Although change detection using MODIS time series is critical for environmental monitoring, it is a highly challenging task due to key MODIS difficulties, e.g., mixed pixels, spatial-spectral-temporal information coupling effect, and background class heterogeneity. This paper presents a novel knowledge-aware Mamba (KAMamba) for enhanced MODIS change detection, with the following contributions. First, to leverage knowledge regarding class transitions, we design a novel knowledge-driven transition-matrix-guided approach, leading to a knowledge-aware transition loss (KAT-loss) that can enhance detection accuracies. Second, to improve model constraints, a multi-task learning approach is designed, where three losses, i.e., pre-change classification loss (PreC-loss), post-change classification loss (PostC-loss), and change detection loss (Chg-loss) are used for improve model learning. Third, to disentangle information coupling in MODIS time series, novel spatial-spectral-temporal Mamba (SSTMamba) modules are designed. Last, to improve Mamba model efficiency and remove computational cost, a sparse and deformable Mamba (SDMamba) backbone is used in SSTMamba. On the MODIS time-series dataset for Saskatchewan, Canada, we evaluate the method on land-cover change detection and LULC classification; results show about 1.5-6% gains in average F1 for change detection over baselines, and about 2% improvements in OA, AA, and Kappa for LULC classification.