CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Andragogy vs Pedagogy: Teaching the Adult Learner in an Online Environment

The purpose of this presentation is to offer a deeper understanding of adult learning and provide tips on how to effectively teach in the online environment. The presenter will compare and contrast two learning theories: andragogy and pedagogy. Furthermore, the roles of the online instructor and e-learner will be outlined. An open discussion at the end of the presentation will allow participants to make implications as to which learning theory is more effective for online learning.

Collaborating Blackboard into Teaching – Case Study

In this presentation, a business instructor will discuss a variety of Blackboard functions and describe how technology enhances teaching and learning. It will also address the challenges and issues facing both instructors and students in an online learning environment.

“Flipped Classroom” for Teaching Business Research in a Business Management Course

This presentation will report on a cross-department collaboration between the library and the business/economics department at Lehman College to conduct information literacy instruction as a “flipped classroom.”

Translation, Communication and 'Learning' : Experiences from teaching a master program in Viet Nam

In Vietnam, as in other Asian countries, co-operation with foreign universities plays an important role for the development of higher education. This paper is based on personal experiences from teaching a Swedish Master Programme in Education Science at Vietnam National University in Hanoi. Using theories developed by Lev Vygotsky and Donald Schon, the programme is explored as an inter-cultural learning process. Three aspects are focused upon. Firstly, the fact that communication between students and teachers is conducted with the help of translators who support both teachers and students in their attempt to understand and make themselves understood. Secondly, the expressed need to connect the ideas and techniques which are studied in the programme to the students´ professional worlds. Thirdly, the need to construct a framework wherein the students can inquire into their own situations and to encourage them to try new and more productive ways to deal with problems they are confronted with.

Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Gymnasieelevers uppfattningar om algebra och problemlösning : En undersökning med utgångspunkt i elevernas kön, slutbetyg i grundskolan och val av gymnasieprogram

Syftet med den här uppsatsen är att undersöka elevers uppfattningar om algebra och problemlösning samt granska hur dessa uppfattningar påverkas beroende på elevernas val av gymnasieprogram, kön och slutbetyg i grundskolan. Syftet är vidare att ta reda på vilka eventuella hinder och svårigheter eleverna själva uppfattar då de använder algebra för att lösa matematiska problem. Som metod för att söka svar på syfte och frågeställningar har valts att genomföra en enkätundersökning med elever som går första året på gymnasiet och som läser antingen naturvetenskapsprogrammet eller bygg- och anläggningsprogrammet. Enkätundersökningen består av två delar, en del som undersöker elevers uppfattningar om matematik i allmänhet och algebra och problemlösning i synnerhet, samt en del som försöker reda ut vilka svårigheter eleverna uppfattar då de ska lösa matematiska problem med algebra. Svaren sammanställs genom en analys av vilka eventuella skillnader och likheter som finns beroende på elevernas val av gymnasieprogram, kön och betyg i grundskolan. Resultatet visar på att elever på naturvetenskapsprogrammet som hade MVG i betyg i grundskolan har en mer positiv inställning till algebra och problemlösning i jämförelse med elever från bygg- och anläggningsprogrammet som fått G i betyg. Vad gäller elevernas kön finns det inte några indikationer på att denna faktor har någon större påverkan på deras uppfattningar. Resultatet kan vara en indikation på att elevernas uppfattningar främst påverkas av deras förståelse för det algebraiska tankesättet. Det eleverna upplever som svårast när de ska lösa problem med hjälp av algebra är att översätta den skrivna texten till en algebraisk framställning. När eleverna löser matematiska problem indikerar även resultatet att de till stor del styrs av sina förväntningar och förutfattade föreställningar om uppgiften. Resultatet ger en indikation om att eleverna behöver arbeta mer med problemlösning i olika former för att genom det kunna träna upp sin resonemangsförmåga och sin förmåga att behärska alla de tre faserna, översättning, omskrivning och tolkning, i den algebraiska cykeln.

Teaching Intercultural Communication in Foreign Language Education through Video Conferencing

Since 1980s, Western linguists and specialists on second language acquisition have emphasized the importance of enhancing students’ intercultural communication competence in foreign language education. At the same time, the demand for intercultural communicative competence increased along with the advances of communication technology with its increasingly global reach and the process of globalization itself.In the field of distance language education, these changes have resulted in a shift of focus from the production and distribution of learning materials towards communication and learning as a social process, facilitated by various internet-based platforms. The current focus on learners interacting and communicating synchronously trough videoconferencing is known as the fourth generation of distance language education. Despite the fact that teaching of Chinese as a foreign language (CFL) faces the same or even greater challenges as teaching other languages, the intercultural communication perspective is still quite a new trend in CFL and its implementation and evaluation are still under development. Moreover, the advocates of the new trends in CFL have so far focused almost exclusively on classroom-based courses, neglecting the distance mode of CFL and leaving it as an open field for others to explore. In this under-researched context, Dalarna University (Sweden), where I currently work, started to provide web-based courses of the Chinese language in 2007. Since 2010, the Chinese language courses have been available only in the distance form, using the same teaching materials as the previous campus-based courses. The textbooks used in both settings basically followed the functional nationalism approach. However, in order to catch up with the main trend of foreign-language education, we felt a need to implement the cross-cultural dimension into the distance courses as well. Therefore in 2010, a pilot study has been carried out to explore opportunities and challenges for implementing a cross-cultural perspective into existing courses and evaluating the effectiveness of this implementation based on the feedback of the students and on the experience of the teacher/researcher.

