812 resultados para On-line mathematics learning


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Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.

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Daniela Ivanova Dureva–Tuparova In this paper 3 pedagogical scenarios of e-learning courses are performed. The courses have been implemented in blended mode with the students in Master program “ICT in primary schools”. The courses apply different didactical methods such as “Jigsaw” interactive technique, on-line simulations, project based learning, etc. Some results from study of students’ attitude to the used didactical methods and technology enhanced educational activities are presented and discussed.

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The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics FCAT results were examined to determine if the GSP produced any effects. Students’ scores were compared based on assignment to the control or experimental group as well as gender and SES. SES measurements were based on whether students qualified for free lunch. The findings of the study revealed a significant difference in the FCAT mathematics scores of students who were taught geometry using GSP compared to those who used the traditional method. No significant differences existed between the FCAT mathematics scores of the students based on SES. Similarly, no significant differences existed between the FCAT scores based on gender. In conclusion, the use of technology (particularly GSP) is likely to boost students’ FCAT mathematics test scores. The findings also show that the use of GSP may be able to close known gender and SES related achievement gaps. The results of this study promote policy changes in the way geometry is taught to 10th grade students in Florida’s public schools.

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A fundamental goal of education is to equip students with self-regulatory capabilities that enable them to educate themselves. Self directedness not only contributes to success in formal instruction but also promotes lifelong learning (Bandura, 1997). The area of research on self-regulated learning is well grounded within the framework of psychological literature attributed to motivation, metacognition, strategy use and learning. This study explored past research and established the purpose of teaching students to self-regulate their learning and highlighted the fact that teachers are expected to assume a major role in the learning process. A student reflective writing journal activity was sustained for a period of two semesters in two fourth-grade mathematics classrooms. The reflective writing journal was analyzed in search of identifying strategies reported by students. Research questions were analyzed using descriptive statistics, frequency counts, cross-tabs and chi-square analyses. ^ Results based on student-use of the journals and teacher interviews indicated that the use of a reflective writing journal does promote self-regulated learning strategies to the extent which the student is engaged in the journaling process. Those students identified as highly self-regulated learners on the basis of their strategy use, were shown to consistently claim to learn math “as well or better than planned” on a weekly basis. Furthermore, good self-regulators were able to recognize specific strategies that helped them do well and change their strategies across time based on the planned learning objectives. The perspectives of the participating teachers were examined in order to establish the context in which the students were working. The effect of “planned change” and/or the resistance to change as established in previous research, from the teachers point of view, was also explored. The analysis of the journal data did establish a significant difference between students who utilized homework as a strategy. ^ Based on the journals and interviews, this study finds that the systematic use of metacognitive, motivational and/or learning strategies can have a positive effect on student's responsiveness to their learning environment. Furthermore, it reflects that teaching students “how to learn” can be a vital part of the effectiveness of any curriculum. ^

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This paper is a case study that describes the design and delivery of national PhD lectures with 40 PhD candidates in Digital Arts and Humanities in Ireland simultaneously to four remote locations, in Trinity College Dublin, in University College Cork, in NUI Maynooth and NUI Galway. Blended learning approaches were utilized to augment traditional teaching practices combining: face-to-face engagement, video-conferencing to multiple sites, social media lecture delivery support – a live blog and micro blogging, shared, open student web presence online. Techniques for creating an effective, active learning environment were discerned via a range of learning options offered to students through student surveys after semester one. Students rejected the traditional lecture format, even through the novel delivery method via video link to a number of national academic institutions was employed. Students also rejected the use of a moderated forum as a means of creating engagement across the various institutions involved. Students preferred a mix of approaches for this online national engagement. The paper discusses successful methods used to promote interactive teaching and learning. These included Peer to peer learning, Workshop style delivery, Social media. The lecture became a national, synchronous workshop. The paper describes how allowing students to have a voice in the virtual classroom they become animated and engaged in an open culture of shared experience and scholarship, create networks beyond their institutions, and across disciplinary boundaries. We offer an analysis of our experiences to assist other educators in their course design, with a particular emphasis on social media engagement.

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[EN]In face recognition, where high-dimensional representation spaces are generally used, it is very important to take advantage of all the available information. In particular, many labelled facial images will be accumulated while the recognition system is functioning, and due to practical reasons some of them are often discarded. In this paper, we propose an algorithm for using this information. The algorithm has the fundamental characteristic of being incremental. On the other hand, the algorithm makes use of a combination of classification results for the images in the input sequence. Experiments with sequences obtained with a real person detection and tracking system allow us to analyze the performance of the algorithm, as well as its potential improvements.

