A preliminary machine presence measure within the community of inquiry framework: How students perceive AI-mediated guidance in multivariable calculus course

Abstract

The integration of generative artificial intelligence (AI) into mathematics learning raises a foundational question for the community of inquiry (CoI) framework: do students perceive guidance provided by an AI tutor as distinguishable from guidance associated with a human teacher (teaching presence), or do they treat the two as interchangeable? This study pursued two aligned aims: (1) to develop and provide an initial psychometric evaluation of a five-item machine presence measure, including a direct test of its perceived distinctiveness from teaching presence; and (2) to examine how perceived machine presence is associated with learner presence and cognitive presence. In a cross-sectional survey of 211 undergraduates who used an AI tutor configured to provide Socratic guidance rather than direct solutions in a multivariable calculus course, the measurement model showed good fit (χ²/df = 1.65, CFI = 0.960, TLI = 0.951, RMSEA = 0.056, SRMR = 0.042) and adequate convergent validity (machine presence average variance extracted = 0.596, composite reliability = 0.880). Machine and teaching presence showed discriminant validity (HTMT = 0.49; Fornell-Larcker criterion satisfied), and a competing-models comparison showed that the two-factor solution was statistically preferable to the one-factor solution (Δχ² (1) = 310.9, p < 0.001; CFI = 0.963 vs. 0.660). Perceived machine presence was positively associated with learner presence (β = 0.62) and cognitive presence (β = 0.34), and learner presence with cognitive presence (β = 0.49); the indirect association via learner presence was significant, consistent with the hypothesized mediation model. Importantly, when the paths from machine and teaching presence to learner and cognitive presence were constrained to equality, model fit did not deteriorate (Δχ² (2) = 0.539, p = 0.764), consistent with a source-attribution interpretation in which students distinguish the agent of guidance while perceiving comparable pedagogical functions. We interpret these results as evidence of perceptual and measurement-level distinctness within one particular AI-tutoring implementation, and we emphasize that measurement separability does not by itself establish that machine presence constitutes a new, functionally independent theoretical dimension of the CoI framework. Given the cross-sectional, single-group, single-context, self-report design, all structural findings are interpreted associationally rather than as evidence of instructional effectiveness or causal direction.