Week+9+questions

Is it just me, or does it seem as if Forman (2003) classify both situated learning (pp. 336-337) and symbolization (in the form of the use of signs, p. 334) as sociocultural? (JE, 3/15)

As we work with pre-service teachers, how can we introduce the idea of community of learning? It is clear that we need to model this in our own classrooms, but how does one teach this concept to novices? CZ 3/15

How can the description of Brown and Stein (1997) be applied to student learning

In last week's reading, Ernest (1994) argues that mathematical discourse is dialogical and that these are seen in textbooks. Forman says the voice of the third person in communication is absent from textbooks and consequently in classroom that tie down to textbooks. What are the similarities and differences between Ernest’s and Forman’s claim about mathematical discourse? (NA)

Figured worlds are defined as “places where agents come together to construct joint meanings and activities” (Boaler & Greeno, 2000, p. 173). As cited in Stein and Brown (1997, p. 163), a community of practice is defined here as “a group of individuals who ‘share understandings concerning what they are doing and what that means in their lives and for their communities’ (Lave and Wenger, 1991, p. 98).” What is the difference then between communities of practice and figured worlds? Maybe it is related to the distinctions made here between ‘place’ and ‘group’, or even ‘construction of’ and ‘shared’ meanings (figured world, and community of practice, respectively). NF 3/15/10

Why are all three voices (Mathematician, Agent, and Person) //necessary// to the genre of mathematical discourse? (see Forman, 2003, p. 342 and beyond) NF 3/15/10

Boaler and Greeno (2000) present different kinds of knowing and how some students prefer one kind to the other (p. 190). The sociocultural theory supports the development of connected knowing. Must every students be a connected knowers to succeed in learning mathematics? Or is this article just exposing us to the different kinds of knowing available in our classrooms for us to balance the learning approach we use? (NA)

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After reflecting on our synthesis from today and our readings this week, I'm still inclined to try to 'classify' each of our readings into some perspective (i.e., situated versus sociocultural). However, I'm wondering if it would be more fruitful to understand how sociocultural/situated constructs are used in similar or different ways by these authors? The use of Lave and Wenger's (1991) framework might be an appropriate context for comparison (it is used in all three of our required readings-and the additional reading!). NF 3/15/10 ======

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On page 334, Forman (2003) states that the third theme found in Vygotsky's  work was that all activity is mediated by signs. Is this synonymous to the "signs" we discussed last meeting? (JH 3/15) ======

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Since identity and enculturation play important roles in education, I wonder about the need for immersion or just "time on task." The standard three credit-hour mathematics course at the university level is (as far as I know) not research based. Would four hours be better? Five? Three with a one hour "lab"? What about coordination between classes? For example, an engineering school (where there are lot of people who need to take mathematics who also need to take physics) would it not be beneficial to coordinate the classes to create a single community of practice into which students are enculturated? (RK, 03/16) ======

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The notion of enculturation seems simultaneously quite important and a bit ill-defined. It seems obvious that students will likely be enculturated into ~some~ culture. But do we have a clear understanding of what the culture of mathematics is? Are the cultures of mathematics consumers the same as that of mathematics developers? For example, mathematicians tend to be very critical of mathematics and tend to derive conviction in "more robust" ways (proof schemes). Statisticians are probably more likely to have external conviction schemes and this seems fine. It also seems from the readings that the mathematics culture of the classroom may be different from the mathematics culture of practice. So, what is this culture into which students are being enculturated? It seems there is a need to make it explicit. (RK, 03/16) ======

Stein and Brown assert on page 188 that " ...readers will have difficulty putting their fingers on what was actually being learned... " Is this an inherent difficulty with using contextual approaches like situated cognition and socio-cultural theory, or do we not yet have the appropriate devices to measure this type of learning? If this is an inherent difficulty (as I believe it is) does this undermine the usefulness of the theory as an educational design tool? How can we be certain that the target audience is learning? (I was unsatisfied with the answers proposed by the authors as they did not in any way attempt to show how progress might be quantified, or at least catagorized.) (JDS 3/16)