Beiträge zum Mathematikunterricht 2015. Vorträge auf der 49. Tagung für Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel [Band 2]

Die Jahrestagung der Gesellschaft für Didaktik der Mathematik fand im Jahr 2015 zum dritten Mal in der Schweiz statt. [...] Mit rund 300 Vorträgen, 16 moderierten Sektionen, 15 Arbeitskreistreffen und 21 Posterpräsentationen eröffnete sich ein breites Spektrum an Themen und unterschiedlichen Zugangsweisen zur Erforschung von Fragen rund um das Lernen und Lehren von Mathematik. (DIPF/Orig.)

Prática de ensino supervisionada em Educação Pré-escolar e Ensino do 1.º Ciclo do Ensino Básico

O presente relatório foi realizado no âmbito da Unidade Curricular de Prática de Ensino Supervisionada (PES), integrada no curso de Mestrado em Educação Pré-escolar (EPE) e Ensino do 1.º Ciclo do Ensino Básico (1.º CEB) e desenvolvida em contexto de Educação Pré-escolar, numa Instituição Particular de Solidariedade Social, com crianças de 3 anos de idade e em contexto do 1.º Ciclo do Ensino Básico, numa escola da rede pública com um grupo/turma de crianças de 5 e 6 anos de idade. A prática foi desenvolvida nos dois contextos, e os dados foram retirados no decorrer das intervenções realizadas através da observação direta e participante, sendo que para a recolha de dados recorremos a notas de campo, registos fotográficos e de áudio e, ainda, às produções das crianças, com a intencionalidade de nos servirem como documentos de análise. Ao longo do processo fomos também realizando registos numa grelha de observação, adaptada de Viana e Ribeiro (2014), para podermos compreender a evolução das crianças no desenvolvimento das suas competências (meta)linguísticas. Partimos da questão-problema: Que estratégias de aprendizagem se podem desenvolver em contexto de Educação Pré-escolar e de 1.º Ciclo Ensino Básico, no sentido de desenvolver competências (meta)linguísticas? Considerando esta interrogação estabelecemos como objetivo: (i) Promover o desenvolvimento linguístico e metalinguístico das crianças num contexto geral de comunicação (oralidade, escrita e leitura). O estudo ajusta-se a uma abordagem qualitativa. Para que fosse possível recolhermos a informação para a presente investigação foi necessário selecionarmos um conjunto de técnicas e de instrumentos de recolha de dados. Durante as atividades que desenvolvemos proporcionamos um ambiente positivo, facilitador da exploração de situações diversificadas de escrita e leitura e propiciamos, também, oportunidades para que cada criança fosse ouvida, respeitada e integrada. Em termos de resultados pensamos poder concluir que nos dois contextos atendemos aos interesses e motivações das crianças, de modo a promover estratégias de aprendizagens de forma a desenvolver competências (meta)linguísticas, como se comprova pela análise dos dados obtidos através das grelhas de observação, bem como nas experiências de ensino e aprendizagem que integramos neste documento e que também dão conta do processo vivenciado ao longo da Prática de Ensino Supervisionada.

Selbstgesteuertes Lernen mit Kompetenzrastern. Ein theoretischer Blick auf das Potenzial eines pädagogischen Instruments zum individualisierten Lernen

