Week14

Sfard
 * Sfard seems to talk about the PM metaphor in a more favorable light than AM citing only an issue of transfer where AM benefits. Are there other benefits to including the AM metaphor? (DOS)
 * What are the main differences between PM and AM? (AJ)

Cobb & Yackel
 * How does their emergent perspective make use of different theoretical perspectives? (AJ)

Across the articles
 * Is Cobb & Yackel's use of //transmission// and //emergence// (p. 186) analogous to Sfard's //acquisition// and //participation// metaphors? Why? (JLK)(JMG)
 * How does Cobb & Yackel's discussion of the distinctions observed between the suburban and inner-city educational cultures connect to Sfard's suggestion of a more "democratic" practice (page 9 & the endnote #6)? What do these articles suggest about reform efforts? (JLK) (DOS)

Simon (2009)
 * On pages 487-488, Simon talks about the lack of attention to justifying theoretical lenses in JRME articles (directly related to a question/concern posed by Dustin on 4/09/12). Simon then briefly talks about the idea of //theoretical framework//. Does this suggest that a theoretical framework can be solely constituted of discussion and justification of the theoretical lenses/tools and orientations employed in a study? (JLK)
 * What are ways we can be good consumers of the many theories of teaching and learning of mathematics? (AJ)

Sfard article:
 * Class notes**

• acquiring something, where knowledge is sometimes referred to as the something, whether it is something you can internally and individually possess or not. • implies a view that the something is a commodity, suggesting ways in which the method to get the something is more efficient or not - this may be viewed as a limitation • Sfard links a broad range of frameworks, including moderate to radical constructivism, interactionism and sociocultural theories (p. 6). This suggests that acquisition is not always individual - in other words, it's both - individual and social. • reflects many previous years of examining knowledge (see p. 5 for list of key words associated with this metaphor). •
 * Acquisition metaphor**

• "learning a subject is now conceived of as a process of becoming a member of a certain community" (p. 6). Emphasis on constant "doing" instead of having something. • knowledge (noun) (AM) vs. knowing (acting) (PM) • does not reject AM entirely, but examine individual's participation in a community •
 * Participation metaphor**

• We need both AM and PM perspectives. • Pro AM... metaphors are (complementary or incommensurable) or "incommensurable rather than incompatible" (p. 11) where incommensurable means "speaking different languages rather than really conflicting each other" (p. 355, Sfard, 2003) (similar to rational and irrational numbers for incommensurable) • PM influences a lot of the reform movement (e.g., NCTM Standards) - raises questions regarding skills in the documents (AM) • Analogy made in Sfard (2003) regarding viewing AM and PM similar to euclidean and non-euclidean geometry, and of course, analogies to light.
 * Looking across AM and PM**


 * Cobb & Yackel**

• Figure 2 would be combined to capture the emergent perspective. • (Cobb's work was driven out of a cognitive perspective into using an emergent perspective from his work in analyzing data) • Emergent perspective is considered a version of social constructivism (p. 176-177). Also found in the conclusion section, "primary purpose is psychological should be conducted against the background of an interactionist analysis of the social situation" (p. 188). • Emergent perspective may be found combining the interactionist and psychological perspectives found in Figure 3. Locally (within the community), the interactionist and psychological perspectives are complementary in this framework. Also important to look at broad cultural perspective as well as the microculture activity in a community.
 * How does Cobb & Yackel's emergent perspective make use of the different theoretical perspectives?**

• Transmission is part of AM. The "something" is being passed down from one generation to another. • Emergence is part of PM. References to participation focusing on emergence described in the footnote 5 on p. 186.
 * Across the Articles**
 * Is Cobb & Yackel's use of //transmission// and //emergence// (p. 186) analogous to Sfard's //acquisition// and //participation// metaphors? Why?**

• See footnote 5 on p. 186 regarding the role of teachers in helping students emerge in the classroom community. • Not sufficient to use interactionist and psychologist perspectives alone. Researchers must also consider the cultural situations (e.g., suburban and inner city educational cultures) for the students and teachers. Not doing so would be not sufficient.
 * How does Cobb & Yackel's discussion of the distinctions observed between the suburban and inner-city educational cultures connect to Sfard's suggestion of a more "democratic" practice (page 9 & the endnote #6)? What do these articles suggest about reform efforts?**


 * Simon (2009)**

• Lester wrote an article on framework: theoretical, conceptual, and analytic framework. Learning theories can be used for theoretical framework (e.g., words use, questions asked, data collected). Research interests and questions may come first before the theory perspective (or sometimes vice versa). From Simon, more demand on a discussion of framework and the justification in the use.
 * On pages 487-488, Simon talks about the lack of attention to justifying theoretical lenses in JRME articles (directly related to a question/concern posed by Dustin on 4/09/12). Simon then briefly talks about the idea of //theoretical framework//. Does this suggest that a theoretical framework can be solely constituted of discussion and justification of the theoretical lenses/tools and orientations employed in a study?**

• Simon would suggest theories as tools and lenses • Avoiding the tendency to superseding of theories • knowledgeable to distinguish between the different theories. Affordances, limitations, and the domain of applicability • incommensurability of theories as opposed to incompatibility • choose a theory that helps inform a research question or vice versa - be careful that your worldviews don't bias your choice of theory so that choosing your theory is based on answering the research questions • if you're answering a larger question, you have to bring together different perspectives • invest serious time and effort beyond the duration of a course in learning theory •
 * What are ways we can be good consumers of the many theories of teaching and learning of mathematics?**

• Learning is both social and individual. What roles do social interaction or the individual play in various different views of learning? What is the balance between the individual and the social/culture? What is at the foreground and background when using both perspectives in research? • Coping with multiple perspectives. How do researchers cope with the multiple perspectives of theories? What are the affordances, limitations, and domain of applicability with each of these perspectives? Under what justifications do researchers choose among these different perspectives? • Epistemology. (e.g., Acquisition and participation, "r" vs. "R") What is knowledge/knowing? How does one come about these ideas? What are the effects of the different epistemological viewpoints on educational psychology? • Piaget & Vygotsky. What are their contributions? What current perspectives are attributed or build from their work? How are their perspectives similar and different? • Implications for teaching from different perspectives. What are they? How are they useful? • Research design (design for learning). How do research questions impact the selection or use of different frameworks? How are theories applied to address research questions? •
 * General themes of the course - major ideas and questions (Ok-Kyeong will design a prelim question related to these ideas).**