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

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

Metacognitions about desire thinking predict the severity of binge eating in a sample of Italian women

In this study, our principal aim was to investigate whether metacognitions about desire thinking predict the severity of binge eating in women and, if so, whether this relationship is independent of age, self-reported body mass index (BMI), negative affect, irrational food beliefs and craving. One hundred and four women, consisting of 32 consecutive patients with binge eating disorder undergoing initial assessment for cognitive therapy for eating disorders, 39 moderate binge eaters, and 33 non-binge eaters (both from the general population), completed the following measures: Self-reported BMI, Hospital Anxiety and Depression Scale, Irrational Food Beliefs Scale, General Craving Scale, Metacognitions about Desire Thinking Questionnaire, and Binge Eating Scale. A series of Spearman's rho correlation analyses revealed that self-reported BMI, anxiety, depression, irrational food beliefs, craving, and all three factors of the metacognitions about desire thinking questionnaire were significantly associated with the severity of binge eating. A stepwise regression analysis identified self-reported BMI, craving, and negative metacognitions about desire thinking as significant predictors of the severity of binge eating. These results, taken together, highlight the possible role of metacognitions about desire thinking in predicting the severity of binge eating. The clinical implications of these findings are discussed

Researching Teachers’ Agentic Orientations to Educational Change in Finnish Schools

Peer reviewe

Konstruktivistische Ansätze in der Erwachsenenbildung und Weiterbildung

Theoretical approaches in the field of further education and advanced vocational training have to face multifaceted demands: the analysis of knowledge aquisition and knowledge transfer and its instructional support as well as the revealment of the mechanisms which influence further education on an organisational level in companies. This article describes, that herefore especially moderate constructivistic approaches are useful. After an introduction to the philosophical tradition of these approaches and important characteristics of adult learning, two examples of constructivistic models are being described particularly: The theory of situated learning environments and career counseling. Concluding it is shown, that a moderate constructive perspective fulfils important criteria for the theoretic modelling of further education processes.Theoretische Ansätze in der Erwachsenen- und insbesondere in der beruflichen Weiterbildung müssen sich vielfältigen Ansprüchen stellen: der Analyse des Wissenserwerbs und Wissenstransfers und seiner instruktionalen Unterstützung ebenso wie der Aufdeckung der Mechanismen, die in den Betrieben auf organisatorischer Ebene die Weiterbildung beeinflussen. In diesem Beitrag wird die Auffassung vertreten, daß dafür insbesondere liberalisierte konstruktivistische Ansätze gut geeignet sind. Nach einer Einführung in die philosophische Tradition dieser Ansätze und wichtiger Merkmale des Lernens im Erwachsenenalter werden zwei Beispiele konstruktivistischer Modelle genauer beschrieben: die Theorie situierter Lernumgebungen und das career counseling. Abschließend wird gezeigt, daß eine liberalisierte konstruktivistische Perspektive wichtige Kriterien für die theoretische Modellierung von Weiterbildungsprozessen erfüllt

Characterizing interactive engagement activities in a flipped introductory physics class

Interactive engagement activities are increasingly common in undergraduate physics teaching. As research efforts move beyond simply showing that interactive engagement pedagogies work towards developing an understanding of how they lead to improved learning outcomes, a detailed analysis of the way in which these activities are used in practice is needed. Our aim in this paper is to present a characterization of the type and duration of interactions, as experienced by students, that took place during two introductory physics courses (1A and 1B) at a university in the United Kingdom. Through this work, a simple framework for analyzing lectures—the framework for interactive learning in lectures (FILL), which focuses on student interactions (with the lecturer, with each other, and with the material) is proposed. The pedagogical approach is based on Peer Instruction (PI) and both courses are taught by the same lecturer. We find lecture activities can be categorized into three types: interactive (25%), vicarious interactive (20%) (involving questions to and from the lecturer), and noninteractive (55%). As expected, the majority of both interactive and vicarious interactive activities took place during PI. However, the way that interactive activities were used during non-PI sections of the lecture varied significantly between the two courses. Differences were also found in the average time spent on lecturer-student interactions (28% for 1A and 12% for 1B), although not on student-student interactions (12% and 12%) or on individual learning (10% and 7%). These results are explored in detail and the implications for future research are discussed