This study examines how and if threshold concepts enable expansive learning and generalization. Expansive learning and generalization are part of the highly contested conceptions of transfer, and these specific conceptions offer a more complex conception of transfer that deals with knowledge transformation (Tuomi-Gr?hn and Engestr?m, Beach). One way that we can see expansive learning and generalization transform knowledge is through the teaching of threshold concepts. In the last decade, there has been a movement toward using threshold concepts in FYC*s that take up writing studies as their curricula (Wardle and Downs, Dew). Even though using threshold concepts seems to be one interesting way of specifically studying expansive learning and generalization, we have no studies examining whether or not teaching threshold concepts encourages expansive learning. The studies we do have do not seem to offer any methodologies that would enable us to study threshold concepts and generalization. Past methods, such as case studies, interviews, and surveys have included small sample sizes to collect their data from (Wardle, Dively and Nelms, Nowacek). A lot of the transfer data does not actually focus on the writing or the texts themselves or the reoccurring moves that students use in those texts. Linguistic discourse analysis offers a promising avenue for examining the generalization of threshold concepts. Using research methods like linguistic discourse analysis in marriage with the best qualitative methods of transfer, like case studies or interviews, could allow for a larger sample size of data collection and allows for us to see how students use these threshold concepts in their writing. Through linguistic discourse analysis and interviews, this study suggests that students* perceptions of writing change after being introduced to some threshold concepts from the Writing About Writing curriculum. The threshold concepts that students are presented to in the Writing About Writing curriculum at UCF tackles misconceptions and helps students change how they view writing. Once they can change this view, they are able to generalize the knowledge they have into their own writing. If students do not use the exact terminology from the curriculum, they are able to generalize those threshold concepts through using their own language or even through analogies.

In order for the benefits of a behavior management skills training program to reach clients, caregivers must use the behavior management skills in the natural environment. The current study took place at a large residential facility for adults with disabilities, in which caregivers had received prior training in which they demonstrated behavior management skills and maintained those skills in contrived role plays. The current study represents a preliminary analysis of generalization of these skills in the natural environment; thus, a measurement system for when caregivers should demonstrate the tools was developed. The specific purpose of this study was to develop and evaluate a program to establish stimulus control over observers' measurement of appropriate behaviors. Researchers systematically developed and validated a measurement system of "good behaviors" that could be used across clients. The process of development and refinement of the measurement system is described. When the system was finalized, three observers' accuracy in using the system was assessed by comparing measured values to that of the code writer. Following feedback on individual instances of behavior, all observers scored the three target behaviors accurately. Ecological validity was assessed by surveying professionals at the facility and ecological validity results suggested a valid measurement system was developed.

Let F and H be two (compatible) classes of functions. We observe that even when both F and H have small capacities as measured by their uniform covering numbers, the capacity of the composition class H o F={h o f| f in F, h in H} can become prohibitively large or even unbounded. To this end, in this thesis we provide a framework for controlling the capacity of composition and extend our results to bound the capacity of neural networks. Composition of Random Classes: We show that adding a small amount of Gaussian noise to the output of cF before composing it with H can effectively control the capacity of H o F, offering a general recipe for modular design. To prove our results, we define new notions of uniform covering number of random functions with respect to the total variation and Wasserstein distances. The bounds for composition then come naturally through the use of data processing inequality. Capacity of Neural Networks: We instantiate our results for the case of sigmoid neural networks. We start by finding a bound for the single-layer noisy neural network by estimating input distributions with mixtures of Gaussians and covering them. Next, we use our composition theorems to propose a novel bound for the covering number of a multi-layer network. This bound does not require Lipschitz assumption and works for networks with potentially large weights. Empirical Investigation of Generalization Bounds: We include preliminary empirical results on MNIST dataset to compare several covering number bounds based on their suggested generalization bounds. To compare these bounds, we propose a new metric (NVAC) that measures the minimum number of samples required to make the bound non-vacuous. The empirical results indicate that the amount of noise required to improve over existing uniform bounds can be numerically negligible. The source codes are available at https://github.com/fathollahpour/composition_noise / Thesis / Master of Science (MSc) / Given two classes of functions with bounded capacity, is there a systematic way to bound the capacity of their composition? We show that this is not generally true. Capacity of a class of functions is a learning-theoretic quantity that may be used to explain its sample complexity and generalization behaviour. In other words, bounding the capacity of a class can be used to ensure that given enough samples, with high probability, the deviation between training and expected errors is small. In this thesis, we show that adding a small amount of Gaussian noise to the output of functions can effectively control the capacity of composition, introducing a general framework for modular design. We instantiate our results for sigmoid neural networks and derive capacity bounds that work for networks with large weights. Our empirical results show that the amount of Gaussian noise required to improve over existing bounds is negligible.

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