Search Results (214)

Mathematical performance in early education is influenced by a complex interplay of cognitive and affective factors, including language skills, working memory, and anxiety. This study investigated whether working memory and math anxiety, in both explicit numerical situations (ENS) and general classroom situations (GCS), mediate the relationship between general and math-specific vocabulary and math performance in a sample of 467 second-grade students in Chile. Structural equation modelling was employed to test a dual-pathway model in which both working memory and math anxiety served as mediators between vocabulary knowledge and math performance. Results indicated that both general and math-specific vocabulary positively predicted working memory and negatively predicted math anxiety in ENS. In turn, working memory and ENS significantly predicted math outcomes, whereas GCS was not a significant predictor. Indirect effects supported a dual mediation structure, with vocabulary influencing math performance through both cognitive and affective mechanisms. Math-specific vocabulary exerted a slightly stronger total effect than general vocabulary, consistent with its closer alignment to the semantic demands of mathematical tasks. These findings suggest that vocabulary supports early mathematical learning not only by enhancing cognitive processing capacity but also by reducing anxiety in task-specific contexts. Full article

The convection-diffusion-reaction (CDR) equation is a fundamental mathematical model for simulating the transport of pollutants. It is a crucial tool for addressing global environmental challenges. However, most existing computational solutions are proprietary and inaccessible, making the development of open-source educational platforms with advanced stabilization capabilities necessary. This study developed and validated a computational framework that solves CDR equations using algebraic sub-grid scale (ASGS) stabilization. The research addressed the fundamental challenge of spurious oscillations that emerge in standard Galerkin formulations when convective transport significantly exceeds diffusive processes. This is a prevalent issue in transport phenomena modeling. A novel, Python-based educational software platform called CDR-Solv was developed to demonstrate the effectiveness of ASGS stabilization across polynomial degrees ranging from linear to cubic approximations. Numerical experiments with minimal diffusion coefficients showed that numerical instabilities were successfully eliminated while maintaining solution accuracy across various source term configurations. The stabilization parameter, ${\tau }_K$, was instrumental in achieving computational stability without compromising mathematical rigor. Comparative analysis revealed the superior performance of higher-order approximations in capturing boundary layer phenomena and sharp gradient regions. The primary contribution of this study is the development of an open-source educational platform that provides access to advanced stabilization techniques and algorithmic transparency. The CDR-Solv framework also allows for the systematic exploration of the effects of selecting different polynomial degrees on solution quality in transport-dominated regimes. Full article

This research examines the impact of practical work and the use of scientific research methods when teaching ten-year-old students interested in the fields of science, technology, engineering, and mathematics (STEM). An increased interest in STEM is encouraging, as it may carry through to higher education institutions and potentially increase students’ ability to contribute to improving Croatian society. The program “Sa STEMom raSTEMo” was approved by the Ministry of Sciences and Education for researching and improving didactic work in STEM fields in elementary schools. A total of 650 participants from four classes in five primary schools were selected. Half of the participants formed the intervention group in which the “Sa STEMom raSTEMo” program was implemented for three months, and the other half formed the control group. Before and after the experimental intervention, a survey to determine interest in STEM fields was conducted in both groups, and the results were compared to verify the impact of the implemented forms of teaching. A questionnaire was then constructed and tested through a pilot study; its understandability and reliability were measured, as well as the validity of the applied measurement scales. Furthermore, a survey of interest in STEM fields was conducted three months after the intervention. All results were analyzed and compared. The results showed that implementing practical work and using scientific research methods in classroom teaching increases students’ interest in STEM. In general, no statistically significant differences in interest in STEM were observed between girls and boys aged 10, and no relevant gender differences were observed in 10-year-olds who participated in the program. Full article

Limited evidence exists on how teachers contribute to student learning gains in early childhood education. This study draws on the Dynamic Model of Educational Effectiveness (DMEE) and investigates the impact of teacher factors on pre-primary students’ mathematics achievement. It also examines whether the five proposed dimensions—frequency, quality, focus, stage, and differentiation—can clarify the conditions under which these factors influence learning. Using a stage sampling procedure, 463 students and 27 teachers from Greek pre-primary schools were selected. Mathematics achievement was assessed at the beginning and end of the school year, while external observations measured the DMEE factors. Analysis of observation data using multi-trait multilevel models provided support for the construct validity of the measurement framework. Teacher factors explained variation in student achievement gains in mathematics. The added value of using a multidimensional approach to measure the functioning of the teacher factor was identified. Implications of the findings are drawn. Full article

