Concept-Rich Instruction is based on the generally accepted constructivist views of effective teaching and takes a clear position on the issues that are still debated. It is founded upon two undisputed principles. One principle is that learning new concepts reflects a cognitive process. The other is that this process involves reflective thinking that is greatly facilitated through mediated learning.
The idea that learning is progressive, structural, cognitive change has been quite common among educators. For example, Bloom's Taxonomy of Educational Objectives described all learning as a progression through five phases: analysis, synthesis, comprehension, application,z and ultimately evaluation. Mathematics education researchers have consistently based their theories upon this idea. Even the behaviorists among them—for example, Robert Gange, a leading experimental psychologist from Florida State University, who prefers to use such verbs as state, define, and identify, rather than know and understand
on statements of educational objectives—explain the learning of mathematical concepts in terms of a hierarchy (Gange, 1985). Obviously, cognitive researchers have done it all along. Bruner (1991) spoke of stages in concept development that progress from enactive, to iconic, and eventually into symbolic. For Richard Skemp, world-renowned British pioneer theorist in the psychology of mathematics, the idea that there are different levels of conceptual understanding was fundamental (Skemp, 1976) and served as an important precursor to the contemporary research on cognition in mathematics (Asiala et al., 1996; Biggs & Collins, 1982; Sfard, 1992; Sfard & Linchevski, 1994; Van Hiele, 1986).