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[EN]Most face recognition systems are based on some form of batch learning. Online face recognition is not only more practical, it is also much more biologically plausible. Typical batch learners aim at minimizing both training error and (a measure of) hypothesis complexity. We show that the same minimization can be done incrementally as long as some form of ”scaffolding” is applied throughout the learning process. Scaffolding means: make the system learn from samples that are neither too easy nor too difficult at each step. We note that such learning behavior is also biologically plausible. Experiments using large sequences of facial images support the theoretical claims. The proposed method compares well with other, numerical calculus-based online learners.

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Purpose: To describe orthoptic student satisfaction in a blended learning environment. Methods: Blended learning and teaching approaches that include a mix of sessions with elearning are being used since 2011/2012 involving final year (4th year) students from an orthoptic program. This approach is used in the module of research in orthoptics during the 1 semester. Students experienced different teaching approaches, which include seminars, tutorial group discussions and e-learning activities using the moodle platform. The Constructivist OnLine Learning Environment Survey (COLLES ) was applied at the end of the semester with 24 questions grouped in 6 dimensions with 4 items each: Relevance to professional practice, Reflection, Interactivity, Tutor support, Peer support and Interpretation. A 5-point Likert scale was used to score each individual item of the questionnaire (1 - almost never to 5 – almost always). The sum of items in each dimension ranged between 4 (negative perception) and 20 (positive perception). Results: Twenty-four students replied to the questionnaire. Positive points were related with Relevance (16.13±2.63), Reflection (16.46±2.45), Tutor support (16.29±2.10) and Interpretation (15.38±2.16). The majority of the students (n=18; 75%) think that the on-line learning is relevant to students’ professional practice. Critical reflections about learning contents were frequent (n=19; 79.17%). The tutor was able to stimulate critical thinking (n=21; 87.50%), encouraged students to participate (n=18; 75%) and understood well the student’s contributions (n=15; 62.50%). Less positive points were related with Interactivity (14.13±2.77) and Peer support (13.29±2.60). Response from the colleagues to ideas (n=11; 45.83%) and valorization of individual contributions (n=10; 41.67%) scored lower than other items. Conclusions: The flow back and forth between face-to-face and online learning situations helps the students to make critical reflections. The majority of the students are satisfied with a blended e-learning system environment. However, more work needs to be done to improve interactivity and peer support.

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In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its  applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP) Official Program.  Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.

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WiBA-Net ist ein Lernnetzwerk zum Thema „Werkstoffe im Bauwesen“ und wird in der universitären Ausbildung von Bauingenieuren und Architekten verwendet. Dieser Aufsatz soll das Konzept von WiBA-Net vorstellen und zeigen, wie neue Technologien und didaktische Konzepte überzeugend angewendet werden können, um „Blended Learning“ umzusetzen und damit den Hochschulalltag sowohl von Studierenden als auch von Professoren zu erleichtern.(DIPF/Orig.)

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In diesem Beitrag geht es um das Projekt E-Lernen auf der ILIAS-Plattform an der Universität der Bundeswehr Hamburg (E-L I-P UniBwH). Ziel des Projekts ist es, die Präsenzlehre mit dem Einsatz elektronischer Medien zu unterstützen. Im Beitrag werden Ansatzpunkte dargestellt, die die Lehrenden zum Gebrauch der E-Lernplattform motivieren. Es werden Bedarfsmöglichkeiten aufgezeigt, für die eine E-Lernplattform eine mögliche Lösung sein kann, sowie die Rahmenbedingungen benannt, unter denen sie eingesetzt wird. Ziel ist es, die Nachhaltigkeit des E-Lernens an der UniBwH zu fördern.(DIPF/Orig.)

