Search Results (636)

Understanding advanced pre-tertiary mathematics, particularly three-dimensional vectors, demands robust spatial reasoning skills that many students find challenging to develop through traditional pedagogical methods. This study proposes and evaluates an innovative educational tool that leverages large vision models to automate the conversion of handwritten vector equations into accurate 3D graphical representations. By interpreting students’ handwritten input using advanced computer vision, the system provides immediate, interactive visual feedback to bridge the cognitive gap between abstract symbolic notation and tangible geometric concepts. We evaluated the system using a dataset of 1000 handwritten vector equations typical of the Singapore-Cambridge GCE ‘A’ Level H2 Mathematics syllabus. Our findings demonstrate that while GPT-4o serves as a capable baseline, achieving 84.6% accuracy with multi-shot prompting, newer variants such as GPT-4.1-mini offer superior performance, reaching 91.4% accuracy with significantly higher computational efficiency. The results confirm that AI-powered visualisation tools can effectively interpret complex spatial mathematical layouts when guided by optimal prompt engineering. Implementing such technology in educational settings presents a viable, scalable, and cost-effective method to democratise learning support, fostering independent study and enhancing students’ conceptual comprehension of spatial mathematics. Full article

This experimental study investigated the impact of embedding social and emotional learning (SEL) in science instruction on the academic and social–emotional outcomes of Arabic-speaking sixth graders, including those with reading difficulties (RD). Children from two schools in northern Israel (n = 101) were randomly assigned to either an intervention group, which received SEL-enriched science lessons featuring collaborative, reflective activities over 30 sessions, or a control group receiving traditional instruction. Pre- and post-tests assessed SEL competencies, motivation towards science, and academic achievements in science and mathematics. Results showed significantly greater gains in SEL skills, and in science motivation and science achievement in the intervention group compared to controls, whereas mathematics outcomes remained unchanged. Typically developing students and those with RD benefited similarly. Integration of SEL into science curricula thus enhances cognitive and social–emotional learning dimensions, particularly in linguistically and socio-economically marginalised populations. Implications for inclusive pedagogy and future research directions are discussed. Full article

This study investigates the effectiveness of a Game-Based Learning (GBL) itinerary designed to enhance mental calculation (MC) skills related to divisibility in primary education. Grounded in the theoretical perspective of MC as a strategic and adaptive process, the study addresses the gap between performance-based outcomes and the qualitative emergence of flexible strategies. A mixed-methods design was employed with 104 Year 5 pupils divided into an experimental group (Mentematiko) and a control group receiving traditional instruction. Quantitative results showed comparable improvements in execution speed, while the GBL group achieved a markedly greater increase in calculation accuracy. Qualitative validation, based on individual post-test interviews conducted with all participants, revealed that the game-based environment promoted the emergence of flexible and relational calculation strategies rather than procedural reproduction. Social interaction and argumentative practices embedded in gameplay appeared to make mathematical reasoning more visible and adaptive. The study’s originality lies in integrating quantitative performance measures with a qualitative validation procedure aimed at distinguishing genuine flexible mental calculation strategies from numerically correct but procedurally reproduced responses. Methodologically, the findings highlight the importance of analysing actual strategy use when evaluating instructional interventions in mathematics education. Full article

The spatial–numerical association of response codes (SNARC) effect refers to the phenomenon in which responses to small numbers are faster when the left hand is used, and responses to large numbers are faster when the right hand is used. Existing research has shown that cognitive load, such as memory load, is crucial in forming the SNARC effect, and the SNARC effect is smaller for math-skilled individuals than for those with low mathematical skills. However, the underlying mechanisms of how cognitive load and mathematical proficiency affect the SNARC effect remain unclear. This study employed a one-back number comparison task in which participants were asked to compare the current number with the N-1 number under a low or high cognitive load. The results showed that participants with low mathematical skills exhibited the SNARC effect under both cognitive loads. In contrast, participants with high mathematical skills showed the SNARC effect only under the high-load condition. These findings suggest that mathematical proficiency might be beneficial for individuals in resolving conflicts in the spatial–numerical association, but this advantage disappears under a high cognitive load. Full article

This paper attempts to answer questions regarding the link between engineering success and spatial skills through three themes. The previous research of the authors in examining the questions surrounding each theme is the focus of this paper; we acknowledge that others around the world may have conducted similar research, but the specific findings of the authors are the main focus of this paper. In the first theme, we examine data from several author-led studies where positive correlations have been found between spatial skill levels and proficiency in tasks that are a part of what it means to be an engineer. Studies in Theme 1 explore the positive contribution of spatial skills in solving mathematical problems, solving engineering problems, coding, designing, and even technical writing. Theme 2 examines how spatial skills naturally develop just by being enrolled in an engineering program. Taking part in the spatially demanding activities inherent to engineering studies appears to improve the spatial skills of students in our programs. In Theme 3, we examine the result of implementing explicit spatial skills training for students with initially weak skills. In this theme, the impact of spatial skills training on spatial skills, grades in technical courses, and retention in engineering is explored. We begin with a review of the literature that informed the author-led studies in each theme. Finally, we conclude with a call for reform, advocating for an engineering education that acknowledges the importance of spatial skills development for student success and committing to ensuring that all who want to can become the future innovators in the profession. Full article

