The process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.

No description available.

Multi-task learning refers to learning multiple tasks simultaneously, in order to avoid tabula rasa learning and to share information between similar tasks during learning. We consider a multi-task Gaussian process regression model that learns related functions by inducing correlations between tasks directly. Using this model as a reference for three other multi-task models, we provide a broad unifying view of multi-task learning. This is possible because, unlike the other models, the multi-task Gaussian process model encodes task relatedness explicitly. Each multi-task learning model generally assumes that learning multiple tasks together is beneficial. We analyze how and the extent to which multi-task learning helps improve the generalization of supervised learning. Our analysis is conducted for the average-case on the multi-task Gaussian process model, and we concentrate mainly on the case of two tasks, called the primary task and the secondary task. The main parameters are the degree of relatedness ρ between the two tasks, and πS, the fraction of the total training observations from the secondary task. Among other results, we show that asymmetric multitask learning, where the secondary task is to help the learning of the primary task, can decrease a lower bound on the average generalization error by a factor of up to ρ2πS. When there are no observations for the primary task, there is also an intrinsic limit to which observations for the secondary task can help the primary task. For symmetric multi-task learning, where the two tasks are to help each other to learn, we find the learning to be characterized by the term πS(1 − πS)(1 − ρ2). As far as we are aware, our analysis contributes to an understanding of multi-task learning that is orthogonal to the existing PAC-based results on multi-task learning. For more than two tasks, we provide an understanding of the multi-task Gaussian process model through structures in the predictive means and variances given certain configurations of training observations. These results generalize existing ones in the geostatistics literature, and may have practical applications in that domain. We evaluate the multi-task Gaussian process model on the inverse dynamics problem for a robot manipulator. The inverse dynamics problem is to compute the torques needed at the joints to drive the manipulator along a given trajectory, and there are advantages to learning this function for adaptive control. A robot manipulator will often need to be controlled while holding different loads in its end effector, giving rise to a multi-context or multi-load learning problem, and we treat predicting the inverse dynamics for a context/load as a task. We view the learning of the inverse dynamics as a function approximation problem and place Gaussian process priors over the space of functions. We first show that this is effective for learning the inverse dynamics for a single context. Then, by placing independent Gaussian process priors over the latent functions of the inverse dynamics, we obtain a multi-task Gaussian process prior for handling multiple loads, where the inter-context similarity depends on the underlying inertial parameters of the manipulator. Experiments demonstrate that this multi-task formulation is effective in sharing information among the various loads, and generally improves performance over either learning only on single contexts or pooling the data over all contexts. In addition to the experimental results, one of the contributions of this study is showing that the multi-task Gaussian process model follows naturally from the physics of the inverse dynamics.

Objective: Fetal alcohol spectrum disorder (FASD) is a permanent developmental disorder that can occur if women drink alcohol while pregnant. Despite substantial variability in FASD as a population, anecdotal evidence and clinical reports suggest that affected individuals have difficulty learning from experience and generalizing information from one situation to another, and tend to make the same mistakes over and over. Consistent with research in cognitive and educational psychology, these difficulties were conceptualized as impairments in “transfer of learning.” This dissertation sought to measure transfer of learning using three experimental transfer measures and an exploratory parental transfer questionnaire. In addition, performance on the experimental transfer measures was investigated in relation to aspects of executive functioning, because abilities thought to underlie successful transfer bear much resemblance to aspects of executive functioning. Participants and Methods: The sample included 16 children diagnosed with FASD and 16 age- and gender-matched control children. Children were screened for intelligence and excluded if their performance on both Vocabulary and Matrix Reasoning from the WISC-IV fell below the 9th percentile. Children completed three transfer tasks: (1) a novel, experimental modification of the Tower of Hanoi involving nested plastic cups and Tupperware containers; (2) a variation of Chen’s (1996) Bead Retrieval Problem; and (3) the Purdue Pegboard. Participants also completed three executive functioning tasks that were selected to measure concept formation and flexibility: (1) Picture Concepts from the WISC-IV; (2) the D-KEFS Color-Word Interference Test; and (3) the Visual-Verbal Test. In addition, parents or caregivers completed an exploratory questionnaire designed to assess children’s transfer of learning abilities in everyday life, along with the ABAS-II, a standardized measure of adaptive functioning. Results: Children with FASD displayed significantly weaker performance on the Transfer Condition of the Tower of Hanoi, even after controlling for intelligence. Group differences were not observed on the Bead Retrieval Problem or on the Purdue Pegboard. On the measures of executive functioning, control children outperformed those with FASD on all measures before controlling for intelligence. In addition, there was a significant relationship between the Tower of Hanoi and the Visual-Verbal Test; the latter was the only executive functioning task related to transfer of learning. This finding, however, did not persist when intelligence was accounted for. After controlling for intelligence, significant group differences also were found on parental ratings of everyday transfer ability and on more complex aspects of adaptive functioning. Conclusions: Two out of four newly created measures in this exploratory dissertation provided partial support for weak transfer of learning in FASD. This was observed on the modified Tower of Hanoi, which shared an identical structure between conditions but differed in surface appearance. Parental ratings also indicated weak transfer of learning, although in children with FASD, these reports did not correlate with transfer abilities on the Tower of Hanoi. Children with FASD also demonstrated weak executive functioning, but this weakness was moderated significantly by intelligence. The relationship between transfer of learning and executive functioning appeared to be driven primarily by cognitive flexibility, although this relationship also was moderated by intelligence.

