A comparison of academic achievement of Montessori and non -Montessori students in a public school setting

Relationships between academic achievement and type of curriculum delivery system, Montessori or traditional, in a diverse group of learners from a public school district were examined in this study. In a repeated measures, within subjects design, students from an elementary Montessori program were paired with agemates from a traditional group on the basis of similar Stanford Achievement Test Scores in reading or math during the baseline year. Two subsequent administrations of the Stanford were observed for each subject to elucidate possible differences which might emerge based on program affiliation over the three year duration of the study. ^ Mathematics scores for both groups were not observed to be significantly different, although following the initial observation, the Montessori group continued to produce higher mean scores than did the traditional students. Marginal significance between the groups suggests that the data analysis should continue in an effort to elucidate a possible trend toward significance at the .05 level. ^ Reading scores for the groups demonstrated marginally significant differences by one analytical method, and significant differences when analyzed with a second method. In the second and third years of the study, Montessori students produced means which consistently outperformed the traditional group. ^ Recommendations included tracking subsequent administrations of the Stanford Achievement Test for all pairs of subjects in order to evaluate emerging trends in both subject areas. ^

Self -regulated learning: The role of a journal in the learning process for students and teachers

A fundamental goal of education is to equip students with self-regulatory capabilities that enable them to educate themselves. Self directedness not only contributes to success in formal instruction but also promotes lifelong learning (Bandura, 1997). The area of research on self-regulated learning is well grounded within the framework of psychological literature attributed to motivation, metacognition, strategy use and learning. This study explored past research and established the purpose of teaching students to self-regulate their learning and highlighted the fact that teachers are expected to assume a major role in the learning process. A student reflective writing journal activity was sustained for a period of two semesters in two fourth-grade mathematics classrooms. The reflective writing journal was analyzed in search of identifying strategies reported by students. Research questions were analyzed using descriptive statistics, frequency counts, cross-tabs and chi-square analyses. ^ Results based on student-use of the journals and teacher interviews indicated that the use of a reflective writing journal does promote self-regulated learning strategies to the extent which the student is engaged in the journaling process. Those students identified as highly self-regulated learners on the basis of their strategy use, were shown to consistently claim to learn math “as well or better than planned” on a weekly basis. Furthermore, good self-regulators were able to recognize specific strategies that helped them do well and change their strategies across time based on the planned learning objectives. The perspectives of the participating teachers were examined in order to establish the context in which the students were working. The effect of “planned change” and/or the resistance to change as established in previous research, from the teachers point of view, was also explored. The analysis of the journal data did establish a significant difference between students who utilized homework as a strategy. ^ Based on the journals and interviews, this study finds that the systematic use of metacognitive, motivational and/or learning strategies can have a positive effect on student's responsiveness to their learning environment. Furthermore, it reflects that teaching students “how to learn” can be a vital part of the effectiveness of any curriculum. ^

The relationship between socioeconomic status, course delivery method, and student success at a state college: A single institution analysis

In an effort to improve instruction and better accommodate the needs of students, community colleges are offering courses delivered in a variety of delivery formats that require students to have some level of technology fluency to be successful in the course. This study was conducted to investigate the relationship between student socioeconomic status (SES), course delivery method, and course type on enrollment, final course grades, course completion status, and course passing status at a state college. ^ A dataset for 20,456 students of low and not low SES enrolled in science, technology, engineering, and mathematics (STEM) course types delivered using traditional, online, blended, and web enhanced course delivery formats at Miami Dade College, a large open access 4-year state college located in Miami-Dade County, Florida, was analyzed. A factorial ANOVA using course type, course delivery method, and student SES found no significant differences in final course grades when used to determine if course delivery methods were equally effective for students of low and not low SES taking STEM course types. Additionally, three chi-square goodness-of-fit tests were used to investigate for differences in enrollment, course completion and course passing status by SES, course type, and course delivery method. The findings of the chi-square tests indicated that: (a) there were significant differences in enrollment by SES and course delivery methods for the Engineering/Technology, Math, and overall course types but not for the Natural Science course type and (b) there were no significant differences in course completion status and course passing status by SES and course types overall and SES and course delivery methods overall. However, there were statistically significant but weak relationships between course passing status, SES and the math course type as well as between course passing status, SES, and online and traditional course delivery methods. ^ The mixed findings in the study indicate that strides have been made in closing the theoretical gap in education and technology skills that may exist for students of different SES levels. MDC's course delivery and student support models may assist other institutions address student success in courses that necessitate students having some level of technology fluency. ^

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.

