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.

Health-related learning needs and interests of selected non-institutionalized elderly

The research question in this study was "How do the noninstitutionalized elderly in the Hamilton-Wentworth Region perceive their learning needs and interests related to health?" The theoretical foundations of instruction for adults were reviewed as well as learning needs and interests in adult education, the assessment of learning needs in general, and the assessment of the learning needs of the elderly. The methodology used was a descriptive design. A research-based questionnaire-interview was developed, refined, and pilot tested. From a random sampling procedure, a participant group of 23 was secured. The questionnaireinterview was administered in a home visit situation. Data, which were collected, were coded, analyzed, processed, and printed. The results indicated that each participant had many learning needs and interests of varying intensities. The participants had many preferences in the delivery of health promotion. The learning needs and interests had several significant correlations with other variables. The implications of the result~ were discussed.

Globalization and Its Impact on Assessment: Moving Toward a New Story

Globalization has resulted in large-scale international and local assessments closely tied to notions of accountability and competitiveness in a globalized economy. Although policy makers seek to ensure citizens meet the demands of a global knowledge-based economy, such assessments may also impede the development of requisite 21st century skills. While standardization currently is viewed as the most effective measurement of student achievement, several Canadian and international jurisdictions are moving toward assessment for learning (AfL). This conceptual study sought to identify whether AfL or standardized assessment most effectively meets 21st century learning goals in the wake of rapid global change. It applies a Story Model theoretical framework to understand the current, the new emerging, and the future ideal story of education from a personal, cultural, and global lens. The study examines the main critiques and/or challenges of standardized testing, the benefits of AfL for student learning, and new teaching and assessment approaches to the development of 21st century learning goals. The study applies the Story Model’s inside-outside/past-future approach to determine the future direction of assessment. Results show that the new story of assessment will most likely entail a model that integrates both standardized testing and in-class assessments in the form of AfL and PBL.

A Teacher’s Formative Assessment Perceptions and Practices in Oral Intermediate English Courses at the Université de Montréal

Au cours des dernières années, les pratiques de l’évaluation comme aide à l’apprentissage (c’est-à-dire l’auto-évaluation, l’évaluation par les pairs, la rétroaction) dans la salle de classe ont été de plus en plus considérées comme des éléments essentiels (Black & Wiliam, 1998; Harlen & Winter, 2004; van de Watering & van der Rijt, 2006). Cependant, dans le domaine de l’apprentissage d’une langue seconde la recherche sur ce sujet est plutôt limitée. En nous fondant sur les études de Colby-Kelly et Turner (2007) et de Lyster et Ranta (1997), nous avons mené une recherche exploratoire visant à combler ce besoin. L’objectif général était de comprendre comment l’évaluation formative se réalise dans deux cours d’anglais intermédiaire à l’Université de Montréal, et de comparer comment ces pratiques sont perçues et vécues par la professeure et ses étudiants. Trois questions de recherche étaient posées: 1. Quelle est la nature de l’évaluation formative dans une salle de classe d’anglais langue seconde? 2. Est-ce que les pratiques de la professeure reflètent ce qu’elle pense de l’évaluation formative? 3. Quels sont les correspondances et différences entre les croyances de la professeure et les perceptions de ses étudiants quant aux bénéfices de l’évaluation formative pour l’apprentissage de l’anglais langue seconde? La collecte de données comprend des observations en classe, des entrevues auprès de la professeure et des questionnaires pour les étudiants. Pour répondre à notre première question de recherche, nous avons analysé la rétroaction donnée par la professeure pendant une production orale réalisée par ses étudiants à partir de la typologie de feedback et de uptake de l’étude de Lyster et Ranta (1997). En ce qui a trait à la deuxième question de recherche, nous avons fait des entrevues avec la professeure en vue d’expliciter ses perceptions relativement à l’évaluation formative. À la fin du trimestre, nous avons comparé ses réponses avec sa pratique à partir des enregistrements vidéo produits en classe. Finalement, pour répondre à notre dernière question de recherche nous avons comparé les réponses données par la professeure aux entrevues avec les réponses des étudiants à un questionnaire adapté à partir de celui de Colby-Kelly et Turner. Finalement, nous présentons et discutons les résultats les plus significatifs obtenus dans cette étude qualitative Nous concluons cette thèse en proposant de avenues pour des recherches futures.

