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1
Esterhuizen, H. L. "Linguistics + Mathematics = twins." Interim : Interdisciplinary Journal, Vol 7, Issue 1 :Central University of Technology Free State Bloemfontein, 2008. http://hdl.handle.net/11462/379.
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Published ArticleLanguage and Mathematics are both so-called "tools" that are used by other disciplines to explain / describe phenomena in those disciplines, but they are scientific disciplines in their own right. Language is a system of symbols, but so is Mathematics. These symbols carry meaning or value. Both originate in the human mind and are then translated into messages of logic. What is important are the relationships between units that are inherent to both disciplines. In practicing the two disciplines, there are elements that correspond. These are a vocabulary, grammar, a community and meaning. Psycholinguists and psychologists are interested in the role that language might have in enabling other functions in the human cognitive repertoire. Some argue that language is a prerequisite for a whole range of intellectual activities, including mathematics. They claim that mathematical structures are, in a way, parasitic on the human linguistic faculty. Some evidence for the language: maths connection comes from neurology. Functional imaging studies of the brain show increased activation of the language areas as certain mathematical tasks / challenges are performed. Lesions to a certain part of the brain impair both the linguistic as well as the mathematical ability. We are looking at a fundamentally shared enterprise, a deeply interwoven development of numerical and linguistic aspects. This co-evolution of number concepts and number words suggests that it is no accident that the same species that possesses the language faculty as a unique trait, should also be the one that developed a systematic concept of number.
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Nefdt, Ryan Mark. "The foundations of linguistics : mathematics, models, and structures." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/9584.
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The philosophy of linguistics is a rich philosophical domain which encompasses various disciplines. One of the aims of this thesis is to unite theoretical linguistics, the philosophy of language, the philosophy of science (particularly mathematics and modelling) and the ontology of language. Each part of the research presented here targets separate but related goals with the unified aim of bringing greater clarity to the foundations of linguistics from a philosophical perspective. Part I is devoted to the methodology of linguistics in terms of scientific modelling. I argue against both the Conceptualist and Platonist (as well as Pluralist) interpretations of linguistic theory by means of three grades of mathematical involvement for linguistic grammars. Part II explores the specific models of syntactic and semantics by an analogy with the harder sciences. In Part III, I develop a novel account of linguistic ontology and in the process comment on the type-token distinction, the role and connection with mathematics and the nature of linguistic objects. In this research, I offer a structural realist interpretation of linguistic methodology with a nuanced structuralist picture for its ontology. This proposal is informed by historical and current work in theoretical linguistics as well as philosophical views on ontology, scientific modelling and mathematics.
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Meyer, Ulrich 1968. "Mathematics, time, and confirmation." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8194.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2001.Includes bibliographical references (leaves 117-128).
This dissertation discusses two issues about abstract objects: their role in scientific theories, and their relation to time. Chapter 1, "Why Apply Mathematics?" argues that scientific theories are not about the mathematics that is applied in them, and defends this thesis against the Quine-Putnam Indispensability Argument. Chapter 2, "Scientific Ontology," is a critical study of W. V. Quine's claim that metaphysics and mathematics are epistemologically on a par with natural science. It is argued that Quine's view relies on a unacceptable account of empirical confirmation. Chapter 3, "Prior and the Platonist," demonstrates the incompatibility of two popular views about time: the "Platonist" thesis that some objects exist "outside" time, and A. N. Prior's proposal for treating tense on the model of modality. Chapter 4, "What has Eternity Ever Done for You?" argues against the widely held view that abstract objects exist eternally ("outside" time), and presents a defense of the rival view that they exist sempiternally (at all times)
Ulrich Meyer.
Ph.D.
4
Uzquiano, Gabriel 1968. "Ontology and the foundations of mathematics." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9370.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1999.Includes bibliographical references.
"Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more, precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences (whose acceptance plays a crucial role in applications) place serious constraints on the sorts of items to which numerals, as we ordinarily use them, can be taken to refer: Numerals cannot be taken to refer to objects that exist contingently such as people, mountains, or rivers, but rather must be taken to refer to objects that exist necessarily such as abstracta. Chapter 2, "Modern Set Theory and Replacement," takes up a challenge to explain the reasons one should accept the axiom of replacement of Zermelo-Fraenkel set theory, when its applications within ordinary mathematics and the rest of science are often described as rare and recondite. We argue that this is not a question one should be interested in; replacement is required to ensure that the element-set relation is well-founded as well as to ensure that the cumulation of sets described by set theory reaches and proceeds beyond the level w of the cumulative hierarchy. A more interesting question is whether we should accept instances of replacement on uncountable sets, for these are indeed rarely used outside higher set theory. We argue that the best case for (uncountable) replacement comes not from direct, intuitive considerations, but from the role replacement plays in the formulation of transfinite recursion and the theory of ordinals, and from the fact that it permits us to express and assert the (first-order) content of the modern cumulative view of the set theoretic universe as arrayed in a cumulative hierarchy of levels. Chapter 3, "A No-Class Theory of Classes," makes use of the apparatus of plural quantification to construe talk of classes as plural talk about sets, and thus provide an interpretation of both one- and two-sorted versions of first-order Morse-Kelley set theory, an impredicative theory of classes. We argue that the plural interpretation of impredicative theories of classes has a number of advantages over more traditional interpretations of the language of classes as involving singular reference to gigantic set-like entities, only too encompassing to be sets, the most important of these being perhaps that it makes the machinery of classes available for the formalization of much recent and very interesting work in set theory without threatening the universality of the theory as the most comprehensive theory of collections, when these are understood as objects.
by Gabriel Uzquiano.
