The Living Economy

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Weighted Dispersive Estimates for Solutions of the Schrödinger Equation

2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.

Business statistics using EXCEL and SPSS

'Takes the challenging and makes it understandable. The book contains useful advice on the application of statistics to a variety of contexts and shows how statistics can be used by managers in their work.' - Dr Terri Byers, Assistant Professor, University Of New Brunswick, Canada A book about introductory quantitative analysis for business students designed to be read by first- and second-year students on a business studies degree course that assumes little or no background in mathematics or statistics. Based on extensive knowledge and experience in how people learn and in particular how people learn mathematics, the authors show both how and why quantitative analysis is useful in the context of business and management studies, encouraging readers to not only memorise the content but to apply learning to typical problems. Fully up-to-date with comprehensive coverage of IBM SPSS and Microsoft Excel software, the tailored examples illustrate how the programmes can be used, and include step-by-step figures and tables throughout. A range of ‘real world’ and fictional examples, including "The Ballad of Eddie the Easily Distracted" and "Esha's Story" help bring the study of statistics alive. A number of in-text boxouts can be found throughout the book aimed at readers at varying levels of study and understanding •Back to Basics for those struggling to understand, explain concepts in the most basic way possible - often relating to interesting or humorous examples •Above and Beyond for those racing ahead and who want to be introduced to more interesting or advanced concepts that are a little bit outside of what they may need to know •Think it over get students to stop, engage and reflect upon the different connections between topics A range of online resources including a set of data files and templates for the reader following in-text examples, downloadable worksheets and instructor materials, answers to in-text exercises and video content compliment the book.

The effects of required/sequenced preparatory courses on academic success and retention at a community college

This dissertation had two purposes: first, to analyze how required sequenced college preparatory courses in mathematics, reading, and writing affect students' academic success and, second, to add to a theoretical model for predicting student retention at a community college. Grade point average, number of degree credits earned, and re-enrollment rate were measured as determinants of academic success. The treatment group had a significantly higher grade point average than the control group. There was no significant difference in the number of degree credits earned or re-enrollment rate for the groups. A series of logistic regressions used the independent variables E-ASSET scores in math, reading, and writing; number of college prep areas required; credits earned; grade point average; students' status; academic restrictions/required course sequencing; sex; race; and socio-economic status to determine the predictor variables for retention. The academic variable that showed the greatest potential as a predictor for retention was grade point average. Overall, receiving financial aid was the greatest predictor for re-enrollment. For a financial aid recipient the odds of re-enrollment were 2.70 times more likely than if no financial aid was received.

The relation of sports participation to academic performance of high school students

Over the past one hundred years, interscholastic athletic programs have evolved to a place of prominence in both public and private education across America. The National Federation of State High School Associations (NFHS) estimates that approximately 3.96 million males and 2.80 million females participated in organized high school athletic programs during the 2001–2002 school year at over 17 thousand public and private high schools. The popularity of interscholastic athletic programs has resulted in continuous investigations of the relationship between high school athletic programs and academic performance. ^ The present study extends earlier investigations by examining the relation of athletic participation to several indicators of academic performance for senior high school students. This research examined: (a) average daily attendance of varsity athletes and non-athletes; (b) final cumulative grade point average; and (c) test scores on the tenth grade Florida Comprehensive Assessment Test (FLAT) in both reading and in mathematics. ^ Data were collected on 2081 randomly selected male and female high school students identified as athletes or non-athletes at ten public senior high schools in the Miami-Dade County Public Schools district. The results of the overall analyses showed a positive and significant relationship between athletic participation and educational performance. On average, athletes were absent fewer days from school per year than non-athletes and athletes earned a significantly higher cumulative grade point average than their non-athlete peers. A significant statistical difference was also found in the tenth grade FCAT test scores in both reading and mathematics for athletes and non-athletes when eighth grade FCAT test scores in reading and mathematics were used as co-variates. Athletes earned significantly higher Grade 10 FCAT test scores in both reading and mathematics than non-athletes. ^ Although cause and effect cannot be inferred from this study, the findings do indicate the potentially beneficial value of athletic programs in public secondary education. The study concluded that Florida high school graduation requirements might seriously consider the role of interscholastic athletic programs as a valid and essential extra-curricular activity. ^

Teacher efficacy of special education teachers of English language learners with disabilities

This research examined the perceived teacher efficacy of special education teachers of English Language Learners (ELLs) with educational disabilities by surveying 202 elementary special education teachers using the EXCEL Teacher Inventory. EXCEL consists of 20 teacher efficacy items, three open-ended questions, and participant demographic items. ^ Overall participant teacher efficacy scores were high. Of the variables assessed, a statistically significant difference in perceived efficacy was found with self-reported proficiency in the language of the target students. No statistically significant differences in teacher efficacy scores were found for (a) levels of teacher preparation; (b) number of years of teaching experience; or (c) socioeconomic status of the students. A multiple regression analysis indicated that, of the variables listed above, proficiency in the language of the target students accounted for significant variance in predicting the level of teachers' perceived efficacy. ^ Responses to the open-ended questions about what was most helpful when working with ELLs with disabilities yielded two major themes: organizational issues and teacher issues. Participants wrote numerous comments about the value of support from educational professionals and parents. Many participants recommended individuals in preservice programs take ESOL content specific courses. ^ The results demonstrate the positive correlation between proficiency in the language of the target students and teacher efficacy. This suggests that teachers of ELLs with disabilities have proficiency in the ELLs' native language (or have support from others who are language proficient) that allows them to distinguish between language difference and language disability and provide instruction in the native language when needed. Further, results from open-ended questions suggest that special education teacher preparation programs should include courses related specifically to strategies for teaching ELLs with disabilities, not just ELLs. ^

