Geometry remains a critical component of mathematics education due to its role in developing spatial reasoning, logical thinking, and problem-solving skills essential for STEM-related fields. However, persistent negative learner attitudes toward geometry continue to hinder achievement and engagement, particularly in under-resourced educational contexts. While existing literature suggests that conducive learning environments positively influence learner attitudes, limited research has explored this relationship specifically within geometry or examined contexts where such relationships may be inconsistent or complex. Therefore, this study investigated the relationship between conducive learning environments and learners’ attitudes toward geometry. Guided by the Community of Inquiry (CoI) framework, the study adopted a mixed-methods approach. Quantitative data were collected through questionnaires and analysed using chi-square tests and contingency coefficients to determine the strength of association between variables. Qualitative data were obtained through semi-structured interviews with mathematics teachers and analysed thematically, with findings interpreted through the lenses of teaching, cognitive, and social presence. The quantitative results revealed a statistically significant and moderately strong relationship between learning environments and learners’ attitudes toward geometry (χ² = 53.146, p < 0.001; V = 0.543). However, qualitative findings indicated that systemic challenges, such as overcrowded classrooms, limited resources, inconsistent pedagogical practices, and weak learner engagement, constrain the effectiveness of these environments. This study contributes to the literature by providing a context-sensitive understanding of the environment–attitude relationship, demonstrating that the alignment of instructional, cognitive, and social factors mediates the impact of conducive learning environments. It further highlights the need for integrated and sustainable interventions to improve geometry learning outcomes.
Historic mosques in Indonesia embody mathematical ideas, yet studies of the Panjunan Red Mosque in Cirebon, built in 1480, have focused on its history and cultural acculturation rather than its mathematical structure. This study aims to identify and map the plane geometry, solid geometry, and geometric transformations embodied in the architecture of the mosque as a source of contextual mathematics learning. A qualitative descriptive design with an ethnographic approach was used. Data were collected through direct observation, a 45–60-minute semi-structured interview with the mosque caretaker, and photographic documentation of eight architectural elements: fence ornaments, roof, pillars, walls, ventilation openings, mihrab, gate, and wall reliefs. The data were analysed with the Miles–Huberman–Saldaña interactive model using inductive open and axial coding, and the transformations were modelled schematically in GeoGebra. The elements contain squares, rectangles, circles, triangles, trapezoids and rhombuses, as well as cylinders, cuboids, a square pyramid and a pyramid frustum. Four transformations were identified: translation in the ventilation openings, approximate reflection symmetry in the mihrab and the split gate, fourfold rotational symmetry in the wall relief (dihedral group D4), and dilation in the concentric square tiers of the gate pillars. The three isometries produce congruent repetition, whereas dilation produces similar figures of decreasing size. These regularities underpin the aesthetic balance of the building and are interwoven with its Javanese, Hindu-Buddhist, Chinese and Islamic meanings. The findings can inform culture-based geometry tasks; because the models are schematic, measured dimensions and classroom trials are needed in future work.
Euclidean geometry is central to mathematics teacher education, yet many pre-service teachers struggle with geometric reasoning and proof. This qualitative follow-up study examined how 12 pre-service teachers from two Colleges of Education experienced learning geometry through either traditional instruction or a van Hiele phase-based model. Data from reflective journals and semi-structured interviews were analysed using interpretive thematic analysis. Findings revealed that van Hiele participants developed the ability to follow proof logic, trusted that difficulty would eventually make sense, described their learning as gradual, and left with a clear vision for teaching geometry. By contrast, traditional instruction participants described memorisation without understanding, disengagement when lost, and uncertainty about future teaching. The findings demonstrate that instructional design shapes not only what pre-service teachers know but also how they reason, persist, and imagine themselves as future geometry teachers. Implications for teacher education programmes are discussed.
Creative thinking has become an important educational competency, particularly following its inclusion as a new domain in PISA 2022. However, empirical evidence regarding its relationship with other academic competencies remains limited, especially in non-OECD educational contexts. This study employed a quantitative secondary data analysis using the PISA 2022 dataset to examine Indonesian students’ creative thinking performance and its association with mathematical literacy. The analysis included approximately 13,000 Indonesian students who participated in PISA 2022 and was conducted using OECD-calibrated plausible values in RStudio. Descriptive and correlational analyses were performed to examine the distribution of creative thinking scores and their relationship with mathematical literacy. The results revealed substantial variation in creative thinking performance among Indonesian students. In addition, a Pearson correlation analysis showed a strong positive association between creative thinking and mathematical literacy (r = 0.67, p < .001). Interpreted through a deep learning lens, these findings suggest that creative thinking and mathematical literacy may share common cognitive foundations related to reasoning, conceptual understanding, and meaningful problem solving. Although the findings do not imply causality, they highlight the importance of learning environments that support deep engagement with mathematical ideas. This study provides empirical evidence on the relationship between creative thinking and mathematical literacy in a non-OECD educational context.
Automatic sliding doors are usually studied as electronic systems, yet their motion offers a concrete context for geometric transformations. This study analyses how translation, reflection, and dilation describe the motion of a two-panel automatic sliding door at the main entrance of a shopping mall in Cirebon, Indonesia. The door was observed in 12 sessions over four days, with approximately 10–15 opening–closing cycles recorded per session, and the panel positions and opening widths were documented on video and mapped onto a Cartesian plane. Each panel moved by a pure horizontal translation along its rail, and the translations of the two panels were reflection-symmetric about the vertical centre line of the doorway. The representative opening width was 30 cm for a single user, 75 cm for two to three users, and 100 cm for a crowd. Taking the single-user opening as the reference aperture, the larger openings correspond to dilation factors k = 2.50 and k = 3.33 about the centre of the door, while the panels themselves remain rigid. Because detection distance and the number of users varied together and the door’s control logic was not accessible, these factors describe the observed openings rather than the controller’s rule. The door thus illustrates a composition of isometries combined with a change of scale of the aperture and can serve as a contextual resource for teaching geometric transformations.
