The reasoning capabilities of Large Language Models (LLMs) are typically developed through the single-turn reinforcement learning, whereas real-world applications often involve multi-turn interactions with human feedback, leading to a potential mismatch between training and deployment conditions. In this work, we study whether multi-turn training with human feedback is necessary for reasoning tasks. We compare conventional single-turn training with three multi-turn strategies and reach contrary conclusions to previous research. We find that models trained in a single-turn setting generalize effectively to both single- and multi-turn evaluations, while models trained with multi-turn strategies exhibit a significant degradation in single-turn reasoning performance. These results suggest that for tasks with complete information, robust single-turn training remains more effective and reliable, as multi-turn training with basic feedback provides limited benefits and can even degrade reasoning capabilities.