Meta-analysis was used to investigate the relationship between visuo-spatial ability and performance in remote environments. In order to be included, each study needed to examine the relationship between the use of an ego-centric perspective and various dimensions of performance (i.e., identification, localization, navigation, and mission completion time). The moderator analysis investigated relationships involving: (a) visuo-spatial construct with an emphasis on Carroll’s (1993) visualization (VZ) factor; (b) performance outcome (i.e., identification, localization, navigation, and mission completion time); (c) autonomy to support mission performance; (d) task type (i.e., navigation vs. reconnaissance); and (e) experimental testbed (i.e., physical vs. virtual environments). The process of searching and screening for published and unpublished analyses identified 81 works of interest that were found to represent 50 unique datasets. 518 effects were extracted from these datasets for analyses. Analyses of aggregated effects (Hunter & Schmidt, 2004) found that visuo-spatial abilities were significantly associated with each construct, such that effect sizes ranged from weak (r = .235) to moderately strong (r = .371). For meta-regression (Borenstein, Hedges, Figgins, & Rothstein, 2009; Kalaian & Raudenbush, 1996; Tabachnick & Fidell, 2007), moderation by visuo-spatial construct (i.e., focusing on visualization) was consistently supported for all outcomes. For at least one of the outcomes, support was found for moderation by test, the reliability coefficient of a test, autonomy (i.e. to support identification, localization, and navigation), testbed (i.e., physical vs. virtual environment), intended domain of application, and gender. These findings illustrate that majority of what researchers refer to as “spatial ability” actually uses measures that load onto Carroll’s (1993) visualization (VZ) factor. The associations between this predictor and all performance outcomes were significant, but the significant iv variation across moderators highlight important issues for the design of unmanned systems and the external validity of findings across domains. For example, higher levels of autonomy for supporting navigation decreased the association between visualization (VZ) and performance. In contrast, higher levels of autonomy for supporting identification and localization increased the association between visualization (VZ) and performance. Furthermore, moderation by testbed, intended domain of application, and gender challenged the degree to which findings can be expected to generalize across domains and sets of participants.

Mit der wachsenden Verbreitung empirischer Schulleistungsleistungen im Large-Scale Assessment gehen eine Reihe methodischer Herausforderungen einher. Die vorliegende Arbeit untersucht, welche Konsequenzen Modellverletzungen in eindimensionalen Item-Response-Modellen (besonders im Rasch-Modell) besitzen. Insbesondere liegt der Fokus auf vier methodischen Herausforderungen von Modellverletzungen. Erstens, implizieren Positions- und Kontexteffekte, dass gegenüber einem eindimensionalen IRT-Modell Itemschwierigkeiten nicht unabhängig von der Position im Testheft und der Zusammenstellung des Testheftes ausgeprägt sind und Schülerfähigkeiten im Verlauf eines Tests variieren können. Zweitens, verursacht die Vorlage von Items innerhalb von Testlets lokale Abhängigkeiten, wobei unklar ist, ob und wie diese in der Skalierung berücksichtigt werden sollen. Drittens, können Itemschwierigkeiten aufgrund verschiedener Lerngelegenheiten zwischen Schulklassen variieren. Viertens, sind insbesondere in low stakes Tests nicht bearbeitete Items vorzufinden. In der Arbeit wird argumentiert, dass trotz Modellverletzungen nicht zwingend von verzerrten Schätzungen von Itemschwierigkeiten, Personenfähigkeiten und Reliabilitäten ausgegangen werden muss. Außerdem wird hervorgehoben, dass man psychometrisch häufig nicht entscheiden kann und entscheiden sollte, welches IRT-Modell vorzuziehen ist. Dies trifft auch auf die Fragestellung zu, wie nicht bearbeitete Items zu bewerten sind. Ausschließlich Validitätsüberlegungen können dafür Hinweise geben. Modellverletzungen in IRT-Modellen lassen sich konzeptuell plausibel in den Ansatz des Domain Samplings (Item Sampling; Generalisierbarkeitstheorie) einordnen. In dieser Arbeit wird gezeigt, dass die statistische Unsicherheit in der Modellierung von Kompetenzen nicht nur von der Stichprobe der Personen, sondern auch von der Stichprobe der Items und der Wahl statistischer Modelle verursacht wird. / Several methodological challenges emerge in large-scale student assessment studies like PISA and TIMSS. Item response models (IRT models) are essential for scaling student abilities within these studies. This thesis investigates the consequences of several model violations in unidimensional IRT models (especially in the Rasch model). In particular, this thesis focuses on the following four methodological challenges of model violations. First, position effects and contextual effects imply (in comparison to unidimensional IRT models) that item difficulties depend on the item position in a test booklet as well as on the composition of a test booklet. Furthermore, student abilities are allowed to vary among test positions. Second, the administration of items within testlets causes local dependencies, but it is unclear whether and how these dependencies should be taken into account for the scaling of student abilities. Third, item difficulties can vary among different school classes due to different opportunities to learn. Fourth, the amount of omitted items is in general non-negligible in low stakes tests. In this thesis it is argued that estimates of item difficulties, student abilities and reliabilities can be unbiased despite model violations. Furthermore, it is argued that the choice of an IRT model cannot and should not be made (solely) from a psychometric perspective. This also holds true for the problem of how to score omitted items. Only validity considerations provide reasons for choosing an adequate scoring procedure. Model violations in IRT models can be conceptually classified within the approach of domain sampling (item sampling; generalizability theory). In this approach, the existence of latent variables need not be posed. It is argued that statistical uncertainty in modelling competencies does not only depend on the sampling of persons, but also on the sampling of items and on the choice of statistical models.

