Teaching and cognitive outcomes in A-levels and Advanced GNVQ's: Case studies from Science and Business Studies Classrooms

The purpose of the paper is to demonstrate how a research diary methodology, designed to analyse A-level and GNVQ classrooms, can be a powerful tool for examining pedagogy and quality of learning at the level of case study. Two subject areas, science and business studies, are presented as cases. Twelve teachers and thirty-four students were studied over a four-week period in May 1997 and contrasts were drawn between lessons from three A-level physics teachers/three Advanced GNVQ science teachers and two A-level business/economics teachers/four Advanced GNVQ business teachers. Lessons were analysed within a cognitive framework which distinguishes between conceptual and procedural learning and emphasizes the importance of metacognition and epistemological beliefs. Two dimensions of lessons were identified: pedagogical activities (e.g. teacher-led explanation, teacher-led guidance on a task, question/answer sessions, group discussions, working with IT) and cognitive outcomes (e.g. structuring and memorizing facts, understanding concepts and arguments, critical thinking, problem-solving, learning core skills, identifying values). Immediately after each lesson, teachers and students (three per class) completed structured research diaries with respect to the above dimensions. Data from the diaries reveal general and unique features of the lessons. Time-ofyear effects were evident (examinations pending in May), particularly in A-level classrooms. Students in business studies classes reported a wider range of learning activities and greater variety in cognitive outcomes than did students in science classes. Science students self-rating of their ability to manage and direct their own learning was generally low. The phenomenological aspects of the classrooms were consistently linked to teachers' lesson plans and what their teaching objectives were for those particular students at that particular time of the year.

The role of advanced glycation end products in retinal microvascular leukostasis

PURPOSE: A critical event in the pathogenesis of diabetic retinopathy is the inappropriate adherence of leukocytes to the retinal capillaries. Advanced glycation end-products (AGEs) are known to play a role in chronic inflammatory processes, and the authors postulated that these adducts may play a role in promoting pathogenic increases in proinflammatory pathways within the retinal microvasculature. METHODS: Retinal microvascular endothelial cells (RMECs) were treated with glycoaldehyde-modified albumin (AGE-Alb) or unmodified albumin (Alb). NFkappaB DNA binding was measured by electromobility shift assay (EMSA) and quantified with an ELISA: In addition, the effect of AGEs on leukocyte adhesion to endothelial cell monolayers was investigated. Further studies were performed in an attempt to confirm that this was AGE-induced adhesion by co-incubation of AGE-treated cells with soluble receptor for AGE (sRAGE). Parallel in vivo studies of nondiabetic mice assessed the effect of intraperitoneal delivery of AGE-Alb on ICAM-1 mRNA expression, NFkappaB DNA-binding activity, leukostasis, and blood-retinal barrier breakdown. RESULTS: Treatment with AGE-Alb significantly enhanced the DNA-binding activity of NFkappaB (P = 0.0045) in retinal endothelial cells (RMECs) and increased the adhesion of leukocytes to RMEC monolayers (P = 0.04). The latter was significantly reduced by co-incubation with sRAGE (P <0.01). Mice infused with AGE-Alb demonstrated a 1.8-fold increase in ICAM-1 mRNA when compared with control animals (P <0.001, n = 20) as early as 48 hours, and this response remained for 7 days of treatment. Quantification of retinal NFkappaB demonstrated a threefold increase with AGE-Alb infusion in comparison to control levels (AGE Alb versus Alb, 0.23 vs. 0.076, P <0.001, n = 10 mice). AGE-Alb treatment of mice also caused a significant increase in leukostasis in the retina (AGE-Alb versus Alb, 6.89 vs. 2.53, n = 12, P <0.05) and a statistically significant increase in breakdown of the blood-retinal barrier (AGE Alb versus Alb, 8.2 vs. 1.6 n = 10, P <0.001). CONCLUSIONS: AGEs caused upregulation of NFkappaB in the retinal microvascular endothelium and an AGE-specific increase in leukocyte adhesion in vitro was also observed. In addition, increased leukocyte adherence in vivo was demonstrated that was accompanied by blood-retinal barrier dysfunction. These findings add further evidence to the thinking that AGEs may play an important role in the pathogenesis of diabetic retinopathy.

Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

Measuring critical thinking skills and dispositions in undergraduate students

This thesis investigates critical thinking with a particular focus on measurement in undergraduate students. A higher education context was chosen because many regard critical thinking development as a primary goal for third level education. Nine studies, both cross-sectional and longitudinal in design, were conducted with undergraduate psychology students (N=387), using the California Critical Thinking Disposition Inventory (CCTDI) and the California Critical Thinking Skills Test (CCTST). Studies 1-3 revealed psychometric weaknesses in the CCTDI and revised the scale with factor analysis and reliability analysis to form the CCTDI United Kingdom revision (CCTDI-UK). Study 4 investigated convergent validity and showed significant inter-correlation between the sub-scales of the CCTDI-UK, and significant correlations with the Openness scale of the NEO Personality Inventory (NEO PI-R). The study also provided evidence for improvement in scores on three of the six sub-scales in the CCTDI-UK (Truth-Seeking, Inquisitiveness, Open-Mindedness) during the course of an undergraduate degree. Study 5 explored a two factor structure for critical thinking dispositions. Study 6 used reliability analysis to revise the CCTST to produce the CCTST-UK. Study 7 showed that the CCTST-UK had a moderate correlation with degree attainment and a slightly higher correlation with a test of non-verbal intelligence (Raven’s Advanced Progressive Matrices short form); in addition, the study showed that scores on the CCTST-UK improved during the course of the degree. Studies 8 and 9 investigated the potential of critical thinking for predicting degree attainment. A-levels predicted approximately 10% of the variance of degree attainment while entry level scores on the CCTST-UK predicted an additional 5%. Exit level scores on the CCTST-UK and the Inquisitive sub-scale of the CCTDI-UK were found to be predictors of degree attainment The main conclusions of the thesis were that these tests had significant potential for predicting degree attainment and that they measured a substantial proportion of the theoretical constructs identified by the major authors in critical thinking.

Mathematical modeling and simulation of heat flow through pultrusion die assembly system for thermoset composites

Pultrusion is an industrial process used to produce glass fibers reinforced polymers profiles. These materials are worldwide used when performing characteristics, such as great electrical and magnetic insulation, high strength to weight ratio, corrosion and weather resistance, long service life and minimal maintenance are required. In this study, we present the results of the modelling and simulation of heat flow through a pultrusion die by means of Finite Element Analysis (FEA). The numerical simulation was calibrated based on temperature profiles computed from thermographic measurements carried out during pultrusion manufacturing process. Obtained results have shown a maximum deviation of 7%, which is considered to be acceptable for this type of analysis, and is below to the 10% value, previously specified as maximum deviation. © 2011, Advanced Engineering Solutions.

Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

Past, present and future mathematical models for buildings (ii)

This article is the second part of a review of the historical evolution of mathematical models applied in the development of building technology. The first part described the current state of the art and contrasted various models with regard to the applications to conventional buildings and intelligent buildings. It concluded that mathematical techniques adopted in neural networks, expert systems, fuzzy logic and genetic models, that can be used to address model uncertainty, are well suited for modelling intelligent buildings. Despite the progress, the possible future development of intelligent buildings based on the current trends implies some potential limitations of these models. This paper attempts to uncover the fundamental limitations inherent in these models and provides some insights into future modelling directions, with special focus on the techniques of semiotics and chaos. Finally, by demonstrating an example of an intelligent building system with the mathematical models that have been developed for such a system, this review addresses the influences of mathematical models as a potential aid in developing intelligent buildings and perhaps even more advanced buildings for the future.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

Alumina porous ceramics: mathematical behavior at different commercial starch concentration

Several researches have been developed in order to verify the porosity effect over the ceramic material properties. The starch consolidation casting (SCC) allows to obtain porous ceramics by using starch as a binder and pore forming element. This work is intended to describe the porous mathematical behavior and the mechanical resistance at different commercial starch concentration. Ceramic samples were made with alumina and potato and corn starches. The slips were prepared with 10 to 50 wt% of starch. The specimens were characterized by apparent density measurements and three-point flexural test associated to Weibull statistics. Results indicated that the porosity showed a first-order exponential equation e(-x/c) increasing in both kinds of starches, so it was confirmed that the alumina ceramic porosity is related to the kind of starch used. The mechanical resistance is represented by a logarithmic expression R = A + B/1+10((Log(x0)-P)C).

Theoretical approaches to forensic entomology: II. Mathematical model of larval development

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Theoretical approaches to forensic entomology: I. Mathematical model of postfeeding larval dispersal

An overall theoretical approach to model phenomena of interest for forensic entomology is advanced. Efforts are concentrated in identifying biological attributes at the individual, population and community of the arthropod fauna associated with decomposing human corpses and then incorporating these attributes into mathematical models. In particular in this paper a diffusion model of dispersal of post feeding larvae is described for blowflies, which are the most common insects associated with corpses.

Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.

Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.