13 resultados para Teaching of mathematics. Combinatorial analysis. Heuristic analysis of combinatorial problems

em Digital Commons at Florida International University


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Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^

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Approximately 200 million people, 5% aged 15-64 worldwide are illicit drug or substance abusers (World Drug Report, 2006). Between 2002 and 2005, an average of 8.2% of 12 year olds and older in the Miami, Fort Lauderdale metropolitan areas used illicit drugs (SAMHSA, 2007). Eight percent of pregnant women, aged 15 to 25, were more likely to have used illicit drugs during pregnancy than pregnant women aged 26 to 44. Alcohol use was 9.8% and cigarette use was 18% for pregnant women aged 15 to 44 (SAMHSA, 2005). Approximately a quarter of annual birth defects are attributed to the exposure of drugs or substance abuse in utero (General Accounting Office, 1991). Physical, psychological and emotional challenges may be present for the illicit drug/substance abuse (ID/SA) mother and infant placing them at a disadvantage early in their relationship (Shonkoff & Marshall, 1990). Mothers with low self efficacy have insecurely attached infants (Donovan, Leavitt, & Walsh, 1987). As the ID/SA mother struggles with wanting to be a good parent, education is needed to help her care for her infant. In this experimental study residential rehabilitating ID/SA mothers peer taught infant massage. Massage builds bonding/attachment between mother and infant (Reese & Storm, 2008) and peer teaching is effective because participants have faced similar challenges and speak the same language (Boud, Cohen, & Sampson 2001). Quantitative data were collected using the General Self-Efficacy and Maternal Attachment Inventory-Revised Scale before and after the 4-week intervention program. A reported result of this study was that empowering ID/SA mothers increased their self-efficacy, which in turn allowed the mothers to tackle challenges encountered and created feelings of being a fit mother to their infants. This research contributes to the existing database promoting evidence-based practice in drug rehabilitation centers. Healthcare personnel, such as nurse educators and maternal-child health practitioners, can develop programs in drug rehabilitation centers that cultivate an environment where the ID/SA rehabilitating mothers can peer teach each other, while creating a support system. Using infant massage as a therapeutic tool can develop a healthy infant and nurture a more positive relationship between mother and infant.

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Approximately 200 million people, 5% aged 15-64 worldwide are illicit drug or substance abusers (World Drug Report, 2006). Between 2002 and 2005, an average of 8.2% of 12 year olds and older in the Miami, Fort Lauderdale metropolitan areas used illicit drugs (SAMHSA, 2007). Eight percent of pregnant women, aged 15 to 25, were more likely to have used illicit drugs during pregnancy than pregnant women aged 26 to 44. Alcohol use was 9.8% and cigarette use was 18% for pregnant women aged 15 to 44 (SAMHSA, 2005). Approximately a quarter of annual birth defects are attributed to the exposure of drugs or substance abuse in utero (General Accounting Office, 1991). Physical, psychological and emotional challenges may be present for the illicit drug/substance abuse (ID/SA) mother and infant placing them at a disadvantage early in their relationship (Shonkoff & Marshall, 1990). Mothers with low self efficacy have insecurely attached infants (Donovan, Leavitt, & Walsh, 1987). As the ID/SA mother struggles with wanting to be a good parent, education is needed to help her care for her infant. In this experimental study residential rehabilitating ID/SA mothers peer taught infant massage. Massage builds bonding/attachment between mother and infant (Reese & Storm, 2008) and peer teaching is effective because participants have faced similar challenges and speak the same language (Boud, Cohen, & Sampson 2001). Quantitative data were collected using the General Self-Efficacy and Maternal Attachment Inventory-Revised Scale before and after the 4-week intervention program. A reported result of this study was that empowering ID/SA mothers increased their self-efficacy, which in turn allowed the mothers to tackle challenges encountered and created feelings of being a fit mother to their infants. This research contributes to the existing database promoting evidence-based practice in drug rehabilitation centers. Healthcare personnel, such as nurse educators and maternal-child health practitioners, can develop programs in drug rehabilitation centers that cultivate an environment where the ID/SA rehabilitating mothers can peer teach each other, while creating a support system. Using infant massage as a therapeutic tool can develop a healthy infant and nurture a more positive relationship between mother and infant.