Ph.D.
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Breet, Felicity Grace. "Verbal interaction in mathematics lessons in Anglophone Cameroon." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/1216/.
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The verbal interaction between students during mathematics lessons Cameroon is the primary focus of Strategies for facilitating language Service Training activities to meet needs of such teachers form a secondary teachers and in Anglophone this study. oriented Inthe training focus. Specifically three research questions are asked. Firstly, how do teachers and students interact in English whilst teaching and learning mathematics? Secondly can a model of these patterns be created and thirdly can such a model be used with teachers to enable them to increase the amount and range of student language in mathematics lessons. Following a review of relevant research-, -the need for a study which will provide answers to these questions is clear. The methodology of such research is also reviewed, 'and thus the present study is rooted in existing practice both in terms of its content and its research design. The data, audio recorded lessons, are transcribed and the patterns of verbal interaction observed classified via a grounded theory. These patterns are described collectively and then individually so that changes made during the phase of intensive INSET can be observed. The study shows that the participating teachers were able to use their new awareness of their own patterns of verbal interaction to experiment with innovative ways of interacting with their learners some of which led to an increase in the amount and range of student language use. The implications of this study for. INSET programmes are many. Enabling teachers to be more aware of their own language use is advantageous and provides the basis for long term changes in classroom procedures. The study also offers a research process which can be used to illuminate verbal interaction in other contexts such as discussions between doctors and their patients or during formalised conflict resolution.
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Bold, Christine Elizabeth. "Making sense of mathematical language in a primary classroom." Thesis, n.p, 2001. http://oro.open.ac.uk/18838.
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Shiers, N. L. "Gaussian latent tree model constraints for linguistics and other applications." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/80590/.
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The relationships between languages are often modelled as phylogenetic trees whereby there is a single shared ancestral language at the root and contemporary languages appear as leaves. These can be thought of as directed acyclic graphs with hidden variables, specifically Bayesian networks. However, from a statistical perspective there is often no formal assessment of the suitability of these latent tree models. A lot of the work that seeks to address this has focused on discrete variable models. However, when observations are instead considered as functional data, the high dimensional approximations are often better considered in a Gaussian context. The high dimensional data is often inefficiently stored and so the first challenge is to project this data to a low dimension while retaining the information of interest. One approach is to use the newly developed tool named separable-canonical variate analysis to form a basis. Extending the techniques for assessing latent tree model compatibility to beyond discrete variables, the complete set of Gaussian tree constraints are derived for the first time. This set comprises equations and inequality statements in terms of correlations of observed variables. These statements must in theory be adhered to for a Gaussian latent tree model to be appropriate for a given data set. Using the separable-canonical variate analysis basis to obtain a truncated representation, the suitability of a phylogenetic tree can then be plainly assessed. However, in practice it is desirable to allow for some sampling error and as such probabilistic tools are developed alongside the theoretical derivation of Gaussian tree constraints. The proposed methodology is implemented in an in-depth study of a real linguistic data set to assess the phylogenies of five Romance languages. This application is distinctive as the data set consists of acoustic recordings, these are treated as functional data, and moreover these are then being used to compare languages in a phylogenetic context. As a consequence a wide range of theory and tools are called upon from the multivariate and functional domains, and the powerful new separable-canonical function analysis and separable-canonical variate analysis are used. Utilising the newly derived Gaussian tree constraints for hidden variable models provides a first insight into features of spoken languages that appear to be tree-compatible.
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Miller, Barbara L. "Grammar Efficiency of Parts-of-Speech Systems." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1300373267.
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Picard, Joseph Romeo William Michael. "Impredicativity and turn of the century foundations of mathematics : presupposition in Poincare and Russell." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12498.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1993.Includes bibliographical references (leaves 145-158).
by Joseph Romeo William Michael Picard
Ph.D.
10
Cardinal, Kumi. "An algebraic study of Japanese grammar /." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29419.
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I present an algebraic language model for Japanese within the framework of a type grammar. The analysis pays attention to both inflectional morphology and to syntax. The mathematics for checking the sentencehood of strings of words invokes a generalization of the notorious group concept.
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Wang, Xiaozhou. "Language shift regarding Canada's French-speaking population: Data comparability and trends from 1971 to 2001." Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/27304.
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The importance of establishing valid language shift trends regarding Canada's French-speaking populations and the historical comparability of Canadian census language data are considered. Based on an empirical theory, comparability breaks in language data since 1971 are identified and evaluated. The proportions of Canadian-born persons of French mother tongue, and of French home language, to the total population of relevant birth regions are then adjusted separately, to reduce the impact of comparability breaks. The resulting language shift trends regarding the French-speaking populations are portrayed using language vitality indices for reference cohorts. It is found that for the whole of Canada, and for the provinces of Quebec and New Brunswick, the vitality of French among the Canadian-born rebounded in 2001, after consistently decreasing from 1971 to 1991. It is also observed that for other regions, the vitality of French went down continuously, indicating a sustained and aggravated assimilation over the past 30 years.
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Wallace, Michelle L. Ellerton Nerida F. "Characterization of high school mathematics and physics language genres." Normal, Ill. : Illinois State University, 2004. http://wwwlib.umi.com/cr/ilstu/fullcit?p3127139.
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Thesis (Ph. D.)--Illinois State University, 2004.Title from title page screen, viewed Jan. 21, 2005. Dissertation Committee: Nerida F. Ellerton (chair), Sherry L. Meier, Sharon Soucy McCrone, Tami S. Martin. Includes bibliographical references (leaves 153-163) and abstract. Also available in print.
