Strategic Fading of Scaffolding to Foster Mathematical Autonomy: Supporting the Shift from Descriptive to Symbolic Thinking in Elementary Proportional Reasoning

Elementary students’ mathematical thinking is frequently constrained by persistent misconceptions and an overreliance on procedural instruction. International assessments of mathematical literacy consistently report lower levels of achievement among students in many developing countries, underscoring the need for instructional approaches that promote conceptual understanding rather than rote learning. Scaffolding, understood as temporary and adaptive instructional support, has been widely acknowledged as an effective means of facilitating students’ conceptual development. Nevertheless, its classroom enactment—particularly the processes through which support is responsively adjusted and gradually withdrawn—remains insufficiently documented and systematically analyzed in empirical research. This study aims to examine the forms of scaffolding employed by teachers, their responsive strategies in addressing student errors, and the observable indicators of scaffolding reduction (fading) in mathematics instruction grounded in visual pattern recognition and comparative reasoning. A descriptive qualitative methodology was adopted, using a case study design involving three upper elementary school students. Data were collected through analyses of students’ written work, classroom interaction observations, and semi-structured interviews. The data were analyzed thematically within the framework of contingent scaffolding. The findings indicate differentiated learning trajectories among the participants. Student MA demonstrated a shift from intuitive verbal descriptions to symbolic comparative reasoning following interactive scaffolding. Student RFM exhibited independent formal reasoning from the outset, requiring minimal instructional support. In contrast, student IAM experienced a substantial conceptual transition after receiving explicit instructional intervention. Notably, all three students were ultimately able to generalize that the number of blue triangles was consistently less than half of the total number of triangles. These results highlight the critical role of adaptive and contingent scaffolding in fostering conceptual understanding and learning autonomy in elementary mathematics. By documenting the forms, timing, and transitions of instructional support, this study contributes to the empirical literature on scaffolding practices in primary education. Importantly, the findings provide a novel account of how scaffolding is dynamically enacted and strategically faded in response to students’ errors, enabling a progression from descriptive to symbolic proportional reasoning. The identification of concrete indicators of scaffolding reduction aligned with students’ emerging autonomy offers theoretically grounded and practice-oriented implications for the design of adaptive instructional support in elementary mathematics classrooms. Keywords: instructional scaffolding; mathematical reasoning; mathematics education; proportional reasoning; gradual fading of support.