Beyond g : putting multiple intelligences theory to the test /

The purpose of this study was to investigate Howard Gardner's (1983) Multiple Intelligences theory, which proposes that there are eight independent intelligences: Linguistic, Spatial, Logical/Mathematical, Interpersonal, Intrapersonal, Naturalistic, Bodily-Kinesthetic, and Musical. To explore Gardner's theory, two measures of each ability area were administered to 200 participants. Each participant also completed a measure of general cognitive ability, a personality inventory, an ability self-rating scale, and an ability self-report questionnaire. Nonverbal measures were included for most intelligence domains, and a wide range of content was sampled in Gardner's domains. Results showed that all tests of purely cognitive abilities were significantly correlated with the measure of general cognitive ability, whereas Musical, Bodily-Kinesthetic, and one of the Intrapersonal measures were not. Contrary to what Multiple Intelligences theory would seem to predict, correlations among the tests revealed a positive manifold and factor analysis indicated a large factor of general intelligence, with a mathematical reasoning test and a classification task from the Naturalistic domain having the highest ^- loadings. There were only minor sex differences in performance on the ability tests. Participants' self-estimates of ability were significantly and positively correlated with actual performance in some, but not all, intelligences. With regard to personality, a hypothesized association between Openness to Experience and crystallized intelligence was supported. The implications of the findings in regards to the nature of mental abilities were discussed, and recommendations for further research were made.

Lien entre l'activité pariéto-occipitale enregistrée pendant une tâche de mémoire à court terme visuelle et les habiletés mathématiques : une étude en magnétoencéphalographie

La mémoire à court terme visuelle (MCTv) est un système qui permet le maintien temporaire de l’information visuelle en mémoire. La capacité en mémoire à court terme se définit par le nombre d’items qu’un individu peut maintenir en mémoire sur une courte période de temps et est limitée à environ quatre items. Il a été démontré que la capacité en MCTv et les habiletés mathématiques sont étroitement liées. La MCTv est utile dans beaucoup de composantes liées aux mathématiques, comme la résolution de problèmes, la visualisation mentale et l’arithmétique. En outre, la MCTv et le raisonnement mathématique font appel à des régions similaires du cerveau, notamment dans le cortex pariétal. Le sillon intrapariétal (SIP) semble être particulièrement important, autant dans la réalisation de tâches liées à la MCTv qu’aux habiletés mathématiques. Nous avons créé une tâche de MCTv que 15 participants adultes en santé ont réalisée pendant que nous enregistrions leur activité cérébrale à l’aide de la magnétoencéphalographie (MEG). Nous nous sommes intéressés principalement à la composante SPCM. Une évaluation neuropsychologique a également été administrée aux participants. Nous souhaitions tester l’hypothèse selon laquelle l’activité cérébrale aux capteurs pariéto-occipitaux pendant la tâche de MCTv en MEG sera liée à la performance en mathématiques. Les résultats indiquent que l’amplitude de l’activité pariéto-occipitale pendant la tâche de MCTv permet de prédire les habiletés mathématiques ainsi que la performance dans une tâche de raisonnement perceptif. Ces résultats permettent de confirmer le lien existant entre les habiletés mathématiques et le fonctionnement sous-jacent à la MCTv.

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

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo

A matemática, o quadro de escrever e os formadores de professores de matemática: interpretando relações

Por muito tempo o quadro de escrever ou quadro de giz foi o referencial de uma educação tradicional, cuja sua função era apenas demonstrar e simbolizar os conhecimentos docentes, uma vez que ao professor perpetuava a condição de detentor do saber e transmissor de todo conhecimento que possuía, sem ao menos refletir a importância e significados do uso do quadro em função a construção coletiva do conhecimento intermediado pelo quadro de escrever. Para desmistificar esses pressupostos foi a proposta desse estudo, uma vez que se buscou compreender quais aspectos relevantes e diferenciados que os formadores de professores de matemática atribuem ao uso do quadro. Ao mesmo tempo em que precisam atender as perspectivas do século XXI. Numa investigação focal procuramos identificar junto as narrativas de constituição dos formadores influências pessoais e coletivas em relação ao magistério e a saberes desenvolvidos em relação ao uso do quadro. Visto que por várias vezes e em discursos diferentes o quadro foi lembrado como apenas “memória auxiliar” da construção do raciocínio matemático. As discussões aqui realizadas foram acerca baseadas em dados coletados através de questionário entrevistas, os quais tem como prioridades a formação docente e suas relações com o quadro de escrever. Além da relevância do quadro de escrever no ensino da matemática e na formação de professores críticos e mediadores de matemática.