No description available.

Thesis (M.A.)--Miami University, Dept. of Psychology, 2007. / Title from first page of PDF document. Includes bibliographical references (p. 21-24).

This study aimed at analyzing and comparing the phonological changes that occur in the different degrees of phonological disorder severity in individuaIs treated with the Modified Maximum Opposition Model (Bagetti,Mota & Keske-Soares, in press) as well as verifYingthe way of approaching the distinctive features in the target sounds (contrast or reinforcement) which lead to major phonological changes. The phonological disorder (PD) diagnosis was carried out by means of phonological and complementary assessments. The subjects' speech data were analyzed through the performance of the Child's Phonological Assessment (CPA) proposed by Yavas, Hemandorena & Lamprecht (1991). After the phonological assessment, the percentage of correct consonants (PCC) proposed by Shriberg & Kwiatkowski (1982) was calculated and the subjects were then classified in the degrees of severity of the phonological disorder: severe (SD), moderate-severe (MSD), mild-moderate (MMD) and mild disorder (MD). The studied group was composed by seven subjects, four males and three females aged from 3:10 to 6:9. For the treatment, the Modified Maximum Opposition Model (Bagetti, Mota & Keske-Soares, in press), which is based on the Maximum Opposition Model (Gierut, 1992), wasused. After 20 therapeutic sessions, the CPA was performed again, the PCC was calculated and the phonological changes referent to the PCC were analyzed, as well as the number of sounds acquired during the therapy and generalizations (to items not used in the treatment, to another position of the word, within a class of sounds and to other classes of sounds). The phonological changes were analyzed before and after the treatment, considering and not considering the way ofpresenting the stimulus (contrast or reinforcement). It was analyzed whether there was a statistically significant difference (Wilcoxon Non-Parametric Test, p<0.05). A comparison of the phonological changes among the different degrees of severity of the PD was performed considering and not considering the form of presenting the stimulus. After, the phonological changes within each degree of PD severity were analyzed, one subject treated by contrast approach and the other by reinforcement approach. The phonological changes among the groups treated by both approaches were also analyzed, as well as whether there was a statistically significant difference among them (Kruskal-Wallis Test, p<0.05). It was verified that in the total group there was a statistically significant increasing of the PCC (p<0.0 17), of the number of acquired phonemes (p<O.O17) and of the generalizations to items not used during the treatment (p=O.OO5), to another position of the word, (p=O.OO7), within a class of sounds (p=O.OO6)and to other classes of sounds (p=O.OOO9) after therapy. The group of subjects treated by the contrast approach showed an increase in the PCC and in the number of the phonemes acquired, but such increment was not statistically significant (p=O.067). They presented a statistically significant evolution in relation to the generalizations to items not used in the treatment (p=0.027), to another position ofthe word (p=O.042),within a class ofsounds (p=O.OI7)and to other classes ofsounds (p=O.017).The major phonological changes in the different degrees of phonological disorder severity without considering the form of presenting the stimulus and the subjects treated by the contrast approach occurred in the groups with intermediate phonological disorder severity (MSD and MMD) when compared to the group with a more severe (SD) or less severe (MD) degree. Among the subjects with different degrees of PD severity treated by the reinforcement approach, the major phonological changes were observed in the subject with SD followed by the MMD and the MD. In the comparative analysis within each degree, it was verified that in the severe and medium degrees, the subjects treated by the reinforcement approach presented the major phonological changes and in the medium-moderate degree and the subject treated by the contrast approach presented the major changes. In relation to the comparative analysis between the total group treated by both approaches, it was observed that both groups presented changes in their phonological systems and there was no statistically significant difference between them. / Este estudo teve como objetivo analisar e comparar as mudanças fonológicas ocorridas nos diferentes graus de severidade do desvio fonológico em sujeitos tratados pelo modelo de Oposições Máximas Modificado (Bagetti, Mota & Keske-Soares, no prelo) e verificar a maneira de abordagem dos .traços distintivos nos sons-alvo ("contraste" ou "reforço") que conduz a maiores mudanças fonológicas. O diagnóstico de desvio fonológico (DF) foi realizado através de avaliações fonoaudiológicas e complementares. Os dados da fala dos sujeitos foram analisados por meio da aplicação da Avaliação Fonológica da Criança (AFC) proposta por Yavas, Hemandorena & Lamprecht (1991). Após a realização da avaliação fonológica, foi calculado o percentual de consoantes corretas (PCC) proposto por Shriberg & Kwiatkowski (1982) e os sujeitos foram classificados nos graus de severidade do desvio fonológico: desvio severo (DS), moderado-severo (DMS), médio-moderado (DMM) e médio (DM). O grupo pesquisado foi constituído por sete sujeitos, quatro do sexo masculino e três do feminino (idades entre 3:10 e 6:9). Foi utilizado para o tratamento o Modelo de Oposições Máximas Modificado (Bagetti, Mota & Keske-Soares, no prelo), baseado no Modelo de Oposições Máximas (Gierut, 1992). Após 20 sessões terapêuticas, aplicou-se novamente a AFC, foi calculado o PCC e analisadas as mudanças fonológicas, referentes ao PCC, número de fonemas adquiridos com a terapia e generalizações (a itens não utilizados no tratamento, para outra posição da palavra, dentro de uma classe de sons e para outras classes de sons). Foram analisadas as mudanças fonológicas, pré e pós-tratamento, sem considerar a forma de apresentação do estímulo e considerando-se a forma de apresentação do estímulo ("contraste" e "reforço") e analisado se houve diferença estatisticamente significante (Teste Não Paramétrico Wilcoxon, p<0,05). Foi realizada uma comparação das mudanças fonológicas entre os diferentes graus de severidade do DF sem considerar a forma de apresentação do estímulo e considerando-se a forma de apresentação do mesmo. Em seguida, foram analisadas as mudanças fonológicas dentro de cada grau de severidade do DF, sendo um sujeito tratado pelo "contraste" e outro pelo "reforço". Também foram analisadas as mudanças fonológicas entre o grupo de sujeitos tratados pelo "contraste" e o grupo tratado pelo 'reforço', e observado se houve diferença estatisticamente significante (Teste Kruskal-Wallis, p<0,05) entre eles. Verificou-se que, no grupo total de sujeitos, houve um aumento estatisticamente significante do PCC (p<0,0 17), do número de sons adquiridos (p<0,0 17) e das generalizações a itens não utilizados no tratamento (p=0,005), para outra posição da palavra (p=0,007), dentro de uma classe de sons (p=0,006) e para outras classes de sons (p=0,0009) após a terapia. O grupo de sujeitos, com diferentes graus de severidade do DF, tratados pelo "contraste", apresentou um aumento no PCC e no número de sons adquiridos, mas este aumento não foi estatisticamente significante (p=0,067). Apresentaram evolução estatisticamente significante em relação às generalizações a itens não utilizados no tratamento (p=0,027), para outra posição da palavra (p=0,042), dentro de uma classe de sons (p=0,017) e para outras classes de sons (p=0,017). O grupo de sujeitos com diferentes graus de severidade do desvio fonológico tratados pelo "reforço" apresentou evolução, mas esta não foi estatisticamente significante em relação ao PCC (p=0,108), número de sons adquiridos (p=O,108) e generalizações a itens não utilizados no tratamento (p=0,67), para outra posição da palavra (p=0,67), dentro de uma classe de sons (p=0,126). Este grupo também apresentou evolução em relação à generalização para outras classes de sons, e esta evolução foi estatisticamente significante (p=0,017). As maiores mudanças fonológicas nos diferentes graus de severidade do desvio fonológico, sem considerar a forma de apresentação do estímulo, como também nos sujeitos tratados pelo "contraste", ocorreram nos grupos com desvios fonológicos com graus de severidade intermediários (DMS e DMM), quando comparados ao grupo com grau de severidade mais acentuado (DS) ou menos acentuado (DM). Nos sujeitos tratados pelo "reforço" com diferentes graus de severidade do DF, as maiores mudanças fonológicas foram observadas no sujeito com DS, seguido do sujeito com DMM e DM. Na análise comparativa dentro de cada grau, verificou-se que, nos graus severo e médio, os sujeitos tratados pelo "reforço" apresentaram maiores mudanças fonológicas, e no grau médio-moderado o sujeito tratado pelo "contraste" apresentou maior mudança fonológica. Quanto à análise comparativa entre o grupo total de sujeitos tratados pelo "contraste" e o grupo tratado pelo "reforço", verificou-se que ambos os grupos apresentaram mudanças em seus sistemas fonológicos e não houve diferença estatisticamente significante entre eles.

