Mathematics word problem solving is a critical component of elementary education, yet many students struggle with the dual cognitive load of linguistic comprehension and mathematical reasoning. While generative artificial intelligence (GenAI) offers promising avenues for educational support, there remains limited understanding of how students interact with AI systems in authentic learning contexts. This study shifts the focus from technological capability to human-AI interaction, examining how primary students engage with a GenAI-enabled learning environment—ChatGPT-supported Mathematics Problem-Solving System (ChatGPT-MPS)—during mathematics word problem solving. The research explores not only learning outcomes but, more importantly, the nature and quality of student-system interactions that shape problem-solving processes and learning experiences. A quasi-experimental study was conducted with 104 fifth-grade students, comparing an experimental group using ChatGPT-MPS with a control group receiving traditional instruction. Findings revealed that students in the experimental group demonstrated significantly greater improvement in problem-solving performance, but more notably, qualitative and quantitative data highlighted rich, iterative dialogic interactions with the system—characterized by clarification requests, strategy exploration, and real-time feedback loops. Students reported high levels of engagement, attributing their motivation to the responsive, conversational, and adaptive nature of the AI. The study underscores the importance of designing AI systems not merely as answer-generating tools, but as interactive partners in learning. It contributes to the emerging discourse on pedagogical human-AI interaction by providing empirical insights into how structured, dialogic engagement with GenAI can scaffold cognitive development and foster deeper mathematical thinking in young learners.