Induction: a formal perspective

The aim of this contribution is to provide a rather general answer to Hume's problem. To this end, induction is treated within a straightforward formal paradigm, i.e., several connected levels of abstraction. Within this setting, many concrete models are discussed. On the one hand, models from mathematics, statistics and information science demonstrate how induction might succeed. On the other hand, standard examples from philosophy highlight fundamental difficulties. Thus it transpires that the difference between unbounded and bounded inductive steps is crucial: While unbounded leaps of faith are never justi�ed, there may well be reasonable bounded inductive steps. In this endeavour, the twin concepts of information and probability prove to be indispensable, pinning down the crucial arguments, and, at times, reducing them to calculations. Essentially, a precise study of boundedness settles Goodman's challenge. Hume's more profound claim of seemingly inevitable circularity is answered by obviously non-circular hierarchical structures

Effectiveness of Instructional Strategies Emphasizing Cooperative Learning in the Acquisition of English by Taiwanese University Students

The primary purpose of this study was to explore and analyze Taiwanese university students in the effectiveness of cooperative learning strategies in the acquisition of English. This study employed the Theory of Second Language Acquisition (SLA) and Cooperative Learning (CL) as the framework to explain the interrelationship among second language learner factors, cooperative learning strategies, and English language proficiency (ELP). This nonexperimental, correlational study used convenience sampling. Participants from Taiwan received e-mail invitations and voluntarily completed the online survey questionnaires. The survey was administered to a sample of undergraduate students who had attended the daytime Fortune Institute of Technology of Kaohsiung in Taiwan and had studied English as a foreign language. There were 396 online questionnaires applicable for data analysis. There were three significant variables in this research, including language learner factors, cooperative learning strategies, and English language proficiency. The independent variables were language learner factors and cooperative learning strategies. The dependent variable was English language proficiency. Language learner factors were measured by Taiwanese university students\u27 perceptions of learning English and included six dimensions: motivational intensity, language classroom anxiety, language aptitude, classroom social distance, frequency of participation in cooperative learning, and English language proficiency. The content of the online survey included two parts. The first part contained socio-demographic characteristics of gender, age, education category and years of experience learning English. The second part inquired about language learner factors, cooperative learning strategies, and English language proficiency. The data analysis employed the statistical software of SPSS to conduct descriptive analysis, multiple regression analysis, reliability analysis, and validity analysis. Findings indicated that learner factors of motivation, anxiety, language aptitude, social distance, and learning strategies had a strong positive and significant relationship with English language proficiency. In addition, frequency of participation in cooperative learning strategies had a moderately strong relationship with English language acquisition proficiency. Findings also indicated age and gender of learner factors rarely appear to affect English language proficiency, but these may be fundamental requirements for English language acquisition proficiency. The practical implications, limitations, and recommendations for future study are further discussed

Disproportionality in Gifted Education

Gifted education has historically involved disproportionate rates of identification and enrollment for both students of color and students from lower socioeconomic backgrounds, depriving these groups of more challenging learning opportunities. Giftedness transcends subgroups, spanning all racial, socioeconomic, and disability categories; still, data indicate that Asian and White students are identified and enrolled in gifted programs at rates exceeding their respective proportions (overrepresented) within the general student population. Conversely, the rates for Black, Hispanic, and American Indian students enrolled in gifted education are smaller than their respective proportions (underrepresented) within the general student population. This dissertation aims to disrupt current educational practices by provoking a reevaluation of gifted policy, bringing multicultural considerations to the forefront, and applying inferential statistics to disproportionality data rather than relying solely on descriptive reports. These studies used a cross-sectional observational design with two research arms. Arm A was designed to determine disproportionality rates within a large and diverse school district; Arm B was constructed to examine national disproportionality rates. The two-pronged, micro/macro approach allowed for the determination of disproportionality rates present in extant databases across special student populations, such as race, gender, SES, disability status, and language proficiency status. The data of participants enrolled in gifted programs were then compared to the total number of students from those special populations, yielding a range of proportionality. In specific terms, Arm A looked at prevalence rates by race/ethnicity, gender, and SES for elementary students enrolled for gifted services, while also asking whether the relevant race/ethnicity, gender, and SES proportions differed from those within the general student population. For its part, Arm B examined Gifted and Talented Education (GATE) program enrollment and focused on whether disproportionalities exist in student populations according to race/ethnicity, IDEA status, and ELL status, while also exploring the ranking of U.S. states in terms of racial disproportionalities in GATE program enrollment. Both studies deployed descriptive and inferential analyses, including a one-sample z test of proportions. Across both arms, results indicated and confirmed statistically significant disproportionalities among all variables, in both local and national samples. Findings specifically showed that each state across the nation contained racial disproportionalities in enrollment data for underrepresented groups. The largest racial disproportionalities among states were almost all located in the south-east region of the U.S. Results indicate causes of disproportionalities lurk beneath assessment and identification procedures, which are the most common arguments made in the literature. The present study argues that disproportionalities in gifted education are rooted in a culture-bound construct that guides our society’s conceptualization of giftedness itself