Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain monotone and smooth conditions. To incorporate such conditions and to alleviate the strong parametric assumption on regressing latent trajectories, a flexible nonparametric prior has been introduced to model the dynamic changes of latent traits for item response theory models over the study period. Suitable Bayesian computation schemes are developed for such analysis of the longitudinal and dichotomous item responses. Simulation studies and a real data example from educational testing have been used to illustrate our proposed methods.