Early patterning skills, particularly those involving linear repeating patterns, are well-established predictors of mathematical development. This relationship has not yet been investigated in visually oriented deaf and hard-of-hearing (DHH) children. It also remains unclear whether a two-dimensional pattern structure contributes to predicting numerical skills in children at the time of school entry. The present study investigates the relationship between repeating patterning skills in two formats (linear and circular) and numerical skills in a total of 38 DHH and typically hearing children. Language competence was additionally assessed in the DHH group to account for its linguistic heterogeneity. In the DHH and hearing groups, repeating patterning skills in each format strongly predicted numerical skills. Among DHH children, prior language experience played a more decisive role in mathematical development. The circular format emerged as a particularly strong predictor for typically hearing children. DHH children, especially those with sign language experience, perform equally well with both formats, and it is argued that this is due to their enhanced visuospatial skills. Full article

Research has demonstrated a link between spatial and mathematics skills, although less research has addressed the directionality of this relation and what factors may impact the spatial–mathematics link. Two such factors may be spatial and mathematics anxiety, which are related to performance in their respective domains, but may also play a cross-domain role in the relation between spatial and mathematics skills. Importantly, these relations are prudent to investigate in children when mathematics and spatial skills are early in their development. To bridge the gap, the present study examined the direction of the relation between spatial and mathematics skills across two waves of data and the domain specificity of cognitive anxieties (spatial and mathematics anxiety) as they relate to their respective skill in children. In a sample of 647 U.S. first-graders (M_age = 6 years 8 months), we found bidirectional relations between spatial and mathematics skills across two waves of data collection. We found domain-specific, but not cross-domain, relations between mathematics anxiety and skills, but no evidence of links between spatial anxiety and spatial or mathematics skills at this age. These results provide support for the bidirectional spatial–mathematics link in young children and suggest that mathematics anxiety may be a useful target for interventions to improve mathematics outcomes. Full article

There is limited understanding regarding whether and how teachers’ talent beliefs evolve across career stages. While most prior research conceptualizes talent beliefs across domains, emerging frameworks emphasize field-specific talent beliefs. An established multidimensional model of talent beliefs provides a theoretically grounded structure for capturing these domain-specific perceptions. Yet comparative evidence across teacher career stages remains limited. Our study examines if verbal and mathematical talent beliefs among in-service teachers and pre-service teachers differ in terms of sources, structure and levels. A total of 307 in-service teachers and 215 pre-service teachers completed validated six-dimensional talent beliefs instruments for both domains and reported sources of their beliefs. Participants—especially pre-service teachers—most strongly attributed their talent beliefs to personal school experiences, while educational science and subject-didactic coursework played a marginal role. Both the mathematical and verbal talent belief scales demonstrated configural and metric invariance, supporting equivalent factor structures and factor loadings across pre-service teachers and in-service teachers. Latent mean comparisons showed that pre-service teachers hold systematically different talent beliefs in comparison to in-service teachers. In-service teachers emphasize talent beliefs concerning domain-specific skills and, for verbal talent, passion—consistent with contemporary talent development frameworks—whereas pre-service teachers focus on external teacher influence and, for mathematical talent, on internal factors. These findings reinforce theoretical claims that talent beliefs are experience-sensitive, multidimensional constructs shaped through socialization in educational contexts. Teacher (further) education should deliberately address the dominance of personal schooling experiences by fostering structured reflection, explicitly targeting belief formation in practice-based courses, and ensuring coherence between higher-education instruction and school-based experiences. Teachers’ impact on their students’ talent development should especially be reflected in further education, since in-service teachers assess their own influence as lower than pre-service teachers do; additionally, passion as a key driver of talent development and the relevance of talent domains should already be highlighted in initial teacher education. Full article

