Introduction to the e-Learning networ in mathematics in Saxony - E-Assessment...metamath
This document introduces an e-learning network in mathematics across universities in Saxony, Germany. The network shares electronic assessments created using ONYX and MAXIMA. Over 50 authors have created more than 1000 questions across various topics in mathematics. The assessments provide interactive practice and feedback for students and inform instructors. OPAL is the central learning platform used by 80,000 members across 11 universities. ONYX allows for different question types and MAXIMA can analyze student responses with random parameters and expressions as answers. The speaker's university courses use 4 online tests throughout a semester to provide practice for approximately 200 students.
Presentation of examples of modern scenarios with digital mediametamath
The document discusses modern teaching and learning methods using digital media. It presents examples of how professors in Saxonian universities are using technologies like digital texts, videos, simulations, and online surveys. Specific examples are given of uses like central distribution of materials, flexibility in timing with video lectures, and demonstrations with digital media. Implications for constructive alignment of learning outcomes, assessments and teaching activities are discussed. The use of social learning technologies like wikis, blogs, and video conferencing are also examined. Throughout, implications for integrating these methods into teaching projects are highlighted.
Quality Assurance in Large Scale E-Assessmentsmetamath
The document discusses quality assurance in large scale e-assessments. It outlines a quality assurance process that involves (1) planning assessments according to constructive alignment principles by defining learning outcomes and designing an assessment blueprint, (2) developing assessments by creating test items and compiling tests, and (3) analyzing and evaluating assessments by analyzing item-level metrics like difficulty and discrimination and test-level reliability. The process aims to ensure assessments are valid, objective, and reliable. Quality assurance is about more than just technical issues - it also requires communication and buy-in from students and faculty.
Introduction to the e-Learning networ in mathematics in Saxony - E-Assessment...metamath
This document introduces an e-learning network in mathematics across universities in Saxony, Germany. The network shares electronic assessments created using ONYX and MAXIMA. Over 50 authors have created more than 1000 questions across various topics in mathematics. The assessments provide interactive practice and feedback for students and inform instructors. OPAL is the central learning platform used by 80,000 members across 11 universities. ONYX allows for different question types and MAXIMA can analyze student responses with random parameters and expressions as answers. The speaker's university courses use 4 online tests throughout a semester to provide practice for approximately 200 students.
Presentation of examples of modern scenarios with digital mediametamath
The document discusses modern teaching and learning methods using digital media. It presents examples of how professors in Saxonian universities are using technologies like digital texts, videos, simulations, and online surveys. Specific examples are given of uses like central distribution of materials, flexibility in timing with video lectures, and demonstrations with digital media. Implications for constructive alignment of learning outcomes, assessments and teaching activities are discussed. The use of social learning technologies like wikis, blogs, and video conferencing are also examined. Throughout, implications for integrating these methods into teaching projects are highlighted.
Quality Assurance in Large Scale E-Assessmentsmetamath
The document discusses quality assurance in large scale e-assessments. It outlines a quality assurance process that involves (1) planning assessments according to constructive alignment principles by defining learning outcomes and designing an assessment blueprint, (2) developing assessments by creating test items and compiling tests, and (3) analyzing and evaluating assessments by analyzing item-level metrics like difficulty and discrimination and test-level reliability. The process aims to ensure assessments are valid, objective, and reliable. Quality assurance is about more than just technical issues - it also requires communication and buy-in from students and faculty.
Intelligent Adaptive Services for Workplace-Integrated Learning on Shop Floorsmetamath
The document discusses intelligent adaptive services to support workplace-integrated learning on the shop floor. It provides context on Industry 4.0 and the transformation of manufacturing workplaces through digitalization and cyber-physical systems. The APPsist project aims to develop assistance and knowledge acquisition services for smart production environments. Services select appropriate work processes, learning content, and assistance based on the user and machine context to guide operators and support flexible on-the-job learning. The services were implemented and tested in pilot scenarios at industry partners.
The document describes a project to develop self-directed e-learning mathematics courses on an online platform to help students from diverse educational backgrounds succeed in their university studies, with features like entry tests, short instructional videos, interactive examples, and online exercises with personalized feedback to support learning both individually and collaboratively before classroom lessons.
