Effect of boundary conditions and convection on thermally induced motion of beams subjected to internal heating

Numerical exercises are presented on the thermally induced motion of internally heated beams under various heat transfer and structural boundary conditions. The dynamic displacement and dynamic thermal moment of the beam are analyzed taking into consideration that the temperature gradient is independent as well as dependent on the beam displacement. The effect of length to thickness ratio of the beam on the thermally induced vibration is also investigated. The type of boundary conditions has its influence on the magnitude of dynamic displacement and dynamic thermal moment. A sustained thermally induced motion is observed with progress of time when the temperature gradient being evaluated is dependent on the forced convection generated due to beam motion. A finite element method (FEM) is used to solve the structural equation of motion as well as the heat transfer equation.     

Models and Paradigms in Kuhn and Halloun

In Modeling Theory in Science Education, Halloun (2004) adopts the word ‘paradigm’, but his use of the term is radically different from that of Kuhn. In this paper, I explore some of the differences between Kuhn’s paradigms and Halloun’s paradigms. Where Kuhn’s paradigms are public, community-defining exemplars of practice, Halloun’s paradigms are private, individualized ways of thinking. Where Kuhn writes of the paradigm shift as a revolutionary, vision-altering conversion experience, Halloun writes of a gradual evolution from one way of thinking to another and an easy back-and-forth switch between paradigms. Since Kuhn’s paradigms are self-enclosed and incommensurable, there is no objective standard by which one paradigm can be shown to be superior to the other. But Halloun uses ‘viability’ as a standard for paradigm choice. Underlying all of this is the more basic question of whether the history of science is an appropriate metaphor for student progress in the classroom. I conclude with some brief thoughts on this question.     

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.     

6- and 8-year-olds’ performance evaluations: Do they differ between self and unknown others?

The current study investigated kindergarteners and second graders’ ability to monitor and evaluate their own and a virtual peer’s performance in a paired-associate learning task. Participants provided confidence judgments (CJs) for their own responses and performance-based judgments (judgments provided after receiving feedback on their performance) for both their own and a virtual peer’s responses. For the performance-based judgments, children were confronted with their own or the peer’s answer as well as the correct answer. Additionally, participants were asked to credit their own and the peer’s correct and incorrect answers while facing feedback. Results indicate an age-related progression in metacognitive monitoring skills, with second graders differentiating more strongly in their confidence judgments between correct and incorrect responses compared to kindergarteners. Regarding performance-based judgments, children of both age groups provided higher judgments for correctly compared to incorrectly recognized items as well as for their own responses in comparison to the responses of the unknown child. Similarly, when crediting, participants of both age groups gave more credits for correct recognition than for incorrect recognition and for their own responses than for the peer’s responses. The significant interaction between age group and recognition accuracy for the crediting shows that second graders gave more credits for correctly recognized items while kindergarteners gave more credits for incorrect answers than the older children – primarily for their own incorrect answers. In conclusion, the study provides new insights into 6- and 8-year-olds’ evaluations of their own and an unknown child’s performance in a paired-associate learning task by showing that children of both age groups generally judged and credited responses in their own favor. These results add to our understanding of biases in children’s performance evaluations, including metacognitive judgments and judgments provided after receiving feedback.     

e-Trust and reputation

Trust online can be a hazardous affair; many are trustworthy, but some people use the anonymity of the web to behave very badly indeed. So how can we improve the quality of evidence for trustworthiness provided online? I focus on one of the devices we use to secure others’ trustworthiness: tracking past conduct through online reputation systems. Yet existing reputation systems face problems. I analyse these, and in the light of this develop some principles for system design, towards overcoming these challenges. In providing better evidence for trustworthiness online, so we can also encourage people actually to be trustworthy more often, which is an ethically welcome outcome.     

Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.