Mathematical inquiry is a process in which students respond to ill-structured, open-ended questions that reflect the authentic problems we encounter in real life. This Is unlike most problems we teach in mathematics ,which are well structured and close-ended. An open-ended ill-structured question has no single correct answer significant progress in identifying causal relationships, describing the reasoning process, and using data as evidence, they showed slight improvement in evaluating explanations.Additionally, the analyses suggest that phases of inquiry provide different kinds of learning opportunities and interact with students’ development of inquiry skill