Exploring the potential of knowledge engineering and hypercard for enhancing teaching and learning in mathematics.

This study adapted the knowledge engineering process from expert systems research and used it to acquire the combined knowledge of a mathematics student and a mathematics teacher. The knowledge base acquired was used to inform the design of a hypercard learning environment dealing with linear and quadratic functions. The researcher, who is also a mathematics teacher, acted as both knowledge engineer and expert. In the role of knowledge engineer, she conducted sixteen sessions with a student-expert. The purpose of the knowledge engineering sessions was to acquire an explicit representation of the student\u27s expertise. The student\u27s expertise was her view of mathematical concepts as she understood them. The teacher also made explicit her understanding of the same mathematical concepts discussed by the student. A graphical representation of the knowledge of both student and teacher was developed. This knowledge base informed the design of a hypercard learning environment on functions. Three major implications for teaching and learning emerged from the research. First, the teacher as knowledge engineer is a compelling new way to conceptualize the teacher\u27s role. In the role of knowledge engineer, the teacher develops an understanding of the student\u27s knowledge base which can inform curriculum. Second, recognizing the student as expert allows the student to be a more active participant in the learning process. Finally, hypercard is an appropriate and promising application for the development of knowledge based systems which will encourage the active participation of teachers and students in the development of curriculum

Unsupervised Deep Single-Image Intrinsic Decomposition using Illumination-Varying Image Sequences

Machine learning based Single Image Intrinsic Decomposition (SIID) methods decompose a captured scene into its albedo and shading images by using the knowledge of a large set of known and realistic ground truth decompositions. Collecting and annotating such a dataset is an approach that cannot scale to sufficient variety and realism. We free ourselves from this limitation by training on unannotated images. Our method leverages the observation that two images of the same scene but with different lighting provide useful information on their intrinsic properties: by definition, albedo is invariant to lighting conditions, and cross-combining the estimated albedo of a first image with the estimated shading of a second one should lead back to the second one's input image. We transcribe this relationship into a siamese training scheme for a deep convolutional neural network that decomposes a single image into albedo and shading. The siamese setting allows us to introduce a new loss function including such cross-combinations, and to train solely on (time-lapse) images, discarding the need for any ground truth annotations. As a result, our method has the good properties of i) taking advantage of the time-varying information of image sequences in the (pre-computed) training step, ii) not requiring ground truth data to train on, and iii) being able to decompose single images of unseen scenes at runtime. To demonstrate and evaluate our work, we additionally propose a new rendered dataset containing illumination-varying scenes and a set of quantitative metrics to evaluate SIID algorithms. Despite its unsupervised nature, our results compete with state of the art methods, including supervised and non data-driven methods.Comment: To appear in Pacific Graphics 201

The Mastery Rubric for Statistics and Data Science: promoting coherence and consistency in data science education and training

Consensus based publications of both competencies and undergraduate curriculum guidance documents targeting data science instruction for higher education have recently been published. Recommendations for curriculum features from diverse sources may not result in consistent training across programs. A Mastery Rubric was developed that prioritizes the promotion and documentation of formal growth as well as the development of independence needed for the 13 requisite knowledge, skills, and abilities for professional practice in statistics and data science, SDS. The Mastery Rubric, MR, driven curriculum can emphasize computation, statistics, or a third discipline in which the other would be deployed or, all three can be featured. The MR SDS supports each of these program structures while promoting consistency with international, consensus based, curricular recommendations for statistics and data science, and allows 'statistics', 'data science', and 'statistics and data science' curricula to consistently educate students with a focus on increasing learners independence. The Mastery Rubric construct integrates findings from the learning sciences, cognitive and educational psychology, to support teachers and students through the learning enterprise. The MR SDS will support higher education as well as the interests of business, government, and academic work force development, bringing a consistent framework to address challenges that exist for a domain that is claimed to be both an independent discipline and part of other disciplines, including computer science, engineering, and statistics. The MR-SDS can be used for development or revision of an evaluable curriculum that will reliably support the preparation of early e.g., undergraduate degree programs, middle e.g., upskilling and training programs, and late e.g., doctoral level training practitioners.Comment: 40 pages; 2 Tables; 4 Figures. Presented at the Symposium on Data Science & Statistics (SDSS) 202

Seidel elements and mirror transformations

The goal of this article is to give a precise relation between the mirror symmetry transformation of Givental and the Seidel elements for a smooth projective toric variety $X$ with $-K_X$ nef. We show that the Seidel elements entirely determine the mirror transformation and mirror coordinates.Comment: 36 pages. We corrected several issues as pointed out by the refere

Are we really that different from each other? The difficulties of focusing on similarities in cross-cultural research.

In this article we argue that there are 2 dominant underlying themes in discussions of strategies for dealing with diversity—similarity and difference. When we are dealing with social groups, a number of basic psychological processes, as well as popular media and research-based narratives, make it easier to highlight difference rather than similarity. This difference-based approach in research is inherently divisive, but the training that we receive as researchers in the field of psychology has taken us down this path. As a first step, we propose that researchers working in the area of cultural diversity should start making explicit attempts to highlight similarities between groups, even if such similarities are only based on the absence of observed statistical differences. Moreover, if we are going to be serious about demonstrating similarity between groups and certain types of universals in behavior, we should start embracing new approaches to data analyses and consider using statistical procedures that test for equivalence. We illustrate these new techniques using our own data. Finally, we argue that shifting our primary focus from difference to similarity is a worthwhile direction to pursue for successfully managing diversity in multicultural societies.Social Sciences and Humanities Research Council (SSHRC

An X-Ray Spectral Classification Algorithm with Application to Young Stellar Clusters

A large volume of low signal-to-noise, multidimensional data is available from the CCD imaging spectrometers aboard the Chandra X-Ray Observatory and the X-Ray Multimirror Mission (XMM-Newton). To make progress analyzing this data,itisessentialtodevelopmethods tosort,classify,and characterize thevastlibrary of X-rayspectrain a nonparametric fashion (complementary to current parametric model fits). We have developed a spectral classification algorithm that handles large volumes of data and operates independently of the requirement of spectral model fits.Weuseprovenmultivariatestatisticaltechniquesincludingprincipalcomponentanalysisandanensembleclassifier consistingofagglomerativehierarchicalclusteringandK-meansclusteringappliedforthefirsttimeforspectralclassification.Thealgorithmpositionsthesourcesinamultidimensionalspectralsequenceandthengroupstheorderedsources into clusters based on their spectra. These clusters appear more distinct for sources with harder observed spectra. The apparent diversity ofsource spectra isreduced toa three-dimensional locus inprincipal component space,withspectral outliers falling outside this locus. The algorithm was applied to a sample of 444 strong sources selected from the 1616 X-ray emitting sources detected in deep Chandra imaging spectroscopy of the Orion Nebula Cluster. Classes form sequencesinNH,AV,andaccretionactivityindicators,demonstratingthatthealgorithmefficientlysortstheX-raysources into a physically meaningful sequence. The algorithm also isolates important classes of very deeply embedded, active young stellar objects, and yields trends between X-ray spectral parameters and stellar parameters for the lowest mass, pre‐main-sequence stars