The area of perceptual decision-making research seeks to understand how our perception of the world affects our judgment. Laboratory investigations of perceptual decision-making concentrate on observers' ability to discriminate among stimuli and their biases towards reporting one stimulus more frequently than others. Choice theories assume that these performance measures are determined by generalization of reinforcement along both stimulus and response dimensions. Historically the majority of research has addressed situations in which the difference among stimuli and resulting consequences of a perceptual decision are static. Consequently, little is known about the dynamics of stimulus and response generalization. The present research investigated the dynamics of discrimination accuracy and response bias by frequently varying differences among stimuli and the outcomes for correct decisions. In Experiment 1, four rats responded in a two-stimulus, two-response detection procedure employing temporal stimuli (short vs. long houselight presentations). Sample stimulus difference was varied over two levels across experimental conditions. A rapid acquisition procedure was employed in which relative reinforcer frequency varied daily. Shifts in response bias were well described by a behavioral model of detection (Davison & Nevin, 1999). Within sessions, bias adjusted rapidly to current reinforcer ratios when the sample stimulus difference was large, but not when the difference was small. In Experiment 2, three rats responded in a five-stimulus, two-response detection procedure employing temporal stimuli. Relative reinforcer frequency was again varied daily. Control by current session reinforcer ratios increased rapidly within sessions in a nearly monotonic fashion. Furthermore, response bias following each sample stimulus was observed within the first few trials of an experimental session. The speed of changes in response bias, especially following an unreinforced probe stimulus, provide strong support for an effective reinforcement process and suggest that this process may operate at a trial-by-trial level. In Experiment 3, three rats responded in a six-stimulus, two-response classification procedure. A repeated-acquisition procedure was employed in which the relationship between classes of short and long sample stimuli and their respective correct comparison locations reversed every 15 sessions. After several reversals, the probabilities of reinforcement for correct classification were also manipulated. In the majority of conditions across subjects, response bias reached half-asymptotic levels more rapidly than did discrimination accuracy. These findings provide some support for a backward chaining account of the acquisition of signal detection performance. An attention-augmented behavioral detection model accurately described the acquisition data; however parameter estimates expressing the probability of attending to sample and comparison stimuli differed widely among subjects. The results of these experiments support the adaptation of dynamic research methodologies to the study of learning in perceptual decision-making tasks. Furthermore, discrimination performance and response bias adapt rapidly to frequent changes in reinforcement contingencies. Quantitative models formulated to describe static performance in detection procedures can be extended to predict dynamic performance. Some theoretical assumptions of these models were supported and others were violated. Overall, this research supports a renewed emphasis on learning in signal detection procedures and suggests that stable behavioral endpoints are at least as much a function of contingency variables as they are of sensory variables.

This study examines the coda clusters in Classical Arabic and how Najdi speakers, modern inhabitants of the central area of Saudi Arabia, pronounce them. Fourteen Najdi participants were asked to read a list of thirty-one words that took into account falling, equal, and rising sonority clusters, consisting of obstruents, nasals, liquids, and glides. The instrument contained one, two, and three steps of sonority for each level of sonority (falling and rising) to determine the minimal sonority distance used in Najdi Arabic. Specifically, obstruent + nasal, nasal + liquid, and liquid + glide were included for falling sonority clusters of one step, obstruent + liquid and nasal + glide were used for falling sonority clusters of two steps, and only obstruent + glide for falling sonority clusters of three steps. To test the rising sonority clusters, the elements in the clusters were transposed for each combination; for example, instead of using obstruent + nasal, clusters of nasal + obstruent were considered. However, for equal sonority clusters, only obstruent + obstruent and nasal + nasal were examined. Obstruents were dealt with separately in the instrument at first to see whether they caused any difference in the results. The results showed that the subjects added epenthesis in the rising sonority clusters and equal sonority clusters containing sonorants. However, they did not add epenthesis in the falling sonority clusters or equal sonority clusters containing obstruents. Thus, no matter the distance in sonority between the two segments in the rising sonority clusters (one, two, or three steps), the participants always epenthesized them. In addition, no matter how many sonority steps there were between the two segments in the falling sonority clusters, the participants always produced them without modification. In case of equal sonority, when the two segments of the cluster were sonorants, the participants added epenthesis; however, when the two segments of the cluster were obstruents, the participants produced them without modification.

