycles, conducing to the development of general design principles for TBT tasks. Full article

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC “Task Design for Math Trails”, with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC’s topics’ task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research. Full article

The current evidence for a relation between children’s heart rate measures and their academic performance and executive functioning is infancy. Despite several studies observing dose-response effects of physical activity on academic performance and executive function in children, further research using objective measures of the relative intensity of physical activity (e.g., heart rate) is warranted. The present study aimed to inspect associations between heart rate response and various academic performance indicators and executive function domains. A total of 130 schoolchildren between the ages of 9 and 13 years (M = 10.69, SD 0.96 years old; 56.9% boys) participated in a cross-sectional study. Children’s heart rate data were collected through participation in physical education classes using the polar Team^TM hardware and software. One week before heart rate measures, academic performance was obtained from the school records in maths, Spanish language, Catalan language, physical education, and Grade point average. Executive function was measured by two domains, cognitive flexibility with the Trail Making Test and inhibition with the Stroop test. Associations between children’s heart rate data and academic performance and executive function were analyzed using regression models. Academic performance was found to be positively related to four heart rate measures (β range, 0.191 to 0.275; all p < 0.040). Additionally, the hard heart rate intensity level was positively related to two academic indicators (β range, 0.183 to 0.192; all p < 0.044). Three heart rate measures were associated with two cognitive flexibility subdomains (β range, −0.248 to 0.195; all p < 0.043), and three heart rate measures were related to one inhibition subdomain (β range, 0.198 to 0.278; all p < 0.028). The results showed slight associations of heart rate responses during physical education lessons with academic performance but did not clearly indicate associations with executive function. Future experimental studies testing associations between different bouts of intensity levels are needed to disentangle the relationship with brain function during childhood. Full article