This study explores how teachers in Swedish preschool classes respond to and elaborate on six-year-old students’ input during mathematics teaching. The aim is to understand how different teacher responses offer different learning opportunities related to numbers and number relations. Data were collected through classroom observations of 145 teaching episodes across 95 preschool classes. Each episode was analyzed using an adapted version of the Mediating Primary Mathematics framework. Four qualitatively different response categories, predefined within the framework, were used to capture variation in how student input was responded to. Although most teaching episodes involved brief confirmations, only a few episodes included elaborations that offered students opportunities to engage more deeply with mathematical ideas. Two teaching episodes were selected for a closer analysis, using variation theory of learning, with the aim of describing the different learning opportunities offered depending on how the teachers responded to and elaborated on student input. The results show that, in both teaching episodes, students were given opportunities to learn that numbers can be represented in different ways. In one episode, the teacher’s elaboration enabled students to learn how to use units of five to count collections larger than five. In the other episode, although groups of five were represented visually, they were not explicitly used as a strategy for determining the total, and no alternative to counting by single units was offered. The study highlights the importance of how teachers respond to student input and how these responses influence what becomes possible to learn in early mathematics education. Full article

Providing students with effective learning resources is essential for improving educational outcomes—especially in complex and conceptually diverse fields such as Mathematics and Computer Science. To better understand how these subjects are communicated, this study investigates the linguistic structures embedded in academic texts from selected subfields within both disciplines. In particular, we focus on meta-languages—the linguistic tools used to express definitions, axioms, intuitions, and heuristics within a discipline. The primary objective of this research is to identify which subfields of Mathematics and Computer Science share similar meta-languages. Identifying such correspondences may enable the rephrasing of content from less familiar subfields using styles that students already recognize from more familiar areas, thereby enhancing accessibility and comprehension. To pursue this aim, we compiled text corpora from multiple subfields across both disciplines. We compared their meta-languages using a combination of supervised (Neural Network) and unsupervised (clustering) learning methods. Specifically, we applied several clustering algorithms—K-means, Partitioning around Medoids (PAM), Density-Based Clustering, and Gaussian Mixture Models—to analyze inter-discipline similarities. To validate the resulting classifications, we used XLNet, a deep learning model known for its sensitivity to linguistic patterns. The model achieved an accuracy of 78% and an F1-score of 0.944. Our findings show that subfields can be meaningfully grouped based on meta-language similarity, offering valuable insights for tailoring educational content more effectively. To further verify these groupings and explore their pedagogical relevance, we conducted both quantitative and qualitative research involving student participation. This paper presents findings from the qualitative component—namely, a content analysis of semi-structured interviews with software engineering students and lecturers. Full article

The primary distinction between technical design and engineering design lies in the role of analysis and optimization. From its inception, descriptive geometry has supported military and engineering applications, and its graphical rules inherently reflect principles of optimization—similar to the core ideas of sparse representation and compressed sensing. This paper explores the geometric and mathematical significance of the center line in symmetrical objects and the axis of rotation in solids of revolution, framing these elements within the theory of sparse representation. It further establishes rigorous correspondences between geometric primitives—points, lines, planes, and symmetric solids—and their sparse representations in descriptive geometry. By re-examining traditional engineering drawing techniques from the perspective of optimization analysis, this study reveals the hidden mathematical logic embedded in geometric constructions. The findings not only support the deeper integration of mathematical reasoning in engineering education but also provide an intuitive framework for teaching abstract concepts such as sparsity and signal reconstruction. This work contributes to interdisciplinary understanding between descriptive geometry, mathematical modeling, and engineering pedagogy. Full article

