Advanced Math Problem Design & Solution: An Exploratory, Intuitive Approach for Gifted Learners

This article explores an innovative pedagogical approach to designing and solving advanced mathematics problems, specifically tailored for gifted learners. The primary purpose is to investigate the efficacy of an exploratory and intuitive methodology that moves beyond traditional rote memorization and algorithmic application. We posit that gifted students can benefit significantly from learning environments that encourage creative thinking, hypothesis generation, and the development of conceptual understanding through hands-on exploration. The research employed a mixed-methods approach, combining qualitative case studies of a select group of gifted high school students with quantitative pre- and post-intervention assessments. Participants engaged in a series of problem-solving tasks designed to foster intuition and deep conceptual engagement. Data collection involved student work samples, think-aloud protocols during problem-solving sessions, surveys on problem-solving attitudes, and achievement tests. Preliminary results indicate that the exploratory, intuitive approach enhances not only problem-solving proficiency but also deepens mathematical understanding and boosts confidence among gifted learners. Students demonstrated an increased ability to approach complex, unfamiliar problems with flexibility and creativity. This study highlights the potential of shifting instructional focus towards conceptual intuition, offering valuable insights for educators seeking to optimize mathematics education for high-achieving students.

کلیدواژه ها:

Mathematics Problem Solving ، Gifted Education ، Intuitive Approach ، Advanced Mathematics