Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

The linguistic construction of business reasoning: Towards a language-based model of decision-making in undergraduate business

This thesis reports on research whose aim is to arrive at a linguistically theorised understanding of the process of decision-making in undergraduate business studies. The use of ‘real-life’ tasks such as country reports – the major assessment task of the interdisciplinary unit Business in the Global Environment at a metropolitan Australian university – is intended to prepare students for the skills of ‘problem-solving’, ‘decision-making’ and professional report writing in international business environments. However, as indicated by the large number of students failing this task, few students possess the sophisticated linguistic resources necessary to build the generic complexity and persuasive rhetoric this high-stakes task demands. This study is concerned with identifying the linguistic demands of demonstrating decision-making in country reports. Current modelling of ‘big texts’ in SFL (Martin, 1994, 1995) is insufficient for understanding longer texts stretching across the many pages tertiary students are generally required to write. This thesis will show through fine-grained linguistic analyses of High Distinction student assignments that not all ‘big texts’ are macrogenres made up of elemental genre complexes and illustrate that embedded genres play a fundamental role in enabling texts of the length of business country reports to grow bigger than a page. Drawing on discourse semantics (Martin, 1992; Martin & Rose, 2007; Martin & White, 2005), this thesis also will also show how business reasoning is construed in undergraduate business reports through different types of grammatical structures and how successful student writers construct cause-effect relations and three major types of rhetorical moves in these texts. By making visible the academically valued meanings by which skillful writers demonstrate the process of decision-making in undergraduate business country reports, this research has pedagogical implications for academic literacy interventions aimed at making explicit the basis of achievement in business studies. It is hoped that this study will open up future research directions for the continued study of knowledge-building in undergraduate business studies

Current issues of the Russian language teaching XIV

Collection of papers “Current issues of the Russian language teaching XIV” is devoted to issues of methodology of teaching Russian as a foreign language, to issues of linguistics and literary science and includes papers related to the use of online tools and resources in teaching Russian. This collection of papers is a result of the international scientific conference “Current issues of the Russian language teaching XIV”, which was scheduled for 8–10 May 2020, but due to the pandemic COVID-19 took place remotely

Some new insights into the semantics of English N+N compounds

This thesis focuses on English N+N compounds and the primary purpose of the study is to investigate the way in which compounded structures acquire their meaning and to check the way in which the semantics of each of the constituents contributes to the overall meaning of the structure. The way in which such contributions are made should be inferable from the linguistic analysis of the structure and meaning of compounds. In order to do this, the thesis looks first at the morphological productivity of the constituents comprising a compound. The second aim is to identify whether the productivity of a compound constituent on the morphological level coincides with the productivity of the semantic relation realised in the constituent family. The discussion of the results obtained from a corpus study provides plausible explanations for the regularities noted in the course of the analysis by using some of the relevant principles from the complex of approaches including the Construction Grammar and Cognitive Grammar approaches. Examples of compounds were collected from the printed media (NZ broadsheets) and the BNC. The analysis of the data used both quantitative and qualitative methods. The quantitative analysis of the data confirms two hypotheses: (1) that a constituent is more productive in just one of the positions (modifier or head), and (2) the more productive a constituent is, the more likely it is to realise a single semantic relation in a constituent family. The qualitative analysis involves consideration of the semantic content of the concepts in each constituent in order to see how this content is reflected in the semantic relations realised by a constituent. It is discovered that the semantic content of the head is a stronger predictor of the relation realised in a compound than that of the modifier. The study is important in order to better understand the factors that govern the formation of compounds and the patterns that speakers use in the process of coining complex lexical items ..

What is “meta-” for? : a Peircean critique of the cognitive theory of metaphor

My thesis aims to anatomize the cognitive theory of metaphor and suggests a Peircean semiotic perspective on metaphor study. As metaphorical essentialists, Lakoff/Johnson tend to universalize a limited number of conceptual metaphors and, by doing this, they overlook the dynamic relation between metaphorical tenor and vehicle. Such notion of metaphor is not compatible with the polysemous nature of the sign. The diversity and multivalency of metaphorical vehicle, in particular, cast serious doubts on the hypothesis of “conceptual metaphors” which, being meta-metaphorical constructs, can tell us nothing but a dry and empty formula “A is B”. Consequently, Lakoff/Johnson’s notion of conceptual metaphor is very much a Chomskyan postulation. Also problematic is the expedient experientialism or embodied philosophy they have put forward as a middle course between objectivism and subjectivism. What is missing from their framework is a structural space for dynamic interpretation on the part of metaphor users. In contrast, cognitive linguists may find in Peirce’s theory of the sign a sound solution to their theoretical impasse. As a logician, Peirce sees metaphor as the realization of iconic reasoning at the language level. His exposition on iconicity and iconic reasoning has laid a solid foundation upon which may be erected a fresh epistemology of metaphor fit for the contemporary study of language and mind. Broadly speaking, metaphor in Peirce can be examined from roughly two perspectives. Macroscopically, metaphor is an icon in general as opposed to index and symbol, whereas, microscopically, it is a subdivided hypoicon on the third level as opposed to image and diagram. Besides, Peirce also emphasized the subjective nature of metaphor. Semioticians after Peirce have further developed his theory on metaphor. For example, through his concept of “arbitrary iconicity”, Ersu Ding stresses the arbitrary nature of metaphorization and tries to shift our attention away from Lakoff/Johnson’s abstract epistemological Gestalt to the specific cultural contexts in which metaphors occur. Umberto Eco, on the other hand, sees interpretation of signs as an open-ended process that involves knowledge of all kinds. Encyclopedic knowledge thus serves as unlimited source for metaphorical association. For Eco, the meaning of a metaphor should be interpreted in the cultural framework based on a specific cultural community. Both Ding’s and Eco’s ideas are in line with Peirce’s theoretical framework where the meaning of a metaphor depends on an interpreter in a particular socio-historical context. They all realize that we should go beyond the ontology of metaphorical expressions to acquire a dynamic perspective on metaphor interpretation. To overcome the need for presupposing an omnipotent subject capable of knowing the metaphor-in-itself, we turn to Habermas’s theory of communicative action in which the meaning of metaphor is intersubjectively established through negotiation and communication. Moreover, we should not overlook the dynamic tension between metaphor and ideology. Aphoristically, we can say that nothing is a metaphor unless it is interpreted as a metaphor, and we need to reconnect metaphors with the specific cultural and ideological contexts in which they appear