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Murakami, Yuko. "Modal logic of partitions." [Bloomington, Ind.] : Indiana University, 2005. http://wwwlib.umi.com/dissertations/fullcit/3162977.
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Thesis (Ph.D.)--Indiana University, Dept. of Philosophy, 2005.Title from PDF t.p. (viewed Dec. 2, 2008). Source: Dissertation Abstracts International, Volume: 66-02, Section: A, page: 0620. Chairs: Lawrence Moss; Michael Dunn.
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Mahofa, Ernest. "Code switching in the learning of mathematics word problems in Grade 10." Thesis, Cape Peninsula University of Technology, 2014. http://hdl.handle.net/20.500.11838/1950.
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Thesis submitted in fulfilment of the requirements for the degree
Master of Education
in the Faculty of Education
at the Cape Peninsula University of Technology
2014This study investigates the effects of code switching in the learning of mathematics word problems in Grade 10. The research used Cummins’ language acquisition theory to inform the study. The study employed ethnographic qualitative research design whereby classroom observations and semi-structured interviews were used as data collection techniques. The use of multiple data collection techniques was to ensure validity and credibility of the study. The sample consisted of sixty learners and two mathematics teachers. The sample was drawn from a population of one thousand two hundred and thirty five learners and forty nine teachers.The study has shown that even though code switching could be beneficial in the learning and teaching of mathematics, it was difficult for learners and teachers to use it in a way that enhances the learning of mathematics word problems because of the barriers in the use of mathematical language. It is recommended that teachers should exercise care when using code switching, especially with the topics that involve word problems; as such topics are more aligned to certain mathematical language that could not be translated to IsiXhosa.
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Raiker, Andrea. "The role of linguistics in the learning, teaching and assessment of mathematics in primary education : a case study of a lower school in the United Kingdom." Thesis, University of Bedfordshire, 2008. http://hdl.handle.net/10547/134963.
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This doctoral research was concerned with the role of language and its implications for the learning, teaching and assessment of mathematics for children aged 4-9 years. Earlier research by the author had established language and assessment as bridges enabling learning although they had the potential to increase the divide between teacher and learner. Reflection raised the question on how children achieved in mathematics despite potential difficulties with language and assessment. Review of the literature concluded that resources and sociocultural norms were also bridges between learner and teacher. A model was established of the relationships and processes between all perceived variables that provided an external, theoretical structure to be evaluated against structuralist, pragmatic and integrational linguistic approaches and empirical outcomes. The overarching approaches adopted were institutional ethnography and case study. An appropriate methodology was devised whereby sophisticated ICT equipment captured all visual and speech events during classroom interactions. Frequency analysis at word level, content analysis at utterance level and discourse analysis at total speech level triangulated with content analysis of interviews and evaluation of documentation completed the empirical research. Data analysis revealed five registers of children’s talk. Evidence suggested that the peer-peer ‘conditioned talk’ used in focused group work was the most effective for learning as it enabled them to discern the small steps in the inferential leaps in discourse made by their teachers, work out problems together, inform their peers, share findings and reinforce each others’ learning. Learners’ language showed aspects of structural, pragmatic and integrational linguistics, confirming a conclusion of the literature review that the various linguistic approaches discussed should be used to support and not exclude each other. The contribution made to knowledge is the ethnomethodology provided by the model, ICT resource and the five registers of talk revealed by the linguistic approach to discourse analysis. Teachers would be able to understand nuances of language used by their pupils and acquire essential skills and tools to put into effect the personalised learning agenda. Peer-peer observation of teachers would be an appropriate platform for the observation of the different registers used by learners, the resources that generate those registers, and their most effective use to close the gap between natural language and the subject specific language of mathematics.
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Pechenick, Eitan. "Exploring the Google Books Corpus: An Information-Theoretic Approach to Linguistic Evolution." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/525.
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The Google Books corpus contains millions of books in a variety of languages. Due to this incredible volume and its free availability, it is a treasure trove that has inspired a plethora of linguistic research.
It is tempting to treat frequency trends from Google Books data sets as indicators for the true popularity of various words and phrases. Doing so allows us to draw novel conclusions about the evolution of public perception of a given topic. However, sampling published works by availability and ease of digitization leads to several important effects, which have typically been overlooked in previous studies. One of these is the ability of a single prolific author to noticeably insert new phrases into a language. A greater effect arises from scientific texts, which have become increasingly prolific in the last several decades and are heavily sampled in the corpus. The result is a surge of phrases typical to academic articles but less common in general, such as references to time in the form of citations. We highlight these dynamics by examining and comparing major contributions to the statistical divergence of English data sets between decades in the period 1800--2000. We find that only the English Fiction data set from the second version of the corpus is not heavily affected by professional texts, in clear contrast to the first version of the fiction data set and both unfiltered English data sets.
We critique a method used by authors of an earlier work to determine the birth and death rates of words in a given linguistic data set. While intriguing, the method in question appears to produce an artificial surge in the death rate at the end of the observed period of time. In order to avoid boundary effects in our own analysis of asymmetries in language dynamics, we observe the volume of word flux across various relative frequency thresholds (in both directions) for the second English Fiction data set. We then use the contributions of the words crossing these thresholds to the Jensen-Shannon divergence between consecutive decades to resolve major factors driving the flux.
Having established careful information-theoretic techniques to resolve important features in the evolution of the data set, we validate and refine our methods by analyzing the effects of major exogenous factors, specifically wars. This approach leads to a uniquely comprehensive set of methods for harnessing the Google Books corpus and exploring socio-cultural and linguistic evolution.
