Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

On the study and difficulties of mathematics /

First edition, 1831.

Real mathematics, intended mainly for practical engineers, as an aid to the study and comprehension of mathematics,

Mode of access: Internet.

Pre-Service Teachers’ Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Thesis (Ph.D.)--University of Washington, 2016-06

Heteronormativity and teaching: A phenomenological study of lesbian teachers

The purpose of this phenomenological study was to understand what impact “heteronormativity” has on a lesbian teacher's perception of her instructional style, content, and context of curriculum taught. Through taped interviews with lesbian educators, this research examined the lived experience of the lesbian teacher. The framework for this study included theories related to historical, sociocultural, and psychosocial development while the methodology included a qualitative design using primary elements of a phenomenological study outlined without ignoring the influence associated with contextualism. Due to the sensitive nature of the study nine women who were the focus of this research were volunteers with the first serving as a “gatekeeper” to assist in the pilot study. The subsequent group evolved as a result of “snowballing” to gain more participants. ^ The data in the form of narrative derived from the interviews was transcribed, color-coded, and organized into four themes and associated sub-themes, based upon the perceptions of these educators. These themes characterized the coming out process of a lesbian, which directly paralleled the personal and professional development of the lesbian educator, emerged as a result of the analysis. They included: (a) self-acknowledgement; (b) self-indentification; (c) coming out to other lesbians by overcoming fear and establishing relationships; (d) coming out to others by overcoming heteronormativity by using support groups in defining a lesbian's role as a teacher. ^ The results of this study showed that the acceptance of the lesbian culture, shared with the acknowledgement, rather than compliance or defiance, of cultural hegemony can allow the lesbian educator to develop a curriculum and a classroom climate that will foster understanding and even generate social change among colleagues, parents, and students, one person at a time. ^

A case study of teaching and learning practice in a Chinese adult institution

Résumé: Cette recherche s'est réalisée dans une institution chinoise de formation des adultes. Il existe très peu d'études présentant la pratique de l'enseignement et de l'apprentissage en Chine. Aussi, il semble que cette étude de cas puisse être utile. Elle porte sur le personnel de formation en administration économique dans un centre de formation de Tianjin. Le but premier de cette recherche est de décrire ce qui se fait à cet institut de formation des adultes. Les aspects couverts vont de la sélection du contenu de formation et des modalités d'enseignement jusqu'à la compréhension de l'enseignement et de l'apprentissage. À partir de l'expérience des professeurs de ce centre de Tianjin, cette étude cherche précisément à décrire leurs perceptions et leurs attitudes en regard d'un enseignement centré sur l'apprentissage et développé selon un mode de collaboration. Les fondements théoriques retenus s'inspirent des conceptions andragogiques de Knowles, de celles de Brookfield qui ont trait aux rôles des formateurs et formatrices d'adultes et de Conti qui présente une conception de l'enseignement qui se développe selon un mode de collaboration. Les données sont été retenues à la suite d'interviews et de questionnaires. Ce dernier instrument a été administré à 70 professeurs de formation aux adultes. Les résultats obtenus sont décrits et analysés. Les principaux éléments indiquent que la pratique actuelle de formation des adultes à ce centre de Tianjin ne tient pas compte des principes de l'éducation des adultes présenté selon un mode de collaboration. La formation est centrée sur l'enseignement. Il est à souhaiter que cette recherche contribuera à développer une meilleure compréhension de l'enseignement et de l'apprentissage en Chine tel que perçus par les formateurs et formatrices. Quelques suggestions de recherche complémentaires sont proposées à la fin.||Abstract: The present study grew out of one Chinese adult institute. Relatively few works are available that present a view of what actually happens in Chinese adult teaching and learning practice. Accordingly, it is believed that a case study on Tianjin Institute of Training Economic Management Personnel (TITEMP) which has been working for years in varions forms of adult programs, will be very useful addition to the knowledge of Chinese adult teaching and learning. The primary purpose of the present study is to serve as an introduction to one Chinese adult institute (TITEMP) in terms of characteristics of teaching, including selecting teaching content and teaching pattern, and to expand the understanding of Chinese adult teaching and learning. Based on the experiences of teachers at TITEMP, the study seeks to investigate the issues of teacher's perceptions and attitudes of teaching and learning to obtain implications toward learning-centred and collaborative mode. The theoretical foundations include andragogical conceptions (Knowles), roles of adult teachers (Brookfield), and conceptions of collaborative teaching and learning mode (Conti). The main sources of data are: the interviews and results of the questionnaire. Questionnaire responses from 70 teachers with knowledge of adult teaching and learning are described and interpreted. The general findings of the study are that the existing adult teaching practice at TITEMP does not adequately account for the principles of adult learning in a collaborative mode with adult students. Adult learning is teaching-centred. Some suggestions for further research are offered. It is hoped and believed that this research will contribute to a better understanding of Chinese adult teaching and learning in general, more particularly to the empirical study of the teachers from teaching and learning perspective in a Chinese adult higher learning setting. The research findings will be used as basis for the exploration of Chinese adult teaching.