Gradient Metaphoricity of the Preposition in: A Corpus-based Approach to Chinese Academic Writing in English

In Cognitive Linguistics, a conceptual metaphor is a systematic set of correspondences between two domains of experience (Kövecses 2020: 2). In order to have an extensive understanding of metaphors, metaphoricity (Müller and Tag 2010; Dunn 2011; Jensen and Cuffari 2014; Nacey and Jensen 2017) has been emphasized to address one of the properties of metaphors in language usage: gradience (Hanks 2006; Dunn 2011, 2014), which indicates that metaphorical expressions can be measured. Despite many noteworthy contributions, studies of metaphoricity are often accused of subjectivity (Müller 2008; Jensen and Cuffari 2014; Jensen 2017), this is why this study uses a big corpus as a database. Therefore, the main aim of this dissertation is to measure the gradient senses of the preposition in in an objective way, thus mapping the highly systematic semantic extension. Based on these gradient senses, the semantic and syntactic features of the preposition in produced by advanced Chinese English-major learners are investigated, combining quantitative and qualitative research methods. A quantitative analysis of the literal and other ten metaphorical senses of the preposition in is made at first. In accounting for the five factors influencing image schemata of each sense: “scale of Landmark”, “visibility”, “path”, “inclusion” and “boundary”, the formula of measuring the gradability of metaphorical degree is deduced: Metaphoricity=[[#Visibility] +[#Path] +[#Inclusion] +[#Boundary]]*[#Scale of Landmark]. The result is that the primary sense has the highest value:12, and all other extended senses have values down to zero. The more shared features with proto-scene, the higher the value of the metaphorical sense, and the less metaphorical the sense. EVENT and PERSON are the “least metaphoric” (value = 9-11); SITUATION, NUMBER, CONTENT and FIELD are “weak metaphoric” (value = 6-8); Also included are SEGMENTATION, TIME and MANNER (value = 3-5), and they are “strong metaphoric”; PURPOSE shares the least feature with proto-scene, and it has the lowest value, so it is “most metaphoric” (value = 0-2). Then, a corpus-based approach is employed, which offers a model for employing a corpus-based approach in Cognitive Linguistics. It compares two compiled sub-corpora: Chinese Master Academic Writing Corpus and Chinese Doctorate Academic Writing Corpus. The findings show that, on the semantic level, Chinese English-major students overuse in with a low level of metaphoricity, even advanced learners use the most metaphorical in rarely. In terms of syntactic behaviours, the most frequent nouns in [in+noun] construction are weakly metaphoric, whilst the nouns in the construction [in the noun of] are EVENT sense, which is least metaphorical. Moreover, action verbs tend to be used in the construction [verb+in] and [in doing sth.] in both master and doctorate groups. In the qualitative study, the divergent usages of the preposition in are explored. The preposition in is often substituted with other prepositions, such as on and at. The fundamental reason for the Chinese learners’ weakness is the negative transfer from their mother tongue (Wang 2001; Gong 2007; Zhang 2010). Although in and its Chinese equivalence zai...li (在...里) share the same proto-scene, there are discrepancies: the metaphorical senses of the preposition in are TIME, PURPOSE, NUMBER, CONTENT, FIELD, EVENT, SITUATION, SEGMENTATION, MANNER, PERSON, while those of zai...li (在...里) are only five: TIME, CONTENT, EVENT, SITUATION and PERSON. Thus the image schemata of each sense cannot be correspondingly mapped onto each other in different languages. This study also provides evidence for the universality and variation of spatial metaphors on the ground of cultural models. Philosophically, it supports the standpoint of Embodiment philosophy that abstract concepts are constructed on the basis of spatial metaphors that are grounded in the physical and cultural experience

Methodological Tools for Linguistic Description and Typology.

International audienc

Applied and Computational Linguistics

Розглядається сучасний стан прикладної та комп’ютерної лінгвістики, проаналізовано лінгвістичні теорії 20-го – початку 21-го століть під кутом розмежування різних аспектів мови з метою формалізованого опису у електронних лінгвістичних ресурсах. Запропоновано критичний огляд таких актуальних проблем прикладної (комп’ютерної) лінгвістики як укладання комп’ютерних лексиконів та електронних текстових корпусів, автоматична обробка природної мови, автоматичний синтез та розпізнавання мовлення, машинний переклад, створення інтелектуальних роботів, здатних сприймати інформацію природною мовою. Для студентів та аспірантів гуманітарного профілю, науково-педагогічних працівників вищих навчальних закладів України