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Hadjipantelis, Pantelis-Zenon. "Functional data analysis in phonetics." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/62527/.
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The study of speech sounds has established itself as a distinct area of research, namely Phonetics. This is because speech production is a complex phenomenon mediated by the interaction of multiple components of a linguistic and non-linguistic nature. To investigate such phenomena, this thesis employs a Functional Data Analysis framework where speech segments are viewed as functions. FDA treats functions as its fundamental unit of analysis; the thesis takes advantage of this, both in conceptual as well as practical terms, achieving theoretical coherence as well as statistical robustness in its insights. The main techniques employed in this work are: Functional principal components analysis, Functional mixed-effects regression models and phylogenetic Gaussian process regression for functional data. As it will be shown, these techniques allow for complementary analyses of linguistic data. The thesis presents a series of novel applications of functional data analysis in Phonetics. Firstly, it investigates the influence linguistic information carries on the speech intonation patterns. It provides these insights through an analysis combining FPCA with a series of mixed effect models, through which meaningful categorical prototypes are built. Secondly, the interplay of phase and amplitude variation in functional phonetic data is investigated. A multivariate mixed effects framework is developed for jointly analysing phase and amplitude information contained in phonetic data. Lastly, the phylogenetic associations between languages within a multi-language phonetic corpus are analysed. Utilizing a small subset of related Romance languages, a phylogenetic investigation of the words' spectrograms (functional objects defined over two continua simultaneously) is conducted to showcase a proof-of-concept experiment allowing the interconnection between FDA and Evolutionary Linguistics.
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Gray, Tyler. "Measuring Linguistic and Cultural Evolution Using Books and Tweets." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1130.
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Written language provides a snapshot of linguistic, cultural, and current events information for a given time period. Aggregating these snapshots by studying many texts over time reveals trends in the evolution of language, culture, and society. The ever-increasing amount of electronic text, both from the digitization of books and other paper documents to the increasing frequency with which electronic text is used as a means of communication, has given us an unprecedented opportunity to study these trends. In this dissertation, we use hundreds of thousands of books spanning two centuries scanned by Google, and over 100 billion messages, or ‘tweets’, posted to the social media platform, Twitter, over the course of a decade to study the English language, as well as study the evolution of culture and society as inferred from the changes in language.
We begin by studying the current state of verb regularization and how this compares between the more formal writing of books and the more colloquial writing of tweets on Twitter. We find that the extent of verb regularization is greater on Twitter, taken as a whole, than in English Fiction books, and also for tweets geotagged in the United States relative to American English books, but the opposite is true for tweets geotagged in the United Kingdom relative to British English books. We also find interesting regional variations in regularization across counties in the United States. However, once differences in population are accounted for, we do not identify strong correlations with socio-demographic variables.
Next, we study stretchable words, a fundamental aspect of spoken language that, until the advent of social media, was rarely observed within written language. We examine the frequency distributions of stretchable words and introduce two central parameters that capture their main characteristics of balance and stretch. We explore their dynamics by creating visual tools we call ‘balance plots’ and ‘spelling trees’. We also discuss how the tools and methods we develop could be used to study mistypings and misspellings, and may have further applications both within and beyond language.
Finally, we take a closer look at the English Fiction n-gram dataset created by Google. We begin by explaining why using token counts as a proxy of word, or more generally, ‘n-gram’, importance is fundamentally flawed. We then devise a method to rebuild the Google Books corpus so that meaningful linguistic and cultural trends may be reliably discerned. We use book counts as the primary ranking for an n-gram and use subsampling to normalize across time to mitigate the extraneous results created by the underlying exponential increase in data volume over time. We also combine the subsampled data over a number of years as a method of smoothing. We then use these improved methods to study linguistic and cultural evolution across the last two centuries. We examine the dynamics of Zipf distributions for n-grams by measuring the churn of language reflected in the flux of n-grams across rank boundaries. Finally, we examine linguistic change using wordshift plots and a rank divergence measure with a tunable parameter to compare the language of two different time periods. Our results address several methodological shortcomings associated with the raw Google Books data, strengthening the potential for cultural inference by word changes.
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Yee, Sean P. "Students' Metaphors for Mathematical Problem Solving." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1340197978.
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Walichinski, Danieli. "Contextualização no ensino de estatística: uma proposta para os anos finais do ensino fundamental." Universidade Tecnológica Federal do Paraná, 2012. http://repositorio.utfpr.edu.br/jspui/handle/1/1252.
