An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

An Innovative Approach to Teaching Structural Induction for Computer Science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

The applied computer science of economic analyses: Internet prioritization and Internet pricing, and software engineering and software pricing for the mass market

This research examines evolving issues in applied computer science and applies economic and business analyses as well. There are two main areas. The first is internetwork communications as embodied by the Internet. The goal of the research is to devise an efficient pricing, prioritization, and incentivization plan that could be realistically implemented on the existing infrastructure. Criteria include practical and economic efficiency, and proper incentives for both users and providers. Background information on the evolution and functional operation of the Internet is given, and relevant literature is surveyed and analyzed. Economic analysis is performed on the incentive implications of the current pricing structure and organization. The problems are identified, and minimally disruptive solutions are proposed for all levels of implementation to the lowest level protocol. Practical issues are considered and performance analyses are done. The second area of research is mass market software engineering, and how this differs from classical software engineering. Software life-cycle revenues are analyzed and software pricing and timing implications are derived. A profit maximizing methodology is developed to select or defer the development of software features for inclusion in a given release. An iterative model of the stages of the software development process is developed, taking into account new communications capabilities as well as profitability. ^

Spirituality and transformational leadership in education

The purpose of this study was to investigate the relationship between school principals' self-reported spirituality and their transformational leadership behaviors. The relationship between spirituality and transactional leadership behaviors was also explored. The study used Bass and Avolio's (1984) Full Range Leadership Model as the theoretical framework conceptualizing transformational leadership. Data were collected using online surveys. Overall, six principals and sixty-nine teachers participated in the study. Principal surveys contained three parts: the Multifactor Leadership Questionnaire (MLQ Form-5X Short), the modified Spirituality Well-Being Scale (SWBS) and demographic information. Teacher surveys included two parts: the MLQ-5X and demographic information. The MLQ-5X was used to identify the degree of principals' transformational and transactional leadership behaviors. The modified SWBS (Existential Well Being) was used to determine principals' degree of spirituality. The correlation coefficients for the transformational leadership styles of inspirational motivation and idealized behavioral influence were significantly related to principals' spirituality. In addition, a multiple regression analysis including the five measures of transformational leadership as predictors suggested that spirituality is positively related to an individual's transformational leadership behaviors. A multiple regression analysis utilizing a linear combination of all transformational leadership and transactional measures was predictive of spirituality. Finally, it appears that the inspirational motivation measure of transformational leadership accounts for a significant amount of unique variance independent of the other seven transformational and transactional leadership measures in predicting spirituality. Based on the findings from this study, the researcher proposed a modification of Bass and Avolio's (1985) Full Range Leadership Model. An additional dimension, spirituality, was added to the continuum of leadership styles. The findings from this study imply that principals' self-reported levels of spirituality was related to their being perceived as displaying transformational leadership behaviors. Principals who identified themselves as "spiritual", were more likely to be characterized by the transformational leadership style of inspirational motivation.

Multicultural Literacy in Education: Meeting the Objectives of the Florida Sunshine State Standards

The purpose of this paper is to show how incorporating multicultural literacy in education can meet the Florida Sunshine State Standards to promote a more equitable approach to classroom discourse and a qualitative teacher-facilitated learning environment for students who reflect a multicultural and global community.

Diversity in Education: Profiles of Students at FIU's School of Hospitality Management

The authors are conducting a study of career patterns for students enrolled in the Florida International University School of Hospitality Management. A preliminary ethnographic phase of the study was to profile a variety of student participants in order to identify potential factors which might affect career patterns. The result is a fascinating and diverse mosaic of ambitious young people and a wealth of insight for corporate recruiting.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

An investigation of mathematics and science instruction in English and Spanish for English language learners

The contextual demands of language in content area are difficult for ELLS. Content in the native language furthers students' academic development and native language skills, while they are learning English. Content in English integrates pedagogical strategies for English acquisition with subject area instruction. The following models of curriculum content are provided in most Miami Dade County Public Schools: (a) mathematics instruction in the native language with science instruction in English or (b) science instruction in the native language with mathematics instruction in English. The purpose of this study was to investigate which model of instruction is more contextually supportive for mathematics and science achievement. ^ A pretest and posttest, nonequivalent group design was used with 94 fifth grade ELLs who received instruction in curriculum model (a) or (b). This allowed for statistical analysis that detected a difference in the means of .5 standard deviations with a power of .80 at the .05 level of significance. Pretreatment and post-treatment assessments of mathematics, reading, and science achievement were obtained through the administration of Aprenda-Segunda Edición and the Florida Comprehensive Achievement Test. ^ The results indicated that students receiving mathematics in English and Science in Spanish scored higher on achievement tests in both Mathematics and Science than the students who received Mathematics in Spanish and Science in English. In addition, the mean score of students on the FCAT mathematics examination was higher than their mean score on the FCAT science examination regardless of the language of instruction. ^

Signal processing of physiological signals for automated assessment of stress in computer users