Metadados bibliográficos duplicados são registros que correspondem a referências bibliográficas semanticamente equivalentes, ou seja, que descrevem a mesma publicação. Identificar metadados bibliográficos duplicados em uma ou mais bibliotecas digitais é uma tarefa essencial para garantir a qualidade de alguns serviços como busca, navegação e recomendação de conteúdo. Embora diversos padrões de metadados tenham sido propostos, eles não resolvem totalmente os problemas de interoperabilidade porque mesmo que exista um mapeamento entre diferentes esquemas de metadados, podem existir variações na representação do conteúdo. Grande parte dos trabalhos propostos para identificar duplicatas aplica uma ou mais funções sobre o conteúdo de determinados campos no intuito de captar a similaridade entre os registros. Entretanto, é necessário escolher um limiar que defina se dois registros são suficientemente similares para serem considerados semanticamente equivalentes ou duplicados. Trabalhos mais recentes tratam a deduplicação de registros como um problema de classificação de dados, em que um modelo preditivo é treinado para estimar a que objeto do mundo real um registro faz referência. O objetivo principal desta tese é o desenvolvimento de um método efetivo e automático para identificar metadados bibliográficos duplicados, combinando o aprendizado de múltiplos classificadores supervisionados, sem a necessidade de intervenção humana na definição de limiares de similaridade. Sobre o conjunto de treinamento são aplicadas funções de similaridade desenvolvidas especificamente para o contexto de bibliotecas digitais e com baixo custo computacional. Os escores produzidos pelas funções são utilizados para treinar múltiplos modelos de classificação heterogêneos, ou seja, a partir de algoritmos de diversos tipos: baseados em árvores, regras, redes neurais artificiais e probabilísticos. Os classificadores aprendidos são combinados através da estratégia de empilhamento visando potencializar o resultado da deduplicação a partir do conhecimento heterogêneo adquirido individualmente pelos algoritmo de aprendizagem. O modelo de classificação final é aplicado aos pares candidatos ao casamento retornados por uma estratégia de blocagem de dois níveis bastante eficiente. A solução proposta é baseada na hipótese de que o empilhamento de classificadores supervisionados pode aumentar a qualidade da deduplicação quando comparado a outras estratégias de combinação. A avaliação experimental mostra que a hipótese foi confirmada quando o método proposto é comparado com a escolha do melhor classificador e com o voto da maioria. Ainda são analisados o impacto da diversidade dos classificadores no resultado do empilhamento e os casos de falha do método proposto. / Duplicated bibliographic metadata are semantically equivalent records, i.e., references that describe the same publication. Identifying duplicated bibliographic metadata in one or more digital libraries is an essential task to ensure the quality of some services such as search, navigation, and content recommendation. Although many metadata standards have been proposed, they do not completely solve interoperability problems because even if there is a mapping between different metadata schemas, there may be variations in the content representation. Most of work proposed to identify duplicated records uses one or more functions on some fields in order to capture the similarity between the records. However, we need to choose a threshold that defines whether two records are sufficiently similar to be considered semantically equivalent or duplicated. Recent studies deal with record deduplication as a data classification problem, in which a predictive model is trained to estimate the real-world object to which a record refers. The main goal of this thesis is the development of an effective and automatic method to identify duplicated bibliographic metadata, combining multiple supervised classifiers, without any human intervention in the setting of similarity thresholds. We have applied on the training set cheap similarity functions specifically designed for the context of digital libraries. The scores returned by these functions are used to train multiple and heterogeneous classification models, i.e., using learning algorithms based on trees, rules, artificial neural networks and probabilistic models. The learned classifiers are combined by stacked generalization strategy to improve the deduplication result through heterogeneous knowledge acquired by each learning algorithm. The final model is applied to pairs of records that are candidate to matching. These pairs are defined by an efficient two phase blocking strategy. The proposed solution is based on the hypothesis that stacking supervised classifiers can improve the quality of deduplication when compared to other combination strategies. The experimental evaluation shows that the hypothesis has been confirmed by comparing the proposed method to selecting the best classifier or the majority vote technique. We also have analyzed the impact of classifiers diversity on the stacking results and the cases for which the proposed method fails.