This document describes the Math-Bridge education solution which provides pre-recorded math courses covering basic to advanced mathematics topics. The courses include videos, exercises, and assessments. Content areas include numbers, arithmetic, algebra, functions, geometry, trigonometry, calculus, probability, and more. The content is organized into collections and designed to be reusable across programs and institutions. Some content has been implemented at Leuphana University in Lüneburg, Germany for a bridging mathematics course.
The document describes the architecture of a math training program called Math-Bridge. It includes components like Apache Tomcat for web delivery, Maverick as a model-view-controller framework, and a core component for system functionality. Content is stored and indexed in a ContentDB using technologies like Java, Lucene and OMDoc. A learner model tracks user progress. Other components include presentation of content, user accounts, exercises that interface with a computer algebra system, and a tutorial component. The program uses technologies like Java, databases, XMLRPC and XSLT to power its functionality.
This document outlines an evaluation methodology for reformed math courses. It proposes conducting a longitudinal study comparing student outcomes between a controlled group taught with old courses and an experimental group taught with new reformed courses. Student outcomes would be assessed using pre-and post-tests, pre-and post-questionnaires, and measures of grades, knowledge gain, drop-out rates, motivation, and student evaluations. Challenges include accounting for differences between groups and ensuring high response rates to electronic questionnaires.
Math-Bridge is an educational software solution that automatically generates math exercises. It uses domain reasoners and a knowledge base to create multi-step exercises that provide feedback, hints, and solutions. Exercises are generated and can be customized through an authoring interface that allows domain experts to construct exercises and feedback for students.
This document provides guidance for authoring advanced math exercises in Math-Bridge, an education solution. It explains that exercise steps should include different interaction types and that the order of transition conditions is important, with the first matching the final correct answer and the default transition last. It also recommends using syntactic comparison for the exact correct answer and semantic comparison for other conditions like correct but simplified answers or typical errors. Partial credit can be given based on syntactic and semantic analysis of responses.
Math-Bridge is an education solution that uses an event framework to facilitate communication between its components. The event framework allows components to publish events about actions taken, which other interested components can subscribe to and listen for. Events contain information about the action, timestamp, and source. Example events include a page being presented in a book, an exercise being started or completed, and individual exercise steps. The event framework supports listening, subscribing, and publishing events to allow components like the student model and exercise subsystem to share information and update each other.
This document discusses learning objects and their representation in the Math-Bridge project. It covers:
1) Different types of learning objects like definitions, axioms, examples, and their relations.
2) Representing learning objects and their relations like "for" and "domain-prerequisite" using XML/OMDoc.
3) Tools like JEditOQMath for developing and testing learning object representations that integrate with Math-Bridge.
The document describes the student interface of a math education solution called Math-Bridge. It summarizes key features such as the main dashboard containing courses, tests, bookmarks and instructional videos. It also describes the registration/login process, an extended book interface with three panels for content, metadata and related concepts. Additional features covered include adaptive course generation, micro-course generation, different exercise types with intelligent feedback, and integration of external multimedia content. Hands-on tasks are provided to demo the student experience.
The document provides troubleshooting tips for common problems that may occur when using the Joint Math-Bridge Training Program. It lists potential issues like an address already being in use, a Derby database being locked, parse errors when loading views, and users being unable to log in. For each problem, it identifies the possible cause and recommends solutions like checking log files, cleaning and restarting projects, deleting lock files, validating XML structure, and copying dtd folders.
- Math-Bridge is an education solution that provides teacher tools in its platform.
- The teacher tools allow teachers to manage users and user groups, content like books and tests, and generate reports on student activity.
- Specifically, teachers can edit user parameters, assign roles, import and export user lists, create and assign user groups, restrict access and assign tutors to groups. Teachers can also create and edit books and tests to include as content.
Math-Bridge is an education solution that allows for the creation of static learning objects (LOs). It features a WYSIWYG authoring tool that allows editing of LO metadata and inclusion of mathematical formulas. Different types of LOs can be defined with their own applicable metadata. The tool allows users to create, edit, translate, and publish LOs. Published LOs are moved from the local workspace to collections for sharing.