Education for Sustainable Development (ESD) has emerged as a key priority in contemporary education systems, emphasizing the need to equip learners with the knowledge and competencies required to address complex environmental and societal challenges. Mathematics education can play an important role in achieving these goals by enabling students to analyse data, interpret real-world problems, and develop critical thinking skills related to sustainability issues. However, despite the growing interest in sustainability-oriented mathematics education, limited empirical evidence exists on how structured mathematical modelling interventions influence pre-service primary teachers’ perceptions, modelling orientation, and confidence in designing sustainability-based mathematics lessons. This study investigates the impact of sustainability-oriented mathematical modelling activities on pre-service primary teachers’ perceptions of integrating sustainability into mathematics education. The study employed a quasi-experimental design involving 68 pre-service primary teachers enrolled in a mathematics education course at a university. Participants engaged in a six-week intervention consisting of modelling activities based on real-world sustainability contexts, including water consumption, energy use, waste management, and sustainable transportation. Data were collected using a pre- and post-intervention questionnaire examining participants’ perceptions of sustainability integration, mathematical modelling, and teaching confidence. Statistical analyses, including reliability analysis, descriptive statistics, paired-sample t-tests, effect size estimates, and correlation analysis, as well as multiple regression analysis, were conducted to examine the impact of the intervention. The results indicate significant improvements in participants’ perceptions of sustainability-oriented mathematics teaching and their confidence in designing modelling-based sustainability activities. The largest improvement was observed in teaching confidence, while mathematical modelling perception emerged as a significant predictor of teaching confidence. The findings suggest that mathematical modelling can serve as an effective pedagogical approach for integrating sustainability topics into mathematics education and preparing future teachers to connect mathematical reasoning with real-world environmental challenges. The study contributes to the growing body of research at the intersection of mathematics education, teacher education, and sustainability education by providing empirical evidence on the potential of modelling-based learning for supporting sustainability-oriented teaching practices. More specifically, it shows how mathematical modelling can function as a concrete pedagogical mechanism for translating Education for Sustainable Development into primary mathematics teacher education. Full article

International graduate students studying Science, Technology, Engineering, and Mathematics (STEM) in the United States (U.S.) diversify universities and contribute to research and innovation. They are critical to the U.S. STEM pipeline, workforce and economy; therefore, it is important to understand their experiences. This systematic literature review investigated international graduate STEM students’ characteristics and the supports and barriers they experience while studying in the U.S., following PRISMA guidelines. Thirty-nine peer-reviewed articles were systematically selected from 552 articles for inclusion in this review. Ecological systems theory situated the study within the broader system of graduate education. Findings revealed great diversity, such as country of origin and cultural identity, gender, STEM fields, and prior experiences. Students expressed differences in their reasons to pursue U.S. education and their post-graduation intentions to remain in the U.S. or leave. Support came from institutions, faculty members/academic advisors, and peers. Reported barriers included unfamiliarity with norms and institutional resources, limited English proficiency and writing skills, issues with advisor and being a teaching assistant, underrepresentation, and family responsibilities. Themes were placed within the levels of the ecological framework; most were in the macrosystem, reflecting the strong influence of society, institutions, culture, and norms on students’ experiences. Full article

This paper presents a dynamic multi-period mixed-integer programming model for the Disaster Volunteer Task Assignment Problem (DVTAP) that advances the humanitarian logistics literature through an integrated treatment of features that have previously appeared only in isolation. Unlike prior formulations that assume volunteer surplus or steady-state conditions, our model reflects the acute-phase reality where tasks far exceed available volunteers and new task arrivals diminish over time as the disaster stabilizes. We incorporate makespan as an optimization objective alongside deprivation-weighted response time, skill matching, workload balance, and volunteer reliability. Ideal-nadir normalization ensures that all objective components contribute meaningfully regardless of their native units. The approach proceeds in two stages. First, we formulate and solve a single-period baseline MIP under volunteer surplus using the CBC solver at four scales (10 to 500 tasks). All four instances are solved to proven optimality, achieving 80 to 100% task coverage with skill-matching rates of 76.9 to 99.6%. Second, we develop a rolling-horizon algorithm that decomposes the multi-period problem into sequential epoch-level MIPs with state transitions, non-homogeneous Poisson task arrivals, fatigue accumulation, and task surplus conditions where the initial task-to-volunteer ratio exceeds 3:1. Computational experiments on three dynamic scenarios (up to 559 mean cumulative tasks) demonstrate that the algorithm achieves mean task completion rates of 84.21 ± 1.92% (Large-Dynamic), 93.74 ± 2.07% (Small-Dynamic), and 94.59 ± 2.03% (Medium-Dynamic) (mean ± standard deviation across 30 Monte Carlo replications) within a 15 h planning horizon, with per-epoch skill-matching rates of 11 to 20% (substantially lower than the static baseline due to triage-mode epochs that force all-volunteer assignment regardless of skill fit). The results reveal a clear regime transition: early epochs operate under severe task surplus where triage dominates, while later epochs transition to volunteer surplus where optimization of secondary objectives becomes feasible. Comparison against a skill-aware greedy heuristic confirms that the MIP’s advantage lies in global multi-objective coordination. This research contributes both a validated mathematical framework and a practical algorithmic approach for multi-period volunteer assignment under demand decay, extending prior work by Sperling and Schryenthrough explicit Poisson dynamics, fatigue state modeling, and makespan optimization. Full article

