Teaching mathematics using Massive Open Online Courses

Distance learning - where students take courses (attend classes, get activities and other sort of learning materials) while being physically separated from their instructors, for larger part of the course duration - is far from being a “new event”. Since the middle of the nineteenth century, this has been done through Radio, Mail and TV, taking advantage of the full educational potential that these media resources had to offer at the time. However, in recent times we have, at our complete disposal, the “magic wonder” of communication and globalization - the Internet. Taking advantage of a whole new set of educational opportunities, with a more or less unselfish “look” to economic interests, focusing its concern on a larger and collective “welfare”, contributing to the development of a more “equitable” world, with regard to educational opportunities, the Massive Open Online Courses (MOOCs) were born and have become an important feature of the higher education in recent years. Many people have been talking about MOOCs as a potential educational revolution, which has arrived from North America, still growing and spreading, referring to its benefits and/or disadvantages. The Polytechnic Institute of Porto, also known as IPP, is a Higher Education Portuguese institution providing undergraduate and graduate studies, which has a solid history of online education and innovation through the use of technology, and it has been particularly interested and focused on MOOC developments, based on an open educational policy in order to try to implement some differentiated learning strategies to its actual students and as a way to attract future ones. Therefore, in July 2014, IPP launched the first Math MOOC on its own platform. This paper describes the requirements, the resulting design and implementation of a mathematics MOOC, which was essentially addressed to three target populations: - pre-college students or individuals wishing to update their Math skills or that need to prepare for the National Exam of Mathematics; - Higher Education students who have not attended in High School, this subject, and who feel the need to acquire basic knowledge about some of the topics covered; - High School Teachers who may use these resources with their students allowing them to develop teaching methodologies like "Flipped Classroom” (available at http://www.opened.ipp.pt/). The MOOC was developed in partnership with several professors from several schools from IPP, gathering different math competences and backgrounds to create and put to work different activities such video lectures and quizzes. We will also try to briefly discuss the advertising strategy being developed to promote this MOOC, since it is not offered through a main MOOC portal, such as Coursera or Udacity.

Educação bilingue em Moçambique: um estudo de caso, na Província de Gaza, centrado nas práticas pedagógicas do ensino básico

Em contextos como o de Moçambique que apresenta uma diversidade linguística, o uso de mais de uma língua no ensino é quase que obrigatório. Assim, urge a necessidade de formalizar a Educação Bilingue (EB) nas escolas moçambicanas. A modalidade de EB em Moçambique é de transição e manutenção, nas primeiras classes (1ª, 2ª e 3ª) usa-se a língua local como meio de instrução e o Português é uma disciplina, a partir da 4ª classe há uma inversão. Dessa estratégia o aluno deve estar em condições na 5ª classe de enfrentar o exame nacional, que é feito em língua oficial Portuguesa, para transitar do 1º para o 2º grau. O trabalho tem como problema esta interrogação: De que modo o programa curricular de Educação Bilingue se traduz nas práticas pedagógicas nas escolas do Ensino Básico que usam a língua Portuguesa e Changana no distrito de Bilene, na província de Gaza? O estudo empírico é de natureza qualitativa e quantitativa, com a utilização de técnicas de recolha de dados como a análise documental, entrevistas, questionário e provas escrita e oral aos alunos. Do estudo conclui-se: i) Não existe um programa de base especificamente para EB; ii) Há incongruência entre o programa e as práticas pedagógicas e iii) Os alunos apresentam maior dificuldades de compreensão, na escrita do que na oralidade, nas provas de conhecimento nas disciplinas básicas (Português e Matemática) em língua Portuguesa.

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.9 (1831)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.3 (1828)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.4 (1828)

A course of instruction in zootomy (vertebrata).

1884

A course of practical instruction in elementary biology, by T. H. Huxley, assisted by H. N. Martin.

1876

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.

Instruction of haematopoietic lineage choices, evolution of transcriptional landscapes and cancer stem cell hierarchies derived from an AML1-ETO mouse model.

The t(8;21) chromosomal translocation activates aberrant expression of the AML1-ETO (AE) fusion protein and is commonly associated with core binding factor acute myeloid leukaemia (CBF AML). Combining a conditional mouse model that closely resembles the slow evolution and the mosaic AE expression pattern of human t(8;21) CBF AML with global transcriptome sequencing, we find that disease progression was characterized by two principal pathogenic mechanisms. Initially, AE expression modified the lineage potential of haematopoietic stem cells (HSCs), resulting in the selective expansion of the myeloid compartment at the expense of normal erythro- and lymphopoiesis. This lineage skewing was followed by a second substantial rewiring of transcriptional networks occurring in the trajectory to manifest leukaemia. We also find that both HSC and lineage-restricted granulocyte macrophage progenitors (GMPs) acquired leukaemic stem cell (LSC) potential being capable of initiating and maintaining the disease. Finally, our data demonstrate that long-term expression of AE induces an indolent myeloproliferative disease (MPD)-like myeloid leukaemia phenotype with complete penetrance and that acute inactivation of AE function is a potential novel therapeutic option.

Innovative Applications : Open Educational Resources and Mobile Resources Repository for the Instruction of Educational Researchers in Mexico

The movement of Open Educational Resources (OER) is one of the most important trends that are helping education through the Internet worldwide. "Tecnológico de Monterrey" (http://tecvirtual.itesm.mx/) in Mexico, with other Mexican higher education institutions, is creating an Internet/web based repository of OERs and Mobile Resources for the instruction and development of educational researchers at undergraduate, Master's and Doctoral level. There is a lack of open educational resources and material available at the Internet that can help and assist the development and education of educational researchers in Spanish speaking countries. This OER repository is part of a project that is experimenting new technology for the delivery of OERs from one repository (http://catedra.ruv.itesm.mx/) through an indexed OER catalog (http://www.temoa.info/) to mobile devices (Ipod, Iphone, MP3, MP4). This paper presentation will describe and comment about this project: outcomes, best practices, difficulties and technological constraints.