Teaching to improve student models (e.g., knowledge distillation) is an extensively studied methodology in LLMs. However, in human education, teaching enhances not only the students but also the teachers by fostering more rigorous and clearer reasoning, as well as deeper knowledge building. We ask: Can LLMs also learn by teaching (LbT) for better reasoning? If the answer is yes, we can potentially unlock the possibility of continuously advancing the models without solely relying on human-produced data or stronger models. In this paper, we provide a preliminary exploration of this question. We show that LbT ideas can be incorporated into existing LLM training/prompting pipelines and bring improvements. Specifically, we design three methods, each mimicking one of the three levels of LbT: observing students' feedback, learning from the feedback, and learning iteratively, with the goal of improving answer accuracy without training or improving models' inherent capability with fine-tuning. We reveal some findings: (1) Teaching materials that make it easier for students to learn (via in-context learning) have clearer and more accurate logic; (2) Weak-to-strong generalization: LbT might help improve strong models by teaching weak models; (3) Diversity in students might help: teaching multiple students could be better than teaching a single student or the teacher alone. We hope that our exploration can inspire future research on LbT and, more broadly, the adoption of advanced education techniques to improve LLMs. The code and website are at https://github.com/imagination-research/lbt and https://sites.google.com/view/llm-learning-by-teaching.