Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

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.