Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Self access and learning English as a second language

A study of the development and implementation of a self-access centre in the University of Khon Kaen to help Thai students learn English as a foreign language. Problems in the teaching of English relate to the nature of Thai culture and the isolated location of the university. Explores the advantages and disadvantages of working in a research team in a department where the principles of action research are still novel.

Travellers’ tales : the expatriate english language teacher in the new global culture

Most of the research into ELT has focused on its linguistic and methodological aspects, which are based on Western scientific traditions. The contributions and experiences of English language teachers themselves, especially their work in overseas contexts, have frequently been overlooked. This volume aims to document the complexity of ELT as 'work' in new global economic and cultural conditions, and to explore how this complexity is realised in the everyday experiences of ELT teachers. The development of ELT from the colonial experience to its current status as a global commodity is explored; ELT is then situated in the discourses of globalisation, specifically within Appadurai's theorisation of global flows of people, images, ideas, technology and money, or scapes. Within this framework, narratives are constructed from the experiences of Native-speaking English teachers. These reveal much about the personal, pedagogical and cultural dimensions of ELT work in non-Centre countries, and will contribute to a greater understanding of the intercultural dimensions of ELT for all those who work in it, and in related educational fields.

Code-switching and teaching Chinese as a second language

This book aims to explore the nature of code-switching. The purpose is to find out how this works and thereby inform language-teaching strategies. It focuses on Chinese / English bilinguals with special emphasis on younger students living in two linguistic worlds (Chinese and English). The book examines code-switching in relation to several aspects: grammatical structures, tonal facilitation, contextual factors, speakers' social background aspects and their participation in school language programs.

Teacher agency and participation in professional learning for new literacies

The proliferation of digital technologies is influencing the relational as well as the technological and meaning-making aspects of literacy learning. There is a renewed focus on student learning that promotes agency and enables new literacies mindsets. However a lack of clarity persists as to the form and content of effective professional learning for teachers of new literacies. Combining elements from various models of professional learning to foster teacher agency and participation mobilises transformed processes and conditions. This article draws on literature from the areas of new literacies, student agency and teacher professional learning to argue for approaches to teacher professional learning that support new literacy learning. It explores the characteristics of models of professional learning for teachers; describes a professional learning program offered to teachers of literacy; outlines a mixed methods research study in the form of a survey of participants engaged in the professional learning program; and analyses teacher perceptions of their experiences of professional learning and how key characteristics influenced their learning.

"The capacity of contrastive analysis to successfully predict the errors of second language learners - a case study"

The aim of this dissertation is to show the power of contrastive analysis in successfully predicting the errors a language learner will make by means of a concrete case study. First, there is a description of what language transfer is and why it is important in the matter of second language acquisition. Second, a brief explanation of the history and development of contrastive analysis will be offered. Third, the focus of the thesis will move to an analysis of errors usually made by language learners. To conclude, the dissertation will focus on the concrete case study of a Russian learner of English: after an analysis of the errors the student is likely to make, a recorded conversation will be examined.

Structural plasticity in the language system related to increased second language proficiency

While functional changes linked to second language learning have been subject to extensive investigation, the issue of learning-dependent structural plasticity in the fields of bilingualism and language comprehension has so far received less notice. In the present study we used voxel-based morphometry to monitor structural changes occurring within five months of second language learning. Native English-speaking exchange students learning German in Switzerland were examined once at the beginning of their stay and once about five months later, when their German language skills had significantly increased. We show that structural changes in the left inferior frontal gyrus are correlated with the increase in second language proficiency as measured by a paper-and-pencil language test. Contrary to the increase in proficiency and grey matter, the absolute values of grey matter density and second language proficiency did not correlate (neither on first nor on second measurement). This indicates that the individual amount of learning is reflected in brain structure changes, regardless of absolute proficiency.