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Michael, I won't pretend to understand all of the issues raised in the field of psychology in relation to the question of "best teaching practice" However my original question was based in educational reform recommendations and here the recommendations are much clearer.?I have pasted an excerpt from an NSF document on math reform.?If one looks at the balance of the national reforms in the U.S. by subject they will find very similar language contained within.?These reforms are typically cited by state governments as a required part of teacher certification.?So while the field of Psychology may not have formed a paradigm about best teaching practice, the field of education has been willing to layout some specific definitions that are helpful in this process. The trick now becomes getting teachers to adopt the beliefs, theories, methods, and strategies that are recommended.? The link to this NSF document if anyone cares to read the rest is http://www.nsf.gov/pubs/2002/nsf02084/start.htm Excerpt from NSF Foundations Document Understanding the pedagogical theories that underlie school mathematics reform Research shows that most mathematics teachers, including prospective teachers, have strongly-held beliefs about student and teacher’s roles, desirable instructional approaches, and students?mathematical knowledge, how students learn and the purposes of schools (Thompson, 1992). These beliefs have mostly developed as a result of the teachers?own schooling. Although rarely made explicit, the following views of knowledge, learning and teaching lie behind what takes place in most traditional classrooms: ?#8486; Knowledge is a body of established facts and techniques that can be broken down and transmitted to novices by experts (positivistic view of knowledge). ?#8486; Learning results from acquiring isolated bits of information and skills through listening, watching, memorizing and practicing (behaviorist view of learning). ?#8486; Teaching is the direct transmission of knowledge from teacher to student; it takes place as long as the teacher provides clear explanations for the students to absorb (direct instruction view of teaching) (Borasi & Siegel, 1992, 2000). In contrast, the teaching practices recommended by the NCTM Standards (NCTM, 2000) and illustrated in our classroom vignette are grounded in views of knowledge, learning and teaching informed by a constructivist perspective (e.g., Brooks & Brooks, 1999; Davis, Maher & Noddings, 1990; Fosnot, 1996). Although different interpretations of constructivism exist, current school mathematics reform efforts are generally characterized by the following constructivist assumptions: ?#8486; Knowledge is socially constructed through human activity, shaped by context and purposes, and validated through a process of negotiation within a community of practice. Thus, it is always tentative rather than absolute. However, although knowledge is provisional in this paradigm, it does not mean that "anything goes." ?#8486; Learning is a generative process of making meaning that builds on personal knowledge and social interactions. This process may be stimulated by perceived dissonance. Prior knowledge, context and purpose play critical roles in the shaping of learning situations. ?#8486; Teaching is facilitating students?learning by creating a learning environment conducive to inquiry, setting up problem-solving situations to stimulate both student interest and cognitive dissonance about important mathematical ideas, and supporting students?attempts to solve problems and make sense of mathematical concepts (Borasi & Siegel, 1992, 2000). To fully appreciate the constructivist pedagogical approach recommended in the NCTM Standards, teachers need to identify and understand the non-traditional theories of teaching and learning mathematics and the research supporting such approaches.