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Acompanha: Sequência de ensino contemplando a estatística nos anos finais do ensino fundamental segundo pressupostos da contextualizaçãoO presente trabalho teve como objetivo analisar as contribuições que uma sequência de ensino pautada nos pressupostos da contextualização poderá trazer para o ensino e aprendizagem de Estatística nos anos finais do Ensino Fundamental. A revisão de literatura referente ao ensino de Estatística apoia-se em Cazorla (2002), Lopes (2003, 2008, 2010a, 2010b), Silva (2007), Andrade (2008), Cazorla, Kataoka e Silva (2010), Jacobini et al. (2010), Campos, Wodewotzki e Jacobini (2011), dentre outros. Quanto a contextualização, a revisão de literatura apoia-se em Brasil (1998b, 1999), Tufano (2001), Pais (2002, 2010), Ramos (2004), Mello (2005), Sadovsky (2007), Luccas (2011), além de outros. Com a intenção de alcançar o objetivo proposto, foi desenvolvida no ano de 2011 uma pesquisa aplicada, qualitativa com análise interpretativa e, descritiva em uma turma de alunos do 7° ano do Ensino Fundamental de um colégio público estadual do município de Ponta Grossa, Paraná. A revisão de literatura referente às características da pesquisa fundamenta-se em Gil (1991, 2006), Chizzotti (2003, 2008), Silva e Menezes (2005), Moreira e Caleffe (2008), Alves-Mazzotti (2011), Sarmento (2011), Teixeira (2011), dentre outros. Primeiramente foi realizada uma análise do desempenho prévio dos alunos em relação a conteúdos básicos de Estatística, tendo como base um instrumento diagnóstico chamado pré – teste. Depois foi aplicada uma sequência de ensino direcionada a conteúdos básicos de Estatística, por meio da utilização de dados coletados na própria turma, ou seja, por meio da contextualização. Verificou-se durante a aplicação da sequência de ensino, um maior interesse e motivação dos alunos para as aulas, além de um maior envolvimento dos educandos com os conteúdos estudados. Os resultados da análise do desempenho dos alunos após a aplicação da sequência de ensino mostraram que essa contribuiu para que houvesse um ganho significativo quanto à aquisição de conteúdos básicos de Estatística por parte de educandos dos anos finais do Ensino Fundamental. Considera-se que as atividades realizadas com os educandos, contribuíram para o desenvolvimento das competências de raciocínio, pensamento e, letramento estatísticos desses, formando a base necessária para que futuramente esses alunos possam atingir o nível de letramento estatístico que a sociedade contemporânea exige. Como produto final deste trabalho foi elaborado um material didático de apoio ao professor contendo uma sequência de ensino contextualizada sobre conteúdos básicos de Estatística voltada ao Ensino Fundamental, o qual se encontra anexado a esta dissertação.
The present study aimed to examine the contributions that a sequence of teaching based on assumptions of contextualization can bring to the teaching of statistics in the final years of basic school. The literature review concerning the teaching of statistics relies on Cazorla (2002), Lopes (2003, 2008, 2010a, 2010b), Silva (2007), Andrade (2008), Cazorla, Kataoka and Silva (2010), Jacobini et al. (2010), Campos, Wodewotzki and Jacobini (2011), among others. As for context, the literature review supported by Brazil (1998b, 1999), Tufano (2001), Pais (2002, 2010), Ramos (2004), (2005), Sadovsky (2007), Luccas (2011), among others. With the intention of achieving the proposed goal, was developed in the year 2011 a applied research, interpretive analysis and qualitative, descriptive in a batch of students of 7° year of basic school to a State public College of the city of Ponta Grossa, Paraná. The review of literature pertaining to the search features based on Gil (1991, 2006), Chizzotti (2003, 2008), Silva and Menezes (2005), Moreira and Caleffe (2008), Alves-Mazzotti (2011), Sarmento (2011), Teixeira (2011), among others. First was conducted an analysis of previous performance of the students on the basic content of statistics, based on a diagnostic instrument called pre-test. Then it was applied a sequence of teaching directed to basic statistical content, through the use of data collected in their own class, i.e. through contextualization. It emerged during the implementation of education, a greater interest and motivation of students to classes, as well as greater involvement of learners with the contents. The results of the analysis of the performance of the students after teaching sequence showed that this contributed to a significant gain on the acquisition of basic statistical content by students of the final years basic school. It is considered that the activities undertaken with learners, contributed to the development of the skills of reasoning, thinking, and statistical literacy of those forming the necessary basis for that in the future these students can reach the level of statistical literacy that contemporary society requires. As the final product of this work was to elaborate a courseware to support teacher education sequence containing a contextualized on basic statistical content aimed at the basic school, which is attached to this dissertation.
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Whale, Susan Gaye. "Using language as a resource: strategies to teach mathematics in multilingual classes." Thesis, Nelson Mandela Metropolitan University, 2012. http://hdl.handle.net/10948/1669.
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South Africa is a complex multilingual country. In the majority of schools in the Eastern Cape, a province in South Africa, the teachers and learners share the same home language, isiXhosa, but teach and learn mathematics in English. The purpose of this study was to encourage teachers to use the home language as a resource to teach mathematics in multilingual classes. The study follows a mixed method design, using both qualitative and quantitative data. Qualitative data were collected from a survey and poetry, which teachers crafted, in which they highlighted their perceptions about language in their lives. They also reflected on their practices and submitted pieces of contemplative writing. Quantitative data were collected from participating teachers who administered a pre-test to their learners as well as a post- test approximately nine months later after conducting an intervention. The results showed that where strategies, such as the implementation of exploratory talk and code switching which used language as a resource, had been introduced mathematical reasoning improved and classroom climate became more positive. The learners’ lack of confidence in being able to express their reasoning in English was prevalent throughout the reflective writing. By enabling learners to use isiXhosa in discussions the teachers felt that the learners gained in both confidence and mathematical understanding. This study has demonstrated that using the learners’ and teachers’ home language unlocks doors to communication and spotlights mathematical reasoning, but there is still an urgency to encourage learners to become fluent in Mathematical English. It is important to note that a positive classroom climate is essential for learners to build confidence and to encourage them to attempt to formulate sentences in English - to start on the journey from informal to formal usage of language as advocated by Setati and Adler (2001:250). My main conclusion is that an intervention that develops exploratory talk by using language as a resource can improve learners’ mathematical reasoning. I wish to emphasise that I am not advocating teaching mathematics in isiXhosa only, but the research has shown the advantages of using the home language as a resource together with English in Eastern Cape multilingual mathematics classes. Learners need to be able to express themselves in English, written and spoken, in order to achieve mathematically. This study therefore shows that teachers can gauge their learners’ improvement in mathematical reasoning after an intervention that develops exploratory talk in class by using the home language as a resource.
