This study focuses on exploring how visualization technology can effectively alleviate the cognitive challenges students encounter when understanding the abstract mathematical concept of function continuity. Given that function continuity often appears elusive to students, this research introduces advanced visualization tools such as GeoGebra, which strive to transform complex mathematical operations into intuitive and perceptible graphics or animations. The aim is to provide students with a more direct and vivid learning experience, helping them gradually build a profound understanding of the essence of function continuity and thereby enhancing their grasp of fundamental mathematical theory systems. The results demonstrate that integrating visualization tools into teaching practice not only significantly improves students’ depth of comprehension of abstract concepts like function continuity but also greatly stimulates their interest in learning, promoting the development of spatial imagination and logical thinking abilities. Based on these findings, we recommend widely adopting visualization tools as powerful instructional aids in future teaching, especially when teaching subjects that involve abstract concepts such as function continuity. This will not only enhance the effectiveness and appeal of classroom teaching but also substantially improve students’ learning outcomes and overall abilities.