Hidden asymmetry in audio-encoded function graph interpretation: An item-level diagnostic study of graph level and local change
DOI:
https://doi.org/10.56183/iberoeds.v6i1.716Palavras-chave:
graph interpretation; covariational reasoning; rate of change; sonification; diagnostic assessment; secondary mathematicsResumo
Interpreting function graphs requires students to coordinate graph level, direction of change, steepness, and changing rate. Yet overall score gains can conceal whether learning is distributed evenly across these ideas. This study examined heterogeneous learning patterns in audio-encoded function interpretation among Grade 11 General Mathematics students in a Philippine public secondary school. Using a pretest-instruction-posttest design, 194 students from seven intact classes completed parallel nine-item audio-to-graph matching forms delivered through a lightweight, offline-capable classroom system. Some tasks used graph-level pitch mapping, in which pitch tracked graph height, whereas others used local-change pitch mapping, in which pitch tracked steepness or rate. Total scores improved from a pretest mean of 2.12/9 (SD = 1.32) to a posttest mean of 3.64/9 (SD = 1.72). Because gain scores were non-normal, a Wilcoxon signed-rank test was used and showed a significant increase, (W = 1972), (p < .001), with a matched-pairs effect size of (r = .601). However, item-level results revealed marked conceptual asymmetry. All three graph-level items improved strongly, including the constant-value item (+53.6 percentage points) and the exponential-growth item (+49.0 percentage points). In contrast, change-coded items showed mixed trajectories: two improved substantially, two were statistically unchanged, and two declined, including a square-root-type concavity item (-26.3 percentage points). Grouped analyses showed strong gains for graph-level recognition and exponential patterning, but no net improvement for the concavity and changing-rate cluster. The findings indicate that audio-rendered graph support was not uniformly effective across concepts. Item-level diagnosis identified graph level as an instructional anchor, whereas local change, concavity, and changing-rate interpretation remained bottleneck concepts.
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