Week11


 * Forman (2003)**
 * In Forman's view, what seems to be the most critical element to successful creation and continuance of mathematical discourse (that aligns with the recommendations from the 1991 teaching standards) in the classroom? How does Forman address this - that is, how does she suggest that this type of mathematical discourse be best sustained? (JLK)
 * Taking into account (1) the influence of Vygotsky's theory, (2) the connection between theory and practice, and (3) the recommendations put forth in the 1991 teaching standards, what seems to be the implication regarding how various stakeholders (teachers, curriculum developers, teacher educators, etc.) could think about the use of mathematical discourse in the classroom? (JLK)
 * On page 348, Forman makes the statement that "may be impossible or unproductive to tattempt to conduct anything approaching a controlled experiment in a school setting." Does this statement hold for only research where the unit of analysis is a community? Is this a generalized claim that is being made about all school mathematics research from all perspectives? (JMG)
 * Forman uses situated cognition and sociocultural approaches as viewpoints for thinking about all students (as articulated in NCTM documents). How do situated cognition and sociocultural approaches differ with this respect? (AJ)


 * Stein & Brown (1997)**
 * What are the key distinguishing features between the two frameworks (communities of practice and utilizing a ZPD to promote transitions towards //unassisted learning//) used by the authors? (JLK)
 * In what ways are Stein & Brown's research approach similar to, and different from, Cobb's progressions in his research? (JLK, AJ)
 * The two views seem to be that learning is evidenced by higher level of involvement in a sociocultural setting on one hand, and increased autonomy on the other. How can these two seemingly opposite views (learning as either increased social involvement or decreased social dependence) come from the same general theory (socio-cultural, not the specific frameworks)? (JMG)
 * On page 189, the authors discuss a second way to discuss the topic of learning by talking about the individuals "actively constructing and making sense of" learning situations, by looking at learning cognitively rather than socioculturally. How would this be more advantageous than using a cognitive/constructive view throughout the research practice, and is the author implying that constructivism is subsumed by socio-cultural theory? (JMG)
 * Learning is viewed from a continuum of peripheral to fuller participation in activities where experts and novices have different nature of roles. How do these ideas differ when the communities of practice are evolving, static, or in creation? (AJ)


 * Boaler & Greeno (2000)**
 * The authors suggest that the ways in which mathematicians engage in the practice of mathematics stands in strong contrast to the student practices promoted in //didactic// forms of instruction. However, they also mention how some students view themselves as successful and/or enjoy mathematics because of their belief in there being "one answer", etc. According to the authors, //should// mathematics be totally facilitated from a discussion-based approach that primarily promotes "connected knowing"? Why/why not? (JLK)

Class Discussion:


 * What is our understanding of sociocultural perspectives? What new insights into socioculutural perspectives did we come to understand from this week’s readings?**


 * A better understanding of "evolutionary" development of learning
 * Social and cultural aspects involved but where are the boundaries... So how similar to/different from Vygotsky's work is sociocultural perspective? Vygotsky's work seems to focus on the individual in relation to the larger group, whereas sociocultural perspectives seem more broad and focus on the practices of groups.
 * sociocultural perspective looks at more of the classroom practices of individuals
 * raise the importance of the research questions and frameworks used to analyze different sets of data
 * Participation is not necessarily from Vygotsky's work. Vygotsky's perspective involves internalization. Participation is important for sociocultural perspective and is critiqued in work in this area (for more on this, see Lave & Wenger's work)
 * The need for reflecting is emphasized more/different areas from a sociocultural perspective, given the emphasis on social aspects in classroom.
 * Relevance and lens to discuss equity issues on mathematics learning (e.g., mathematical discourse, different arguments)


 * What questions do you have regarding the frameworks found in the articles?**
 * Stein & Brown: Differences in the framework: Social vs individual aspects for them. How does the whole community progress as opposed to an individual?
 * Assisted performance vs. scaffold: assisted performance involves a co-constructed or "togetherness" or co-participation
 * peripheral to fuller participation on p.164-165 was helpful in understanding... Lave & Wegner discuss breadth and depth... participating in a wider breadth (range of activities) you're moving from peripheral to fuller... also if moving from a shallow to deeper participation (more about the roles) you're moving from peripheral to fuller participation.
 * Boaler & Greeno - discuss identity as a key component. These identities are portrayed by the different examples from school situations. Identities are often discussed as shifts.


 * What are some general themes of sociocultural approaches in mathematics education?**
 * Emphasis on communication, discourse, use of signs
 * Implications for classroom practice (discursive patterns: IRE, IRF Forman p. 341)
 * Distinctions between didactic and discussion-based teaching (Boaler & Greeno)
 * Focus on the group or individual situated within the group (unit of analysis)
 * Communities of practice
 * Incorporates beliefs, goals, attitudes, dispositions, cultural backgrounds
 * Methodologies: investigative and descriptive, lend themselves for qualitative approaches
 * Differences of the communities create opportunities for learning


 * How does sociocultural perspectives compare/contrast to situated cognition?**
 * Situated cognition focuses on the individual.
 * Situated cognition's use of an object, there is some inherent meaning within it. Whereas in sociocultural perspectives, it makes use of semiotics, an artifact becomes useful when utilizing schemas.
 * Sociocultural perspectives take into account "r" or "R" aspects.