Kompetenzraster sind pädagogische Instrumente, die zum kompetenzorientierten, individualisierten und selbstgesteuerten Lernen in beruflichen Schulen eingesetzt werden. Sie werden üblicherweise im Rahmen eines pädagogischen Gesamtkonzeptes genutzt, indem die Raster oft ein zentrales Instrument in einem komplexen Gefüge schulischer Lern- und Lehrprozesse sind. Kompetenzraster sind häufig der Fixpunkt, an dem sich andere Instrumente (wie Checklisten und Lernjobs) orientieren und sie definieren die Ausgangs- und Zielpunkte der Lernprozesse. Dabei werden den Schülern üblicherweise Freiheitsgrade eingeräumt, so dass sie (mit-) entscheiden ob, was, wann, wie und woraufhin sie lernen. Die schulische Arbeit mit den Rastern kann als ein Versuch angesehen werden, die Lernenden in den Mittelpunkt pädagogischen Denkens und Handelns zu stellen. Dieser Beitrag hat das Ziel, selbstgesteuertes Lernen aus einer distanzierten, vom einzelnen pragmatischen Modell abstrahierenden und eher theoretischen Perspektive auf das individualisierte Lernen mit Kompetenzrastern zu beziehen. Im Kern wird ein Systematisierungsansatz entwickelt, in dem die komplexen Zusammenhänge des Lernens mit Kompetenzrastern im Kontext von selbstgesteuertem Lernen dargestellt werden. Damit soll ein Beitrag zur Elaboration des Lernens mit Kompetenzrastern in beruflichen Schulen geleistet werden. Konkret wird die folgende Frage fokussiert: Was können Kompetenzraster im Rahmen selbstgesteuerten Lernens leisten? (DIPF/Orig.)

Aplicação das ciências forenses no ensino secundário: um conjunto de actividades para a disciplina de Física e Química A

A popularidade das séries televisivas que abordam as Ciências Forenses (CSI 1 Mentes Criminosas, Casos Arquivados...) permite construir actividades que envolvem os alunos numa exploração científica de modo a que dominem os conceitos e apreciem a natureza da Ciência. Estes recursos educativos aplicam uma abordagem Ciência­ Tecnologia-Sociedade -Pensamento Crítico (CTS-PC) e podem ser explorados segundo uma metodologia de Aprendizagem Baseada na Resolução de Problemas (ABRP). Neste trabalho são propostas actividades laboratoriais, a decorrer no contexto formal das aulas da disciplina de Física e Química A (FQ·A), utilizando sensores e a calculadora gráfica. Num contexto não-formal, e baseadas nas técnicas analíticas utilizadas em Ciências Forenses, foram desenvolvidas actividades para um Clube de Ciência ou Laboratórios Abertos, complementadas por um blogue (CSI-Mafra). Estes recursos foram posteriormente partilhados com outros professores de Física e Química, numa acção de formação, proposta pela autora, e cujo objectivo principal foi a diversificação das estratégias de ensino e aprendizagem. O entusiasmo dos alunos na realização das tarefas propostas e os resultados nos questionários de grau de satisfação e de opinião, aplicados a alunos e professores, sugere que as actividades desenvolvidas podem contribuir na motivação dos alunos para o estudo da Física e da Química e promover a literacia científica da comunidade escolar. ABSTRACT; The high popularity between teenagers of the television series that have Forensic Sciences and Criminal lnvestigations as central theme, such as CSI, Dexter, Criminal Minds and Cold Case, can be used to develop learning activities that involves the students into a scientific exploration which aim is leading the students to learn Chemistry and Physics with pleasure, motivation and curiosity. The educational resources developed in this thesis make use of the strategy Science-Technology-Society-Critical Thinking (STS-CP) and can be exploited according the teaching methodology Problem Based Learning (PBL). ln this work we propose a number of laboratory activities that can be used on the classes of the High School course Physic and Chemistry A (FQ-A) and a different set of activities to be used in a non-formal teaching environment, which are based on the analytical techniques used in Forensic Sciences. The non-formal activities were developed as part of the activities of a Science Club and complemented with an interactive blog. The teaching resources developed by us were also used in a professional training course to physics and chemistry teachers aimed to teach how to introduce new teaching­ learning strategies. The enthusiasm of the students shown during the activities and the extremely positive results of the questionnaires, applied to students and teachers after the activities, clearly indicates that the learning resources developed in this thesis contribute to the student's motivation to learn Physic and Chemistry and to promote the scientific Iiteracy of the scholar community.