The document provides steps for installing and configuring the Math-Bridge system, including installing Java, copying system files, compiling, configuring the system properties and ports, adding courses, starting and stopping the server, and finalizing the administrator user configuration. It also provides tips for production settings like adjusting JVM settings and enabling caching.
Intelligent Adaptive Services for Workplace-Integrated Learning on Shop Floorsmetamath
The document discusses intelligent adaptive services to support workplace-integrated learning on the shop floor. It provides context on Industry 4.0 and the transformation of manufacturing workplaces through digitalization and cyber-physical systems. The APPsist project aims to develop assistance and knowledge acquisition services for smart production environments. Services select appropriate work processes, learning content, and assistance based on the user and machine context to guide operators and support flexible on-the-job learning. The services were implemented and tested in pilot scenarios at industry partners.
The document describes a project to develop self-directed e-learning mathematics courses on an online platform to help students from diverse educational backgrounds succeed in their university studies, with features like entry tests, short instructional videos, interactive examples, and online exercises with personalized feedback to support learning both individually and collaboratively before classroom lessons.
This document describes the Math-Bridge education solution which provides pre-recorded math courses covering basic to advanced mathematics topics. The courses include videos, exercises, and assessments. Content areas include numbers, arithmetic, algebra, functions, geometry, trigonometry, calculus, probability, and more. The content is organized into collections and designed to be reusable across programs and institutions. Some content has been implemented at Leuphana University in Lüneburg, Germany for a bridging mathematics course.
The document describes the architecture of a math training program called Math-Bridge. It includes components like Apache Tomcat for web delivery, Maverick as a model-view-controller framework, and a core component for system functionality. Content is stored and indexed in a ContentDB using technologies like Java, Lucene and OMDoc. A learner model tracks user progress. Other components include presentation of content, user accounts, exercises that interface with a computer algebra system, and a tutorial component. The program uses technologies like Java, databases, XMLRPC and XSLT to power its functionality.
This document outlines an evaluation methodology for reformed math courses. It proposes conducting a longitudinal study comparing student outcomes between a controlled group taught with old courses and an experimental group taught with new reformed courses. Student outcomes would be assessed using pre-and post-tests, pre-and post-questionnaires, and measures of grades, knowledge gain, drop-out rates, motivation, and student evaluations. Challenges include accounting for differences between groups and ensuring high response rates to electronic questionnaires.
Math-Bridge is an educational software solution that automatically generates math exercises. It uses domain reasoners and a knowledge base to create multi-step exercises that provide feedback, hints, and solutions. Exercises are generated and can be customized through an authoring interface that allows domain experts to construct exercises and feedback for students.
This document provides guidance for authoring advanced math exercises in Math-Bridge, an education solution. It explains that exercise steps should include different interaction types and that the order of transition conditions is important, with the first matching the final correct answer and the default transition last. It also recommends using syntactic comparison for the exact correct answer and semantic comparison for other conditions like correct but simplified answers or typical errors. Partial credit can be given based on syntactic and semantic analysis of responses.
Math-Bridge is an education solution that uses an event framework to facilitate communication between its components. The event framework allows components to publish events about actions taken, which other interested components can subscribe to and listen for. Events contain information about the action, timestamp, and source. Example events include a page being presented in a book, an exercise being started or completed, and individual exercise steps. The event framework supports listening, subscribing, and publishing events to allow components like the student model and exercise subsystem to share information and update each other.
This document discusses learning objects and their representation in the Math-Bridge project. It covers:
1) Different types of learning objects like definitions, axioms, examples, and their relations.
2) Representing learning objects and their relations like "for" and "domain-prerequisite" using XML/OMDoc.
3) Tools like JEditOQMath for developing and testing learning object representations that integrate with Math-Bridge.
The document describes the student interface of a math education solution called Math-Bridge. It summarizes key features such as the main dashboard containing courses, tests, bookmarks and instructional videos. It also describes the registration/login process, an extended book interface with three panels for content, metadata and related concepts. Additional features covered include adaptive course generation, micro-course generation, different exercise types with intelligent feedback, and integration of external multimedia content. Hands-on tasks are provided to demo the student experience.
