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Exploring the role of cognitive style and APOS-based scaffolding in developing students’ advanced mathematical thinking on function limits
Infinity Journal · Vol. 15 No. 4 (2026) · hlm. 1011–1030
- ISSN
- 2460-9285, 2089-6867
- Terbit
- 2026-09-22
- Penerbit
- IKIP Siliwangi Bandung
Abstrak
This qualitative case study explored how field dependence-independence shaped students’ access to Action-Process-Object-Schema (APOS)-based scaffolding and how stage-specific support contributed to the qualitative development of advanced mathematical thinking (AMT) on function limits. In this study, developing denotes the observable emergence or reorganization of mathematical constructions during scaffolded activity, not a statistically measured learning gain. The bounded classroom case involved 24 mathematics education students at an Islamic university in Sumatra, Indonesia. The Group Embedded Figures Test classified 6 students as field-independent (FI) and 18 as field-dependent (FD); four information-rich cases, comprising 2 FI and 2 FD students, were selected for cross-case analysis. APOS-based scaffolding was implemented in four 135-minute Calculus I sessions and examined further through stimulated-recall interviews. Initial written solutions provided the primary evidence, post-prompt explanations and revisions documented students’ responses to Action-, Process-, Object-, and Schema-oriented support, and classroom observation records verified the enactment and gradual fading of the planned scaffolds. FI-1 constructed a complete Schema and required only fading prompts. FI-2 moved from correct but disconnected Objects toward an integrated Schema after a Schema-oriented prompt. FD-1 corrected an invalid limit value after Process-oriented prompts stabilized the transformation sequence. FD-2 moved from direct substitution and 0/0 toward guided algebraic Actions and an emerging Process after explicit Action-oriented cues. The findings indicate that cognitive style influenced task entry and the amount of external structure used, whereas APOS identified the construction that support needed to target. The observed shifts support a diagnostic account of AMT development while avoiding causal or long-term claims.
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- State University of Semarang
- Universitas Tidar
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- Organisasi sama
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Tampilkan sebagai tabel
| Rekan penulis | Organisasi | Artikel bersama |
|---|---|---|
| Stevanus Budi Waluya | State University of Semarang | 4 |
| Endang Retno Winarti | State University of Semarang | 3 |
| St. Budi Waluya | Afiliasi tidak diketahui | 2 |
| Aisyah Fany Achmalia | Afiliasi tidak diketahui | 2 |
| Sugiman Sugiman | Afiliasi tidak diketahui | 2 |
| Masrukan Masrukan | State University of Semarang | 2 |
| Emi Pujiastuti | State University of Semarang | 2 |
| Sumliyah Sumliyah | State University of Semarang | 2 |
| Nyree Ani | Afiliasi tidak diketahui | 2 |
| Kartono Kartono | State University of Semarang | 2 |
| Mulyono Mulyono | State University of Semarang | 2 |
| Iwan Junaedi | State University of Semarang | 1 |
| Lathifatun Ni’mah | Afiliasi tidak diketahui | 1 |
| Scolastika Mariani | State University of Semarang | 1 |
| Farida Nursyahidah | State University of Semarang | 1 |
| Kristina Wijayanti | State University of Semarang | 1 |
| Vena Agustina | State University of Semarang | 1 |
| Megita Dwi Pamungkas | Universitas Tidar | 1 |
| Isnarto Isnarto | State University of Semarang | 1 |
| Zaenal Abidin | State University of Semarang | 1 |
| Dyah Rini Indriyanti | State University of Semarang | 1 |
| Marshanda Antika Putri | State University of Semarang | 1 |
| Ratna Wahyuningtyas | State University of Semarang | 1 |
| Bayu Murti Suryonegoro | State University of Semarang | 1 |
| Agung Setiawan | State University of Semarang | 1 |
| Ifan Badra Wijaya | State University of Semarang | 1 |
| Zidna Nurus Sakinah | State University of Semarang | 1 |
| Irfan Fajar Prihantoro | State University of Semarang | 1 |
| Bayu Rizky Pratama | Afiliasi tidak diketahui | 1 |
| Sugiman Sugiman | State University of Semarang | 1 |
| Hendri Handoko | State University of Semarang | 1 |
| Li Wei Ming | Afiliasi tidak diketahui | 1 |
| Rochmad Rochmad | State University of Semarang | 1 |
| Ricky Yusuf Susanto | State University of Semarang | 1 |
| Eko Purwanti | State University of Semarang | 1 |
| Trinil Wigati | Afiliasi tidak diketahui | 1 |
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