A comparative study of block scheduling and traditional scheduling on academic achievement

The purpose of this study was to evaluate the effectiveness of an alternate day block schedule design (n = 419) versus a traditional six-period schedule design (n = 623) on the academic achievement of the graduating classes in two schools in which the design was used respectively. Academic achievement was measured by (a) two standardized tests: the Florida Comprehensive Assessment Test Sunshine State Standards (FCAT-SSS) in mathematics and reading for 9th and 10th grade and the Scholastic Reading Inventory Test (SRI) for 9 th, 10th, and 11th grade; (b) three school grades: the mathematics final course grades for 9th, 10th, and 11th grade, the English final course grades for 9th, 10th, 11th, and 12th grade and the graduating GPA. A total of five repeated measure analyses of variance (ANOVAs) were conducted to analyze the difference between the two schools (representing the two designs) with respect to five achievement indicators (FCAT-SSS mathematics scores, FCAT-SSS reading scores, SRI scores, mathematics final course grades, and English final course grades). The between-subject factor for the five ANOVAs was the schedule design and the within-subject factor was the time the tests were taken or the time the course grades were issued. T-tests were performed on all eighth grade achievement indicators to ensure there were no significant differences in achievement between the two cohorts prior to entering high school. An independent samples t-test was conducted to analyze the difference between the two schedule designs with respect to graduating GPA. Achievement in the alternate day block schedule design was significantly higher than in the traditional six-period schedule design for some of the locally assigned school grades. The difference between the two types of schedule designs was not significant for the standardized measures (the FCAT-SSS in reading and mathematics and the SRI). This study concludes that the use of an alternate day block schedule design can be considered an educational tool that can help improve the academic achievement of students as measured by local indicators of achievement; but, apparently the design is not an important factor in achievement as measured by state examinations such as the FCAT-SSS or the SRI.

The effect of instruction on the study behaviors and academic achievement of community college students

The purpose of this study was twofold. It was designed to determine (a) the efficacy of an intervention designed to increase the frequencies of appropriate study behaviors on the part of community college students who were preparing for academic mathematics activities and (b) whether any increase in appropriate study behavior frequency was accompanied by increased academic achievement in college preparatory mathematics classes. A total of 126 Miami Dade College students participated in this study. Two developmental (remedial) mathematics classes were randomly assigned as the experimental group, and two others were assigned as the control group. All students also took a College Survival (SLS) class. The Study Behavior Inventory (SBI) and the Computerized Placement Test (CPT) were administered to the four classes. The SBI was used as a pre- and post-test. The SLS curriculum and classroom time were the same for both groups. However, students in the treatment groups received instruction designed to increase the frequency of effective study behaviors associated with the three factors identified in the SBI, while the students in the control group participated in activities that did not emphasize study behaviors. A series of analysis of covariance procedures were used to analyze four hypotheses. The first three hypotheses proposed that students who were instructed in the use of appropriate study behaviors would score higher on the three factors of the Study Behavior Inventory than those who were not. The fourth hypothesis proposed that a greater proportion of mathematics students who were instructed in the use of appropriate study behaviors would receive a passing grade in their course than students who were in the control group. The four hypotheses were tested at the .05 level of significance. This study revealed that students who received instruction in appropriate study behaviors scored higher in the use of appropriate study behaviors and in mathematics achievement than students who did not. Additional research is needed to investigate whether these effects would persist over time, or be found in subjects other than mathematics.

A Study of Teacher Efficacy of Special Education Teachers of English Language Learners with Disabilities

This research examined the perceived teacher efficacy of special education teachers of English Language Learners with disabilities. The results demonstrate the positive correlation between proficiency in the language of the target students and teacher efficacy. An analysis of responses yielded two major themes, organizational and teacher issues, affecting teacher performance.

