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.

Language and thought in bilinguals: the case of grammatical number and nonverbal classification preferences

Recent research shows that speakers of languages with obligatory plural marking (English) preferentially categorize objects based on common shape, whereas speakers of nonplural-marking classifier languages (Yucatec and Japanese) preferentially categorize objects based on common material. The current study extends that investigation to the domain of bilingualism. Japanese and English monolinguals, and Japanese–English bilinguals were asked to match novel objects based on either common shape or color. Results showed that English monolinguals selected shape significantly more than Japanese monolinguals, whereas the bilinguals shifted their cognitive preferences as a function of their second language proficiency. The implications of these findings for conceptual representation and cognitive processing in bilinguals are discussed.

Language and thought in a multilingual context: the case of isiXhosa

Situated within the grammatical aspect approach to motion event cognition, this study takes a first step in investigating language and thought in functional multilinguals by studying L1 isiXhosa speakers living in South Africa. IsiXhosa being a non-aspect language, the study investigates how the knowledge and use of additional languages with grammatical aspect influence cognition of endpoint-oriented motion events among L1 isiXhosa speakers. Results from a triads-matching task show that participants who often used aspect languages and had greater exposure to English in primary education were less prone to rely on endpoints when categorising motion events.

Duality of thought and language; an outline of original research,

Mode of access: Internet.

Philosophic grammar of the English language : in connection with the laws of matter and of thought ... designed for private students, foreigners, and the higher classes in schools /

Includes index.

Freedom of thought in the aftermath of the Charlie Hebdo attacks

Peer reviewed

The language of neofeudal corporatism and the war on Iraq

In this paper we argue that the term “capitalism” is no longer useful for understanding the current system of political economic relations in which we live. Rather, we argue that the system can be more usefully characterised as neofeudal corporatism. Using examples drawn from a 300,000 word corpus of public utterances by three political leaders from the “coalition of the willing”— George W. Bush, Tony Blair, and John Howard—we show some defining characteristics of this relatively new system and how they are manifest in political language about the invasion of Iraq.

Gifted young adolescents and email : developing a personal language of self

This paper reports on the use of email as a means to access the self-constructions of gifted young adolescents. Australian research shows that gifted young adolescents may feel more lonely and misunderstood than their same-age counterparts, yet they are seldom asked about their lives. Emerging use of online methods as a means of access to individual lives and perceptions has demonstrated the potential offered by the creation of digital texts as narrative data. Details are given of a qualitative study that engaged twelve children aged between 10 and 14 years, who were screened for giftedness, in a project involving the generation of emailed journal entries sent over a period of 6 months. With emphasis on participatory principles, individual young adolescents produced self-managed journal entries that were written and sent to the researcher from personal computers outside the school setting. Drawing from a theoretical understanding of self as constructed within dialogic relationships, the digital setting of email is proposed as a narrative space that fosters healthy self-disclosure. This paper outlines the benefits of using email as a means to explore emotions, promote reflective accounts of self and support the development of a personal language for self-expression. Individual excerpts will be presented to show that the harnessing of personal narratives within an email context has potential to yield valuable insights into the emotions, personal realities and experiences of gifted young adolescents. Findings will be presented to show that the co-construction of self-expressive and explanatory narratives supported by a facilitative adult listener promoted healthy self-awareness amongst participants. This paper contributes to appreciative conversations about using online methods as a flexible and practical avenue for conducting educational research. Furthermore, digital writing in email form will be presented as having distinct advantages over face-to-face methods when utilised with gifted young adolescents who may be unwilling to disclose information within school-based settings.