Formação docente e conhecimento profissional: desafios para o ensino da matemática na EJA

As for the Education for Youth and Adult (EYA), the challenge of training these teachers is to provide tools to understand and act on the teaching of mathematics. It is realized just how special education in this modality and as such teaching is lacking in an adequate and solid training in the area of knowledge. One of the major problems affecting this type of education is the high dropout and failure rates, and lack of motivation among students. Thus the need to provide differentiated profile with a professional to teach youth and adults students, so that they are able to mobilize didactic-pedagogic knowledge, methodologies and theoretical frameworks that serve as a basis for school-developed teaching practice. This thesis aims to investigate how the math teacher, who acts in adult education from elementary school, has developed its didactic and pedagogical action, and that professional knowledge has been mobilized to teach? It has highlighted the importance of initial and continuing training and professionalization of teachers dedicated to this specific type of education, when teachers should be the protagonists of their professional development. The methodological approach was begun with a literature review, then the research was anchored mainly on the ideas by Gauthier, Nuñez and Ramalho (2004); Imbernon (2011), Garcia (2006); Perrenoud (2000); Tardif (2007 ); Haddad, Di Pierro (2000), D'Ambrosio (2002), Mendes (2006, 2009), Freire (1996, 2011), and other theorists and official documents of field of adult education here and abroad. That work leads us to the understanding of the present moment from a foray into historical and conceptual aspects, as well as educational policies of EYA, as well as training, professionalism, knowledge and skills necessary for professional practice. Then, the subjects and the locus of research and the instrument for data collection were set up and led by the object of study. To consolidate the study was selected a sample of 27 mathematics teachers, working in municipal EYA Network Teaching of Natal. This research is in an investigative nature, within the quantitative and qualitative approaches focused on the responses of study subjects from the content analysis by Bardin (1977). Results from the analyzes have revealed that the initial training of mathematics teachers of adult education needs to be reconfigured in order to formalize the knowledge base of professionals (the mathematical content, didactics and professional knowledge). Thus the study suggests that this base knowledge is embedded in the pedagogical practice of these teachers, so that there is a completion of the teaching and learning process for young people and adults. The study also has pointed out that there is a need for teachers to participate in a continuing education plan that prioritizes learning situations of mathematical content considering the previous knowledge of the students. The final analyses thus indicate that knowledge of mathematics and the didactic and pedagogical strategies to be mobilized by teachers must be able to motivate the students in such a way that they feel need to incorporate in their knowledge, mathematical knowledge capable of making them more likely to have access to social, economic and labor market

Conteúdos de matemática do ensino médio com abordagem de raciocínio recursivo e questões do ENEM e OBMEP

In this work, we have the purpose of reminding the math teacher of High School the recursive process so that he/she can use this tool to introduce contents, using recursion as an alternative to the teaching of mathematics. For this, we used questions taken from the Exame Nacional do Ensino M´edio (ENEM) [National Examination of High School] and from the Olimp´ıada Brasileira de Matem´atica das Escolas P´ublicas (OBMEP) [Brazilian Mathematics Olympiad of Public Schools], in addition to present some contents of mathematics that are defined by recursion. In this dissertation, we also showed some activities that involved the recursive reasoning and were applied in a 3rd grade class of high school in a public school in Natal / RN.

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.

Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

Aprendizaje basado en problemas, ABP : una propuesta para transformar la enseñanza-aprendizaje de las aplicaciones de la trigonometría en la solución de triángulos en el grado 10º

