Combining Analyses of Cognitive Processes, Meanings, and Social Participation: Understanding Symbolic Representations

We propose three analytic representations of collaborative problem solving. Activity nests, a generalization of goal-subgoal trees, represent functional decompositions of task activity into components, using nesting to indicate operations that satisfy task functions. Semiotic networks, an extension of semantic networks, represent meanings as refers-to relations between symbolic expressions and other signifiers, and relations in situations and situation types, along with general relations between these meanings. Contribution Vagrants, an adaptation of contribution trees (Clark & Schaefer, 1989), represent how turn sequences collectively achieve task components. W e developed these representations to analyze how pairs of middle-school students constructed tables to represent quantitative properties of a simple physical device that models linear functions. Variations between activity nests of dififerent pairs support an explanation of activity in terms of attimement to constraints and to affordances and abilities, rather than following procedures. The semiotic networks support a hypothesis that task components are completed through accomplishing alignments of refers-to relations.which is a generalization of goal satisfaction. Similarities between the contribution diagrams support a general pattern that we call the turn structure of collaborative operations, in which task information is recognized and task operations are initiated, performed, and accepted. Interaction is organized into this structure in order to support mutually aligned intentions, understandings, actions, and agreements

Managing Disagreement in Intellectual Conversations: Coordinating Interpersonal and Conceptual Concerns in the Collaborative Construction of Mathematical Explanations

This paper reports research into how mathematical explanations are constructed during conversation based on videotapes of pairs of student math teachers collaboratively writing explanations in geometry. In particular, we analyzed how disagreements about parts of their explanations were managed in these conversations. In contrast to research on disagreement in everyday conversation, explanation disagreements were more likely to overlap with preceding turns and to be stated baldly without prefaces, token agreements or qualifications. However, the observed frequencies of different kinds of disagreements were not consistent with a model favoring explicit substantive disgreement either. Instead, it is proposed that both the interpersonal concerns that would motivate a preference for agreement and the conceptual concerns for a quality explanation that would motivate a preference for substantive disagreement are being managed by participants. Disagreements are co-constructed, and conversants are seen to jointly employ complex devices for introducing and managing disagreement across turns that can satisfy both kinds of concerns with much less conflict betweeen them than might have been expected

Conservation of information-processing capacity in paired-associate memorizing

Data that impose constraints on hypotheses regarding the role of temporal variables in memorizing are reviewed, including results that apparently disconfirm Greeno's (1967) time-sharing hypothesis. An alternative hypothesis is proposed, in which it is assumed that S occasionally attenuates his rate of processing information for memory, with the probability of attentuation being relatively high when the item being presented is still in short-term memory as a result of a recent presentation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32693/1/0000060.pd

Interpretation of the two-stage analysis of paired-associate memorizing

Four groups were run with response difficulty and stimulus difficulty varied factorially. A two-stage Markov model fit the data adequately. The parameter associated with the first stage depended on stimulus difficulty as well as response difficulty, refuting an interpretation of the first stage as response learning. The learning parameters associated with the second stage seemed to depend only on stimulus difficulty. The results suggest that the first stage of learning involves storage of the stimulus-response pair in memory, and the second stage involves learning to retrieve the item reliably.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32746/1/0000115.pd

Matrix analysis of identifiability of some finite markov models

Methods developed by Bernbach [1966] and Millward [1969] permit increased generality in analyses of identifiability. Matrix equations are presented that solve part of the identifiability problem for a class of Markov models. Results of several earlier analyses are shown to involve special cases of the equations developed here. And it is shown that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45730/1/11336_2005_Article_BF02291365.pd

An analysis of some conditions for representing N state Markov processes as general all or none models

Recently Markov learning models with two unidentifiable presolution success states, an error state, and an absorbing learned state, have been suggested to handle certain aspects of data better than the three state Markov models of the General All or None model type. In attempting to interpret psychologically, and evaluate statistically the adequacy of various classes of Markov models, a knowledge of the relationship between the classes of models would be helpful. This paper considers some aspects of the relationship between the class of General All or None models and the class of Stationary Absorbing Markov models with N error states, and M presolution success states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45728/1/11336_2005_Article_BF02290602.pd

Equivalence classes of functions of finite Markov chains

A matrical representation of a Markov chain consists of the initial vector and transition matrix of the chain, along with matrices that specify which observable response occurs for each state. The likelihood function based on a Markov model can be stated in a general way using the components of the model's matrical representation. It follows directly from that statement that two models are equivalent in likelihood if they are related through matrix operations that constitute a change of basis of the matrical representation. Two necessary properties of a change matrix associating two Markov models that are members of the same equivalence class with respect to likelihood are derived. Examples are provided, involving use of the results in analyzing identifiability of Markov models, including a useful application of diagonalization that provides a connection between the problem of identifiability and the eigenvalue problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22239/1/0000675.pd

The Impact of Shame, Self-Criticism and Social Rank on Eating Behaviours in Overweight and Obese Women Participating in a Weight Management Programme

Recent research has suggested that obesity is a stigmatised condition. Concerns with personal inferiority (social rank), shame and self-criticism may impact on weight management behaviours. The current study examined associations between social comparison (shame, self-criticism), negative affect and eating behaviours in women attending a community based weight management programme focused on behaviour change. 2,236 participants of the programme completed an online survey using measures of shame, self-criticism, social comparison, and weight-related affect, which were adapted to specifically address eating behaviour, weight and body shape perceptions. Correlation analyses showed that shame, self-criticism and social comparison were associated with negative affect. All of these variables were related to eating regulation and weight control (p < 0.001). Path analysis revealed that the association of shame, hated-self, and low self-reassurance on disinhibition and susceptibility to hunger was fully mediated by weight-related negative affect, even when controlling for the effect of depressive symptoms (p < 0.050 to p < 0.010). In addition, feelings of inadequacy and unfavourable social comparisons were associated with higher disinhibition and susceptibility to hunger, partially mediated through weight-related negative affect (p = 0.001). These variables were negatively associated with extent of weight loss during programme attendance prior to the survey, while self-reassurance and positive social comparisons were positively associated with the extent of weight loss prior to the survey (p < .050). Shame, self-criticism, and perceptions of inferiority may play a significant role in self-regulation of eating behaviour in overweight people trying to manage their weight

Understanding learning culturally: Overcoming the dualism between social and individual views of learning.

This paper identifies limitations within the current literature on understanding learning. Overcoming these limitations entails replacing dualist views of learning as either individual or social, by using a theory of learning cultures and a cultural theory of learning, which articulate with each other. To do this, we argue that it is possible and indeed necessary to combine major elements of participatory or situated views of learning with elements of Deweyan embodied construction. Bourdieu’s concepts of habitus and field are used to achieve this purpose, together with the use of ‘becoming’ as a metaphor to help understand learning more holistically. This theorizing has a predominantly heuristic purpose, and we argue that it enables researchers to better explain data. We also suggest that a cultural approach of the sort proposed here leads toward the asking of better questions about learning and its improvement and has high practical significance