An Examination of the Genesis, Maintenance, and Manifestation of the Pedagogical Beliefs of a Novel Instructor - A Case Study

The great preponderance of research in undergraduate mathematics, especially as it pertains to students transitioning into post-secondary education, tends to problematize the student or the difference in the educational environment. What appears to be lacking, however, is research into the ways that the instructor may be exacerbating this transition. Fundamental to the concerns of the quality and appropriateness of contemporary post-secondary mathematics instruction is the ability to envision alternatives to traditional approaches. This case study identified one individual, whose practice fell well beyond the norms at the institution in which they found employment and explored how they developed their teacher-identity, how they maintained that teacher-identity as they entered into their department and the profession in general, and how they have engaged in praxis. Data collected included interviews, course observations, and course document analysis. Analysis of these data revealed that a number of personal and/or professional crises prompted the evolution of the participant's teacher- and researcher-identity and these evolutions resulted in the need to reimagine the enactment of his affordances regarding teaching, resulting in an envisioning of his praxis as an interrelated system of praxis as an application of the creative process and praxis as an application of mathematical problem solving

Productive Failures: From Class Requirement to Fostering a Support Group

Mistakes occur frequently in mathematics. Reframing mistakes into positive moments can be psychologically important in a student’s educational journey. We investigated two tertiary math classes that explicitly valued mistakes through a pedagogical requirement called “productive failure”. For a percentage of their grade, students demonstrated how they made mistakes in their problem solving and, most importantly, how they overcame those mistakes. Through interviews, video-stimulated recalls, and evaluations of the course all from students, we initially looked for affectual responses to the pedagogical allowance and student-led demonstration. Many of the responses, both benefits and drawbacks of the productive failure, were interpreted by the research group to resemble the psychology literature on peer-led support groups. Descriptions of both productive failure and support groups, as well as quotes from the students, aim to shed light on psychological benefits of valuing mistakes. Finally, we believe that productive failures benefitted many students because it made the human aspect of mathematics more explicit

The trend of disruption in the functional brain network topology of Alzheimer’s disease

Alzheimer’s disease (AD) is a progressive disorder associated with cognitive dysfunction that alters the brain’s functional connectivity. Assessing these alterations has become a topic of increasing interest. However, a few studies have examined different stages of AD from a complex network perspective that cover different topological scales. This study used resting state fMRI data to analyze the trend of functional connectivity alterations from a cognitively normal (CN) state through early and late mild cognitive impairment (EMCI and LMCI) and to Alzheimer’s disease. The analyses had been done at the local (hubs and activated links and areas), meso (clustering, assortativity, and rich-club), and global (small-world, small-worldness, and efficiency) topological scales. The results showed that the trends of changes in the topological architecture of the functional brain network were not entirely proportional to the AD progression. There were network characteristics that have changed non-linearly regarding the disease progression, especially at the earliest stage of the disease, i.e., EMCI. Further, it has been indicated that the diseased groups engaged somatomotor, frontoparietal, and default mode modules compared to the CN group. The diseased groups also shifted the functional network towards more random architecture. In the end, the methods introduced in this paper enable us to gain an extensive understanding of the pathological changes of the AD process

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Forecasting: theory and practice

peer reviewedForecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Quantitative 18F-AV1451 Brain Tau PET Imaging in Cognitively Normal Older Adults, Mild Cognitive Impairment, and Alzheimer's Disease Patients

Recent developments of tau Positron Emission Tomography (PET) allows assessment of regional neurofibrillary tangles (NFTs) deposition in human brain. Among the tau PET molecular probes, 18F-AV1451 is characterized by high selectivity for pathologic tau aggregates over amyloid plaques, limited non-specific binding in white and gray matter, and confined off-target binding. The objectives of the study are (1) to quantitatively characterize regional brain tau deposition measured by 18F-AV1451 PET in cognitively normal older adults (CN), mild cognitive impairment (MCI), and AD participants; (2) to evaluate the correlations between cerebrospinal fluid (CSF) biomarkers or Mini-Mental State Examination (MMSE) and 18F-AV1451 PET standardized uptake value ratio (SUVR); and (3) to evaluate the partial volume effects on 18F-AV1451 brain uptake.Methods: The study included total 115 participants (CN = 49, MCI = 58, and AD = 8) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Preprocessed 18F-AV1451 PET images, structural MRIs, and demographic and clinical assessments were downloaded from the ADNI database. A reblurred Van Cittertiteration method was used for voxelwise partial volume correction (PVC) on PET images. Structural MRIs were used for PET spatial normalization and region of interest (ROI) definition in standard space. The parametric images of 18F-AV1451 SUVR relative to cerebellum were calculated. The ROI SUVR measurements from PVC and non-PVC SUVR images were compared. The correlation between ROI 18F-AV1451 SUVR and the measurements of MMSE, CSF total tau (t-tau), and phosphorylated tau (p-tau) were also assessed.Results:18F-AV1451 prominently specific binding was found in the amygdala, entorhinal cortex, parahippocampus, fusiform, posterior cingulate, temporal, parietal, and frontal brain regions. Most regional SUVRs showed significantly higher uptake of 18F-AV1451 in AD than MCI and CN participants. SUVRs of small regions like amygdala, entorhinal cortex and parahippocampus were statistically improved by PVC in all groups (p < 0.01). Although there was an increasing tendency of 18F-AV-1451 SUVRs in MCI group compared with CN group, no significant difference of 18F-AV1451 deposition was found between CN and MCI brains with or without PVC (p > 0.05). Declined MMSE score was observed with increasing 18F-AV1451 binding in amygdala, entorhinal cortex, parahippocampus, and fusiform. CSF p-tau was positively correlated with 18F-AV1451 deposition. PVC improved the results of 18F-AV-1451 tau deposition and correlation studies in small brain regions.Conclusion: The typical deposition of 18F-AV1451 tau PET imaging in AD brain was found in amygdala, entorhinal cortex, fusiform and parahippocampus, and these regions were strongly associated with cognitive impairment and CSF biomarkers. Although more deposition was observed in MCI group, the 18F-AV-1451 PET imaging could not differentiate the MCI patients from CN population. More tau deposition related to decreased MMSE score and increased level of CSF p-tau, especially in ROIs of amygdala, entorhinal cortex and parahippocampus. PVC did improve the results of tau deposition and correlation studies in small brain regions and suggest to be routinely used in 18F-AV1451 tau PET quantification