Differential outcomes of two -way and transitional programs on English language learners at different entry levels

This study investigated the effects of two types of bilingual education programs (two-way and transitional) on the academic performance, attitudes, and metacognitive awareness of 5th grade students who entered kindergarten or first grade with different levels of English proficiency. The multi-stage sample consisted of students who had participated in each program for a period of at least five years. A mixed model design allowed for the collection of quantitative and qualitative data that were analyzed accordingly and integrated. ^ The findings indicated no significant differences between the two groups on measures of academic achievement in English. Significant differences were found in the number of semesters required for the students to become proficient English speakers. An important conclusion, based on these findings, was that the students enrolled in the two-way bilingual education (TWBE) programs learned English faster. Moreover, they maintained a high level of proficiency in Spanish, scoring significantly higher than the transitional bilingual education group on measures of Spanish reading ability.^ Questionnaire and interview data indicated that the students in the two-way bilingual education programs tended to use more Spanish for recreational purposes and tended to rate themselves as more proficient Spanish speakers than their peers. Conversely, the students enrolled in the transitional bilingual education programs tended to rate themselves as more proficient in English than their peers. ^ The level of English language proficiency upon entering school (five years later) was found to make a difference in academic achievement, as measured by standardized tests. Five years of schooling did not fully eliminate the gap in academic performance between students with different ESOL entry levels at kindergarten. However, entry level did not have an effect on attitudes towards bilingualism. ^ It is concluded that, although there was no significant difference between the two groups on measures of academic achievement in English, TWBE and transitional programs have differential effects. Students in the TWBE programs acquired oral language at a faster rate, developed literacy skills in their native language, and acquired more positive attitudes towards bilingualism. Theoretical, methodological, and policy implications of the findings are discussed. ^

Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

The effects of required/sequenced preparatory courses on academic success and retention at a community college

This dissertation had two purposes: first, to analyze how required sequenced college preparatory courses in mathematics, reading, and writing affect students' academic success and, second, to add to a theoretical model for predicting student retention at a community college. Grade point average, number of degree credits earned, and reenrollment rate were measured as determinants of academic success. The treatment group had a significantly higher grade point average than the control group. There was no significant difference in the number of degree credits earned or re-enrollment rate for the groups. A series of logistic regressions used the independent variables E-ASSET scores in math, reading, and writing; number of college prep areas required; credits earned; grade point average; students' status; academic restrictions/required course sequencing; sex; race; and socio-economic status to determine the predictor variables for retention. The academic variable that showed the greatest potential as a predictor for retention was grade point average. Overall, receiving financial aid was the greatest predictor for reenrollment. For a financial aid recipient the odds of reenrollment were 2.70 times more likely than if no financial aid was received.

História da matemática e teatro nas aulas sobre Teorema de Tales: um script proposto

This study will present the results of an investigation of how the history of mathematics and theater can contribute to the construction of mathematical knowledge of students in the 9th year of elementary school, through the experience, preparation and execution of a play, beyond presentation of the script. This brings a historical approach, defining space and time of events, putting the reader and viewer to do the route in the biography of Thales of Miletus (624-546 a.C), creating situations that led to the study and discussion of the content related to the episode possible to measure the height of the pyramid Khufu and the Theorem of Thales. That said, the pedagogical proposal implemented in this work was based on theoretical and methodological assumptions of the History of Mathematics and Theatre, drawing upon authors such as Mendes (2006), Miguel (1993), Gutierre (2010), Desgrandes (2011), Cabral (2012). Regarding the methodological procedures used qualitative research because it responds to particular issues, analyzing and interpreting the data generated in the research field. As methodological tools we have used participant observation, the questionnaire given to the students, field diary and dissertativos texts produced by students. The processing and analysis of data collected through the questionnaires were organized, classified and quantified in tables and graphs for easy viewing, interpretation, understanding and analysis of data. Data analysis corroborated our hypothesis and contributed to improving the use and display of the play as a motivating activity in mathematics classrooms. Thus, we consider that the script developed, ie the educational product proposed will bring significant contributions to the teaching of Mathematics in Primary Education

A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Cenário da produção acadêmica em história da matemática no ensino de matemática: uma análise reflexiva das teses e dissertações (1990-2010)

This research aims to make a reflective analysis about the academic production originated in the stricto sensu post graduation programs in the country, produced in the period of 1990 to 2010, in the field of History of Mathematics, especifically on works about the History of Mathematics in Mathematics education and that present pedagogical proposals that make use of the History of Mathematics in order to teach Mathematics. Defending the thesis that the researches on mathematics education with goals turned to the use of didactic proposals related to the history of mathematic that take in consideration the coherency between epistemological aspects inherent to mathematics history and anthological elements materialized on the conceptions of mathematics and mathematics history and of apprenticeship (implicitly or explicitly exposed) may originate significant contribution to the field of history of mathematics on education. Among these, nine were Master’s Degree dissertations and five PHD’s theses. The reflective analysis was accomplished from two matrixes; one from theoretical nature and the other, ontologic nature, elaborated from the pretexts of Sanches Gamboa, about the epistemological analysis from academic production in the field of Mathematics Education and the following theoretical perspectives in the field of History of Mathematics Education, that are: linear evolutionary theory, structural construtivist operative, evolutionary discontinuous, historical and socialcultural investigation and the use of activities estimulating the usage of verbal and nonverbal expressions. These perspectives were based on the works of Miguel and Miorim, Mendes and Radford. As results, we have detected some established dissonances between the categories related to theoretical and ontologic levels and the pedagogical proposal presented in these researches. On the other hand, we have discovered works that are able to establish consonances between the theoretical and ontological elements and the presented pedagogical proposal. These works carry significative contributions to the field of History of Mathematics applied to Mathematics pedagogical practice, inclusively presenting significative theoretical elements to the production of knowledge recognized as scientific in the Mathematics field