A Case Comparative Study on Open Mathematical Modeling between Gifted and Ordinary High School Mathematics Students

This study selected a representative gifted student and an ordinary student as case subjects, and explored the performance differences between the two in the process of open mathematical modeling through observation, work analysis and other methods. Based on Leiß and Blum 's seven-step cycle schema for mathematical modeling, a comparative study of open mathematical modeling cases was conducted. The study found that gifted students can quickly understand the meaning of the questions, convert the questions into sub-questions to build a reasonable model framework, and have flexible thinking in the modeling process, and can quickly call on existing mathematical knowledge; while ordinary students have certain difficulties in understanding the problems, are prone to give up when encountering obstacles, and are not flexible in the application of mathematical knowledge ; both of them perform poorly in testing and adjusting the model. Through comparative analysis, the different characteristics and gaps between the two in the development of mathematical modeling ability are revealed, which provides a reference for teaching students in accordance with their aptitude and improving the mathematical modeling literacy of students at different levels, and helps high school mathematics education better meet the personalized development needs of students.