Behavior and interactions of children in cooperative groups in lower and middle elementary grades

The study investigated the behaviors and interactions of children in structured and unstructured groups as they worked together on a 6-week social studies activity each term for 3 school terms. Two hundred and twelve children in Grade 1 and 184 children in Grade 3 participated in the study. Stratified random assignment occurred so that each gender-balanced group consisted of 1 high-, 2 medium-, and 1 low-ability student. The results show that the children in the structured groups were consistently more cooperative and they provided more elaborated and nonelaborated help than did their peers in the unstructured groups. The children in the structured groups in Grade 3 obtained higher reading and learning outcome scores than their peers in the unstructured groups.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

Cue competition between elementary trained stimuli: US miscuing, interference, and US omission

The present series of experiments was designed to assess whether rule-based accounts of Pavlovian learning can account for cue competition effects observed after elemental training. All experiments involved initial differential conditioning training with A-US and B alone presentations. Miscuing refers to the fact that responding to A is impaired after one B-US presentation whereas interference is the impairment of responding to A after presentation of C-US pairings. Omission refers to the effects on B of A alone presentations. Experiments 1-2a provided clear evidence for miscuing whereas interference was not found after 1, 5 or 10 C-US pairings. Moreover, Experiments 3 and 3a found only weak evidence for interference in an A-US, B I C-US, D I A design used previously to show the effect. Experiments 4 and 5 failed to find any effect of US omission after one or five omission trials. The present results indicate that miscuing is more robust than is the interference effect. Moreover, the asymmetrical effects of US miscuing and US omission are difficult to accommodate within rule-based accounts of Pavlovian conditioning. (C) 2002 Elsevier Science (USA). All rights reserved.

Ten Australian elementary teachers' discourse and reported pedagogical practices during cooperative learning

This article describes the types of discourse 10 Australian grade 4-6 teachers used after they had been trained to embed cooperative learning in their curriculum and to use communication skills to promote students' thinking and to scaffold their learning. One audiotaped classroom social science lesson involving cooperative learning was analyzed for each teacher. We provide vignettes from 2 teachers as they worked with groups and from 2 student groups. The data from the audiotapes showed that the teachers used a range of mediated-learning behaviors in their interactions with the children that included challenging their perspectives, asking more cognitive and metacognitive questions, and scaffolding their learning. In turn, in their interactions with each other, the children modelled many of the types of discourse they heard their teachers use. Follow-up interviews with the teachers revealed that they believed it was important to set expectations for children's group behaviors, teach the social skills students needed to deal with disagreement in groups, and establish group structures so children understood what was required both from each other and the task. The teachers reported that mixed ability and gender groups worked best and that groups should be no larger than 5 students. All teachers' programs were based on a child-centered philosophy that recognized the importance of constructivist approaches to learning and the key role interaction plays in promoting social reasoning and learning.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

Quantum spin ladder systems associated with su(2 vertical bar 2)

Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2 \2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

The Saskatchewan Pediatric Bone Mineral Accrual Study: Bone mineral acquisition during the growing years

To investigate bone mineral accretion in growing children, the Saskatchewan Pediatric Bone Mineral Accrual Study was initiated in 1991. The study involves the collection of dietary and physical activity information along with anthropometric growth and maturity measurements every 6 months and dual-energy X-ray absorptiometer (DXA) bone scans of the whole body, AP lumbar spine and proximal femur taken annually, The study has now finished its 6th year and 68 males and 72 females from an original sample of 228 elementary schoolchildren are still involved, To investigate how bone mineral at clinically important sites proceeds in relation to maturation we developed distance and velocity growth curves for height and bone mineral content (BMC) for the AP lumbar spine, the femoral neck and the whole body, In both boys and girls, over 35% of total body and AP spine bone mineral and over 27% of the bone mineral at the femoral neck was laid down during the 4-year adolescent period surrounding peak linear growth velocity. The clinical significance of these values can be appreciated by consideration of the fact that as much bone mineral will be laid down during these 4 adolescent growing years as most people will lose during all of adult life.

Children's cooperative behavior and interactions in trained and untrained work groups in regular classrooms

This study examined group and individual factors that facilitate changes in cooperation and learning outcomes in trained and untrained work groups of elementary school-age children. The study had two foci. The first was to determine if the cooperative behaviors and interactions of children in classroom groups who were trained in cooperative learning skins were different from those of children who were given no training, and the second was to investigate small group interactions and achievement in these groups over time. The results showed that there were observable differences between student interactions in the two conditions and these differences were maintained over time. Compared with children in the untrained groups, those in the trained groups were consistently more cooperative and helpful to each other; they actively tried to involve each other in the learning task by using language which was more inclusive (e.g., frequent use of ''we''), and they gave more explanations to assist each other as they worked together. It appeared that as the children worked together over time, they became more responsive to the learning needs of each other. Furthermore, the children in the trained groups performed significantly better on the learning outcomes questionnaire than those in the untrained groups. (C) 1997 Society for the Study of School Psychology. Published by Elsevier Science Ltd.