Week+5+questions

Type in your questions on the readings for Week 5 here. Add your initials in the parentheses at the end of each of your questions.

Can the perspective of moderate empiricism articulated by Goldin be criticized as being symptomatic of a Cartesian anxiety? Could one support calls for data from a perspective of radical constructivism? (RK, 02/08)

What role do experts play in defining and shaping sociocultural practices? Who are the experts in our field, and what role do we expect them to play? (RK, 02/08)

I have some questions but am not sure they'll all lead to a fruitful discussion of our readings... (NF 2/8/10) - How do others understand how scheme theory fits with children's stages of development (see Confrey, 1995, p. 197)? - Confrey (1995) rejects "the assumption that structures lie awaiting discovery in concepts, in that such a view treats knowledge as a static, impersonal, independent object" (p. 214). Is this notion of "structure" the same as what Bruner advocates (think new math reform and structure in mathematics)? Must structure be contrasted with the notion of knowledge as an active process? - What new definitions and historical timeline pieces have you been adding to your bank of knowledge this week? (this is more for developing a more clear organization of main ideas and concepts)

Is social constructivism the bridge between the contsturctivism of Piaget and the social-cultural psychology of Vygotsky? (JE, 2/9) “As a cognitive position, construction assert that all mental activity is constructive (Davis, Maher and Noddings, p. 14)” This implies rote memorization is constructive because it is a mental activity. I think this is accommodating an already existing knowledge, which the learner cannot claim ownership of. It shouldn’t be construction at all. (NA) “I have a hard time understanding what it means to say “the constructivist position is post-epeistemological (Davis, Maher and Noddings, p. 12)” (NA)

piaget argues that in explaining the development of mathematical structures it is better to rely on reflective abstraction. Reflective abstraction is the process of interiorizing our physical operations on objects. He claimed, as we move the objects about, we come to understand mathematical operations such as commutativity, associativity, and reversibility. What happens to the properties of the objects? Are they held constant? (NA)

Constructive agree that “All knowledge is constructed” and that “Purposive activity induces transformation of existing structures.” Consider a child who is very hungry and the mother puts hot food on the table. This child immediately puts the hand in it to start eating, but is burned by the food and withdraws the hand. From that day on, this child learns never to touch hot very food again. Is this learning in the constructivist perspective? Was this activity purposive? Did it transform existing structures? Can error in procedure not lead to real construction of knowledge? (NA)

How does it come about that the reality we construct is in many ways remarkably stable? (NA)

In Ernest (1996), why is information-processing theory included with the three forms of constructivism, if itself is not a form of constructivism (see p. 339)? (JE, 2/9)

I am having a hard time with questioning the definition of "knowledge" (as in the Noddings article). This seems to be a philosophical argument that isn't practical to those of us "in the trenches." It seems that the more interesting question mathematics educators face concerning this is how do we judge when students know and when they do not (p. 11)? CZ

It seems that there is an a priori assumption that some constructions are better than others (Noddings pg 13). Is there a heirarchy of constructions? Or is there just good and bad ones? How do we know the difference? (JDS)

Noddings described ways to "induce engagement" in students so they perform powerful constructions, such as group work. This has been recommended for children, but is this similarly effective for older students? (JH, 2/9)

I would like to know more about non-constructive learning. What are actual examples of this? (JH 2/9)