Despite widespread recognition by science educators, researchers and K-12 frameworks that scientific inquiry should be an essential part of science education, typical classrooms and assessments still emphasize rote vocabulary, facts, and formulas. One of several reasons for this is that the rigorous assessment of complex inquiry skills is still in its infancy. Though progress has been made, there are still many challenges that hinder inquiry from being assessed in a meaningful, scalable, reliable and timely manner. To address some of these challenges and to realize the possibility of formative assessment of inquiry, we describe a novel approach for evaluating, tracking, and scaffolding inquiry process skills. These skills are demonstrated as students experiment with computer-based simulations. In this work, we focus on two skills related to data collection, designing controlled experiments and testing stated hypotheses. Central to this approach is the use and extension of techniques developed in the Intelligent Tutoring Systems and Educational Data Mining communities to handle the variety of ways in which students can demonstrate skills. To evaluate students' skills, we iteratively developed data-mined models (detectors) that can discern when students test their articulated hypotheses and design controlled experiments. To aggregate and track students' developing latent skill across activities, we use and extend the Bayesian Knowledge-Tracing framework (Corbett & Anderson, 1995). As part of this work, we directly address the scalability and reliability of these models' predictions because we tested how well they predict for student data not used to build them. When doing so, we found that these models demonstrate the potential to scale because they can correctly evaluate and track students' inquiry skills. The ability to evaluate students' inquiry also enables the system to provide automated, individualized feedback to students as they experiment. As part of this work, we also describe an approach to provide such scaffolding to students. We also tested the efficacy of these scaffolds by conducting a study to determine how scaffolding impacts acquisition and transfer of skill across science topics. When doing so, we found that students who received scaffolding versus students who did not were better able to acquire skills in the topic in which they practiced, and also transfer skills to a second topic when was scaffolding removed. Our overall findings suggest that computer-based simulations augmented with real-time feedback can be used to reliably measure the inquiry skills of interest and can help students learn how to demonstrate these skills. As such, our assessment approach and system as a whole shows promise as a way to formatively assess students' inquiry.

Despite widespread recognition by science educators, researchers and K-12 frameworks that scientific inquiry should be an essential part of science education, typical classrooms and assessments still emphasize rote vocabulary, facts, and formulas. One of several reasons for this is that the rigorous assessment of complex inquiry skills is still in its infancy. Though progress has been made, there are still many challenges that hinder inquiry from being assessed in a meaningful, scalable, reliable and timely manner. To address some of these challenges and to realize the possibility of formative assessment of inquiry, we describe a novel approach for evaluating, tracking, and scaffolding inquiry process skills. These skills are demonstrated as students experiment with computer-based simulations. In this work, we focus on two skills related to data collection, designing controlled experiments and testing stated hypotheses. Central to this approach is the use and extension of techniques developed in the Intelligent Tutoring Systems and Educational Data Mining communities to handle the variety of ways in which students can demonstrate skills. To evaluate students' skills, we iteratively developed data-mined models (detectors) that can discern when students test their articulated hypotheses and design controlled experiments. To aggregate and track students' developing latent skill across activities, we use and extend the Bayesian Knowledge-Tracing framework (Corbett & Anderson, 1995). As part of this work, we directly address the scalability and reliability of these models' predictions because we tested how well they predict for student data not used to build them. When doing so, we found that these models demonstrate the potential to scale because they can correctly evaluate and track students' inquiry skills. The ability to evaluate students' inquiry also enables the system to provide automated, individualized feedback to students as they experiment. As part of this work, we also describe an approach to provide such scaffolding to students. We also tested the efficacy of these scaffolds by conducting a study to determine how scaffolding impacts acquisition and transfer of skill across science topics. When doing so, we found that students who received scaffolding versus students who did not were better able to acquire skills in the topic in which they practiced, and also transfer skills to a second topic when was scaffolding removed. Our overall findings suggest that computer-based simulations augmented with real-time feedback can be used to reliably measure the inquiry skills of interest and can help students learn how to demonstrate these skills. As such, our assessment approach and system as a whole shows promise as a way to formatively assess students' inquiry.

<p dir="ltr">The generalization error of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higher-dimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected n-times and the best classifier among those n, based on its performance on training data, is chosen. </p><p dir="ltr">We show that this type of classifier is extremely flexible, as it is likely to approximate, to an arbitrary precision, any continuous function on a compact set as well as any Boolean function on a compact set that splits the support into measurable subsets. In particular, given full knowledge of the class conditional densities, the error of these low-complexity classifiers would converge to the optimal (Bayes) error as k and n go to infinity. On the other hand, if only a training dataset is given, we show that the classifiers will perfectly classify all the training points as k and n go to infinity. </p><p dir="ltr">We also bound the generalization error of our random classifiers. In general, our bounds are better than those for any classifier with VC dimension greater than O(ln(n)). In particular, our bounds imply that, unless the number of projections n is extremely large, there is a significant advantageous gap between the generalization error of the random projection approach and that of a linear classifier in the extended space. Asymptotically, as the number of samples approaches infinity, the gap persists for any such n. Thus, there is a potentially large gain in generalization properties by selecting parameters at random, rather than optimization. </p><p dir="ltr">Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. </p><p dir="ltr">We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.</p>