The need to provide computers with the ability to distinguish the affective state of their users is a major requirement for the practical implementation of affective computing concepts. This dissertation proposes the application of signal processing methods on physiological signals to extract from them features that can be processed by learning pattern recognition systems to provide cues about a person's affective state. In particular, combining physiological information sensed from a user's left hand in a non-invasive way with the pupil diameter information from an eye-tracking system may provide a computer with an awareness of its user's affective responses in the course of human-computer interactions. In this study an integrated hardware-software setup was developed to achieve automatic assessment of the affective status of a computer user. A computer-based "Paced Stroop Test" was designed as a stimulus to elicit emotional stress in the subject during the experiment. Four signals: the Galvanic Skin Response (GSR), the Blood Volume Pulse (BVP), the Skin Temperature (ST) and the Pupil Diameter (PD), were monitored and analyzed to differentiate affective states in the user. Several signal processing techniques were applied on the collected signals to extract their most relevant features. These features were analyzed with learning classification systems, to accomplish the affective state identification. Three learning algorithms: Naïve Bayes, Decision Tree and Support Vector Machine were applied to this identification process and their levels of classification accuracy were compared. The results achieved indicate that the physiological signals monitored do, in fact, have a strong correlation with the changes in the emotional states of the experimental subjects. These results also revealed that the inclusion of pupil diameter information significantly improved the performance of the emotion recognition system. ^

An analysis of the themes of environmental sustainability in the United States curriculum science content standards

This study examined how the themes of environmental sustainability are evident in the national, state and local standards that guide k–12 science curriculum. The study applied the principles of content analysis within the framework of an ecological paradigm. In education, an ecological paradigm focuses on students' use of a holistic lens to view and understand material. The intent of this study was to analyze the seventh grade science content standards at the national, state, and local textbook levels to determine how and the extent to which each of the five themes of environmental sustainability are presented in the language of each text. The themes are: (a) Climate Change Indicators, (b) Biodiversity, (c) Human Population Density, (d) Impact and Presence of Environmental Pollution, (e) Earth as a Closed System. The research study offers practical insight on using a method of content analysis to locate keywords of environmental sustainability in the three texts and determine if the context of each term relates to this ecological paradigm. Using a concordance program, the researcher identified the frequency and context of each vocabulary item associated with these themes. Nine chi squares were run to determine if there were differences in content between the national and state standards and the textbook. Within each level chi squares were also run to determine if there were differences between the appearance of content knowledge and skill words. Results indicate that there is a lack of agreement between levels that is significant p < .01. A discussion of these results in relation to curriculum development and standardized assessments followed. The study found that at the national and state levels, there is a lack of articulation of the goals of environmental sustainability or an ecological paradigm. With respect to the science textbook, a greater number of keywords were present; however, the context of many of these keywords did not align with the discourse of an ecological paradigm. Further, the environmental sustainability themes present in the textbook were limited to the last four chapters of the text. Additional research is recommended to determine whether this situation also exists in other settings.

Factors influencing university performance of associate in arts graduates transferring to the state university system

The purpose of this study was to examine the factorsbehind the failure rates of Associate in Arts (AA)graduates from Miami-Dade Community College (M-DCC) transferring to the Florida State University System (SUS). In M-DCC's largest disciplines, the university failure rate was 13% for Business & Management, 13% for Computer Science, and 14% for Engineering. Hypotheses tested were: Hypothesis 1 (H1): The lower division (LD) overall cumulative GPA and/or the LD major field GPA for AA graduates are predictive of the SUS GPA for the Business Management, Computer Science, and Engineering disciplines. Hypothesis 2 (H2): Demographic variables (age, race, gender) are predictive of performance at the university among M-DCC AA graduates in Engineering, Business & Management, and Computer Science. Hypothesis 3 (H3): Administrative variables (CLAST -College Level Academic Skills Test subtests) are predictive of university performance (GPA) for the Business/Management, Engineering, and Computer Science disciplines. Hypothesis 4 (H4): LD curriculum variables (course credits, course quality points) are predictive of SUS performance for the Engineering, Business/Management and Computer Science disciplines. Multiple Regression was the inferential procedureselected for predictions. Descriptive statistics weregenerated on the predictors. Results for H1 identified the LD GPA as the most significant variable in accounting for the variability of the university GPA for the Business & Management, Computer Science, and Engineering disciplines. For H2, no significant results were obtained for theage and gender variables, but the ethnic subgroups indicated significance at the .0001 level. However, differentials in GPA may not have been due directly to the race factor but, rather, to curriculum choices and performance outcomes while in the LD. The CLAST computation variable (H3) was a significant predictor of the SUS GPA. This is most likely due to the mathematics structure pervasive in these disciplines. For H4, there were two curriculum variables significant in explaining the variability of the university GPA (number of required critical major credits completed and quality of the student's performance for these credits). Descriptive statistics on the predictors indicated that 78% of those failing in the State University System had a LD major GPA (calculated with the critical required university credits earned and quality points of these credits) of less than 3.0; and 83% of those failing at the university had an overall community college GPA of less than 3.0.