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

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

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

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 fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Researching Teachers’ Agentic Orientations to Educational Change in Finnish Schools

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