Conversion Discriminative Analysis on Mild Cognitive Impairment Using Multiple Cortical Features from MR Images

Neuroimaging measurements derived from magnetic resonance imaging provide important information required for detecting changes related to the progression of mild cognitive impairment (MCI). Cortical features and changes play a crucial role in revealing unique anatomical patterns of brain regions, and further differentiate MCI patients from normal states. Four cortical features, namely, gray matter volume, cortical thickness, surface area, and mean curvature, were explored for discriminative analysis among three groups including the stable MCI (sMCI), the converted MCI (cMCI), and the normal control (NC) groups. In this study, 158 subjects (72 NC, 46 sMCI, and 40 cMCI) were selected from the Alzheimer's Disease Neuroimaging Initiative. A sparse-constrained regression model based on the l2-1-norm was introduced to reduce the feature dimensionality and retrieve essential features for the discrimination of the three groups by using a support vector machine (SVM). An optimized strategy of feature addition based on the weight of each feature was adopted for the SVM classifier in order to achieve the best classification performance. The baseline cortical features combined with the longitudinal measurements for 2 years of follow-up data yielded prominent classification results. In particular, the cortical thickness produced a classification with 98.84% accuracy, 97.5% sensitivity, and 100% specificity for the sMCI–cMCI comparison; 92.37% accuracy, 84.78% sensitivity, and 97.22% specificity for the cMCI–NC comparison; and 93.75% accuracy, 92.5% sensitivity, and 94.44% specificity for the sMCI–NC comparison. The best performances obtained by the SVM classifier using the essential features were 5–40% more than those using all of the retained features. The feasibility of the cortical features for the recognition of anatomical patterns was certified; thus, the proposed method has the potential to improve the clinical diagnosis of sub-types of MCI and predict the risk of its conversion to Alzheimer's disease

Early role of vascular dysregulation on late-onset Alzheimer's disease based on multifactorial data-driven analysis

Multifactorial mechanisms underlying late-onset Alzheimer's disease (LOAD) are poorly characterized from an integrative perspective. Here spatiotemporal alterations in brain amyloid-β deposition, metabolism, vascular, functional activity at rest, structural properties, cognitive integrity and peripheral proteins levels are characterized in relation to LOAD progression. We analyse over 7,700 brain images and tens of plasma and cerebrospinal fluid biomarkers from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Through a multifactorial data-driven analysis, we obtain dynamic LOAD–abnormality indices for all biomarkers, and a tentative temporal ordering of disease progression. Imaging results suggest that intra-brain vascular dysregulation is an early pathological event during disease development. Cognitive decline is noticeable from initial LOAD stages, suggesting early memory deficit associated with the primary disease factors. High abnormality levels are also observed for specific proteins associated with the vascular system's integrity. Although still subjected to the sensitivity of the algorithms and biomarkers employed, our results might contribute to the development of preventive therapeutic interventions

Global variation in subjective well-being predicts seven forms of altruism

The geographic prevalence of various altruistic behaviors (non-reciprocal acts that improve others' welfare) is non-uniformly distributed. But whether this reflects variation in a superordinate construct linked to national-level outcomes or cultural values is unknown. We compiled data on seven altruistic behaviors across 48-152 nations, and found evidence that these behaviors reflect a latent construct positively associated with national-level subjective well-being (SWB) and individualist values, even controlling for national-level wealth, health, education, and shared cultural history. Consistent with prior work, we found that SWB mediates the relationship between two objective measures of well-being (wealth and health) and altruism (N=130). Moreover, these indirect effects increase as individualist values increase within the subset of countries (N=90) with available data. Together, results indicate that altruism increases when resources and cultural values provide objective and subjective means for pursuing personally meaningful goals, and that altruistic behaviors may be enhanced by societal changes that promote well-being