The current study examined the perceptions of elite high school students in the United Arab Emirates about their experiences in learning and acquiring mathematical concepts and skills through the ALEKS system that stands for Assessment and Learning in Knowledge Spaces. ALEKS is an e-assessment and tutoring platform that facilitates the teaching and learning of mathematics for students in Grades 5–12 using versatile and personalized teaching functions. Eight participants of equally mixed gender participated in the study, four Grade 9 and four Grade 10 students. A qualitative research design in the form of one-to-one semi-structured interviews was used to have a deeper understanding of students’ ALEKS experiences, identify the challenges encountered while studying with it, and pinpoint the benefits and advantages of using ALEKS. Results showed that participating students frequently used ALEKS because of two main factors, including rewards promised by teachers and immediate feedback and feeling of immediate achievement provided by the platform. Challenges related to ALEKS were language barriers among the Arabic-speaking students studying in English, a lack of human interaction and support, time management issues, and the necessity for supplementary resources. Multiple advantages were also found, most noticeably how the ALEKS individualized adaptive learning environment helped participants gain more knowledge of mathematical concepts and develop their mathematics skills. Recommendations for mathematics teachers and policymakers include allowing students to utilize ALEKS in small groups in school, aligning ALEKS themes and topics with textbooks learning goals and objectives, giving systematic and personal guidance for increased independent use at home, and making bilingual editions and Arabic-language assets (e.g., tutorial videos) available. Full article

In this quantitative study, we investigated the conditional mediating role of students’ mathematical language self-efficacy in the relationship between self-regulation and mathematics anxiety. The study employed a relational research design and included survey data from 706 middle school students attending public schools in Turkey. Findings indicated that both self-regulation and perceived self-efficacy in mathematical language use were significantly associated with mathematics anxiety. Moreover, the effect of self-regulation on mathematics anxiety was significantly mediated by students’ perceptions of their ability to understand and use mathematical language self-efficacy. The indirect effect was negative while the direct effect was positive, indicating a suppression (competitive mediation) effect, whereby self-regulation exerts both anxiety-reducing and potentially anxiety-inducing influences through different pathways. Conditional mediation analysis further revealed that this mediating effect varied as a function of students’ perceived academic support, with the indirect effect being non-significant for students who did not receive support. Measurement invariance across gender and grade level was examined to ensure that the constructs were measured equivalently across groups. These findings highlight the importance of fostering both self-regulation skills and mathematical language proficiency, particularly in contexts where students may lack sufficient support. These findings provide a theoretically grounded and practically relevant framework for understanding mathematics anxiety within inclusive mathematics education contexts. Full article

This study developed and validated a curriculum-aligned instrument to assess preservice primary teachers’ geometric reasoning skills. Addressing the limited availability of domain-specific tools in teacher education research, the study examined preservice teachers’ conceptual strengths and weaknesses across key geometry domains relevant to primary mathematics teaching. A two-phase quantitative research design was employed. In Study 1, Confirmatory Factor Analysis (CFA) and Item Response Theory (IRT) were used to evaluate the psychometric properties of the instrument with a sample of 221 preservice teachers, providing evidence of construct validity and internal consistency. Geometric reasoning was conceptualised as a four-factor structure comprising Conceptualisation of Geometric Properties (GP), Geometric Transformation Reasoning (GT), Reasoning with Representations of Three-Dimensional Objects (RE), and Measurement Reasoning (MS). In Study 2, the validated Geometric Reasoning Test (GRT) was administered to a larger sample of 406 preservice primary teachers from three education colleges in Myanmar. Descriptive statistics and group comparisons were conducted using Welch’s t-tests and Welch’s ANOVA to examine differences by gender, year level, and institution. The findings indicate that preservice primary teachers’ geometric reasoning remains underdeveloped across training stages, highlighting the need for greater emphasis on geometry and spatial reasoning in teacher education. Full article

Self-assessment plays an important role in the teaching-learning process, as it helps students actively construct their own knowledge. This article aims to develop a methodology for creating quizzes for e-learning platforms, with the goal of addressing students’ difficulties in mathematics and promoting active learning. The proposed methodology begins with identifying the processes that students need to activate and analyzing the most common errors related to them. A key element is the integration of the MATH taxonomy to determine what is necessary or what is intended to be assessed with this type of question. In addition, Niss’s skills are used, i.e., the skills that students need to answer these questions. An important part of the methodology is also the selection of mathematical language, which can be simple and close to everyday language or more sophisticated, verbal, symbolic or mixed, depending on the educational objective. This approach aims to create diagnostic and personalized questions designed to support self-assessment and independent learning in digital environments. Full article