Mapping the language of science and science teaching practices : a case study of early childhood school science

Concerns raised in educational reports about school science in terms of students. outcomes and attitudes, as well as science teaching practices prompted investigation into science learning and teaching practices at the foundational level of school science. Without science content and process knowledge, understanding issues of modern society and active participation in decision-making is difficult. This study contended that a focus on the development of the language of science could enable learners to engage more effectively in learning science and enhance their interest and attitudes towards science. Furthermore, it argued that explicit teaching practices where science language is modelled and scaffolded would facilitate the learning of science by young children at the beginning of their formal schooling. This study aimed to investigate science language development at the foundational level of school science learning in the preparatory-school with students aged five and six years. It focussed on the language of science and science teaching practices in early childhood. In particular, the study focussed on the capacity for young students to engage with and understand science language. Previous research suggests that students have difficulty with the language of science most likely because of the complexities and ambiguities of science language. Furthermore, literature indicates that tensions transpire between traditional science teaching practices and accepted early childhood teaching practices. This contention prompted investigation into means and models of pedagogy for learning foundational science language, knowledge and processes in early childhood. This study was positioned within qualitative assumptions of research and reported via descriptive case study. It was located in a preparatory-school classroom with the class teacher, teacher-aide, and nineteen students aged four and five years who participated with the researcher in the study. Basil Bernstein.s pedagogical theory coupled with Halliday.s Systemic Functional Linguistics (SFL) framed an examination of science pedagogical practices for early childhood science learning. Students. science learning outcomes were gauged by focussing a Hallydayan lens on their oral and reflective language during 12 science-focussed episodes of teaching. Data were collected throughout the 12 episodes. Data included video and audio-taped science activities, student artefacts, journal and anecdotal records, semi-structured interviews and photographs. Data were analysed according to Bernstein.s visible and invisible pedagogies and performance and competence models. Additionally, Halliday.s SFL provided the resource to examine teacher and student language to determine teacher/student interpersonal relationships as well as specialised science and everyday language used in teacher and student science talk. Their analysis established the socio-linguistic characteristics that promoted science competencies in young children. An analysis of the data identified those teaching practices that facilitate young children.s acquisition of science meanings. Positive indications for modelling science language and science text types to young children have emerged. Teaching within the studied setting diverged from perceived notions of common early childhood practices and the benefits of dynamic shifting pedagogies were validated. Significantly, young students demonstrated use of particular specialised components of school-science language in terms of science language features and vocabulary. As well, their use of language demonstrated the students. knowledge of science concepts, processes and text types. The young students made sense of science phenomena through their incorporation of a variety of science language and text-types in explanations during both teacher-directed and independent situations. The study informs early childhood science practices as well as practices for foundational school science teaching and learning. It has exposed implications for science education policy, curriculum and practices. It supports other findings in relation to the capabilities of young students. The study contributes to Systemic Functional Linguistic theory through the development of a specific resource to determine the technicality of teacher language used in teaching young students. Furthermore, the study contributes to methodology practices relating to Bernsteinian theoretical perspectives and has demonstrated new ways of depicting and reporting teaching practices. It provides an analytical tool which couples Bernsteinian and Hallidayan theoretical perspectives. Ultimately, it defines directions for further research in terms of foundation science language learning, ongoing learning of the language of science and learning science, science teaching and learning practices, specifically in foundational school science, and relationships between home and school science language experiences.

The language of optimism : how entrepreneurs sell the sizzle in business plan offer documents

Existing macro level research on the new venture creation process recognises the entrepreneur as a central agent in the process yet generally avoids, at each stage of the process, an examination of the micro level psychological behaviour of the individual entrepreneur. By integrating two theoretical approaches to entrepreneurship research, the psychology of the entrepreneur and the entrepreneurship process, this paper examines, using content analysis, the language used by new venture founders in documents directly linked to their capital raising activity. The study examined the language of 108 offer documents (information memorandum’s) which were divided between 54 new ventures that were successful in raising capital and 54 new ventures that either did not proceed further or were not successful in raising capital through the Australian Small Scale Offerings Board. Specifically, we were interested in examining the level of optimism evident in these narratives given that entrepreneurs have been previously described in the literature as being excessively optimistic.