Recreational Mathematics - Only For Fun?

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment?

Building a Learning Architecture : e-Learning and e-Services

With the rapid advancement of the webtechnology, more and more educationalresources, including software applications forteaching/learning methods, are available acrossthe web, which enables learners to access thelearning materials and use various ways oflearning at any time and any place. Moreover,various web-based teaching/learning approacheshave been developed during the last decade toenhance the capability of both educators andlearners. Particularly, researchers from bothcomputer science and education are workingtogether, collaboratively focusing ondevelopment of pedagogically enablingtechnologies which are believed to improve theinfrastructure of education systems andprocesses, including curriculum developmentmodels, teaching/learning methods, managementof educational resources, systematic organizationof communication and dissemination ofknowledge and skills required by and adapted tousers. Despite of its fast development, however,there are still great gaps between learningintentions, organization of supporting resources,management of educational structures,knowledge points to be learned and interknowledgepoint relationships such as prerequisites,assessment of learning outcomes, andtechnical and pedagogic approaches. Moreconcretely, the issues have been widelyaddressed in literature include a) availability andusefulness of resources, b) smooth integration ofvarious resources and their presentation, c)learners’ requirements and supposed learningoutcomes, d) automation of learning process interms of its schedule and interaction, and e)customization of the resources and agilemanagement of the learning services for deliveryas well as necessary human interferences.Considering these problems and bearing in mindthe advanced web technology of which weshould make full use, in this report we willaddress the following two aspects of systematicarchitecture of learning/teaching systems: 1)learning objects – a semantic description andorganization of learning resources using the webservice models and methods, and 2) learningservices discovery and learning goals match foreducational coordination and learning serviceplanning.

Teaching Mathematics in English to Swedish Speaking Students : The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School

Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

Machine translation and the disruption of foreign language learning activities

This study examines the question of how language teachers in a highly technology-friendly university environment view machine translation and the implications that this has for the personal learning environments of students. It brings an activity-theory perspective to the question, examining the ways that the introduction of new tools can disrupt the relationship between different elements in an activity system. This perspective opens up for an investigation of the ways that new tools have the potential to fundamentally alter traditional learning activities. In questionnaires and group discussions, respondents showed general agreement that although use of machine translation by students could be considered cheating, students are bound to use it anyway, and suggested that teachers focus on the kinds of skills students would need when using machine translation and design assignments and exams to practice and assess these skills. The results of the empirical study are used to reflect upon questions of what the roles of teachers and students are in a context where many of the skills that a person needs to be able to interact in a foreign language increasingly can be outsourced to laptops and smartphones.

Development of on-line courses focusing on quality

The purpose of this paper is to show by which means quality in on-line education is achieved at Dalarna University. As a leading provider of online university courses in northern Europe, both in terms of number of students conducting their studies entirely on-line compared to the whole student body, (approximately 70% on-line students all subjects included), Dalarna University has acquired de facto extensive practical experience in the field of information technologies related to distance education. It has been deemed essential, to ensure that the quality of teaching reflects the principles governing the assessment of learning so that on-line education is deemed as comparative to campus education, both from a legal and cognitive point-of-view. Dalarna University began on-line courses in 2002 and it soon became clear that the interaction between the teacher and the student should make its mark in all stages of the learning process in order to both maintain the learners' motivation and ensure the assimilation of knowledge. We will illustrate these aspects by giving examples of what has been done in the recent years in on-line teaching of languages. As this method of teaching is not limited to learning basic language skills, but also to the study of literature, social issues and the language system of the various cultures, our presentation will offer a broad range of areas where the principles of quality in education are provided on a daily basis.

Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.