Providing 98 demonstrates that students’ errors emerge from the interaction between developmental readiness, geometric levels

The gap

Evidence profile

Sourced from the future work and limitations of the source papers, classified as general, spanning 3 journals.

Supporting evidence — 4 representative gaps

• From Misconception To Conceptual Understanding: Hypothetical Learning Trajectory Design In Similarity Learning (2026) · Koordinat Jurnal MIPA · doi

  these establish five a theoretical comprehensive didactical foundation for interpreting student errors not merely as failures but as indicators of ongoing cognitive development. Such an cognitive 84 that from progressively integrative stance aligns with Tall (2004) conceptualization of the “three worlds of mathematics” embodied, symbolic, and learners formal which emphasizes transition visual representations to symbolic reasoning and ultimately to deductive abstraction, guided by conceptual reflection (Dreyfus, 2015; Tall, 2011). Within framework, conceptual errors are viewed as natural markers of students’ operation within a that mathematical world distinct from expected by formal instruction, rather than as deficiencies to be corrected. this to and later through practice, facilitate To bridge the divide between learning the classroom theory framework of Hypothetical Learning Trajectory (HLT) initially conceptualized by (Simon, 1995) and refined by (Gravemeijer, & Cobb, 2006) offers a systematic model for designing conceptually grounded instruction. HLT delineates the anticipated developmental pathway of three students’ understanding essential components: (1) the learning goals, (2) the hypothetical progression of learners’ thinking, and (3) the instructional activities that progression intended (Bakker & Smit, 2018; Irawan et al., 2025). This design-oriented approach has been widely applied in mathematics education research to construct learning trajectories for topics such as functions (Nogueira et al., 2021), fractions (Stark Guss et al., 2022), and geometric transformations (Bakker & Smit, 2018; Gravemeijer & Cobb, 2006). Doorman, demphasized the inclusion of reflective and diagnostic dimensions within HLT the connection between student errors and the dynamics of learning progression (Alonzo & von Aufschnaiter, 2018; Hiebert et al., 2018; Mosher, 2022). frameworks strengthen to Nevertheless, the application of HLT to the topic of geometric similarity remains limited, particularly within the Indonesian mathematics education context, which is grounded in a constructivist curriculum framework. Most national studies have concentrated on identifying and classifying students’ misconceptions without explicitly theoretically linking findings learning informed prospective these and to Vira Pitriatunnazwa, Dedi Muhtadi, Sukirwan trajectories (Didi et al., 2019; Firdaus & Mutaqin, 2019). This highlights a persistent research gap between two major paradigms in mathematics education research : (a) diagnostic studies, which focus on analyzing what students misunderstand, and (b) didactical design research, which seeks to explore how instructional interventions can such be to 2009; misunderstandings Gravemeijer & 1999). for

  generalfuture work
  Keywords: learning mathematics within students errors framework gravemeijer progression education didactical student cognitive tall three symbolic
• From Misconception To Conceptual Understanding: Hypothetical Learning Trajectory Design In Similarity Learning (2026) · Koordinat Jurnal MIPA · doi

  provide 98 demonstrates that students’ errors emerge from the interaction between developmental readiness, geometric levels, problem- representational solving processes, and social mediation. competence, reasoning from suggests trajectory A major contribution of this study is the development of an evidence-informed Hypothetical Learning Trajectory (HLT) for geometric similarity derived the systematic synthesis of empirical literature.

  generalfuture work
  Keywords: geometric trajectory provide demonstrates students errors emerge interaction developmental readiness levels problem representational solving processes
• Teacher Noticing of Students’ Mathematical Thinking in Geometry: A Qualitative Analysis Using the Air Framework (2026) · East African Journal of Education Studies · doi

  to enhance Future research should examine teacher noticing across a larger and more diverse sample of teachers the generalizability of findings. Longitudinal studies could explore how teachers’ noticing practices evolve through development. sustained Additionally, integrating classroom observations with analysis of students’ written work may provide a more comprehensive understanding of how teacher noticing operates in practice. professional CONCLUSION This study addressed three research questions concerning how senior high school mathematics teachers attend to, interpret, and respond to students’ mathematical thinking in Geometry. The findings reveal that teachers’ noticing practices were three largely procedural across all the Attend–Interpret–Respond dimensions of (AIR) framework. In the attending phase, teachers focused primarily on the visible features of students’ work, such as the correctness of answers, the use of formulas, and the presentation. In the interpreting phase, students’ errors were predominantly viewed as procedural mistakes rather than as indicators of underlying conceptual misunderstandings. the responding phase, teachers’ instructional actions emphasising were demonstrating correct procedures rather than probing students’ reasoning. corrective, Similarly, largely during 359 | This work is licensed under a Creative Commons Attribution 4.0 International License. East African Journal of Education Studies, Volume 9, Issue 2, 2026 Article DOI: https://doi.org/10.37284/eajes.9.2.4924 reasoning. conceptual understanding to explore students’ These themes highlight limited engagement with students’ and Consequently, mathematical thinking, opportunities including alternative strategies and partial understandings, were often overlooked. This suggests that strengthening teachers’ noticing practices, particularly by shifting from procedural to more conceptually oriented approaches, is instruction. improving geometry critical for interpret teachers’ capacity

  generalfuture work
  Keywords: teachers students noticing practices interpret procedural phase teacher across explore understanding three attend respond mathematical
• Innovating higher education pedagogy: integrating RADEC learning model and virtual laboratory to promote pre-service elementary teachers’ conceptual change (2026) · Frontiers in Education · doi

  in data but to connect the development of adaptive professional Furthermore, these issues are exacerbated by low confidence, anxiety toward science, and persistent difficulties in classroom lesson planning during field experiences. management and Many pre-service theoretical teachers struggle knowledge with practical classroom application, particularly when dealing with abstract scientific concepts, which severely limits judgment essential for high-quality teaching (Dumbrajs and Keinonen, 2009; Faikhamta, 2011; Riegle-Crumb et al., 2015). As a result, these this body of evidence underscores imperative problems for improving teacher education programs to systematically tackle misconceptions, emphasize argumentation and inquiry-based pedagogy, and deliberately scaffolded, and reflective, foster deep (Morris, 2025). conceptually learning environments Without such structural reforms, the persistence of superficial learning and procedural teaching among pre-service teachers instruction and hinder will perpetuate meaningful learning outcomes across generations. is not optional but strategically educational quality, urging learning rich low-quality science that addressing improvement through student in Conceptual change, a process where learners actively reconstruct incompatible prior knowledge, is deeply rooted in a constructivist epistemological framework perceives learning as an active process of meaning-making rather than merely receiving information, thereby making it a framework.

  generallimitationsevidence 5/5
  Keywords: learning quality science classroom service teachers knowledge teaching process framework making connect development adaptive professional

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