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Agency problems that helped cause the banking crisis in the United States in the 1980s impacted hotel appraisals competed for the Resolution Trust Corporation (RTC). Lower appraised values would help make more bids acceptable, helping to sell more assets quickly. The results indicate appraised hotel values were much lower than sales prices in states with a high number of bank failures.

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Taiwan's technical vocational educational system includes three levels: (1) institutes of technology (two and four year programs), (2) junior colleges (two, three and five year programs), and (3) senior vocational schools. Two-year junior colleges enroll their students through two channels: (1) based on results of the Particular Screening Entrance Examination (PSEE), (2) based on the Joint College Entrance Examination (JCEE). The PSEE has two categories: Category I includes on-time graduates with excellent performance, which means that they are within the top ten of their classes; Category II students include award-winning students in talent contests who have achieved a minimum grade point average of 75%. The JCEE is a regular entrance examination given to any senior vocation school graduate.^ Basic courses have a great impact on the students' academic performance. The purpose of the study was to focus on the effectiveness of teaching mathematics in two-year junior colleges and to analyze and correlate the results of two-year junior college students' performance in calculus and on-time graduation. The target group consisted of 521 students enrolled at National Taipei Institute of Technology in 1993.^ Calculus is a very important course for engineering majors in two-year junior colleges and has a great impact on the students' academic performance. This retrospective study showed that there was a correlation between students' performance in calculus and on-time graduation after two years of study.^ The conclusions of the study urge the Ministry of Education to reform two-year junior college curriculum standards to emphasize basic rudimentary courses. It is recommended that engineering majors receive three hours of calculus per week as the current requirement of only two hours per week is inadequate. The future job market will require a technologically advanced labor force that can be trained in a higher education system. More channels of higher education for two-year junior college graduates should be made available for those wishing to pursue bachelor degrees. Additional work in calculus will not only enhance the opportunities for two-year junior college graduates to continue their pursuit of an advanced academic degree, but also serve them well as they seek career advancement. ^

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This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.

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In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. ^ Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. ^ In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data. ^

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In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data.

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The major barrier to practical optimization of pavement preservation programming has always been that for formulations where the identity of individual projects is preserved, the solution space grows exponentially with the problem size to an extent where it can become unmanageable by the traditional analytical optimization techniques within reasonable limit. This has been attributed to the problem of combinatorial explosion that is, exponential growth of the number of combinations. The relatively large number of constraints often presents in a real-life pavement preservation programming problems and the trade-off considerations required between preventive maintenance, rehabilitation and reconstruction, present yet another factor that contributes to the solution complexity. In this research study, a new integrated multi-year optimization procedure was developed to solve network level pavement preservation programming problems, through cost-effectiveness based evolutionary programming analysis, using the Shuffled Complex Evolution (SCE) algorithm.^ A case study problem was analyzed to illustrate the robustness and consistency of the SCE technique in solving network level pavement preservation problems. The output from this program is a list of maintenance and rehabilitation treatment (M&R) strategies for each identified segment of the network in each programming year, and the impact on the overall performance of the network, in terms of the performance levels of the recommended optimal M&R strategy. ^ The results show that the SCE is very efficient and consistent in the simultaneous consideration of the trade-off between various pavement preservation strategies, while preserving the identity of the individual network segments. The flexibility of the technique is also demonstrated, in the sense that, by suitably coding the problem parameters, it can be used to solve several forms of pavement management programming problems. It is recommended that for large networks, some sort of decomposition technique should be applied to aggregate sections, which exhibit similar performance characteristics into links, such that whatever M&R alternative is recommended for a link can be applied to all the sections connected to it. In this way the problem size, and hence the solution time, can be greatly reduced to a more manageable solution space. ^ The study concludes that the robust search characteristics of SCE are well suited for solving the combinatorial problems in long-term network level pavement M&R programming and provides a rich area for future research. ^