Prática de ensino supervisionada em educação pré-escolar e ensino do 1º ciclo do ensino básico: explorando a simetria na infância

O presente relatório é referente à investigação realizada no âmbito das unidades curriculares da Prática de Ensino Supervisionada em Pré-Escolar e 1.º Ciclo do Ensino Básico, do Mestrado em Educação Pré-Escolar e Ensino do 1.º Ciclo do Ensino Básico, da Universidade de Évora. A investigação foi realizada em contexto de uma sala de Pré-Escolar e em contexto de 1.º Ciclo do Ensino Básico, numa turma de 2.º ano. Os dois contextos fazem parte da Escola Manuel Ferreira Patrício, sede do Agrupamento de Escolas n.º 1 de Évora. A respetiva investigação teve como objetivos compreender, analisar e refletir acerca da exploração da simetria de reflexão em Pré-Escolar e em 1.º Ciclo do Ensino Básico. Deste modo, era pretendido responder às seguintes questões: “Como lidam as/os crianças/alunos com a identificação e a exploração de simetria de reflexão?” e “Que práticas devo desenvolver que contribuam para a compreensão e utilização da simetria de reflexão por parte das crianças?”. No decorrer da investigação foi desenvolvida uma intervenção didática em cada contexto, consistindo em sequências de tarefas de exploração de simetria que se caracterizaram por recorrer a diversos materiais e ao computador com o programa SIMIS, em 1.º Ciclo, com tarefas abertas de natureza exploratória. A recolha de dados apoiou-se nos cadernos de formação relativos às PES, nas planificações, nas produções das crianças, em respostas às tarefas e excertos dos diálogos havidos. Esta investigação permitiu verificar que é possível explorar a simetria no Pré- Escolar e 1.ºCiclo de Ensino Básico, uma vez que as crianças reconheceram figuras com simetria, conseguiram identificar eixos de simetria em figuras e construíram figuras simétricas. Para tal, desenvolveram-se práticas que contribuíram para a compreensão e utilização da simetria, através de estratégias de ensino-aprendizagem exploratório da Matemática, com recurso a materiais manipuláveis e a software específico, que mostraram ser ferramentas essenciais nas tarefas de exploração e identificação de simetria; ABSTRACT: The present report refers to research developed in the context of Supervised Teaching Practice in Pre-school Education and in Primary School, integrated in Master’s degree in Pre-school Education and Teaching Primary School at University of Évora. The research was conducted in context of a pre-school room and in context of 1st cycle of basic education, in a 2nd class year. The two contexts are part of the Manuel Ferreira Patrício School, headquarters of cluster of Évora schools. The respective research has aimed understand, analyze and reflect about reflection symmetry exploration, in Pre-school and in Primary School. Thus, was intented to answer the questions: “How childrens deal with the identification and exploration of reflection symmetry?" And "What practices should be developed to contribute to the understanding and use of reflection symmetry by childrens?". During the research it was developed a didactic intervention, in each context, consisting of sequences of symmetry exploration tasks that featured by resorting to diverse materials and the computer with the SIMIS program in the Primary School, with open tasks exploratory. Data collection builds on the training books on STP, the flat patterns, in productions of children, in response tasks and excerpts from the additions accruing dialogues. This research has shown that it is possible to explore the symmetry in Preschool and Primary School, since children recognized figures with symmetry, they were able to identify lines of symmetry in figures and built symmetrical figures. For such practices have developed that have contributed to the understanding and use of symmetry, through exploratory teaching and learning strategies of mathematics, using manipulatives and specific software, which proved to be essential tools in the exploration tasks and identification symmetry.

O ensino e aprendizagem da programação de computadores no ensino a distância : uma proposta de instanciação do modelo pedagógico virtual da Universidade Aberta

