Graph neural network (GNN) based algorithms have achieved superior performance in recommendation tasks due to their advanced capability of exploiting high-order connectivity between users and items. However, most existing GNN-based recommendation models ignore the dynamic evolution of nodes, where users will continuously interact with items over time, resulting in rapid changes in the environment (e.g., neighbor and structure). Moreover, the heuristic normalization of embeddings in dynamic recommendation is de-coupled with the model learning process, making the whole system suboptimal. In this paper, we propose a novel framework for generating satisfying recommendations in dynamic environments, called Dynamic Graph Evolution Learning (DGEL). First, we design three efficient real-time update learning methods for nodes from the perspectives of inherent interaction potential, time-decay neighbor augmentation, and symbiotic local structure learning. Second, we construct the re-scaling enhancement networks for dynamic embeddings to adaptively and automatically bridge the normalization process with model learning. Third, we leverage the interaction matching task and the future prediction task together for joint training to further improve performance. Extensive experiments on three real-world datasets demonstrate the effectiveness and improvements of our proposed DGEL. The code is available at https://github.com/henrictang/DGEL.