This research examines the influence of integrating generative artificial intelligence (GAI) in education, focusing on its acceptance and utilization among elementary education students. Grounded in the Task-Technology Fit (TTF) Theory and an expanded iteration of the Unified Theory of Acceptance and Use of Technology (UTAUT) model, the study analyzes key constructs--Performance Expectancy, Effort Expectancy, Social Influence, and Facilitating Conditions--on students' behavioral intentions and usage behaviors concerning GAI. The UTAUT model, which integrates elements from multiple theories and is widely applied in educational contexts to understand technology adoption behaviors, provides a robust theoretical framework. Additionally, TTF theory, emphasizing the alignment of technology with specific instructional tasks, enhances our understanding of GAI acceptance. This study also investigates the moderating effects of TTF and gender within this framework. Data analysis, conducted through PLS-SEM, is based on responses from 279 elementary education students in China who completed an 8-week course incorporating GAI. Results indicate that Performance Expectancy, Social Influence, and Effort Expectancy significantly influence Behavioral Intention, while Facilitating Conditions have the strongest impact on actual Use Behavior, surpassing their influence on Behavioral Intention. Furthermore, Task-Technology Fit moderates both Performance Expectancy and Effort Expectancy in students' consideration of GAI use. However, gender does not demonstrate a moderating effect in the overall model. These findings deepen our understanding of elementary school students' acceptance of GAI technology and provide practical guidance for developers, educational policymakers, teachers, and researchers to effectively integrate GAI into elementary education while maintaining teaching quality.