Accurate segmentation of medical images is essential for many clinical applications and is now typically achieved by training deep learning models on large annotated datasets. However, acquiring sufficient labeled images remains challenging, as pixel-level manual annotations are highly time-consuming. To substantially reduce the manual effort, we developed a novel semi-supervised segmentation method, termed dual-decoder mutual teaching (DDMT), which incorporates a smoothed exponential moving average (sEMA) scheme and a shape consistency constraint (SCC) scheme into the classical mean teacher (MT) framework. The sEMA scheme enhances the stability of the student and teacher models during training, while the SCC scheme ensures consistent learning of shape characteristics across the two different decoders within each model. With these two innovative components, DDMT achieves promising segmentation performance when trained on limited labeled images and abundant unlabeled images. Experiments on public datasets for left atrium, pancreas, and optic disc segmentation demonstrated that DDMT consistently outperforms several state-of-the-art semi-supervised learning (SSL) methods (e.g., MT, UAMT, DTC, and MCNet) across varying proportions of labeled images. The source code is publicly available at https://github.com/wmuLei/ddmt.