Week14+questions

To what extent is Cobb's comparisons and contrasts among the four theoretical perspectives similar (or dissimilar) to Sfard (1998) and Simon (2009)? (JE, 4/18/10)

Related to Jonathan's question, am I correct to say that the pragmatic realism described in Cobb is "post-epistemological?" I feel fairly certain of this and I feel it's the reason he can put forward a view of science as "co-existence and conflict" rather than "relentless march of progress" (p. 31). This view of science is, I think, necessary if one wants to accept the proliferation of incommensurable theories. (RK, 4/19/10)

Cobb seems to set Karl Popper's falsifiability criterion aside as a "rule of thumb." My own limited understanding of Popper is that this criterion was put forward to distinguish scientific pursuits from non-scientific pursuits. If one cannot design an experiment which will refute a particular idea, then that idea is not a scientific idea. In particular, Popper was attacking the Marxist theory of historicism as unscientific. Cobb claims that in applying this rule of thumb, we rely on our "wisdom and judgment" (p. 14). But these things seem cultural and to some extent relative. What would prevent us from adopting the "wisdom and judgment" of thinkers such as Marx or Engel? It seems to me as though we must think carefully before adopting pragmatic realism as our philosophy and that there is a need to be able to carefully articulate the value of such a decision. (RK, 4/19/10). ---For example, Michael Apple (Davis (1997) cited Apple's 1992 article in JRME as a reason to spend time "wondering and worrying ... about the moral and ethical status of our chosen careers", p. 366) is a neo-Marxist. --Rob, you stole my question, though I would not have phrased it so eloquently :-). I really wanted to know how frameworks which do not derive support from empirical data can ever be rejected. Related to that idea is whether pragmatic realism will lead to an inevitable explosion of competing theories, beyond any individual's ability to cope. (JDS 4/20)

Cobb mentions several examples that seem to show the difference between the real and the Real. What is the difference between these two states? CZ, 4/20. I need to understand this too. (NA)

Based on what we know now about how people learn, I want to go back to my question at the beginning: what are best strategies that teachers can employ to monitor students' capacity and inclination to do and understand mathematics? (JH, 4/20)

Which of situational and structural rationale for learning mathematics is dominant among students today? What are the advantages and disadvantages of each? Which learning theory supports each and why? (NA)