Week+2

Post Week 2 Questions here:

Lave, Murtaugh, & de la Rocha (1984) Scribner (1984) Saxe (1988) Across the articles:
 * In Lave et al (1984) what is meant in the paragraph that talks about "high ethnographic standards" (page 69 - the last full paragraph on the page). (JLK)
 * In Lave et al (1984), choice has an impact on how shoppers select items at the grocery store (see page 80, for example); does this treatment of choice connect in some way to Cobb's (2007) discussion of "Reality" and "reality"? I ask this as the shopping experience is shown to include consideration of multiple variables, multiple rationalization strategies (price, product preference, etc.). (JLK)
 * The discussion of shoppers using alternatives to arithmetic problem-solving seems important for weighing the authors' conclusions (e.g., one alternative is the abandonment of calculation discussed on pp. 90-92). How does the dialectical approach to problem solving explain why shoppers abandon calculations? (AJ)
 * The author cites a 98% success rate with calculations in the grocery shopping 'arena,' and the impression I got was that abandoned calculations were not counted against the subjects. I'd like to know what the percentage is when considering abandoned calculations, and also whether a correct outcome was reliant on the exactly correct numerical decision being reached or simply the most favorable outcome being selected, and whether or not that level of mathematics was genuinely represented in the comparison test. (JMG)
 * The shopper creates a probable solution in her mind from the general principle, "bigger is cheaper" and realizes there are counterexamples. What is the arithmetic equivalent of this situation? What general principles do students enter arithmetic with and how should they be dealt with? Additionally, what about promoting general principles that might be true in an elementary classroom but not beyond? For example, "Addition makes things bigger" (until negatives come along) (DOS)
 * What implications might Scribner's (1984) work, particularly the notion of flexible use of strategies, have for the current promotion of //College and Career Readiness//? (JLK)
 * What are the strengths and weaknesses of Scribner's methodology (selection of subjects, data instruments and collection, etc.)? (JLK) (JMG)
 * The author references Vygotsky on page 29 and refers to items filling a "sign-function" in mental operations. I was unclear what is meant by this. (Likely I will be able to answer this question for us as I continue to prepare for my Vygotsky presentation.) (DOS)
 * What is the nature of typical "school mathematics" problems experienced by students? How are they similar to or different from the types (and progression) of tasks candy sellers experience? And how does this relate to the methods and assessed tasks used in this study? (AJ)
 * Does Saxe's conclusion about the 'breach between school mathematics and mathematics used in everyday tasks' stand the test of time, in particular in the light of the ever-increasing emphasis on problem solving? (JMG)
 * Scribner (1984, pg 12) and Saxe (1988, pg 16) each use the term //orthography//. Do these authors use the term in a similar sense? How does orthography connect to the mathematical practice of problem-solving in the real-world? (JLK, AJ, DOS)
 * What are the consistent results across all three of the readings (grocery shopping, candy sellers, and the dairy plant), with regards to mathematical problem-solving? (JLK)


 * Class Discussion:**

Common characterizations of out-of-school mathematics:
 * Contextual settings
 * Practical goal-directed activity
 * Optimization and efficiency were seen as important
 * Novice/Expert continuum, influenced heavily by experience
 * Social and cultural activity