Little attention is given to how the processes of scientific inquiry should be taught. It is apparently assumed that once teacher candidates graduate from institutions of higher learning they understand how to conduct scientific inquiry and can effectively pass on appropriate knowledge and skills to their students. This is often not the case due to the nature of university-level instruction that is often didactic. Scientific inquiry processes, if formally addressed at all, are often treated as an amalgam of non-hierarchical activities. There is a critical need to synthesize a framework for more effective promotion of inquiry processes among students at all levels. The author presents a new hierarchy of teaching practices and Intellectual processes that can help science teachers, science teacher educators, and curriculum writers promote an increasingly more sophisticated understanding of scientific inquiry among students.