The document provides troubleshooting tips for common problems that may occur when using the Joint Math-Bridge Training Program. It lists potential issues like an address already being in use, a Derby database being locked, parse errors when loading views, and users being unable to log in. For each problem, it identifies the possible cause and recommends solutions like checking log files, cleaning and restarting projects, deleting lock files, validating XML structure, and copying dtd folders.
- Math-Bridge is an education solution that provides teacher tools in its platform.
- The teacher tools allow teachers to manage users and user groups, content like books and tests, and generate reports on student activity.
- Specifically, teachers can edit user parameters, assign roles, import and export user lists, create and assign user groups, restrict access and assign tutors to groups. Teachers can also create and edit books and tests to include as content.
Math-Bridge is an education solution that allows for the creation of static learning objects (LOs). It features a WYSIWYG authoring tool that allows editing of LO metadata and inclusion of mathematical formulas. Different types of LOs can be defined with their own applicable metadata. The tool allows users to create, edit, translate, and publish LOs. Published LOs are moved from the local workspace to collections for sharing.
The document provides steps for installing and configuring the Math-Bridge system, including installing Java, copying system files, compiling, configuring the system properties and ports, adding courses, starting and stopping the server, and finalizing the administrator user configuration. It also provides tips for production settings like adjusting JVM settings and enabling caching.
Магистерская программа «Распределённые системы и компьютерные сети»ARCCN
Доклад Смелянского Руслана Леонидовича, чл.-корр. РАН, профессор, д.ф.-м-.н., МГУ им. М.В.Ломоносова, факультет ВМК, Кафедра АСВК, Лаборатория Вычислительных Комплексов, на ежегодном заседании участников Консорциума университетов по SDN технологиям, май 2017
Презентация с семинара ИТМО "Формализация знаний и искусственный интеллект в образовании" (http://iam.ifmo.ru/ru/viewnews/17227/formalizaciya_znaniy_i_iskusstvennyy_intellekt_v_obrazovanii.htm). Доклад "Информационные системы поддержки активного обучения: облачные технологии, управление знаниями и коллаборативные платформы".
ЛЕКЦИЯ 0. Описание курса. Общие вопросы, структура курса, требования. Содержание курса. Полезные ресурсы
Курс "Параллельные вычислительные технологии" (ПВТ), весна 2015
Сибирский государственный университет телекоммуникаций и информатики
Пазников Алексей Александрович
к.т.н., доцент кафедры вычислительных систем СибГУТИ
http://cpct.sibsutis.ru/~apaznikov
Probability Theory and Mathematical Statistics in Tver State Universitymetamath
Project MetaMath outlines a probability theory and mathematical statistics course offered at Tver State University. The course is offered over two semesters for a total of 9 credits. It includes lectures, laboratory work, seminars, course projects each semester, and exams. The goal of the course is to present basic information about probability models that account for random factors. Upon completing the course, students should have mastered key probability and statistics concepts and techniques. The course also discusses modernizing elements like pre-testing students and incorporating online homework assignments.
This document compares the Discrete Mathematics curricula and courses between OMSU (National Research Ogarev Mordovia State University) in Russia and TUT (Tampere University of Technology) in Finland. It analyzes the competencies, topics, and learning outcomes covered in the Discrete Mathematics courses based on three levels of difficulty. Overall, the OMSU course covers more topics like set theory, combinatorics, algebraic structures, and coding theory over a longer duration, while the TUT course focuses more on number theory over a shorter period. The document proposes increasing engineering applications and using an online learning system to help modernize the Discrete Mathematics courses.
This document outlines a course of calculus for IT students at Lobachevsky State University of Nizhni Novgorod. The course is divided into 3 terms covering sequences, differential calculus, integral calculus, and series. Tests and exams are given throughout each term to assess student competency in mathematical thinking and problem solving. The course aims to develop skills in applying modern mathematical tools. Plans are discussed to modernize the course by adding an introductory section to address low student preparation, using online tools like METAMATH to support independent work, and testing key concepts to address educational problems.
The document discusses the discrete mathematics curriculum at Saint-Petersburg Electrotechnical University. It provides an overview of which discrete math topics are covered in each year of study for different degree programs. It also compares course parameters like credits and hours between the university and TUT. Key modules covered in the second year Math Logic and Algorithm Theory course are outlined. Competencies addressed in the curriculum are mapped to SEFI levels, with additional competencies covered uniquely at the university. Suggested modifications to improve the curriculum structure are presented.