El estudio tuvo como propósito determinar la efectividad relativa del ABP, comparado con el método tradicional para desarrollar habilidades de resolución de problemas en el aprendizaje de las aplicaciones de la solución de triángulos en el grado 10º de la Institución Educativa El Progreso, de El Carmen de Viboral, Antioquia. La enseñanza-aprendizaje de las matemáticas sustentadas con la estrategia didáctica Aprendizaje Basado en Problemas permite a los estudiantes y docentes aproximarse al conocimiento de una manera similar a como lo hacen los científicos; el primer paso es una situación de duda, perplejidad del estudiante provocada por la Situación Problema planteada por el docente, el segundo un momento de “sugerencias” en las que la mente salta hacia adelante en busca de una posible solución (Dewey, 1933, p. 102). El tercer paso “intelectualización” de la dificultad que se ha percibido para convertirlo en un problema que debe solucionarse (Dewey, 1933, p. 103). La cuarta es “la idea conductora o hipótesis”, las cuales se basan en la formulación de explicaciones sugeridas o soluciones posibles (Dewey, 1933, p. 104). El quinto paso sería el “razonamiento”, consiste en la elaboración racional de una idea que se va desarrollando de acuerdo a las habilidades de cada persona (Dewey, 1933, p. 105). El paso final es la “comprobación de hipótesis” en situaciones reales. Este proceso se evidenció a través de cuatro Situaciones-Problema enfocadas desde un contexto auténtico “la remodelación del parque principal de El Carmen de Viboral” con el objetivo de motivar a los estudiantes para el aprendizaje de algunos conceptos matemáticos y el desarrollo de habilidades de resolución de problemas. La metodología de la investigación fue un diseño cuasi-experimental con grupo experimental compuesto por 38 estudiantes del grado 10º2 y grupo control con 37 estudiantes del grado 10º1. Se empleó como técnica de recolección de la información una prueba pre-test antes del tratamiento y una prueba post-test que se aplicó después del tratamiento a ambos grupos; se aplicó también una escala de satisfacción de los estudiantes con la metodología tradicional en ambos grupos y una escala de satisfacción con la estrategia didáctica ABP sólo al grupo experimental; la observación directa, y el portafolio que evidenciaba todas las construcciones de los estudiantes. La aplicación de la estrategia didáctica experimental se aplicó durante 4 meses, con una intensidad horaria de cuatro horas semanales, tiempo durante el cual se implementaron las cuatro Situaciones-Problema. Se concluyó entre otros aspectos que el 86,5% de los estudiantes encuentran las clases de matemáticas como interesantes, contextualizadas, aplicables y significativas, mientras que antes del tratamiento sólo el 44,4% se encontraba satisfecho con las clases de matemáticas, con una diferencia en cambio de actitud de 42,1% frente a las clases de matemáticas con la metodología tradicional. En el análisis comparativo de adquisición de competencias específicas se demuestra que el grupo experimental demostró ser matemáticamente más competente con respecto al grupo control en todas las competencias evaluadas: capacidad de modelación, inductiva, comunicativa y habilidad procedimental. Además, el proyecto de investigación tuvo un valor agregado: 10 estudiantes tuvieron la oportunidad de conocer más sobre su cultura ceramista mediante el diseño y construcción de mosaicos que los ofreció la casa de la cultura en forma gratuita.

Estatística com projetos: uma alternativa de ensino e aprendizagem

This work presents the use of projects as an alternative for teaching statistics, for that it was elaborated a Project that involves the educational socioeconomic reality from the families of the students and built a link between the reality and the scholastic knowledge. This project was applied in Sesi School - Pato Branco between the months of August to September 2014 with 25 students from the 1o and 2o grades from High School. To work the statistics concepts a questionnaire was applied for the parents of the students of the Project´s, they answer it and through these answers the students made frequency tables and graphs, besides measure calculations on measures of central tendency and dispersion measure. All of the construction were realized manually and in the Excel spreadsheet and some of them were chosen to be in this work to with the purpose of showing the hits and the mistakes done. The students worked in groups of 5 students, except in the last class when it was done a test referring to the contents taught in the classroom and a questionnaire for them to evaluate the project´s application. The results show that the teaching of Statistics trough projects motivate the students interest, stimulating the statistical reasoning, in addition made the students know a Math that was different from the one they have already known, with a lot of calculation but with no final objective.

Educação financeira no ensino médio: uma abordagem por meio da análise de produtos financeiros com ênfase em consórcios

This paper presents a differential approach of financial mathematics developed in high school, focusing on financial education. We seek through the insertion of texts, analysis of some financial products and by the interpretation of problems to contribute to the financial training of students. Aiming to make financial mathematics more attractive and accessible to the day-today, there are available for studies some practical tools like the citizen calculator which are available for computers and mobile phones. As well as spreadsheets and software Geogebra, that allow you to compare and analyze the financial costs of consortia, financing and financial applications,in addition to being allied in the preparation and control of personal and family budget. By applying the teaching sequence proposed in a nocturnal class of high school, we realized some difficulties that have limited the financial learning of math concepts.Yet identified progress regarding the financial education of students. These observations were made through qualitative and quantitative analysis from notes in the field diary and also answers given by students in specific form.