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Bergvall, Ida. "Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS." Doctoral thesis, Uppsala universitet, Institutionen för pedagogik, didaktik och utbildningsstudier, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-284096.
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The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language. Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language. The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS). In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language. The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic. The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.
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Williams, Jake Ryland. "Lexical mechanics: Partitions, mixtures, and context." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/346.
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Highly structured for efficient communication, natural languages are complex systems. Unlike in their computational cousins, functions and meanings in natural languages are relative, frequently prescribed to symbols through unexpected social processes. Despite grammar and definition, the presence of metaphor can leave unwitting language users "in the dark," so to speak. This is not problematic, but rather an important operational feature of languages, since the lifting of meaning onto higher-order structures allows individuals to compress descriptions of regularly-conveyed information. This compressed terminology, often only appropriate when taken locally (in context), is beneficial in an enormous world of novel experience. However, what is natural for a human to process can be tremendously difficult for a computer. When a sequence of words (a phrase) is to be taken as a unit, suppose the choice of words in the phrase is subordinate to the choice of the phrase, i.e., there exists an inter-word dependence owed to membership within a common phrase. This word selection process is not one of independent selection, and so is capable of generating word-frequency distributions that are not accessible via independent selection processes. We have shown in Ch. 2 through analysis of thousands of English texts that empirical word-frequency distributions possess these word-dependence anomalies, while phrase-frequency distributions do not. In doing so, this study has also led to the development of a novel, general, and mathematical framework for the generation of frequency data for phrases, opening up the field of mass-preserving mesoscopic lexical analyses. A common oversight in many studies of the generation and interpretation of language is the assumption that separate discourses are independent. However, even when separate texts are each produced by means of independent word selection, it is possible for their composite distribution of words to exhibit dependence. Succinctly, different texts may use a common word or phrase for different meanings, and so exhibit disproportionate usages when juxtaposed. To support this theory, we have shown in Ch. 3 that the act of combining distinct texts to form large 'corpora' results in word-dependence irregularities. This not only settles a 15-year discussion, challenging the current major theory, but also highlights an important practice necessary for successful computational analysis---the retention of meaningful separations in language. We must also consider how language speakers and listeners navigate such a combinatorially vast space for meaning. Dictionaries (or, the collective editorial communities behind them) are smart. They know all about the lexical objects they define, but we ask about the latent information they hold, or should hold, about related, undefined objects. Based solely on the text as data, in Ch. 4 we build on our result in Ch. 2 and develop a model of context defined by the structural similarities of phrases. We then apply this model to define measures of meaning in a corpus-guided experiment, computationally detecting entries missing from a massive, collaborative online dictionary known as the Wiktionary.
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Albuquerque, Rosangela Nieto de. "Alguns fatores lingüísticos que interferem na intelecção dos problemas matemáticos no ensino fundamental I." Universidade Católica de Pernambuco, 2007. http://www.unicap.br/tede//tde_busca/arquivo.php?codArquivo=127.
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O presente trabalho é o resultado da análise de alguns problemas matemáticos dos livros didáticos e tem como objetivo identificar as causas da dificuldade de interpretação e intelecção dos problemas matemáticos pelos alunos que estão iniciando a leitura, na 1 série do Ensino Fundamental I. Nossa hipótese é que os fatores lingüísticos relativos aos enunciados dos problemas matemáticos interferem na sua compreensão, conforme a articulação entre os fenômenos da língua e a construção deste tipo textual. Buscamos, então, os estudos dos mecanismos enunciativos e de textualização. A metodologia deste estudo consiste na análise do texto, baseada nos estudos da lingüística textual, relativos ao nível semântico-pragmático-léxico da construção textual, tendo em vista a complexidade dos enunciados dos problemas matemáticos. Acreditamos que as estratégias textuais, as categorias de referenciação (endofórica, anafórica, catafórica e exofórica) e dos dêiticos (tempo, lugar e pessoa), são fatores lingüísticos, que, conforme a articulação na construção do enunciado, dificultam a intelecção e interpretação dos problemas matemáticos, sobretudo, pelos educandos que estão iniciando a leitura e, nesse período, apresentam dificuldades nas relações espaciais e temporais. A pesquisa compreendeu, basicamente, dois momentos fundamentais: a escolha dos problemas matemáticos, e a análise dos dados. Primeiramente buscamos, construir um instrumento metodológico para identificar e selecionar, através do corpus constituído, os problemas matemáticos, cuja construção do enunciado poderá induzir ao erro do educando na resolução do problema. Selecionamos fragmentos textuais, aleatoriamente, conforme a natureza da superfície textual, buscando alguns fatores lingüísticos que interferem na interpretação e intelecção dos problemas matemáticos, sem nos preocuparmos no entanto com a quantidade de problemas analisados. Posteriomente, partimos para a análise dos dados, fundamentada nas relações lingüísticas, e na questão de compreensão textual, considerando os aspectos sócio-culturais em que o educando está inserido. Propomos, pois, ao longo desta pesquisa, embora reconheçamos que não esgotamos o assunto, suscitar uma nova reflexão nos autores dos livros didáticos, na construção dos enunciados dos problemas matemáticos, que no nosso entender, facilitará a intelecção e interpretação dos problemas matemáticos aos alunos de 1 série do Ensino Fundamental I.The present work is the result of the analysis of some mathematical problems of didactic books, and has as objective identify the causes of the interpretation difficulty and intelection of the mathematical problems for the pupils who are initiating the reading, in first years of basic school. Our hypothesis is linguistic factors into the statments of the mathematical problems intervenes in the understanding, as the joint between the phenomon of the language and the construction of this text type. So we study, the enunciative mechanisms and textmake. The methodology of this study consists in the analysis of the text, based in studies of text linguistics, in the level semantic-pragmatic-lexicon in the text construction, in view of complexity of the statements of the mathematical problems. We believe that the text strategies, referencing categories (endofórica, anafórica, catafórica and exofórica) and the dêiticos (time, place and person), they are linguistic factors, in the construction of statement, they make difficult the understanding of the mathematical problems, over all, for the educating that are initiating reading, and show in this period special difficulties with space and secular relations. The research understood, basically, two basic moments: the choice of the mathematical problems, and the analysis of the informations. First, we search a methodological instrument to identify and select, through the corpus, mathematical problems, whose statement construction will be able to induce the educating to the error in resolution of the problem. We select text fragments, randomly, as the nature of the text surface, searching some linguistic factors that interven in the interpretation and understanding of the mathematical problems, without special about the amount of analyzed problems. Lately, we have analysed the research, buy the social-culture aspects whose the educating is inserted. We meant to reflect about the didatical book, that will be easier to the educating understand the statements of the mathematical problems of the first years of basic school
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Hulse, I. "Linguistic realism in mathematical epistemology." Thesis, University College London (University of London), 2008. http://discovery.ucl.ac.uk/1444275/.
