Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

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.

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)

Epitaxial growth and properties of AlGaN-based UV-LEDs on Si(111) substrates

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2010

Wachstumsoptimierung und Charakterisierung von MOVPE-basierten GaN Pufferstrukturen auf Si(111) Substraten

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2014

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.

S. Johannes Chrysostomus, Homiliae (1-82v, 87v-111, 132v-226v), De compunctione cordis (226v-264v), Tractatus de reparatione lapsi (264v-303).

Abbaye Saint-Maur-des-Fossés ; cf. B. de Montfaucon, Bibliotheca bibliothecarum, II, 1739, p. 1141-1143 : "60. 1083. S. Joan. Chrysostomi Homiliae de diversis.". Ex-libris : F. Bv : « Iste liber est sancti Petri... », suivi d'un anathème (Xe-XIe s.) ; f. B : "Sti Germani a Pratis" ; f. 1 : « ex libris monasterii Sancti Germani a pratis Parisiorum ». France.

Uniform Manual Real Property Acquisition and Relocation Assistance Section II - Chapter 111 Uniform Rules and Procedures April, 2006

The purpose of this chapter is to implement Iowa Code chapter 316 and sections 6B.42, 6B.45, 6B.54 and 6B.55, as required by the Uniform Relocation Assistance and Real Property Acquisition Policies Act of 1970, Pub. L. 91-646, as amended by the Uniform Relocation Act Amendments of 1987, Title IV, Pub. L. No. 100-17 , Sec. 104, Pub. L. 105-117, and federal regulations adopted pursuant thereto.

Biokinetics and dosimetry of 111 In-DOTA-NOC-ATE compared with 111In-DTPA-Octreotide

Aim: Biokinetics and dosimetry of 111In-DOTA-NOC-ATE (NOCATE) and 111In-DTPA-octreotide (Octreoscan?, OCTREO) were comparatively studied in the same patients. Patients and Methods: Seventeen patients (10 males, 7 females), mean age 60 years referred for an Octreoscan? because of carcinoid (N=9), unspecified neurodendocrine tumors (N=6), thymoma (N=1) or medullary thyroid carcinoma (N=1) accepted a second study with NOCATE. Four patients had no detectable tumor at the time of scanning. Whole-body (WB) anterior-posterior scans were recorded 0.5 (100% reference scan), 4, 24 and 48 hrs (N=17) and 120 hrs (N=6) after injection. OCTREO (178±15 MBq) preceded NOCATE (108±14 MBq) imaging with 16±5 days in 16 patients while 1 patient had first NOCATE followed 14 days later by OCTREO. Blood samples were taken 5, 15, 30, 60, 240 and 1440 min after injection. Background corrected geometric mean counts of WB, lung, kidney, liver, spleen and blood counts expressed in % of the initial composite WB and blood counts, respectively were fitted to bi- or single exponential curves and dosimetry was performed for male and female patients using MIRDOSE3.1 and OLINDA/EXM. Results: Initially, WB, lung and kidney activity was similar but retention was significantly higher for NOCATE compared with OCTREO. Liver and spleen uptake of NOCATE was higher from beginning (p<0.001) and remained so over time. Activity in rest of body showed similar α and β half-lives, but the β half-life fraction of NOCATE was much higher than OCTREO (49% vs. 19%, respectively). Blood T1/2β was longer for NOCATE compared with OCTREO (19 vs. 6h). Residence times were similar in male and female patients while they were in both genders higher for NOCATE than OCTREO. Consequently, effective dose (ED) for NOCATE (ED 114 and 134 μSv/MBq for man and women, respectively) exceeded that of OCTREO (ED = 61 and 71 μSv/MBq), the latter results being close to the ICRP-published radiation dose of OCTREO (ED = 54 and 71 µSv/MBq, respectively). Differential activity measurement in blood cells and plasma showed that only a minor fraction of NOCATE and OCTREO (<5 % in the mean) was bound to globular blood components. Conclusions: NOCATE showed higher retention in normal organs and delivered roughly twice the radiation dose of OCTREO. The ED of OCTREO in these patients was similar to ICRP80 report when adopting a bladder voiding interval of 2 hours.

Biokinetics and dosimetry of (111)In-DOTA-NOC-ATE compared with (111)In-DTPA-octreotide.

PURPOSE: The biokinetics and dosimetry of (111)In-DOTA-NOC-ATE (NOCATE), a high-affinity ligand of SSTR-2 and SSTR-5, and (111)In-DTPA-octreotide (Octreoscan?, OCTREO) were compared in the same patients. METHODS: Seventeen patients (10 men, 7 women; mean age 60 years), referred for an OCTREO scan for imaging of a neuroendocrine tumour (15), thymoma (1) or medullary thyroid carcinoma (1), agreed to undergo a second study with NOCATE. Whole-body anterior-posterior scans were recorded 0.5 (100 % reference scan), 4, 24 and 48 h (17 patients) and 120 h (5 patients) after injection. In 16 patients the OCTREO scan (178 ± 15 MBq) was performed 16 ± 5 days before the NOCATE scan (108 ± 14 MBq) with identical timing; 1 patient had the NOCATE scan before the OCTREO scan. Blood samples were obtained from 14 patients 5 min to 48 h after injection. Activities expressed as percent of the initial (reference) activity in the whole body, lung, kidney, liver, spleen and blood were fitted to biexponential or single exponential functions. Dosimetry was performed using OLINDA/EXM. RESULTS: Initial whole-body, lung and kidney activities were similar, but retention of NOCATE was higher than that of OCTREO. Liver and spleen uptakes of NOCATE were higher from the start (p < 0.001) and remained so over time. Whole-body activity showed similar α and β half-lives, but the β fraction of NOCATE was double that of OCTREO. Blood T (1/2)β for NOCATE was longer (19 vs. 6 h). As a result, the effective dose of NOCATE (105 μSv/MBq) exceeded that of OCTREO (52 μSv/MBq), and the latter result was similar to the ICRP 106 value of 54 μSv/MBq. Differential activity measurement in blood cells and plasma showed an average of <5 % of NOCATE and OCTREO attached to globular blood components. CONCLUSION: NOCATE showed a slower clearance from normal tissues and its effective dose was roughly double that of OCTREO.