Hoje em dia o ensino e aprendizagem a distância online de nível universitário é, em grande medida, baseado em estratégias de aprendizagem colaborativa, onde, além de aprender sozinho, os estudantes também participam de ações colaborativas dentro de uma classe virtual. O nível de interação do estudante online representa um fator fundamental para o sucesso do processo de ensino-aprendizagem pois é a base da partilha de informação e construção do conhecimento entre estudantes e professores, enquanto todas as ações e atividades integram um modelo pedagógico comum. Existem muitas diferenças e desafios nas áreas de ensino em termos de instanciação do modelo pedagógico e adoção das estratégias de ensino-aprendizagem, como por exemplo, entre as áreas das ciências sociais e das engenharias. Uma área que atrai especial atenção como um todo é a das ciências da computação (CS), e de forma específica, a da programação de computadores. A programação de computadores exige, em primeiro lugar, o desenvolvimento de um bom raciocínio lógico e uma estratégia de resolução segundo uma abordagem “dividir para conquistar”, onde os principais problemas são divididos em problemas menores que são resolvidos individualmente. A programação exige também uma combinação entre o trabalho individual e em grupo, com elevados níveis de revisão e depuração do código fonte em desenvolvimento. O ensino online de programação de computadores é constituído por estes aspectos, exigindo um elevado grau de interação entre estudantes e entre estudantes e professor. Neste capítulo, vamos discutir e apresentar a nossa experiência no ensino online da programação de computadores com base no modelo pedagógico virtual da Universidade Aberta, e propor a sua instanciação e extensão específica para incluir novas estratégias de aprendizagem colaborativa e uma abordagem construtivista para o processo global de aprendizagem.

Las inteligencias múltiples en el proceso del aprendizaje de EGB

En el marco de la investigación: Las inteligencias múltiples en el proceso del aprendizaje de EGB, situada en el área de la Psicología Educativa y el Currículo, sebusca dar una contribución dentro del aprendizaje y de la planificación, presentando estrategias de enseñanza – aprendizaje, para desarrollar las inteligencias dentro de la Actualización y Fortalecimiento Curricular correspondiente a los siete primeros años de Educación General Básica (EGB). El propósito de esta tesis es encontrar la relación entre las inteligencias múltiples y el proceso de aprendizaje en EGB, planteando estrategias metodológicas que desarrollen destrezas con criterio de desempeño que potencien las inteligencias múltiples, en las diferentes áreas del aprendizaje y en los distintos niveles de educación. La metodología a usar en esta investigación fue la bibliográfica documental. Se revisaron artículos científicos, tesis, monografías relacionadas con las categorías de la investigación. La investigación intentó responder las siguientes preguntas: ¿Qué son las inteligencias múltiples?¿Cuál es la relación entre las inteligencias múltiples y los aprendizajes de EGB?¿Quéplantea la Actualización y Fortalecimiento Curricular sobre el trabajo de las inteligencias? ¿Existen actividades de enseñanza – aprendizaje en el currículo de EGB que recurre a las inteligencias múltiples?Para dar respuesta a cada una de las interrogantes se utilizó la metodología descriptiva. Un resultado alcanzado es que es posible la relación de las inteligencias múltiples con las destrezas con criterio desempeño pues como verán más adelante varias destrezas desarrollan las IM planteadas. Por otro lado, la presente investigación muestra estrategias para el desarrollo de cada inteligencia.

The Relationship between Faculty Perceptions and Implementation of Elements of Transactional Distance Theory and Online Web-Based Course Completion Rates

The purpose of this study was to explore the relationship between faculty perceptions, selected demographics, implementation of elements of transactional distance theory and online web-based course completion rates. This theory posits that the high transactional distance of online courses makes it difficult for students to complete these courses successfully; too often this is associated with low completion rates. Faculty members play an indispensable role in course design, whether online or face-to-face. They also influence course delivery format from design through implementation and ultimately to how students will experience the course. This study used transactional distance theory as the conceptual framework to examine the relationship between teaching and learning strategies used by faculty members to help students complete online courses. Faculty members’ sex, number of years teaching online at the college, and their online course completion rates were considered. A researcher-developed survey was used to collect data from 348 faculty members who teach online at two prominent colleges in the southeastern part of United States. An exploratory factor analysis resulted in six factors related to transactional distance theory. The factors accounted for slightly over 65% of the variance of transactional distance scores as measured by the survey instrument. Results provided support for Moore’s (1993) theory of transactional distance. Female faculty members scored higher in all the factors of transactional distance theory when compared to men. Faculty number of years teaching online at the college level correlated significantly with all the elements of transactional distance theory. Regression analysis was used to determine that two of the factors, instructor interface and instructor-learner interaction, accounted for 12% of the variance in student online course completion rates. In conclusion, of the six factors found, the two with the highest percentage scores were instructor interface and instructor-learner interaction. This finding, while in alignment with the literature concerning the dialogue element of transactional distance theory, brings a special interest to the importance of instructor interface as a factor. Surprisingly, based on the reviewed literature on transactional distance theory, faculty perceptions concerning learner-learner interaction was not an important factor and there was no learner-content interaction factor.