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One project in the epistemology of mathematics is to find a defensible account of what passes for mathematical knowledge. This study contributes to this project by examining philosophical theories of mathematics governed by certain basic assumptions. Foremost amongst these is the "linguistic realism" of the title. Roughly put, this is the view that the semantics of mathematical sentences should be taken at face value. Two approaches to mathematics are considered, realist and fictionalist. Mathematical realism affirms the existence of mathematical objects, taking much of what passes for mathematical knowledge as knowledge of such things. It faces the challenge of explaining how such knowledge is possible. The main strategies here are to appeal to the faculty of reason, to a faculty of intuition or to the faculty of sense perception. Recent examples of each strategy are considered and it is argued that the prospects for a satisfactory mathematical realism are limited. Mathematical fictionalism does not affirm the existence of mathematical objects, claiming that mathematics is, or should be considered to be, a form of pretence. It faces the challenge of explaining how a form of pretence can discharge the roles mathematics has in empirical applications. Strategies here are to argue that mathematics is an eliminable convenience or, acknowledging that this may not be the case, that the roles played by mathematics in empirical applications are played in similar contexts by acknowledged forms of pretence. It is argued that the first strategy is not promising but that there is a version of the second that can be defended against objections. In closing, consequences of the conclusions reached are explored and directions for future research indicated.
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Shilamba, Julia Ndinoshisho. "An investigation into the prevalence and use of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia: a case study." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1001683.
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This research report focuses on an investigation of the prevalence and nature of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia. The existence of code switching in these classrooms was established by administering a survey to all grade 8 teachers in the region, while the nature of these practices was explored by interviewing and observing selected teachers using a case study research methodology. The data from the survey was analysed quantitatively using descriptive statistics, while the qualitative data from the case study which comprised of audio and video transcripts was analysed within the framework of Probyn’s (2006) code switching categories. These categories looked at code switching in terms of: explaining concepts; clarifying statements or questions; emphasising points; making connections with learners’ own contexts and experiences; maintaining the learners’ attention with question tags; classroom management and maintaining discipline; and affective purposes. The study found that code switching is widespread in most of the grade 8 mathematics classrooms in the Ohangwena region. It also revealed that the teachers’ code switching practices aligned well with most of Probyn’s framework. The criterion of maintaining learner’s attention with question tags was however not found in this study. The results of the study showed that teachers code switch because the majority of the learners’ language proficiency is not good. Code switching is mostly used as a strategy to support and promote learners understanding in mathematics. The study recommends that it is high time that code switching is acknowledged as a legitimate practice and recognised as an important and meaningful teaching strategy to assist learners who are learning mathematics in their second language. Code switching needs to be de-stigmatised and teachers should be supported in using this practice effectively and efficiently.
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Hale, Scott A. "Global connectivity, information diffusion, and the role of multilingual users in user-generated content platforms." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:3040a250-c526-4f10-aa9b-25117fd4dea2.
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Internet content and Internet users are becoming more linguistically diverse as more people speaking different languages come online and produce content on user-generated content platforms. Several platforms have emerged as truly global platforms with users speaking many different languages and coming from around the world. It is now possible to study human behavior on these platforms using the digital trace data the platforms make available about the content people are authoring. Network literature suggests that people cluster together by language, but also that there is a small average path length between any two people on most Internet platforms (including two speakers of different languages). If so, multilingual users may play critical roles as bridges or brokers on these platforms by connecting clusters of monolingual users together across languages. The large differences in the content available in different languages online underscores the importance of such roles. This thesis studies the roles of multilingual users and platform design on two large, user-generated content platforms: Wikipedia and Twitter. It finds that language has a strong role structuring each platform, that multilingual users do act as linguistic bridges subject to certain limitations, that the size of a language correlates with the roles its speakers play in cross-language connections, and that there is a correlation between activity and multilingualism. In contrast to the general understanding in linguistics of high levels of multilingualism offline, this thesis finds relatively low levels of multilingualism on Twitter (11%) and Wikipedia (15%). The findings have implications for both platform design and social network theory. The findings suggest design strategies to increase multilingualism online through the identification and promotion of multilingual starter tasks, the discovery of related other-language information, and the promotion of user choice in linguistic filtering. While weak-ties have received much attention in the social networks literature, cross-language ties are often not distinguished from same-language weak ties. This thesis finds that cross-language ties are similar to same-language weak ties in that both connect distant parts of the network, have limited bandwidth, and yet transfer a non-trivial amount of information when considered in aggregate. At the same time, cross-language ties are distinct from same-language weak ties for the purposes of information diffusion. In general cross-language ties are smaller in number than same-language ties, but each cross-language tie may convey more diverse information given the large differences in the content available in different languages and the relative ease with which a multilingual speaker may access content in multiple languages compared to a monolingual speaker.
