This study examined early childhood preservice teachers’ (PSTs) critical thinking skills (CTS) and mathematics performance (MP) and how they perceived and experienced mathematics learning after the integration of OpenAI tools such as ChatGPT, focusing on CTS as predictors of MP in twenty-first-century competencies aligned with SDG 4 (Quality Education). Using an explanatory sequential mixed-methods approach, the researchers collected data through quantitative measures of CTS and MP, as well as through focus group discussions. Before AI integration, participants reported low engagement, limited mathematical background, and reliance on rote learning, which corresponded to low CTS scores (Challenged to Practicing) and a mean MP of 74% (Failed). Following AI integration, participants (n = 66) demonstrated significant improvements, with CTS scores rising to the Advanced level and MP increasing to 90% (Very Good, p < 0.001). Qualitative findings highlighted enhanced conceptual understanding, reflective reasoning, and confidence in problem-solving. Correlational and regression analyses confirmed CTS as a strong predictor of MP. The results suggest that when generative AI tools are employed as instructional supports rather than as answer-providing shortcuts, they can enhance both measurable academic outcomes and twenty-first-century skills. These findings underscore the potential of AI to support effective mathematics learning while emphasizing the importance of responsible use and guided pedagogical implementation.
Saudi educational reform has long emphasized professional development and educational technology. However, interactive whiteboards (IWBs) remain unevenly integrated into mathematics classrooms, and less is known about how organizational conditions interact within Saudi private international schools. This qualitative multiple-case study examined IWB implementation in six private international schools in Riyadh through semi-structured interviews with twelve mathematics teachers and seven school leaders, supported by six classroom observations. The analysis combined Fullan’s theory of educational change with Howard’s risk-aversion framework. Findings show three context-bound patterns of implementation: integrated use, partial use, and symbolic use. The distinction did not depend on hardware availability alone. It reflected configurations of leadership expectations, subject-specific professional development, technical reliability, classroom access, and teachers’ appraisal of pedagogical value and risk. Teachers reported that IWBs supported visualization, explanation, time management, and engagement, but the study did not independently measure achievement. The contribution lies in showing how private-school autonomy can accelerate acquisition while still producing uneven pedagogical use. Sustainable integration requires organizational alignment and support for teachers’ pedagogical judgment, not compulsory device use alone.
Developing students’ problem-solving capabilities is an important goal of physics and STEM (Science, Technology, Engineering, and Mathematics) education, particularly in contexts requiring systematic, contextual, interactive, and experiential learning. This study investigates students’ learning needs, current physics learning conditions, and self-reported problem-solving difficulties as an empirical basis for developing a STEM-based learning syntax through the Engineering Design Process (EDP), modified into the Analyze, Need, Design, Implement, and Optimize (ANDIO) stages. A descriptive mixed-methods approach was used, combining quantitative questionnaire data with qualitative interviews. Quantitative data were collected from one hundred seventy-five students across thirteen secondary schools through a Google Forms questionnaire, while qualitative data were obtained through semi-structured interviews with twenty-two students. Quantitative data were analyzed using descriptive statistics, Pearson correlation, and gap analysis, while qualitative data were analyzed thematically. The results showed that students’ need for learning syntax was high (M = 3.10, SD = 0.45), whereas problem-solving difficulties (M = 2.48, SD = 0.60) and current learning conditions (M = 2.22, SD = 0.55) were low. A significant positive relationship was found between problem-solving difficulties and current learning conditions (r = 0.558, p < 0.01; R2 = 0.311). Interview findings indicated preferences for systematic, contextual, interactive, student-centered, and experiment-based learning. Problem-solving difficulties were also significantly related to learning syntax needs (r = 0.287, p < 0.01), whereas current learning conditions were not significantly related to learning syntax needs (r = 0.148, p = 0.051). These findings provide an empirical basis for developing EDP–ANDIO; however, its instructional effectiveness requires further validation.
Data literacy has become an essential component of mathematics education and digital competence in increasingly data-driven societies. Although previous research has increasingly examined data literacy in mathematics education, relatively little attention has been given to how data literacy competencies are systematically integrated across national mathematics curricula, particularly beyond statistical literacy and within Eastern European contexts. This study examines the integration of data literacy competencies within the Latvian mathematics curriculum for basic education (Grades 1–9). Using Schüller’s data literacy framework, the research applies deductive qualitative content analysis to investigate curriculum progression across six dimensions of data literacy: establishing data culture, providing data, evaluating data, interpreting results, interpreting data, and deriving actions. Curriculum elements were coded using a three-point integration scale and transformed into quantitative indicators. The findings reveal a systematic progression of data literacy competencies from foundational representational skills in Grade 3 to advanced analytical and interpretative competencies in Grade 9. Data visualization achieved the highest cumulative integration score (6), whereas data protection and security received no explicit curriculum representation (0). Source evaluation and societal impact received comparatively less curriculum attention than data analysis, visualization, and interpretation. The study contributes to curriculum research by demonstrating that the Latvian mathematics curriculum predominantly develops statistical literacy while giving comparatively limited attention to critical data literacy. These findings provide a framework for evaluating curriculum-level data literacy integration and support the inclusion of ethical, critical, and socio-digital dimensions in mathematics education.
This qualitative case study formulates a theoretical model for understanding homotopies through mathematical argumentation among undergraduate mathematics students at a Peruvian university. The study addresses a documented gap in the literature: although mathematical argumentation and homotopy theory have been studied as separate fields, no prior research integrates them pedagogically at the university level. Data were collected through an open-question questionnaire and semi-structured interviews with five purposively selected participants and analyzed via thematic analysis (TA) using Atlas.ti v9, generating seventy-eight codes organized into four categories. The results reveal three argumentation components—initial data (hypotheses), axiomatic substrate, and conclusion (thesis)—and three epistemologically grounded thinking modes: synthetic-geometric (SG), analytic-topological (ATp), and analytic-algebraic (AAg), connected by conceptual articulators. A fourth emergent category—comprehension obstacles—documents specific epistemological errors (EPs) and conceptual difficulties in topological contexts. The proposed model was validated through expert judgment, obtaining Aiken’s V = 1.00 across all evaluated dimensions. The findings advance the understanding of mathematical argumentation in formal proof contexts and offer a theoretically grounded framework applicable to the teaching of advanced topology in higher education.