L'Intégration d'un Module d'Étude Internet Dans la Classe de Comptabilité: Perceptions des Élèves et les Résultats Académiques

Implemented in the context of Business Administration students enrolled in a college level three year technology program, this research investigated students’ perceptions and academic results concurrent with the implementation of an online web module designed to facilitate student self-study. The students involved in this research were enrolled in a program that, while offering a broad education in business disciplines, specialized in the field of accounting. As a result, students were enrolled in academically rigorous accounting courses in each of the six semesters of the program. The weighting of these accounting courses imposes a significant self-study component – typically matching or exceeding the time spent in class. In this context many of the students enrolled in the Business Administration Program have faced difficulties completing the self-study component of the course effectively as demonstrated in low homework completion rates, low homework grade averages and ultimately low success rates in the courses. In an attempt to address this situation this research studied the implementation of a web-based self-study module. Through this module students could access a number of learning tools that were designed to facilitate the self-study process under the premise that more effective self-study learning tools will help remove obstacles and provide more timely confirmation of learning during student self-study efforts. This research collected data from a single cohort of students drawn from the first three sequential accounting courses of the Business Administration Program. The web-based self-study module was implemented in the third of the three sequential accounting courses. The first two of these courses implemented a traditional manual self-study environment. Data collected from the three accounting courses included homework completion rates, homework, exam and final grades for the respective courses. In addition the web-study module allowed the automatic reporting of student usage of a number of specific online learning tools. To complement the academic data, students were surveyed to gain insight into their perceptions of the effectiveness of the web-based system. The research provided a number of interesting insights. First among these was a confirmation of the importance of the self-study process in the academic achievement of the learners. Regardless of the self-study environment, manual or web-enhanced, a significant positive correlation existed between the students’ self-study results, demonstrated in both homework completion rates and homework averages and the corresponding final grades. These results confirm the importance of self-study found generally in the prevailing academic literature regarding students enrolled in higher education. In addition, the web-enhanced learning environment implemented during the third accounting course coincided with significantly higher homework completion rates and corresponding homework averages: homework completion rates in particular increased from a combined average of 63% in the first two accounting courses to 93% in the web-enhanced context of the third accounting course. Moreover, the homework completion rates of the web-enhanced course were evenly distributed across the cohort of students. A quartile-based analysis was subsequently completed. Quartiles were constructed by ranking the students according to their combined average homework completion rates from the first two manual self-study courses, Accounting I and II. The quartile-based homework completion rates for the manual self-study courses Accounting I and II were subsequently compared to the results these same quartiles of students achieved in the web-based self-study within Accounting III. While the first two courses demonstrated significantly uneven homework completion rates across the quartiles ranging from 31% to 91% homework completion rates, the differences among the four quartiles within the web-enhanced module, with an average homework completion rate of 93%, were statistically insignificant. Congruent with the positive academic results observed in the third, web-enhanced course, through the corresponding survey, students expressed a strong attitude in favor of the online self-study environment. This research was designed to add to the existing research that studies the implementation of learning in an online setting. Specifically, the research was designed to explore a middle ground of online learning – a web-enhanced course – a context that supplements the classroom experience rather than replacing it. The web-enhanced accounting course demonstrated impressive favorable results, both academically and in terms of students' perception of the system; these results suggest that a web-enhanced environment can provide learning tools that facilitate the self-study process while providing a structured learning environment that can help developing learners reach their potential.

