Noumerico: Journal of Technology in Mathematics Education
Vol. 4 No. 2 (2026): Noumerico, September 2026

From Concrete to Abstract: Mapping the Zone of Proximal Development through Dynamic Assessment and Scaffolding in Grade VII Algebra Learning

Sindi Setiandari (Universitas Pendidikan Muhammadiyah Sorong)
Sahidi (Universitas Pendidikan Muhammadiyah Sorong)
Syamsulrizal (Universitas Pendidikan Muhammadiyah Sorong)



Article Info

Publish Date
30 Sep 2026

Abstract

This study mapped Grade VII students’ operational Zone of Proximal Development (ZPD) in algebra and examined score changes across a concrete–semi-concrete–abstract instructional sequence supported by differentiated scaffolding. This sequential explanatory mixed-methods study involved 32 students at SMP Negeri 11 Kabupaten Sorong during the 2024/2025 academic year, with data collected from February to April 2025. Instruments comprised a 20-item Algebra Diagnostic Test (Aiken’s V = 0.87; Cronbach’s α = 0.847), a graduated Dynamic Assessment Protocol, a scaffolding observation sheet, and semi-structured clinical interviews. We summarized quantitative data descriptively and analyzed them using paired Wilcoxon tests, while we analyzed qualitative data thematically and integrated them with the quantitative findings. Dynamic assessment classified 53.13% of students at Level 2, 25.00% at Level 1, 15.63% at Level 3, and 6.25% at Level 0. Mean scores increased from 52.34 at baseline to 81.88 after the abstract phase. Pairwise Wilcoxon comparisons were statistically significant (p < 0.001), with rank-biserial effect estimates ranging from 0.855 to 0.874. Qualitative findings showed differentiated scaffolding patterns across ZPD levels. The results provide preliminary evidence for the feasibility of the Z-CRA framework linking dynamic assessment, representational progression, and contingent scaffolding; controlled studies should examine causal effectiveness.

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Journal Info

Abbrev

noumerico

Publisher

Subject

Computer Science & IT Education Mathematics Social Sciences

Description

The aim of this Journal is to promote a principled approach to research on technology in mathematics education and related concerns by encouraging enquiry into relationship between theoretical and practical studies. The journal welcomes contributions in such areas of current analysis in: 1. Use of ...