COGNITIVE BARRIERS IN HANDLING ADDITIVE STRUCTURES: CASE ANALYSIS IN SECOND GRADE

Abstract

This qualitative exploratory-descriptive research analyzed cognitive barriers faced by second-grade students when interpreting verbal statements with additive structures. A multiple case study methodology was employed with 15 students aged 7 to 9 years distributed across three public institutions in Antioquia, Colombia, during the 2016-2017 period. Data collection was conducted through three written instruments based on numerical thinking theory, evaluating dimensions such as numerical sequence, place value, cardinality, and problem-solving. Analysis was based on triangulation of student responses, direct observations, and theoretical contrast, identifying five emerging categories through manual coding. Findings reveal that place value constitutes the most widespread barrier, affecting 93.3% of participants who manipulate symbols without semantic understanding of positional notation. No student reached the bidimensional chain level, contradicting curricular expectations. Dependence on concrete materials was evident with differences exceeding 50 percentage points between problems with and without visual support. Problems with unknowns in initial position showed only 20% successful resolution. Difficulty patterns converged notably among the three institutions regardless of their contextual differences. The need to implement differentiated diagnostics by numerical sequence levels, gradual transition toward abstraction, and prolonged focus on place value that transcends mechanical exercises to construct semantic referents through physical grouping experiences is concluded.