The significance of flexibility in mathematics classrooms, particularly in interactive mathematics classrooms where students learn through hands-on experience, cannot be overstated. Teachers play a pivotal role in fostering students' mathematical understanding by selecting appropriate tasks and providing expert guidance. Additionally, the patterns of interactions between teachers and students, such as elicitation and discussion patterns, and their relationship with teacher flexibility are examined. Developing adaptive expertise in mathematics involves the ability to think flexibly about mathematical concepts, which can be enhanced by teaching math in a way that promotes the development of expertise. Mathematical flexibility, a crucial aspect of mathematical competence, involves the creative and innovative use of mathematical concepts, numerical relations, and strategies. It requires a combination of procedural and conceptual knowledge, skills, and understanding, as well as motivational and affective dispositions. Pedagogical flexibility can significantly contribute to innovating classroom teaching and learning, and exploring the relationships between teachers' pedagogical flexibility and students' potential and actual mathematical flexibility development. The article also emphasizes the importance of developing adaptive competencies in mathematics education to prepare students for an uncertain future, with creativity being considered a key competency and flexibility being viewed as a vital element of creativity.