Documenter les façons de faire d'enseignants de la 6e année du primaire dans toutes les étapes de la démarche d'évaluation

Le changement de paradigme amené par l'approche par compétences dans le système éducatif québécois au début des années 2000 devait conduire les enseignants à adopter de nouvelles façons de faire prescrites par la Politique en évaluation des apprentissages (MEQ, 2003) qui s’inscrivent dans une évaluation au service de l’apprentissage. Brookhart (2004) pour sa part, considère que la recherche en ce qui concerne les apprentissages et l'évaluation au primaire sont limitées et Boutin (2007) se questionne sur le changement effectif des pratiques considérant les vives critiques suscitées quant à l'implantation de l'approche par compétences dans les écoles québécoises. Cette recherche vise à apporter un éclairage quant aux façons de faire d'enseignants de la 6e année du primaire à toutes les étapes de la démarche d'évaluation en lecture, écriture et mathématique en les situant dans des perspectives nouvelles ou traditionnelles de l'évaluation et en observant si la fréquence des énoncés reliés aux façons de faire diffère selon les caractéristiques personnelles des enseignants. Suivant une méthodologie de type simultanée imbriquée, 55 enseignants ont rempli un questionnaire et 14 d'entre eux ont participé à des entrevues semi-dirigées. L’analyse des données montre que tout au long de la démarche d'évaluation, les façons de faire des enseignants varient, et ce, dans les trois matières: ils utilisent des façons de faire qui sont situées tantôt dans un continuum allant des perspectives traditionnelles aux perspectives nouvelles de l'évaluation comme dans la planification, la collecte de données, l'interprétation et la communication et tantôt dans les nouvelles perspectives de l'évaluation comme dans l'étape du jugement, et ce, selon leurs caractéristiques sociodémographiques. Nous avons ainsi pu catégoriser les enseignants selon le modèle de Schwartz, Bransford et Sears (2005) en distinguant ceux qui sont efficients de ceux qui ne le sont pas, même s'ils innovent. Afin d’améliorer les pratiques des enseignants à chaque étape de la démarche d’évaluation, nous pensons qu'il serait intéressant de valider un tableau synthèse inspiré de Scallon (2004) et l'OCDE (2005) afin de créer une métagrille pour analyser la pertinence et la cohérence des façons de faire des enseignants en cours de cycle dans une optique d’évaluation intégrée à l’apprentissage.

Conception d’un guide d’élaboration d’une épreuve de mathématiques dans une visée certificative pour la fin du cycle primaire au Burkina Faso

La présente recherche s’inscrit dans la mouvance actuelle orientée vers l’approche par compétences (APC) en Afrique de l’ouest. Née des exigences économiques et professionnelles à l’échelle mondiale, l’APC a connu son essor dans les années 1990. Par conséquent, le mode de recrutement sur le marché de l’emploi est basé sur les compétences des postulants. Il était donc légitime que l’école intègre cette nouvelle donne afin que les finissants puissent remplir les exigences socioprofessionnelles en temps opportun. De Ketele (2001, dans Hirtt 2009, p.6) est de cet avis quand il soutient que : « c’est en effet le monde socio-économique qui a déterminé la notion de compétence parce que les adultes que l’école a formés n’étaient pas suffisamment aptes à entrer dans la vie professionnelle ». L’APC rompt donc le caractère insulaire de l’école en faisant intervenir de nouveaux enjeux au niveau de l’enseignement, de l’apprentissage, des pratiques évaluatives des enseignants et des encadrements légaux dans les pays qui l’ont adoptée. Pour des contraintes socioéconomiques, le Burkina Faso a résolument opté de mettre en oeuvre une approche éclectique qui emprunte à l’APC certaines bases didactiques et pédagogiques. Cette option vise à doter le système éducatif burkinabé de mécanismes efficaces et efficients pour un enseignement de qualité tout en assurant la réussite et l’intégration socioprofessionnelle du plus grand nombre des sortants de l’école. Notre étude se situe dans cette nouvelle donne et vise l’amélioration du processus d’évaluation des élèves en fin du cycle primaire. Pour ce faire, nous avons conçu et validé un guide d’élaboration d’épreuves de mathématique dans une visée certificative pour ledit niveau afin de soutenir prioritairement les agents chargés de l’élaboration des épreuves officielles. En nous basant sur le paradigme de l’apprentissage, le constructivisme et la démarche méthodologique de Loiselle et Harvey (2009), nous avons examiné, dans un premier temps, les épreuves nationales développées au Québec et au Burkina Faso. Cette analyse a permis d’en relever les caractéristiques et d’identifier les éléments devant être retenus dans le cahier des charges au regard du profil des sortants défini dans le programme burkinabé. Dans un deuxième temps, un cahier des charges (version initiale.) a été développé en quatre sections afin de présenter les principes qui le sous-tendent : (1) l’élaboration des situations d’évaluation, (2) l’élaboration des outils d’administration de l’épreuve, (3) l’élaboration des outils de correction et de consignation et (4) les grilles d’évaluation. Dans un troisième temps, un groupe d’experts canadiens et deux groupes d’experts burkinabé se sont exprimés sur le degré de pertinence et de clarté de chaque section à partir de l’une ou l’autre version du Guide. Leurs observations et commentaires nous ont permis de le bonifier. D’une manière générale, les pourcentages des degrés d’accord pour la pertinence et la clarté des contenus développés au niveau de chaque section sont satisfaisants. Cependant, les recommandations des experts ont suscité des ajustements sur : 1) le contenu du guide soit de conserver une seule épreuve en mathématiques et de retirer les énoncés concernant les volets lecture et écriture en français; 2) le contenu de certains tableaux : à compléter ou à fusionner et; 3) la qualité de la langue : certaines phrases ont été reformulées, les erreurs de numérotation de certaines sous-sections ont été corrigées. La version finale serait celle qui est adaptée au contexte burkinabé. Ce guide est destiné aux structures chargées de l’évaluation des apprentissages et des acquis des élèves au Burkina Faso. Il constitue aussi un référentiel pour la formation initiale et continue des enseignants et des encadreurs. Bien que la recherche ait rempli des conditions méthodologiques et éthiques, la mise en oeuvre de ses résultats se limite au contexte burkinabé. Cependant, ils pourront soutenir ou orienter d’autres recherches qui s’inscrivent dans la même dynamique.

