Wesley Calvert

We examined the limitations of observed course DFWI rates (% of D and F grades, withdrawals, and incompletes) as evaluation metrics, which obscure student characteristics, course design, instruction, structure, and latent factors, posing challenges in identifying courses that need improvement. An artificial neural network (ANN) was trained using student data to model risk, accounting for variations in student characteristics. The model’s predictions on test data were averaged at the course level, producing expected DFWI rates based on student composition. Courses with high observed DFWI rates and large deviations between observed and predicted DFWI rates (the GAP) were ranked and prioritized for review, as they may reflect aspects of course design, structure, or instructional practices warranting further qualitative evaluation. Our predictions are non-causal, and modeling calibration varies across subgroups; therefore, the original GAP rankings, robust to a post-hoc calibration check, are presented as risk-adjusted indicators for prioritizing courses for further review rather than as definitive causal measures of course quality. Rankings based on observed DFWI rates differ substantially from risk-adjusted GAP rankings, indicating that relying on observed DFWI rates alone may misidentify high-risk courses. Our methodology can assist educators and administrators in making fair resource allocation decisions and improving student outcomes.

In a previous paper, entitled "Structural Highness Notions," we defined several classes of degrees that are high in senses related to computable structure theory. Each class of degrees is characterized by a structural feature (e.g., an isomorphism) that it can compute if such a feature exists. In this paper, we examine each of these classes and characterize them based on what they do if no such object exists. We describe, in particular, reticent, loquacious, and collegiate senses of being high. These, respectively, reflect the case where a computation from the degree can give output only if the desired feature exists, the case where it will give output of some kind whether or not the feature exists, and the case where the degree will either compute the feature or the best available approximation to it.

We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of that are random according to our definition. We show that there are noncomputable algebraic fields which are not random. We also partially characterize the index set, relative to an oracle, of the set of random algebraic fields computable relative to that oracle.In order to carry out this investigation of randomness for fields, we develop computability in the context of the infinite Galois theory (where the relevant Galois groups are uncountable), including definitions of computable and computably enumerable Galois groups and computability of Haar measure on the Galois groups.