The Effectiveness of a Program Based on Flipperentiated Instruction for developing Higher-Order Mathematical Thinking Skills and Self-Efficacy among Faculty of Education Students, Mathematics Specialization

    The research aimed to develop Higher-Order Mathematical Thinking Skills and Self-Efficacy among Faculty of Education Students, Mathematics Specialization through a program based on Flipperentiated Instruction; To achieve this goal, a list of Higher-Order Mathematical Thinking Skills that should developed for mathematics specialization students was prepared. Additionally, the components of the proposed program were designed, and educational materials were developed for student teachers, along with a faculty member guide for implementation. Research tools were also prepared, including a Higher-Order Mathematical Thinking Skills Test supplemented with an Open-Ended Questionnaire to explore student teachers' opinions on their testing experience, as well as a Self-Efficacy Scale. The study employed a Mixed Research Methodology with an explanatory design for a single group, using a pre-post application of quantitative and qualitative research tools. The research sample consisted of (42) third-year mathematics specialization students at the Faculty of Education, University of Sadat City, during the second semester of the 2024/2025. The quantitative and qualitative analysis of the research findings demonstrated the significant effectiveness of the Flipperentiated Instruction-based program for developing both Higher-Order Mathematical Thinking Skills (Critical Mathematical Questioning, Formulating Accurate Mathematical Predictions, Analyzing and Modeling Real-Life Mathematical Data, Solving Mathematical Challenge Problems, and Enhancing Mathematical Thinking Outcomes) and Self-Efficacy and its Behavioral, Cognitive, and Emotional dimensions among Faculty of Education Students, Mathematics Specialization. Furthermore, a strong positive and statistically significant correlation (at the 0.01 level) was found between the students' post-test scores in Higher-Order Mathematical Thinking Skills and their Self-Efficacy Scale scores.