Mathematical language is a cornerstone of a child’s mathematical development, and children can effectively acquire this language through storytelling with a knowledgeable and engaging partner. In this study, we leverage the recent advances in large language models to conduct free-form, creative conversations with children. Consequently, we developed Mathemyths, a joint storytelling agent that takes turns co-creating stories with children while integrating mathematical terms into the evolving narrative. This paper details our development process, illustrating how prompt-engineering can optimize LLMs for educational contexts. Through a user study involving 35 children aged 4-8 years, our results suggest that when children interacted with Mathemyths, their learning of mathematical language was comparable to those who co-created stories with a human partner. However, we observed differences in how children engaged with co-creation partners of different natures. Overall, we believe that LLM applications, like Mathemyths, offer children a unique conversational experience pertaining to focused learning objectives.