Mental calculation is key to the development of number sense and flexibility in thinking, but in practice, it is often neglected in favour of written algorithms. The aim of this study was to examine the relationship between the success in mental calculation and the number of strategies used, as well as to explore differences between age groups and genders. The study included 233 participants from various age groups, and data were collected through a mental calculation test and individual interviews regarding the strategies employed. The study follows quantitative, cross-sectional, correlational-comparative design, and the data was analyzed using key statistical techniques including the Kolmogorov–Smirnov test, Pearson’s correlation analysis, linear regression, one-way ANOVA with Bonferroni post hoc correction, and two-way ANOVA to examine main effects and interactions. The results showed a statistically significant positive correlation between the number of strategies and success in mental calculation. Differences between age groups were marginally significant; it was found that upper primary and secondary school students used a greater number of strategies. Additionally, boys, on average, applied more strategies than girls. In conclusion, the variety of mental calculation strategies positively correlates with accuracy in mental calculation, and teaching a greater number of strategies may contribute to the development of flexibility and confidence in mathematical thinking. It is recommended that greater emphasis is placed on the development of mental strategies within formal education. Full article

This systematic review explores the number and role of the UNO^® card game and UNO-type learning media across different levels of mathematics education. UNO^®-inspired games have gained recognition as innovative pedagogical tools that promote engagement, motivation, and active learning among students in various mathematics topics in the last few years. This review synthesises existing research on the application of these games in preschool, primary, secondary, and higher education settings. We employed a hybrid approach, combining database searches and the snowball method, to ensure a comprehensive and thorough selection of the relevant literature for our systematic review. Published research studies between January 1980 and June 2025 that employed UNO^® or UNO-type card games in education were collected. Forty-one research studies met the inclusion criteria for this review. We sought answers to three research questions. At first, we made a time analysis to organise the collected records. Based on the collection, we identified the mathematical topics for which teachers and researchers used the original UNO^® game or developed UNO-type games at various educational levels, as well as the role of UNO^® and UNO-type games in mathematics education. In approximately 68.29% of the cases, the authors introduce their own educational games modelled after UNO^®. In contrast, just less than one-third of the records (31.71%) utilise the original UNO^® playing cards in the teaching–learning process. The findings indicate that UNO-type educational maths games can enhance conceptual understanding, foster collaborative skills, and improve learning outcomes when appropriately integrated into curricula. This review also offers educators recommendations for effectively introducing these games at various educational levels. We aim to provide an evidence-based, well-structured insight into the potential of UNO^® and UNO-type learning tools. Full article

The education sector in Tanzania faces significant challenges, especially in public primary schools. Unmanageably large classes and critical teacher–pupil ratios hinder the provision of tailored tutoring, impeding pupils’ educational growth. However, artificial intelligence (AI) could provide a way forward. Advances in generative AI can be leveraged to create interactive and effective intelligent tutoring systems, which have recently been built into embodied systems such as social robots. Motivated by the pivotal influence of teachers’ attitudes on the adoption of educational technologies, this study undertakes a qualitative investigation of Tanzanian primary school mathematics teachers’ perceptions of contextualised intelligent social robots. Thirteen teachers from six schools in both rural and urban settings observed pupils learning with a social robot. They reported their views during qualitative interviews. The results, analysed thematically, reveal a generally positive attitude towards using social robots in schools. While commended for their effective teaching and suitability for one-to-one tutoring, concerns were raised about incorrect and inconsistent feedback, language code-switching, response latency, and the lack of support infrastructure. We suggest actionable steps towards adopting tutoring systems and social robots in schools in Tanzania and similar low-resource countries, paving the way for their adoption to redress teachers’ workloads and improve educational outcomes. Full article

Academic performance has become a consolidated indicator of a nation’s educational and social equity. Consequently, increasing attention has been paid to determining the factors associated with school performance, particularly in the case of students with extreme academic outcomes. The aim of this study is to identify and compare the factors related to the level of mathematical competence of Spanish students with low and high levels of achievement, based on data from the Spanish sample of PISA 2022 (n = 30,800). The results of the multilevel quantile regression analysis reveal that the social, economic, and cultural status of the students have a significant and positive effect on both groups. Other variables, such as gender, grade repetition, and length of pre-primary education, show differentiated effects depending on the level of competence. Moreover, school-related factors, such as school location and competition among centres, exhibit opposite effects. Finally, aspects such as school ownership, average class size, and the degree of curricular autonomy only have a significant impact on the mathematical competence of low-achieving students. These findings highlight the need for differentiated educational policies that address the specific needs of each group of students. Full article