ICT as a tool in English teaching : A literature review on the use of ICT for Swedish students with learning difficulties and their literacy learning in grades 7-9

Information and communication technology (ICT) is a subject that is being discussed as a tool that is used within education around the world. Furthermore it can be seen as a tool for teachers to individualize students´ education. Students with literacy difficulties, such as dyslexia, are in constant need of new ways to learn, and new ways to be motivated to learn. The aim of this study is to see what research says in regard to how ICT can be used as a tool to help students with literacy difficulties. Literacy difficulties can be due to a number of things, such as the student has not been taught how to read, trouble within the family which can cause distress, or a neurological disorder such as dyslexia. Furthermore, the main research questions will focus on how ICT can be compared to traditional education forms, such as books and a more teacher centered education within the classroom, and whether ICT can be preferred. The results of this literature review indicates that ICT can be seen as a way for teachers to help students with literacy difficulties gain more self-esteem – something the literature tells us students with learning difficulties lack. The results also show how ICT can lead to a more individualized education. This is due to tools that increase reading comprehension and tools that give direct response when working with ICT, which helps students work more independently.

Teaching grammar: A study of the common English grammar errors and grammar teaching methods that can be relevant for Swedish upper secondary schools

Grammar has always been an important part of language learning. Based on various theories, such as the universal grammar theory (Chomsky, 1959) and, the input theory (Krashen, 1970), the explicit and implicit teaching methods have been developed. Research shows that both methods may have some benefits and disadvantages. The attitude towards English grammar teaching methods in schools has also changed and nowadays grammar teaching methods and learning strategies, as a part of language mastery, are one of the discussion topics among linguists. This study focuses on teacher and learner experiences and beliefs about teaching English grammar and difficulties learners may face. The aim of the study is to conduct a literature review and to find out what scientific knowledge exists concerning the previously named topics. Along with this, the relevant steering documents are investigated focusing on grammar teaching at Swedish upper secondary schools. The universal grammar theory of Chomsky as well as Krashen’s input hypotheses provide the theoretical background for the current study. The study has been conducted applying qualitative and quantitative methods. The systematic search in four databases LIBRIS, ERIK, LLBA and Google Scholar were used for collecting relevant publications. The result shows that scientists’ publications name different grammar areas that are perceived as problematic for learners all over the world. The most common explanation of these difficulties is the influence of learner L1. Research presents teachers’ and learners’ beliefs to the benefits of grammar teaching methods. An effective combination of teaching methods needs to be done to fit learners’ expectations and individual needs. Together, they will contribute to the achieving of higher language proficiency levels and, therefore, they can be successfully applied at Swedish upper secondary schools.

A Story of English Language Learning – How Can Children’s Literature be Used in Teaching Vocabulary to Young English Language Learners? : - A Literature Review

This study aims to find research relating to the use of children’s literature to promote vocabulary development in young children, particularly English language learners in Sweden. The main questions address how (methods) children’s literature can be used and why (reasons) children’s literature is often recommended for the teaching of vocabulary to young learners. The study also aims to explore reasons against the use of children’s literature in vocabulary teaching found in previous research. A systematic literature review was carried out, including results from five empirical studies. The studies involved native speakers, second language learners and foreign language learners from various backgrounds. The results suggest that while research has shown children’s literature to be a good tool to use with young learners, careful lesson planning needs to be carried out. Direct instruction and scaffolding using pictures, technology and gestures is recommended. Hence, the teacher plays an important part for the vocabulary development using children’s literature in the classroom.

Pedagogical methods in web-based language teaching-mapping

The purpose of this presentation is to introduce the research project progress in “the mapping of pedagogical methods in web-based language teaching" by Högskolan Dalarna (Dalarna University). This project will identify the differences in pedagogical methods that are used for online language classes. The pedagogical method defined in this project is what the teachers do to ensure students attain the learning outcomes, for example, planning, designing courses, leading students, knowing students' abilities, implementing activities, etc. So far the members of this project have analyzed the course plans (in the language department at Dalarna University) and categorized the learning outcomes. A questionnaire was constructed based on the learning outcomes and then either sent out remotely to teachers or completed face to face through interviews. The answers provided to the questionnaires enabled the project to identify many differences in how language teachers interact with their students but also, the way of giving feedback, motivating and helping students, types of class activities and materials used. This presentation introduces the progress of the project and identifies the challenges at the language department at Dalarna University. Finally, the advantages and problems of online language proficiency courses will be discussed and suggestions made for future improvement.