Aprendizaje activo

El Centro de Enseñanza Aprendizaje de la Universidad del Rosario (cea-ur), acorde con su compromiso por el mejoramiento continuo y la búsqueda de la innovación en los procesos de enseñanza-aprendizaje, pone a disposición de la comunidad académica el Boletín Reflexiones Pedagógicas. Esta colección presentará diversas alternativas para mejorar nuestros procesos didácticos y fortalecer los procesos de aprendizaje de nuestros estudiantes, de una manera sencilla y fácil de entender. En este primer número se presenta el tema de aprendizaje activo centro de nuestro proyecto educativo enunciado en el pei 2014.En él encontrarán no solo a qué se refiere este tipo de aprendizaje, sino también la descripción de algunas estrategias para desarrollarlo y referencias para profundizar en este tema.

The interactive dynamics in the university context: the classroom environment

Interpersonal relationships in human communities gained a great value since the begging of mankind, these relationships are constructed on interaction and socialization. The educational context is not exempt of these interactive and communicative processes, and it is specifically in the classroom where they can be found. The classroom can be identified as a physical and a humane space, in which dynamics are developed from the interactions between teachers and students, learning content, learning strategies and the class environment. All of these aspects are presented in the classroom as part of the teaching and learning processes. It is interesting to analyze the classroom environment and the interactive dynamics that are developed in it, regardless of the student’s age, wether in the case of infants, adolescents or adults. In this particular case, we analyze the classroom environment at the university level. Understanding the interactive dynamics that are being developed in the classroom, determine whether or not an environment is appropriate for the teaching and learning processes, which must be considered, if someone chooses an integral and quality of education.

Maleku: A Culture in Danger of Extinction

This paper is about the Maleku, one of the indigenous languages that is still alive in the country; though the linguistic community that uses it, composed of less than 400 people, tends to reduce rapidly. There is a high risk that in the near future this language will disappear. This paper is the result of a research project that proposes the construction and implementation of learning strategies that would help to include the customs, traditions and the native language of the Malekus in the schools, to strengthen the identity and culture of this Costa Rican indigenous population.The research project includes a brief overview of the history and problems of the indigenous Maleku population, and an analysis on the importance of the language and oral expression. It also makes a review of how the indigenous languages in Costa Rican schools are currently taught. It later includes a diagnosis of the current situation of language from the perspective of different members of the Maleku community. This diagnosis is based on the research conducted and it will facilitate focusing on the integration of the Maleku and rural curriculums. Finally, there are some reflections about the bilingual intercultural education.

How to Achieve Professional Skills in Higher Education?

During the last decade, higher education has tried to focus education on the achievement of professional skills. It is interesting to see how the learning strategies implemented may facilitate or make more difficult the achievement of competencies. By dealing with the challenge of a competency-based education approach, higher education points out the need of knowing how to build such competencies, i.e. how to design a learning strategy. Not much importance has been given to this issue, probably because the competencies can be confused with abilities, skills and attitudes and, therefore, the model can be associated to in- or out-of-classroom activities without a strategy to articulate the knowledge acquired with the cultural, social and economic contexts of the community and labor spheres, i.e., as a whole (Tobón, 2005). This paper analyzes the epistemological development of the competency-based approach in higher education, focusing on the implementation of professional competencies in the Sociology degree “Licenciatura en Sociología”, in two campuses of the Universidad Autónoma de Baja California: Ensenada and Mexicali. This paper describes how competencies are built and explores different theoretical trends, their conceptualization and formation, based on in-depth interviews applied to students and teachers. It provides a mixed study to understand, based on the student’s point of view, the achievements of this study program in terms of professional competencies.

Independent learning skills, self-determination theory and psychological well-being : strategies for supporting the first year university experience

The purpose of this article is to explain why the first year in higher education experience of Australian tertiary students can be improved through the explicit teaching of independent learning skills. Becoming an independent learner has many benefits, but the focus of this piece is upon the connection between independent learning and the improvement of student psychological well-being. High psychological distress levels appear to start in the first year of university education. We argue that explicitly teaching students independent learning skills is an important curriculum-based strategy that will contribute to the significant task of addressing this issue.