A matemática do sensível pelas mãos do artesão: marcas da aprendizagem matemática e da cultura material dos ceramistas de Icoaraci

Esta tese aborda a discussão a respeito do raciocínio matemático manifestado no saber/ fazer dos artesãos ceramistas do Distrito Municipal de Icoaraci (Belém/ PA), visando o entendimento cognitivo e cultural desta prática, para abstrair contribuições à educação matemática – área de conhecimento na qual se inscreve, especialmente no âmbito da educação matemática. Trabalhado essa última, a tese analisa a realidade dos sujeitos mediante a Teoria dos Campos Conceituais, do educador matemático Gérard Vergnaud, que desenvolve estudos na linha construtivista, do psicólogo da educação Jean Piaget, possibilitando abordar na prática cotidiana do artesão, seus Campos Conceituais, a possibilidade ou não da existência de teoremas e conceitos-em-ato, fato esse que irá constatar ou não a essência ou „matematicidade‟ dos estudos educacionais matemáticos trabalhados por etnomatemáticos, pedagogos, especialistas de modelagem matemática, sociólogos e arqueólogos matemáticos. A epistemologia da educação matemática, disciplina filosófica, surge norteando esse entendimento sobre o raciocínio matemático, através da matemática do sensível, que acha origens na antiguidade grega, através dos ideários pitagórico, platônico e aristotélico, estendendo essa visão à matemática do mundo presente. Assim, a tese procura explicitar a manifestação de um raciocínio matemático por parte do artesão, que no seu fazer predominantemente não conhece e/ ou não utiliza a matemática acadêmica ou formal, como comprovado em outros estudos. Essa presença ou não de entendimentos matemáticos será constatada através de abordagem etnográfica e qualitativa, sob o enfoque fenomenológico, utilizando técnicas de observação, anotações de campo, inventário cultural e entrevistas, no intuito de analisar as representações existentes em suas obras e o fazer/ pensar manifestados nessa produção.

Efeitos da microgravidade no raciocínio lógicomatemático, proposta de experimentação

O trabalho a seguir apresentado tem por objetivo procurar perceber se o nosso raciocínio se processa da mesma maneira em presença de microgravidade ou se, pelo contrário, sofre alguma alteração. A nossa questão foca-se mais especificamente num teste de matemática e, a partir da análise das diferentes variantes intervenientes na resolução do mesmo e das condições em causa (ambiente de microgravidade), inferirmos a possibilidade de o resultado do teste poder ser melhor do que quando elaborado em condições de gravidade normal.

Illustrating Cognitive Connections between Math and Language in Pre-Service Teachers’ Perceptions of Common or Everyday Terms

This paper introduces a new construct that we term Math Mediated Language (MML) focusing on the notion that common or everyday terms with mathematical meanings are important building blocks for students’ mathematical reasoning. A survey given to 96 pre-service early childhood educators indicated clear patterns of perceptions of these terms.

The Effect of Using Portfolios on Student-Parent and Parent-Teacher Communication

This action research project studied how portfolios enhance the communication between students, parents, and the teacher. While using portfolios in my class, students experienced more dialogue with their parents regarding their effort, the topics being taught, and explanations requiring communication with mathematical reasoning.

Sistema de contagem com morfologia matemática fuzzy

Mathematical Morphology presents a systematic approach to extract geometric features of binary images, using morphological operators that transform the original image into another by means of a third image called structuring element and came out in 1960 by researchers Jean Serra and George Matheron. Fuzzy mathematical morphology extends the operators towards grayscale and color images and was initially proposed by Goetherian using fuzzy logic. Using this approach it is possible to make a study of fuzzy connectives, which allows some scope for analysis for the construction of morphological operators and their applicability in image processing. In this paper, we propose the development of morphological operators fuzzy using the R-implications for aid and improve image processing, and then to build a system with these operators to count the spores mycorrhizal fungi and red blood cells. It was used as the hypothetical-deductive methodologies for the part formal and incremental-iterative for the experimental part. These operators were applied in digital and microscopic images. The conjunctions and implications of fuzzy morphology mathematical reasoning will be used in order to choose the best adjunction to be applied depending on the problem being approached, i.e., we will use automorphisms on the implications and observe their influence on segmenting images and then on their processing. In order to validate the developed system, it was applied to counting problems in microscopic images, extending to pathological images. It was noted that for the computation of spores the best operator was the erosion of Gödel. It developed three groups of morphological operators fuzzy, Lukasiewicz, And Godel Goguen that can have a variety applications

GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.

Humor in mathematics teaching

HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade

Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.

GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.

Ambiente digital de aprendizagem promotor do desenvolvimento do raciocínio matemático em alunos com perturbações do espetro do Autismo

A utilização das tecnologias é considerada um meio eficaz para trabalhar conteúdos académicos com alunos com Perturbações do Espetro do Autismo (PEA) possibilitando a criação de ambientes criativos e construtivos onde se podem desenvolver atividades diferenciadas, significativas e de qualidade. Contudo, o desenvolvimento de aplicações tecnológicas para crianças e jovens com PEA continua a merecer pouca atenção, nomeadamente no que respeita à promoção do raciocínio dedutivo, apesar desta ser uma área de grande interesse para indivíduos com esta perturbação. Para os alunos com PEA, o desenvolvimento do raciocínio matemático torna-se crucial, considerando a importância destas competências para o sucesso de uma vida autónoma. Estas evidências revelam o contributo inovador que o ambiente de aprendizagem descrito nesta comunicação poderá dar nesta área. O desenvolvimento deste ambiente começou por uma etapa de criação e validação de um modelo que permitiu especificar e prototipar a solução desenvolvida que oferece modalidades de adaptação dinâmica das atividades propostas ao perfil do utilizador, procurando promover o desenvolvimento do raciocínio matemático (indutivo e dedutivo). Considerando a heterogeneidade das PEA, o ambiente desenvolvido baseia-se em modalidades de adaptação dinâmica e em atividades ajustadas ao perfil dos utilizadores. Nesta comunicação procurámos dar a conhecer o trabalho de investigação já desenvolvido, bem como perspetivar a continuidade do trabalho a desenvolver.