Week+1+questions

Week 1: Questions
 * 1) I would benefit from some discussion of the differences between the four perspectives outlined in Cobb's chapter. In particular, I would like to discuss the differences between cognitive psychology and sociocultural theory. (Rob)
 * 2) Numerous variants of constructivism are discussed by Cobb (2007) (e.g., starting on page 10). How is constructivism defined and how can we make sense of the key distinctions between radical constructivism as compared to other types? Furthermore, why is this theory considered pragmatic realism? (Nicloe)
 * 3) If the four perspectives that Cobb outlines are incommensurable, then it seems unlikely that there can be an objective method for constructing a "bricolage" of the perspectives. Won't the decisions a researcher makes regarding what perspectives to include in his or her theoretical framework will be value-laden and subjective? (Rob)
 * 4) Is Cobb (2007) arguing that transforming psychological perspectives into instructional strategies is not a productive way to connect or relate theory to practice? In particular, in referring to constructivist teaching, among others, Cobb contends that, “pedagogical proposals developed in this manner involve a category error wherein the central tenets of a descriptive theoretical perspective are transformed directly into instructional prescriptions” (p. 5). If this is the case, then what is an appropriate way to connect theory and practice? How is this connection made evident in the Teaching Principle of PSSM (NCTM, 2000) and is it appropriate? (Nicole)
 * 5) Question 2: Research is supposed to inform teacher education programs. How effective has this been? (Napthalin)
 * 6) What are best strategies that teachers can employ to monitor students' capacity and inclination to do and understand mathematics (Principles of School Mathematics, p. 19)? (Janice)
 * 7) Who should be the ultimate enforcer of both the Teaching and Learning Principles? (Jonathan)
 * 8) I don’t understand what is meat by what Cobb (2007) refers to as a central problem of epistemology, “that of the opposition between philosophical realism and constructivist positions that deny that ontological reality is knowable” (p. 4). I am hoping that as we learn more and become more comfortable with these traditions this distinction will make more sense. (Nicole)
 * 9) Cobb does a good job of putting forth arguments both for and against the merit behind experimental psychology as a philosophy behind mathematics education research. Yet, why is there such a push for these types of studies (as seen in funding requirements), over the other theoretical perspectives Cobb expores? (Jonathan)
 * 10) What are the implications of the following statement, “it is quite possible for mathematics educators to make rational decisions about instructional goals while acknowledging that what counts as improvement in students’ mathematical learning is itself open to revision” (Cobb, 2007, p.9)? (Nicoe)
 * 11) Are there more concrete examples of the limitations of distributed cognition (Cobb, p. 27)? The examples given were more theoretical than I could grasp, and I would like to understand more about them. (Janice)
 * 12) On page 17, last paragraph, of the NCTM article says "This kind of knowledge is beyond what most teachers experience in standard preservice mathematics courses in the United States." What are the factors responsible for preservice mathematics courses in the US falling short of the essential ingredients for effective mathematics teaching? How can the situation be remedied? (Napthalin)