Probability Theory and Mathematical Statisticsmetamath
This document provides information about a Probability Theory and Mathematical Statistics course taught at KNITU, Russia. It includes details about the course such as the number of students, preliminary courses required, distribution of working time, topics covered in lectures and workshops/laboratories. It also compares the methodology and topics studied in this course to a similar course taught at TUT, Finland. Key differences highlighted include the use of Matlab at TUT and more emphasis on practical work/tutorials versus lectures. Overall competencies covered are also summarized and compared between the two courses based on the SEFI framework.
This document compares the optimization methods courses between KNITU (Russia) and TUT (Finland).
The KNITU course is mandatory, has fewer credits (3 vs 5), and less time spent (108 student hours vs 138). Key topics are similar but KNITU spends less time on lectures (10 vs 28) and nonlinear optimization.
The main difference is KNITU has fewer lectures, almost half that of TUT. This could be addressed by using an online math platform like Math-Bridge to provide additional lecture material and practice problems. Mid-term tests on Math-Bridge could help evaluate knowledge gained from the extra online content.
This document summarizes the course content and structure for Discrete Mathematics at the National Research Ogarev Mordovia State University. The course is divided into 4 modules covering set theory, graph theory, algebraic structures, and coding theory. Students take exams and write 3 essays throughout the semester to assess their understanding of each module. Pedagogical methods include lectures, practice problems, subgroup work, computer programming assignments, and a final exam to evaluate students on a 100 point scale.
SEFI comparative study: Course - Algebra and Geometrymetamath
The document describes a course in Algebra and Geometry for Informatics and Computer Science (ICS) and Programming Engineering (PE) majors. It analyzes the course content based on the SEFI framework and finds that the course covers most competencies in linear algebra and geometry at the core and level 1 levels. Some level 2 and 3 competencies are also covered. However, not all competencies are addressed as some assume knowledge from secondary school, others are covered in other courses, and some are not necessary for the ICS and PE profiles.
This document discusses the mathematical foundations of fuzzy systems, including:
- The curriculum covers theory of fuzzy sets, theory of possibility, crisp vs. fuzzy values, model tasks, and possibilistic optimization tasks over two semesters for a total of 324 hours.
- The theory of possibility introduced in 1978 uses axiomatic approach and possibility measures to define possibilistic space and possibilistic (fuzzy) variables characterized by possibility distributions.
- Model tasks and possibilistic optimization tasks are presented, where the coefficients can be crisp or possibilistic variables.
Calculus - St. Petersburg Electrotechnical University "LETI"metamath
This document provides an overview of the calculus concepts covered in school and in various university courses at the Electrotechnical University “LETI” in Saint Petersburg, Russia. It outlines the key competencies developed in functions, sequences, series, logarithmic/exponential functions, rates of change, differentiation, integration, and other topics. The levels of mastery increase across the core courses in Calculus, Computing Mathematics, and some additional advanced topics covered in only two specialized groups.
1. The document outlines discrete mathematics competencies covered at different levels in the undergraduate curriculum at Saint-Petersburg Electrotechnical University.
2. Many competencies are covered in the discrete mathematics course in the first year, while others are covered in courses like mathematical logic and algorithm theory in later years.
3. LETI aims to develop additional competencies beyond the SEFI levels, such as skills in mathematical logic, graphs, algorithms, and finite state machines.
Probability Theory and Mathematical Statisticsmetamath
This document discusses a computer tutorial on probability theory and mathematical statistics that was developed for a bachelor's degree program in computer science and engineering. It provides details on the course, including the typical number and gender of students, prerequisite courses, and time allocation. It also outlines the history of the degree program and standards from 1990 to 2014. The document describes the contents, structure, and development of the computer tutorial, and shows some screenshots of different learning management systems used to deliver the tutorial over time, including Lotus Learning Space, IBM Workplace Collaborative Learning, and Blackboard.
