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"The famous Swiss psychologist Jean Piaget stated: "to understand is to invent", highlighting the active nature of the learner. The above discussion provides an outline of the theoretical foundation on which Inquiry-Based Learning rests. Furthermore, it provides a summary of the mounting evidence that students who are given the opportunity to learn mathematics through inquiry develop better strategic competence and deeper conceptual understanding of mathematics. "

A practical list of Math teaching/learning methods that embrace inquiry for deep understanding.

"So according to our "big tent" model of PBL, some of the newer "X-BLs" -- problem-, challenge- and design-based -- are basically modern versions of the same concept. They feature, to varying degrees, all of BIE's 8 Essential Elements of PBL, although each has its own distinct flavor. (And by the way, each of these three, along with project-based learning, falls under the general category of inquiry-based learning -- which also includes research papers, scientific investigations, Socratic Seminars or other text-based discussions, etc."