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With the publication of A Nation at Risk (1983) educational reform has had a prominent place on the agenda of virtually every one of the sovereign states. As in many other states California focused much of its reform effort on the teaching of reading. In a political battle over the reading curriculum, California went from the English/Language Arts Framework of 1987, widely viewed as giving the state's imprimatur to whole language (an approach rooted in the learner's experience), to the English/Language Arts Frameworks (a more traditional or basic approach) of 1998 that called for the inclusion of phonemic awareness as the building block of reading instruction in all elementary schools. This study examined the historical record to determine the major forces behind this curriculum change. The results of this study are helpful to those who wish to better understand the relationship between political forces and curriculum change in the current age of educational reform. ^ This study utilized qualitative research methods and is presented as humanistic historical research (Landes & Tilly, 1971). The organizational framework for the study is taken from the work of M. Frances Klein (1991) which identifies seven different levels of curriculum decision-making. In this analysis particular attention was paid to the interaction of academic, formal, and societal levels, as the problem under consideration casts curriculum decision-making in the political realm. Three sources of information were used to provide the historical record. They include articles from popular newspapers and magazines, government documents, and interviews with individuals directly involved in the political process. ^ The results of this study demonstrate the power of societal forces over formal authority in making curriculum policy decisions. ^

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This research was conducted in Chia-Yi, Taiwan to study the needs of adult education participants to determine the factors necessary to provide direction for the development of university adult education curriculum and supportive government educational policies. Factors researched were characteristics of the adult learner, theories of adult learning, demands of adult education, and implications of university adult education as the theoretical foundation for the development of specific curriculum development efforts. The study investigated adult learning needs and their relationship with demographic variable. Analyzing the needs of adult education participant and the relative factors through a survey resulted in recommendations for the development of adult education program plans, content of curriculum, and teaching. Research questions were analyzed using descriptive statistics, frequencies, chi square, one-way analysis of variance (ANOVA), and post hoc analysis. ^ The study showed that most participants in these adult education activities were under forty, middle class, of above average educational levels, and either living or working in the city. People who were older, of lesser social and economic positions, with lower educational standards, and living/working in the country, did not participate as much in adult education opportunities. Recommendations included that in the planning or setting up of adult education activities, attention be given to all the possible barriers or problems that are likely to occur in people's participation, e.g., motivation, interests, content of courses, teaching methods, willingness of participation, qualification of teachers, time, funds, locations, and so on. It is suggested that the resolution of these problems can significantly increase the participation of adult education. ^

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Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

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This dissertation reports the results of a study that examined differences between genders in a sample of adolescents from a residential substance abuse treatment facility. The sample included 72 males and 65 females, ages 12 through 17. The data were archival, having been originally collected for a study of elopement from treatment. The current study included 23 variables. The variables were from multiple dimensions, including socioeconomic, legal, school, family, substance abuse, psychological, social support, and treatment histories. Collectively, they provided information about problem behaviors and psychosocial problems that are correlates of adolescent substance abuse. The study hypothesized that these problem behaviors and psychosocial problems exist in different patterns and combinations between genders.^ Further, it expected that these patterns and combinations would constitute profiles important for treatment. K-means cluster analysis identified differential profiles between genders in all three areas: problem behaviors, psychosocial problems, and treatment profiles. In the dimension of problem behaviors, the predominantly female group was characterized as suicidal and destructive, while the predominantly male group was identified as aggressive and low achieving. In the dimension of psychosocial problems, the predominantly female group was characterized as abused depressives, while the male group was identified as asocial, low problem severity. A third group, neither predominantly female or male, was characterized as social, high problem severity. When these dimensions were combined to form treatment profiles, the predominantly female group was characterized as abused, self-harmful, and social, and the male group was identified as aggressive, destructive, low achieving, and asocial. Finally, logistic regression and discriminant analysis were used to determine whether a history of sexual and physical abuse impacted problem behavior differentially between genders. Sexual abuse had a substantially greater influence in producing self-mutilating and suicidal behavior among females than among males. Additionally, a model including sexual abuse, physical abuse, low family support, and low support from friends showed a moderate capacity to predict unusual harmful behavior (fire-starting and cruelty to animals) among males. Implications for social work practice, social work research, and systems science are discussed. ^