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Educational dialogue systems have been used to support students and teachers for decades. Such systems rely on explicit pedagogically motivated dialogue rules. With the ease of integrating large language models (LLMs) into dialogue systems, applications have been arising that directly use model responses without the use of human-written rules, raising concerns about their use in classroom settings. Here, we explore how to constrain LLM outputs to generate appropriate and supportive teacher-like responses. We present results comparing the effectiveness of different constraint variations in a zero-shot prompting setting on a large mathematics classroom corpus. Generated outputs are evaluated with human annotation for Fluency, Relevance, Helpfulness, and Adherence to the provided constraints. Including all constraints in the prompt led to the highest values for Fluency and Helpfulness, and the second highest value for Relevance. The annotation results also demonstrate that the prompts that result in the highest adherence to constraints do not necessarily indicate higher perceived scores for Fluency, Relevance, or Helpfulness. In a direct comparison, all of the non-baseline LLM responses were ranked higher than the actual teacher responses in the corpus over 50% of the time.