This document provides an overview of optimization methods. It discusses both single-variable and multi-variable optimization techniques, including necessary and sufficient conditions for local minima. Specific optimization methods covered include golden section search, dichotomous search, gradient descent, Newton's method, the simplex method for linear programming problems, and the method of Lagrange multipliers for constrained optimization problems. The document is intended to provide information about an optimization methods course, including preliminary courses, time distribution, and types of optimization techniques taught.
Math Education for STEM disciplines in the EUmetamath
The document discusses math education reforms in the EU. It notes declining math skills among students and describes efforts across Europe to shift from a content-focused approach to developing mathematical competencies. Recommendations include changing curricula to emphasize real-world problem solving, improving teacher training, and leveraging technology as a teaching tool while maintaining the important role of educators. Overall, the document outlines the need for pedagogical reforms to address shortcomings identified by assessments like PISA and better prepare students for STEM careers.
International Activities of the University in academic fieldmetamath
The document summarizes the international activities of Kazan National Research Technical University (KNRTU-KAI) in academic fields. It outlines several milestones in the university's international relations starting from the 1950s when it first hosted foreign students. It then discusses KNRTU-KAI's participation in international projects, associations, and TEMPUS programs. The document also provides details on international accreditation of academic programs, the new German-Russian Institute of Advanced Technologies, and KNRTU-KAI's approach to developing new curricula/modules based on the qualifications framework of the European Higher Education Area.
TSU course 2 Probability Theory and Math Statistics
1. Project MetaMath
Пример модернизации дисциплины “Теория вероятностей и математическая
статистика”
Захарова И.В. Тверской государственный университет
2. ТВиМС. Структура дисциплины
Длительность : 2 семестра (37 недель)
Год обучения/семестр: 2, 3 / 4, 5
Необходимые курсы: Линейная алгебра, Математический анализ,
Дифференциальные уравнения
Количество кредитов – 9 (1 зачетная единица≡36 часов)
324 часа (148 часов – аудиторная нагрузка, 176 – самостоятельная
работа )
3. ТВиМС в ТвГУ
Требуемые базовые навыки:
• владение инструментарием теории множеств;
• работа с элементами комбинаторики;
• работа с простейшими функциями;
• работа с прогрессиями;
• изображение множества точек на плоскости;
• навыки дифференцирования и интегрирования элементарных функций.
4. ТВиМС. Модерниация курса
• Предварительный тест;
• Выравнивающий курс, развивающий требуемые базовые навыки
• Подкрепление основного курса системой электронного обучения
5. Выравнивающий курс
1. Тридцать человек разбиты на три группы по 10 человек в каждой. Сколько может
различных составов групп?
2. Сколько четырехзначных чисел, составленных из цифр 0,1,2,3,4,5 содержат цифру 3?
3.Садовник должен в течение 3-х дней посадить 10 деревьев. Сколькими способами он
может распределить по дням работу, если будет сажать не менее 1 дерева в день?
4. Расписание одного дня содержит 4 семинара. Определить количество таких расписаний
из 9 дисциплин.
6. Выравнивающий курс
5. Какова вероятность того, что при двух подбрасываниях монеты герб появится один раз?
6. В группе 35 студентов. Каждый из них пользуется хотя бы одним из видов городского
транспорта: метро, автобусом и троллейбусом. Всеми тремя видами транспорта пользуются
6 студентов, метро и автобусом – 15 студентов, метро и троллейбусом – 13 студентов,
троллейбусом и автобусом – 9 студентов. Сколько студентов используют только один вид
транспорта?
8. Найти суммы бесконечно убывающих прогрессий.
9. Построить графики функций.
7.
8.
9.
10.
11.
12.
13. in SEFI offline
ADD:
• Conditional distribution and conditional mean (3/5 semester)
• characteristic functions (3/5 semester)
• effective estimates (3/5 semester)
• information Fischer, inequality of Rao-Cramer (3/5 semester)
• central statistics, the construction of confidence intervals using central statistics (3/5 semester)
• methods of construction estimates (3/5 semester)
• likelihood function (3/5 semester)
14.
15.
16.
17. Probability theory and mathematical statistics
in TSU: Modernization course
Год
ы
2006 2007 2008 2009 2010 2011
Млн
.чел
.
4788
5
4811
4
4628
3
4503
7
4541
2
45817