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Tactile Reinforcement for Early Calculus Concepts: Grocery Bags and Laser Beams

Abstract In order to facilitate student participation in freshman-level undergraduate mathematics classes, we describe two hands-on activities that engage the interest, and promote tactile involvement, of students in early calculus concepts. These activities are: using manipulatives to teach and reinforce concepts surrounding the chain rule in single-variable calculus, and creating an interactive exercise to motivate the use of elementary numerical approximations (e.g., the trapezoidal and simpson rules) of integrals.