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Der Einsatz von Fallstudien kann als wichtiges Bindeglied zur Verknüpfung von Theorie und Praxis betrachtet werden. Fallstudien ermöglichen die Anwendung theoretischen Grundlagenwissens und die Entwicklung überfachlicher Kompetenzen. Damit können sie einen wichtigen Beitrag zur beruflichen Handlungskompetenz genau dort leisten, wo praktische Erfahrungen im Rahmen der Aus-und Weiterbildung nicht möglich sind. Der Einsatz von Fallstudien sollte aus diesem Grund nicht nur den „klassischen“ Anwendungsdisziplinen wie den Rechtswissenschaften, der Betriebswirtschaftslehre oder der Psychologie vorbehalten sein. Auch im Bereich der Informatik können sie eine wichtige Ergänzung zu den bisher eingesetzten Methoden darstellen. Das im Kontext des Projekts New Economy1 entwickelte und hier vorgestellte Konzept zur didaktischen und technischen Aufbereitung von Fallstudien am Beispiel der IT-Aus- und Weiterbildung soll diese Diskussion anregen. Mit Hilfe des vorgestellten Ansatzes ist es möglich, unterschiedliche methodische Zugänge zu einer Fallstudie für eine computerbasierte Präsentation automatisch zu generieren und mit fachlichen Inhalten zu verknüpfen. Damit ist ein entscheidender Mehrwert gegenüber den bisherigen statischen und in sich geschlossenen Darstellungen gegeben. Der damit zu erreichende Qualitätssprung im Einsatz von Fallstudien in der universitären und betrieblichen Aus- und Weiterbildung stellt einen wichtigen Beitrag zur praxisorientierten Gestaltung von Blended Learning-Ansätzen dar.(DIPF/Orig.)

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Die Entwicklung der Akustik-Lern-CD hatte das Ziel, den Anwendungsbezug von theoretischem Wissen bei Regelverstärkern zu fördern. Die Studenten konnten nach dem theoretischen Unterricht zwar Hüllkurven zeichnen und Kompressionsraten berechnen, hatten aber Probleme, in konkreten Situationen wie z.B. beim Übersteuern von Instrumenten den korrekten Regelverstärker auszuwählen. Um einen besseren Wissenstransfer zu erreichen, werden bei der Lern-CD dem Lerner Situationen angeboten, in denen eigene Konstruktionsleistungen möglich sind und in denen kontextgebunden, interaktiv gelernt werden kann.(DIPF/Orig.)

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Das Notebook-Seminar stellte ein M-Learning-Szenario dar, welches durch die Integration des Notebooks in die Lehre eine Verbesserung derselben erwirken soll. Methodischer Schwerpunkt ist das projektorientierte Lernen, welches neben der Vermittlung von Fachinhalten zum Ziel hat, auch fachübergreifende Kompetenzen zu vermitteln. Auf Basis einer ein Semester umfassenden Projektaufgabe werden bestimmte Lernhandlungen von den Studierenden absolviert. Diese Lernhandlungen fassen bestimmte Lernziele, die in Fach-, Methoden und Sozialkompetenz aufgeteilt sind. Das Paper beleuchtet Aspekte des M-Learnings und konzipiert vor diesem Hintergrund das Notebook-Seminar. Danach wird das in die Praxis umgesetzte Konzept vorgestellt und die gemachten Erfahrungen, sowie die Ergebnisse der Evaluation diskutiert.(DIPF/Orig.)

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Mit dem Einsatz der neuen Medien, insbesondere des Internet, im Bereich des Lehrens und Lernens werden – auch nach dem Abklingen der ersten Euphorie – hohe Erwartungen verbunden. Dabei spielen neue, pädagogisch interessante Nutzungsmöglichkeiten, aber auch wirtschaftliche Interessen eine wesentliche Rolle. Die damit verbundenen Fragen (z.B. nach der Sicherung von Qualität und Gewährleistung von Rentabilität) führen zu einem steigenden Interesse an Metadaten zur Beschreibung von telematischen Lehr-/Lernmaterialien (zum Begriff „telematisch“ vgl. Zimmer, 1997, S. 111). Der folgende Beitrag befasst sich mit Erwartungen und Schwierigkeiten bei der Entwicklung und dem Einsatz pädagogischer Metadaten. Im Anschluss an eine kurze allgemeine Darstellung der Funktion von Metadaten wird unter Rückgriff auf Vorschläge verschiedener Gremien zur Bestimmung pädagogischer Metadaten gezeigt, welche Probleme bei deren Findung, Benennung und Implementierung auftreten: So stellen sich z.B. Fragen nach der interkulturellen Übertragbarkeit, nach den unterschiedlichen Perspektiven von Contentanbietern und Lernenden sowie auch die grundsätzliche Frage nach der Möglichkeit der Standardisierung pädagogischer Kategorien. Anhand des Praxisbeispiels der Virtuellen Fachhochschule für Technik, Informatik und Wirtschaft werden projekttypische Entwicklungsstufen von (pädagogischen) Metadaten dargestellt. Vorschläge zur Lösung der beschriebenen Probleme und ein Ausblick mit Forschungsfragen schließen den Beitrag ab.(DIPF/Orig.)