Week+4


 * __From Brainerd (2003):__**
 * Piaget's experiments (and the experiments of those whose work paralleled his) aligned with the notion of 'tutorial' training. From this chapter, what exactly do we think that tutorial training IS? What are the affordances and constraints of this type of "training", and what are the potential implications for school mathematics? (JLK, JMG)
 * Many of the experiments described in this chapter followed the design of pre-test post-test, and more than one included some measure of durability of learning outcomes. Looking back at this research, what possible improvements could be made to improve the research design, if researchers wanted to take the research further? (JLK)
 * On page 258, the Brainerd connects Piaget's work to a "classical readiness perspective coupled with..." What is meant by a "classical readiness perspective"? I did some searching online, but was unable to find a satisfactory answer. Does it simply mean that "all children are ready to learn"? (JLK)


 * __From Piaget (1964):__**
 * (This may seem silly), Is Piaget's discussion of constructive processes in this spech/journal article restricted to the individual. Why/why not? (JLK)
 * Piaget gives examples of the young lad counting pebbles and the notion of the transitivity of equality, amongst other early-mathematical notions. What are some potential implications from observations and results such as these (pertaining to mathematics learning and instruction)? (JLK DOS)
 * On page 179 he describes that the concept of conservation of mass can not be learned through experience. Are there other examples that fit in this category? (DOS)
 * On page 182 he describes that learning is based on stimulus-response but that a stimulus is only really a stimulus if there is a response. This was the idea that I wanted to capture in our definition of learning when I wanted to add an aspect of usefulness or practicality to our definition. Learning is only really learning if there is some sort of meaningful response. How do others think this effects our definition of learning, if at all? (DOS)
 * What is the relationship between internalization/externalization and zone of proximal development? (AJ)


 * __From Tudge & Scrimsher (2003):__**
 * The authors quote Vygotsky in saying "play creates a zone of proximal development of the child. In play a child always behaves beyond his average age, above his daily behavior". First, what do we think the authors intended to communicate by the use of this quote? Second, do we agree with this view on the role of play? (JLK)
 * The authors' descriptions of the zone of proximal development point to the role of reflection by the learner, interaction in the social context, and the transformation of natural instincts and functions (see page 215, for example). What are some potential implications (from this chapter) for the notion of eliciting multiple solution strategies to mathematical problems in the classroom? (JLK)


 * __From Vygotsky (1978):__**
 * How might we summarize the notion of the zone of proximal development, and what do we think are the strongest implications of this theory for mathematics teaching and learning? (JLK)
 * Where would we say that Vygotsky's work falls on the spectrum from quantitative to qualitative design, and why? (JLK)
 * My interpretation is that internalization the process of moving a "function" from the proximal level to the actual level. I am somewhat less clear on what role externalization plays on learning; the way it is presented sounds more like a way for students to express what they have internalized but doesn't bear much on new learning. Is there something else to externalization? (JMG)
 * Vgotsky states, "The zone of proximal development defines those functions that have not yet matured but are in the process of maturation, functions that will mature tomorrow but are currently in an embryonic state" (p. 86). How does the zone of proximal development account for "new" knowledge in complex tasks, perhaps beyond the potential development? (AJ)
 * Does the zone of proximal development take into specific individuals or a "collective" group when many students are engaged in a task together? (AJ)


 * __Across the readings__**
 * When Vygotsky talks about the actual level of development, is it analogous to Piaget's stages of development or is he thinking of development more along a continuum then in steps? (JMG)

__**In-class Discussion**__

Commonalities:
 * Learning as resolving internal conflict.
 * Individual is engaged in active (and dynamic?) processes in goal-directed (as opposed to mimic or meaningless mechanical) activities
 * cognitive development stages (Piaget - internal structure based on operations vs Vygotsky - levels of linguistic development: egocentric, inner speech, higher functions, etc.)
 * learning provoked rather than spontaneous
 * rejects behavioral approaches (PIaget/Vygotsky look at mental structures [S-M-R], not simply stimulus/response)
 * clinical studies to know what children are thinking (as opposed to experimental behaviorists)

Differences/distinctive features: >
 * Relation between development and learning (Piaget: develop then learn; Vygotsky: together interrelated)
 * Vygotsky emphasizes the social role or the learner in context (it's "THE" influence) whereas Piaget has social interaction as part of the environment (not special)
 * Piaget notion of readiness based on developmental stages vs. Vygotsky ZPD (defining what your future goal is)
 * Vygotsky discusses mediation of tools and signs (highly cited in distributed cognition) vs. Piaget's not special environment
 * Piaget - internal structure based on operations vs Vygotsky - levels of linguistic development: egocentric, inner speech, higher functions, etc.