Constructivist and Gibsonian approaches disagree over the possibility of di
rect perceptual use of advanced information. A trenchant instance concerns
visual perception of underlying dynamic properties as specified by kinemati
c patterns of events. For the paradigmatic task of discrimination of relati
ve mass in observed collisions, 2 mathematical models are developed, 1 mode
l representing a direct, invariant-based approach, and 1 representing a cue
-heuristic approach. The models enable a critical experimental design with
distinct predictions concerning performance data and confidence ratings. Al
though pretraining results were mixed, the invariant-based model was empiri
cally confirmed after a minimal amount of training: Competence entails the
use of advanced kinematic information in a direct-perceptual ("sensory") mo
de of apprehension, in contrast to beginners' use of simpler cues in an inf
erential ("cognitive") mode.