This classroom-embedded study investigates whether low-cost, paper/cardboard manipulatives can strengthen students' perceived competence on core three-dimensional topics in Multivariable Calculus. We implemented a foldable, L-shaped modeling base with tangible surface pieces to support hands-on exploration of surfaces, accumulation for multiple integrals, and coordinate transformations, coupled with a standardized lesson sequence (conceptual activation, guided construction and exploration, representation bridge, exit ticket, and reuse). Four course sections (¿ 100 students) used the materials; inferential analyses focus on one representative section with anonymous pre (n=29) and post (n=26) surveys. Two self-efficacy items targeted translations of planar curves and the representation of 2 D equations as 3 D surfaces. The share selecting the top two confidence categories increased from 0.707 to 0.923(¿=0.216; Cohen's h=0.58; two-sided p=0.0040; 95% CI [0.078,0.354]; normalized gain g=0.74). Item-level contrasts were 69.0% to 88.5% for translations (z=1.75, p=0.0805) and 72.4% to 96.2% for 2D to 3D representation (z=2.38, p=0.0175). Results suggest that haptic-visual coupling, when explicitly bridged to sketches and symbolic expressions, is a scalable way to enhance students' readiness to engage surfaces, solids, and coordinate changes. Limitations include self-report outcomes, unpaired samples, and a single-site context.