The use of augmented reality (AR) tools and innovative learning environments in education have increased over the last few years due to the rapid advancement of technology. In this study, an AR mathematics learning intervention has been proposed which consisted of the creation of 3D multibase blocks to perform AR arithmetic calculations conducted through active methodologies in the future classroom lab (FCL). The aim of this study was to analyze pre-service teachers’ (PSTs) affective domain (emotion, self-efficacy, and attitude), engagement, motivation, and confidence. The sample consisted of 97 PSTs enrolled on the second year of the Primary Education degree, who were attending the “Mathematics and its Didactics” subject. The findings revealed a significant increase in PSTs’ satisfaction, fun, confidence, and pride, and a decrease in uncertainty, nervousness, and concern. Regarding PSTs’ self-efficacy, a significant improvement was observed in knowing the necessary steps to teach mathematical concepts and work in the FCL. No significant differences were found in attitude, engagement, and motivation; however, the PSTs showed a high disposition in all of them before starting the intervention. Additionally, the PSTs reported to be more confident, and it enhanced their knowledge in the use of 3D design and AR applications to create multibase blocks to support the teaching–learning content of arithmetic operations. Full article

On the basis of the hypothesis that has emerged from recent research studies, this article discusses the new pedagogical training model for primary school pre-service teachers (PSTs), namely the Meta Discussion on a Pedagogical model (MDPm). The study was conducted with 400 PSTs enrolled in a primary education mathematics course. The MDPm is a collective discussion involving PSTs and their facilitator about the prior teaching experience based on a Mathematical Discussion (MD) model. In this article we try to give a more detailed definition of MDPm by analyzing different examples drawn from a collection of data gathered in the frame of different teacher training experiments. The results indicate that engaging PSTs in both a direct MD and a subsequent reflective meta-discussion leads to enhanced awareness of the teacher’s role and a more robust conceptualization of the MD model. These experiments aimed to help future teachers recognize the characteristics of their instructional actions within a pedagogical model, engaging them actively in their training, in and from practice. In this setting, PSTs assumed a dual role as both students and future teachers. The research has been conducted in a technological environment, which assumed a fundamental role in supporting the processes involved in the teaching experiment. The examples are analyzed through a specific lens aimed at identifying key elements supporting and refining the MDPm, with the aim of more precisely characterizing it. Full article

The transition stage to pre-primary school represents a key event, in which the support received from family and teachers is essential in facilitating the transition and in ensuring an effective adjustment to the school environment. Our study aimed to investigate the impact of mathematical prerequisites on cognitive development, compared to the impact of reading and writing prerequisites, from the perspective of parents and early childhood educators. Thus, we quantified the impact of reading–writing and math prerequisites on children’s transition from kindergarten to school, analyzing the challenges, opportunities, and possibilities that arise. The sample consisted of 685 parents and 188 teachers, using the preschool prerequisites screening standardized questionnaire developed by the company Cognitrom, a questionnaire-survey, and the focus group method. Initially, the fidelity of the research instrument was assessed by calculating Cronbach’s alpha coefficient. The data distribution was tested using the skewness and kurtosis coefficients. Subsequently, descriptive analyses were carried out in order to provide an overview of the data collected by performing a multiple linear regression analysis. In addition, the Phi coefficient and V Cramer’s V coefficient were used to analyze the association between the research variables. By corroborating the obtained results, we can state that, from the parents’ and early childhood teachers’ perspective, math prerequisites have a greater influence on children’s cognitive development in the transition process from kindergarten to school compared to reading–writing prerequisites, confirming the general hypothesis. Full article

Collaboration skills are an important component of 21st century skills and a critical skill for citizens of the future. In this work, we propose collaboration-oriented robotics education (CORE), a methodology aimed at fostering the development of collaboration skills in primary school students aged 11–12 via an adjusted approach to the teaching of educational robotics. In order to assess the existence and level of collaboration skills in a student, a suitable tool is also proposed. Using a collaboration-oriented performance evaluation test (COPE) for both a pre- and post-intervention measurement and applying both the conventional and CORE approaches to teaching educational robotics to 32 students, split into control and intervention groups, we demonstrate the effectiveness of the proposed approach. Specifically, the experimental implementation shows that CORE statistically significantly increases the performance of the experimental group compared to the conventional way of teaching educational robotics. These results, in addition to validating CORE itself, demonstrate that the conventional approach to STEAM (Science, Technology, Engineering, Arts, Mathematics) education is not necessarily already optimized, thus facilitating an overall re-evaluation of the field. Full article