Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Perception of affordances in multi-scale dynamics as an alternative explanation for equivalence of analogical and inferential reasoning in animals and humans

Recent claims of equivalence of animal and human reasoning are evaluated and a study of avian cognition serves as an exemplar of weaknesses in these arguments. It is argued that current research into neurobiological cognition lacks theoretical breadth to substantiate comparative analyses of cognitive function. Evaluation of a greater range of theoretical explanations is needed to verify claims of equivalence in animal and human cognition. We conclude by exemplifying how the notion of affordances in multi-scale dynamics can capture behavior attributed to processes of analogical and inferential reasoning in animals and humans.

Systematic variations in polymer gel dosimeter calibration due to container influence and deviations from water equivalence

There are a number of gel dosimeter calibration methods in contemporary usage. The present study is a detailed Monte Carlo investigation into the accuracy of several calibration techniques. Results show that for most arrangements the dose to gel accurately reflects the dose to water, with the most accurate method involving the use of a large diameter flask of gel into which multiple small fields of varying dose are directed. The least accurate method was found to be that of a long test tube in a water phantom, coaxial with the beam. The large flask method is also the most straightforward and least likely to introduce errors during setup, though, to its detriment, the volume of gel required is much more than other methods.

A comparative study of the effect of calibration conditions on the water equivalence of a range of gel dosimeters

Gel dosimeters are of increasing interest in the field of radiation oncology as the only truly three-dimensional integrating radiation dosimeter. There are a range of ferrous-sulphate and polymer gel dosimeters. To be of use, they must be water-equivalent. On their own, this relates to their radiological properties as determined by their composition. In the context of calibration of gel dosimeters, there is the added complexity of the calibration geometry; the presence of containment vessels may influence the dose absorbed. Five such methods of calibration are modelled here using the Monte Carlo method. It is found that the Fricke gel best matches water for most of the calibration methods, and that the best calibration method involves the use of a large tub into which multiple fields of different dose are directed. The least accurate calibration method involves the use of a long test tube along which a depth dose curve yields multiple calibration points.

A comparative study of the effect of calibration conditions on the water equivalence of a range of gel dosimeters

Gel dosimeters are of increasing interest in the field of radiation oncology as the only truly three-dimensional integrating radiation dosimeter. There are a range of ferrous-sulphate and polymer gel dosimeters. To be of use, they must be water-equivalent. On their own, this relates to their radiological properties as determined by their composition. In the context of calibration of gel dosimeters, there is the added complexity of the calibration geometry; the presence of containment vessels may influence the dose absorbed. Five such methods of calibration are modelled here using the Monte Carlo method. It is found that the Fricke gel best matches water for most of the calibration methods, and that the best calibration method involves the use of a large tub into which multiple fields of different dose are directed. The least accurate calibration method involves the use of a long test tube along which a depth dose curve yields multiple calibration points.

Offsetting methane emissions : an alternative to emission equivalence metrics

It is widely recognised that defining trade-offs between greenhouse gas emissions using ‘emission equivalence’ based on global warming potentials (GWPs) referenced to carbon dioxide produces anomalous results when applied to methane. The short atmospheric lifetime of methane, compared to the timescales of CO2 uptake, leads to the greenhouse warming depending strongly on the temporal pattern of emission substitution. We argue that a more appropriate way to consider the relationship between the warming effects of methane and carbon dioxide is to define a ‘mixed metric’ that compares ongoing methane emissions (or reductions) to one-off emissions (or reductions) of carbon dioxide. Quantifying this approach, we propose that a one-off sequestration of 1 t of carbon would offset an ongoing methane emission in the range 0.90–1.05 kg CH4 per year. We present an example of how our approach would apply to rangeland cattle production, and consider the broader context of mitigation of climate change, noting the reverse trade-off would raise significant challenges in managing the risk of non-compliance. Our analysis is consistent with other approaches to addressing the criticisms of GWP-based emission equivalence, but provides a simpler and more robust approach while still achieving close equivalence of climate mitigation outcomes ranging over decadal to multi-century timescales.

Dispositional resistance to change : measurement equivalence and the link to personal values across 17 nations

The concept of dispositional resistance to change has been introduced in a series of exploratory and confirmatory analyses through which the validity of the Resistance to Change (RTC) Scale has been established (S. Oreg, 2003). However, the vast majority of participants with whom the scale was validated were from the United States. The purpose of the present work was to examine the meaningfulness of the construct and the validity of the scale across nations. Measurement equivalence analyses of data from 17 countries, representing 13 languages and 4 continents, confirmed the cross-national validity of the scale. Equivalent patterns of relationships between personal values and RTC across samples extend the nomological net of the construct and provide further evidence that dispositional resistance to change holds equivalent meanings across nations.

Measurement equivalence of the dispositional resistance to change scale

Intended to bridge the gap between the latest methodological developments and cross-cultural research, this interdisciplinary resource presents the latest strategies for analyzing cross-cultural data. Techniques are demonstrated through the use of applications that employ cross national data sets such as the latest European Social Survey. With an emphasis on the generalized latent variable approach, internationally?prominent researchers from a variety of fields explain how the methods work, how to apply them, and how they relate to other methods presented in the book. Syntax and graphical and verbal explanations of the techniques are included. [from publisher's website]

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Start Over and Survive : A Brief Intervention For Substance Abuse in Early Psychosis

Over the last decade, brief intervention for alcohol problems has become a well-validated and accepted treatment, with bried interventions frequently showing equivalence in terms of outcome to more extended treatments (Bien et al, 1993). A recent review of this studies found that heavy drinkers who received interventions of less than 1 h were almost twice as likely to moderate their drinking over the following 6-12 months as did those not receiving intervention (Wilk etal, 1997).Some studies have used motivational interviewing (MI) strategies (Monti et al, 1999); others have simply given information ajnd advice to reduce drinking (Fleming et al, 1997). Leaflets or information on strategies to assist in the attempt or follow-up sessions are sometimes provided (Fleming et al, 1997). In general practice research, provision of one or more follow-up sessions increases the reliability of intake reductions across studies (Poikolainen, 1999).

Social effects on coworker reliance and individual contributions to intercultural teams

Which social perceptions and structures shape coworker reliance and contributions to team products? When people form an intercultural team, they launch a set of working relationships that may be affected by social perceptions and social structures. Social perceptions include beliefs about interpersonal similarity and also expectations of behavior based on professional and national memberships. Social structures include dyadic relationships and the patterns they form. In this study, graduate students from three cohorts were consistently more likely to rely on others with whom they had a professional relationship, while structural equivalence in the professional network had no effect. In only one of the cohorts, people were more likely to rely on others who were professionally similar to themselves. Expectations regarding professional or national groups had no effect on willingness to rely on members of those groups, but expectations regarding teammates' nations positively influenced individual contributions. Willingness to rely on one's teammates did not significantly influence individual contributions to the team. Number of professional ties to teammates increased individual contributions, and number of external ties decreased contributions. Finally, people whose professional networks included a mixture of brokerage and closure (higher ego network variance) made greater contributions to their teams.