Competencies Required in Education Research and Teaching Systematization according to Students from the Preschool, Primary and Secondary Education Programs of the University of Costa Rica

The purpose of this paper is to present the results of two online forums carried out with the participation of 42 students of the Licenciaturas  in Preschool Education, Primary Education and Secondary Education of the University of Costa Rica. The main purpose of the forums was to determine the insights of the participant students about the competencies they have achieved in the field of education research, and which have been the essential tools for them to systematize their own teaching practices. The discussion forums were part of the course FD5091 Métodos de Investigación Educativa [Education Research Methods] of the School of Teacher Education, delivered from March-April 2010.  Of the sample, 60 percent were students of the Preschool teaching program, 35 percent were from the Primary Education teaching program and 5 percent were from the Secondary Education teaching program in the fields of Science, Mathematics and Social Studies. According to the insights and beliefs showed by the participants –both, the future teachers and the profession practitioners–, there are no opportunities for research or systematization of their own teaching mediation, in the current work situation.(1) Translator’s Note: In Costa Rica, the “Licenciatura” is a one-year post-Bachelor study program, usually including thesis. “Primary Education” refers to students from the 1st to 6th grades, and “Secondary Education” refers to students from the 7th to 11th grades.

Sharing best practices in introducing and teaching ethics principles to public administration employees : research report

O projeto, financiado pelo Programa Aprendizagem ao Longo da Vida, decorreu entre 1 de agosto de 2011 e 31 de julho de 2013 e foi coordenado pelo Instituto de Administração Pública de Praga, tendo como parceiros a Escola de Economia e Direito de Berlim, a Escola Nacional de Administração Pública da Polónia e o INA, de Portugal. A coordenação portuguesa do estudo esteve a cargo da Prof. Doutora Helena Rato e da Dra. Matilde Gago, com a colaboração do Prof. Doutor César Madureira e da Dra. Margarida Quintela, ex investigadores do INA, atualmente na DGAEP.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Marketing education, distance learning and hypermedia : teaching 'current issues in marketing' in a virtual campus

This article reports on a project at the Universitat Oberta de Catalunya (UOC: The Open University of Catalonia, Barcelona) to develop an innovative package of hypermedia-based learning materials for a new course entitled 'Current Issues in Marketing'. The UOC is a distance university entirely based on a virtual campus. The learning materials project was undertaken in order to benefit from the advantages which new communication technologies offer to the teaching of marketing in distance education. The article reviews the main issues involved in incorporating new technologies in learning materials, the development of the learning materials, and their functioning within the hypermedia based virtual campus of the UOC. An empirical study is then carried out in order to evaluate the attitudes of students to the project. Finally, suggestions for improving similar projects in the future are put forward.

