Perturbation with diverse unlabeled data has proven beneficial for semi-supervised medical image segmentation (SSMIS). While many works have successfully used various perturbation techniques, a deeper understanding of learning perturbations is needed. Excessive or inappropriate perturbation can have negative effects, so we aim to address two challenges: how to use perturbation mechanisms to guide the learning of unlabeled data through labeled data, and how to ensure accurate predictions in boundary regions. Inspired by human progressive and periodic learning, we propose a progressive and periodic perturbation mechanism (P3M) and a boundary-focused loss. P3M enables dynamic adjustment of perturbations, allowing the model to gradually learn them. Our boundary-focused loss encourages the model to concentrate on boundary regions, enhancing sensitivity to intricate details and ensuring accurate predictions. Experimental results demonstrate that our method achieves state-of-the-art performance on two 2D and 3D datasets. Moreover, P3M is extendable to other methods, and the proposed loss serves as a universal tool for improving existing methods, highlighting the scalability and applicability of our approach.