We consider the problem of tactile discrimination, with the goal of estimating an underlying state parameter in a sequential setting. If the data is continuous and high- dimensional, collecting enough representative data samples becomes difficult. We present a framework that uses active learning to help with the sequential gathering of data samples, using information-theoretic criteria to find optimal actions at each time step. We consider two approaches to recursively update the state parameter belief: an analytical Gaussian approximation and a Monte Carlo sampling method. We show how both active frameworks improve convergence, demonstrating results on a real robotic hand-arm system that estimates the viscosity of liquids from tactile feedback data.