Ensembling predictions of student post-test scores for an intelligent tutoring system.

________________________________________________________________________ Over the last few decades, there have been a rich variety of approaches towards modeling student knowledge and skill within interactive learning environments. There have recently been several empirical comparisons as to which types of student models are better at predicting future performance, both within and outside of the interactive learning environment. A recent paper (Baker et al., in press) considers whether ensembling can produce better prediction than individual models, when ensembling is performed at the level of predictions of performance within the tutor. However, better performance was not achieved for predicting the post-test. In this paper, we investigate ensembling at the post-test level, to see if this approach can produce better prediction of post-test scores within the context of a Cognitive Tutor for Genetics. We find no improvement for ensembling over the best individual models and we consider possible explanations for this finding, including the limited size of the data set

Carelessness and Affect in an Intelligent Tutoring System for Mathematics

We investigate the relationship between students' affect and their frequency of careless errors while using an Intelligent Tutoring System for middle school mathematics. A student is said to have committed a careless error when the student's answer is wrong despite knowing the skill required to provide the correct answer. We operationalize the probability that an error is careless through the use of an automated detector, developed using educational data mining, which infers the probability that an error involves carelessness rather than not knowing the relevant skill. This detector is then applied to log data produced by high-school students in the Philippines using a Cognitive Tutor for scatterplots. We study the relationship between carelessness and affect, triangulating between the detector of carelessness and field observations of affect. Surprisingly, we find that carelessness is common among students who frequently experience engaged concentration. This finding implies that a highly engaged student may paradoxically become overconfident or impulsive, leading to more careless errors. In contrast, students displaying confusion or boredom make fewer careless errors. Further analysis over time suggests that confused and bored students have lower learning overall. Thus, their mistakes appear to stem from a genuine lack of knowledge rather than carelessness

Discovery with Models: A Case Study on Carelessness in Computer-based Science Inquiry

In recent years, an increasing number of analyses in Learning Analytics and Educational Data Mining (EDM) have adopted a "Discovery with Models" approach, where an existing model is used as a key component in a new EDM/analytics analysis. This article presents a theoretical discussion on the emergence of discovery with models, its potential to enhance research on learning and learners, and key lessons learned in how discovery with models can be conducted validly and effectively. We illustrate these issues through discussion of a case study where discovery with models was used to investigate a form of disengaged behavior, i.e., carelessness, in the context of middle school computer-based science inquiry. This behavior has been acknowledged as a problem in education as early as the 1920s. With the increasing use of high-stakes testing, the cost of student carelessness can be higher. For instance, within computer-based learning environments careless errors can result in reduced educational effectiveness, with students continuing to receive material they have already mastered. Despite the importance of this problem, it has received minimal research attention, in part due to difficulties in operationalizing carelessness as a construct. Building from theory on carelessness and a Bayesian framework for knowledge modeling, we use machine-learned detectors to predict carelessness within authentic use of a computer-based learning environment. We then use a discovery with models approach to link these validated carelessness measures to survey data, to study the correlations between the prevalence of carelessness and student goal orientation. The second construct, carelessness, refers to incorrect answers given by a student on material that the student should be able to answer correctly Rodriguez-Fornells & Maydeu-Olivares, 2000). The application of discovery with models involves two main phases. First, a model of a construct is developed using machine learning or knowledge engineering techniques, and is then validated, as discussed below. Second, this validated model is applied to data and used as a component in another analysis: For example, for identifying outliers through model predictions; examining which variables best predict the modeled construct; finding relationships between the construct and other variables using correlations, predictions, associations rules, causal relationships or other methods; or studying the contexts where the construct occurs, including its prevalence across domains, systems, or populations. For example, in One essential question to pose prior to a discovery with model analysis is whether the model adopted is valid, both overall, and for the specific situation in which it is being used. Ideally, a model should be validated using an approach such as cross-validation, where the model is repeatedly trained on one portion of the data and tested on a different portion, with model predictions compared to appropriate external measures, for example assessments made by humans with acceptably high inter-rater reliability, such as field observations of student behavior for gaming the system (cf. Even after validating in this fashion, validity should be re-considered if the model is used for a substantially different population or context than was used when developing the model.. An alternative approach is to use a simpler knowledge-engineered definition, rationally deriving a function/rule that is then applied to the data. In this case, the model can be inferred to have face validity. However, knowledge-engineered models often DISCOVERY WITH MODELS: A CASE STUDY ON CARELESSNESS 6 produce different results than machine learning-based models, for example in the case of gaming the system. Research studying whether student or content is a better predictor of gaming the system identified different results, depending on which model was applied (cf. Baker, 2007a

Advanced localization of massive black hole coalescences with LISA

The coalescence of massive black holes is one of the primary sources of gravitational waves (GWs) for LISA. Measurements of the GWs can localize the source on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depending on source redshift, and a minor axis which is 2--4 times smaller. The distance (and thus an approximate redshift) can be determined to better than a per cent for the closest sources we consider, although weak lensing degrades this performance. It will be of great interest to search this three-dimensional `pixel' for an electromagnetic counterpart to the GW event. The presence of a counterpart allows unique studies which combine electromagnetic and GW information, especially if the counterpart is found prior to final merger of the holes. To understand the feasibility of early counterpart detection, we calculate the evolution of the GW pixel with time. We find that the greatest improvement in pixel size occurs in the final day before merger, when spin precession effects are maximal. The source can be localized to within 10 square degrees as early as a month before merger at $z = 1$; for higher redshifts, this accuracy is only possible in the last few days.Comment: 11 pages, 4 figures, version published in Classical and Quantum Gravity (special issue for proceedings of 7th International LISA Symposium

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.

First LIGO search for gravitational wave bursts from cosmic (super)strings

We report on a matched-filter search for gravitational wave bursts from cosmic string cusps using LIGO data from the fourth science run (S4) which took place in February and March 2005. No gravitational waves were detected in 14.9 days of data from times when all three LIGO detectors were operating. We interpret the result in terms of a frequentist upper limit on the rate of gravitational wave bursts and use the limits on the rate to constrain the parameter space (string tension, reconnection probability, and loop sizes) of cosmic string models.Comment: 11 pages, 3 figures. Replaced with version submitted to PR

Implications For The Origin Of GRB 051103 From LIGO Observations

We present the results of a LIGO search for gravitational waves (GWs) associated with GRB 051103, a short-duration hard-spectrum gamma-ray burst (GRB) whose electromagnetically determined sky position is coincident with the spiral galaxy M81, which is 3.6 Mpc from Earth. Possible progenitors for short-hard GRBs include compact object mergers and soft gamma repeater (SGR) giant flares. A merger progenitor would produce a characteristic GW signal that should be detectable at the distance of M81, while GW emission from an SGR is not expected to be detectable at that distance. We found no evidence of a GW signal associated with GRB 051103. Assuming weakly beamed gamma-ray emission with a jet semi-angle of 30 deg we exclude a binary neutron star merger in M81 as the progenitor with a confidence of 98%. Neutron star-black hole mergers are excluded with > 99% confidence. If the event occurred in M81 our findings support the the hypothesis that GRB 051103 was due to an SGR giant flare, making it the most distant extragalactic magnetar observed to date.Comment: 8 pages, 3 figures. For a repository of data used in the publication, go to: https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=15166 . Also see the announcement for this paper on ligo.org at: http://www.ligo.org/science/Publication-GRB051103/index.ph