Coneixement lingüístic i matemàtic d'escolars de nivel sociocultural baix en programes d'immersió = Linguistic and mathematic knowledge in pupils of low sociocultural level in immersiom programmes

This piece of research compares knowledge of Catalan, Castilian and mathematics, as well as the attitudes to these two languages, of a sample of non-Catalan speaking pupils of low sociocultural level in their fourth year of primary school. Some of the pupils had followed an immersion programme in Catalan, whereas others had approached Catalan through their habitual language (Castilian). The findings show that not only did the immersion pupils obtain significantly better results in L2 (Catalan), but their mother tongue (Castilian) competence was undiminished and their performance on the mathematics test was superior to that of the other group. Moreover, the findings indicate that in pupils starting out from less favourable conditions (a low sociocultural level and a low I.Q.) the effect of the educational approach variable is greater than in other cases

Conflicto, colaboración y consenso en la enseñanza de las ciencias sociales = Conflict, collaboration and consensus in the teaching of the Social sciences

This article suggests the study of the key concept of conflict as a means of implementing a critical and communicativecurriculum based on the study of relevant social themes. To this end we put forward the principal characteristics of thecritical/communicative curriculum. We offer a didactic proposal about conflict and explain the results of its application intwo Secondary Education classrooms

Integrating environmental education in primary school education in Tanzania : teachers’ perceptions and teaching practices

The study focuses on primary school teachers’ perceptions of environmental education, its integration into primary school education and teachers’ teaching practices in Tanzania. The thesis is based on empirical research. The theoretical underpinnings of the study are based on Palmer’s (1998) model of environmental education. According to the model, meaningful environmental education should include education about, in or through and for the environment. The study is supported by national and international literature from research done on environmental education and education for sustainable development and policy statements. The study is qualitative in nature, adopting phenomenography and phenomenology as points of departure. The empirical data was collected from four primary schools in Morogoro region in Tanzania. The study sample consisted of 31 primary school teachers. Data was collected through interviews and lesson observations. According to the results of the study, primary school teachers expressed variations in their perceptions of environmental education and education for sustainable development. Most of the teachers focused on the aspect of knowledge acquisition. According to Tanzanian education and training policy, environmental education has to be integrated into all subjects. Although there is environmental education in the primary school curriculum, it is not integrated on an equal footing in all subjects. Some subjects like science, social studies and geography have more environmental content than other subjects. Teachers claim that the approach used to integrate environmental education into the school curriculum was not favoured because many claimed that what is to be taught as environmental education in the various subjects is not shown clearly. As a result, many teachers suggested that to ensure that it is taught properly it should be included in the curriculum as an independent subject or as specific topics. The study revealed that teachers’ teaching practices in integrating environmental education varied from one subject to another. Although most of the teachers said that they used participatory methods, lesson observations showed that they limited themselves to question and answer and group discussion. However, the teachers faced a number of barriers in the teaching of environmental education, some of which include lack of teaching and learning resources, time and large class size. The role of teachers in the implementation of environmental education in developing an environmentally literate citizenry is of great significance. The responsibility of the government in developing a curriculum with clear goals and content, developing teachers’ capacity in the teaching of environmental education and provision of teaching and learning materials needs to be taken seriously by the government in educational plans and programs.

Learning through role-playing games: an approach for active learning and teaching

This study evaluates the use of role-playing games (RPGs) as a methodological approach for teaching cellular biology, assessing student satisfaction, learning outcomes, and retention of acquired knowledge. First-year undergraduate medical students at two Brazilian public universities attended either an RPG-based class (RPG group) or a lecture (lecture-based group) on topics related to cellular biology. Pre- and post-RPG-based class questionnaires were compared to scores in regular exams and in an unannounced test one year later to assess students' attitudes and learning. From the 230 students that attended the RPG classes, 78.4% responded that the RPG-based classes were an effective tool for learning; 55.4% thought that such classes were better than lectures but did not replace them; and 81% responded that they would use this method. The lecture-based group achieved a higher grade in 1 of 14 regular exam questions. In the medium-term evaluation (one year later), the RPG group scored higher in 2 of 12 questions. RPG classes are thus quantitatively as effective as formal lectures, are well accepted by students, and may serve as educational tools, giving students the chance to learn actively and potentially retain the acquired knowledge more efficiently.