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Recreational Mathematics - Only For Fun?

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment?

Building a Learning Architecture : e-Learning and e-Services

With the rapid advancement of the webtechnology, more and more educationalresources, including software applications forteaching/learning methods, are available acrossthe web, which enables learners to access thelearning materials and use various ways oflearning at any time and any place. Moreover,various web-based teaching/learning approacheshave been developed during the last decade toenhance the capability of both educators andlearners. Particularly, researchers from bothcomputer science and education are workingtogether, collaboratively focusing ondevelopment of pedagogically enablingtechnologies which are believed to improve theinfrastructure of education systems andprocesses, including curriculum developmentmodels, teaching/learning methods, managementof educational resources, systematic organizationof communication and dissemination ofknowledge and skills required by and adapted tousers. Despite of its fast development, however,there are still great gaps between learningintentions, organization of supporting resources,management of educational structures,knowledge points to be learned and interknowledgepoint relationships such as prerequisites,assessment of learning outcomes, andtechnical and pedagogic approaches. Moreconcretely, the issues have been widelyaddressed in literature include a) availability andusefulness of resources, b) smooth integration ofvarious resources and their presentation, c)learners’ requirements and supposed learningoutcomes, d) automation of learning process interms of its schedule and interaction, and e)customization of the resources and agilemanagement of the learning services for deliveryas well as necessary human interferences.Considering these problems and bearing in mindthe advanced web technology of which weshould make full use, in this report we willaddress the following two aspects of systematicarchitecture of learning/teaching systems: 1)learning objects – a semantic description andorganization of learning resources using the webservice models and methods, and 2) learningservices discovery and learning goals match foreducational coordination and learning serviceplanning.

Teaching Mathematics in English to Swedish Speaking Students : The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School

Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

Machine translation and the disruption of foreign language learning activities

This study examines the question of how language teachers in a highly technology-friendly university environment view machine translation and the implications that this has for the personal learning environments of students. It brings an activity-theory perspective to the question, examining the ways that the introduction of new tools can disrupt the relationship between different elements in an activity system. This perspective opens up for an investigation of the ways that new tools have the potential to fundamentally alter traditional learning activities. In questionnaires and group discussions, respondents showed general agreement that although use of machine translation by students could be considered cheating, students are bound to use it anyway, and suggested that teachers focus on the kinds of skills students would need when using machine translation and design assignments and exams to practice and assess these skills. The results of the empirical study are used to reflect upon questions of what the roles of teachers and students are in a context where many of the skills that a person needs to be able to interact in a foreign language increasingly can be outsourced to laptops and smartphones.

Comportamento matemático: relações ordinais e inferência transitiva em pré-escolares

Um repertório matemático elementar pode ser diretamente ensinado a pré-escolares em risco de dificuldades de aprendizagem. Nesta pesquisa, examinou-se o controle do comportamento por relações ordinais em 14 crianças (idade média: 5 anos e 1 mês) com baixo rendimento escolar numa escola municipal de Vitória. Inicialmente, os estudantes foram avaliados de modo individualizado, em seguida aplicou-se um procedimento de ensino informatizado para ensinar desempenhos ordinais e avaliou-se a ocorrência de desempenhos gerativos. Todas as crianças alcançaram o critério de ensino, estabelecendo-se o controle do comportamento por relações ordinais. Na avaliação da transferência de funções de estímulo 14 crianças ordenaram novas seqüências de estímulos com o procedimento informatizado e oito crianças com o procedimento não informatizado. Conclui-se que habilidades básicas para o aprendizado da matemática podem ser diretamente ensinadas, apesar das falhas no repertório inicial da criança.

O uso de blogs como tecnologia educacional narrativa para a forma/ação inicial docente

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A matemática financeira e a estatística como ferramentas para uma gestão financeira consciente

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)