Generative AI has the potential to help teachers rapidly create classroom-ready visual materials, particularly in mathematics where diagrams and visual representations must be pedagogically meaningful and instructionally correct. However, current generative tools primarily support prompting and post-hoc editing, leaving open a key question for correctness-sensitive educational authoring: when in the generation pipeline should teachers exert control? In this paper, we investigate how the timing of human control in AI-assisted generation shapes teachers' visual authoring practices in correctness-sensitive tasks. We introduce a design space of three stages of control: pre-generation control, where users specify intent solely through natural language prompts before generation; mid-generation control, where users inspect and confirm an explicit layout structure before the system completes generation; and post-generation control, where users directly modify AI-generated visuals after generation through object-level edits. In a within-subject, mixed-methods study with 24 primary mathematics teachers, post-generation control received higher ratings on predictability and correctness, while other subjective measures showed no reliable differences. Qualitative findings explain these differences by revealing workflow trade-offs: highly automated, pre-generation control supports rapid ideation but reduces perceived agency and predictability; mid-generation control improves structural alignment at the cost of additional effort; and post-generation control preserves user agency through low-cost, direct verification and correction. Together, these results suggest that in correctness-sensitive educational tasks, effective generative tools should align system behavior with teacher intent and support stage-dependent workflows that combine automation with direct manipulation.

翻译：生成式AI有潜力帮助教师快速创建适用于课堂的视觉材料，尤其在数学领域，图表和视觉表示必须兼具教学意义与指导正确性。然而，当前生成工具主要支持提示词输入与事后编辑，这引出了一个对正确性敏感的教育创作关键问题：教师在生成流程的哪个阶段应施加控制？本文探究了AI辅助生成中人类控制时机如何影响教师在正确性敏感任务中的视觉创作实践。我们提出了包含三个控制阶段的设计空间：生成前控制（用户仅通过自然语言提示在生成前指定意图）、生成中控制（用户在系统完成生成前检查并确认显式布局结构）以及生成后控制（用户在生成后通过对象级编辑直接修改AI生成的视觉内容）。通过一项针对24名小学数学教师的被试内混合方法研究，生成后控制在可预测性和正确性方面获得更高评分，而其他主观指标无显著差异。定性研究结果揭示了这些差异背后的工作流权衡：高度自动化的生成前控制支持快速构思但降低感知能动性与可预测性；生成中控制改善结构对齐但增加额外努力；生成后控制通过低成本直接验证与修正保留用户能动性。综合结果表明，在正确性敏感的教育任务中，有效生成工具应使系统行为与教师意图对齐，并支持结合自动化与直接操作的阶段依赖工作流。