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Lai, Mun-yee, and 黎敏兒. "Teacher's linguistic features in mathematics classroom: an exploratory study." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31962270.
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Lai, Mun-yee. "Teacher's linguistic features in mathematics classroom : an exploratory study /." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk:8888/cgi-bin/hkuto%5Ftoc%5Fpdf?B23451415.
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Hermann, Karl Moritz. "Distributed representations for compositional semantics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1c995f84-7e10-43b0-a801-1c8bbfb53e76.
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The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional approaches—meaning distributed representations that exploit co-occurrence statistics of large corpora—have proved popular and successful across a number of tasks. However, natural language usually comes in structures beyond the word level, with meaning arising not only from the individual words but also the structure they are contained in at the phrasal or sentential level. Modelling the compositional process by which the meaning of an utterance arises from the meaning of its parts is an equally fundamental task of NLP. This dissertation explores methods for learning distributed semantic representations and models for composing these into representations for larger linguistic units. Our underlying hypothesis is that neural models are a suitable vehicle for learning semantically rich representations and that such representations in turn are suitable vehicles for solving important tasks in natural language processing. The contribution of this thesis is a thorough evaluation of our hypothesis, as part of which we introduce several new approaches to representation learning and compositional semantics, as well as multiple state-of-the-art models which apply distributed semantic representations to various tasks in NLP. Part I focuses on distributed representations and their application. In particular, in Chapter 3 we explore the semantic usefulness of distributed representations by evaluating their use in the task of semantic frame identification. Part II describes the transition from semantic representations for words to compositional semantics. Chapter 4 covers the relevant literature in this field. Following this, Chapter 5 investigates the role of syntax in semantic composition. For this, we discuss a series of neural network-based models and learning mechanisms, and demonstrate how syntactic information can be incorporated into semantic composition. This study allows us to establish the effectiveness of syntactic information as a guiding parameter for semantic composition, and answer questions about the link between syntax and semantics. Following these discoveries regarding the role of syntax, Chapter 6 investigates whether it is possible to further reduce the impact of monolingual surface forms and syntax when attempting to capture semantics. Asking how machines can best approximate human signals of semantics, we propose multilingual information as one method for grounding semantics, and develop an extension to the distributional hypothesis for multilingual representations. Finally, Part III summarizes our findings and discusses future work.
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Milanda, Ibrahim. "Matematikundervisning för andraspråkselever : En kvalitativ studie om lärares arbetssätt i matematik." Thesis, Södertörns högskola, Lärarutbildningen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-5661.
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Norgaard, Holly Luttrell. "Assessing Linguistic, Mathematical, and Visual Factors Related to Student Performance on the Texas Assessment of Knowledge and Skills, Eighth Grade Mathematics Test." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4849/.
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The No Child Left Behind Act and National Council of Teachers of Mathematics' Principles and Standards both had a significant impact on the format and content of the Texas Assessment of Knowledge and Skills (TAKS) math test. Content analysis of the 2004 TAKS eighth grade math test identified the prevalence of linguistic complexity, mathematical rigor, and visual presentation factors and explored their relationship to student success on individual test items. Variables to be studied were identified through a review of literature in the area of reading comprehension of math word problems. Sixteen variables of linguistic complexity that have been significantly correlated with student math test performance were selected. Four variables of visual presentation were identified and ten variables of mathematical rigor. An additional five variables of mathematical rigor emerged from preliminary study of the 2003 TAKS math test. Of the 35 individual variables, only four reached a significant level of correlation with the percent of students correctly answering a given test item. The number of digits presented in the problem statement and number of known quantities both exhibited a significant positive correlation with the dependent variable. The number of times a student had to perform a multiplication operation had a significant negative correlation with the percent of correct responses, as did the total number of operations required. Stepwise regression of these four variables revealed total number of operations and known quantities to be the best combination of predictors of correct responses. When grouped in categories by problem type and compared, items involving mathematical reasoning but no mathematical operations had a significantly higher percentage of correct responses than those requiring at least one operation. Further categorization revealed problems involving applications only (without computation) associated with the highest levels of correct responses, followed by those involving only computation. Items requiring both applications and computations had a significantly lower percent of correct responses.
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Jung, Darryl 1962. "The Logic of Principia Mathematica." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/11766.
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Landry, Elaine. "Category-theoretic realism, a linguistic approach to the philosophy of mathematics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/NQ32318.pdf.
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Carlén, Irina. "PLUSSA, LÄGGA IHOP OCH ADDERA - Verb i läromedel i matematikämnet för grundskolans tidigare år." Thesis, Malmö universitet, Fakulteten för lärande och samhälle (LS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-30509.
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Research points at the textbook as the main source for mathematics development in the early school ages. The study enhances the concept of relational and instrumental understanding as means to address the teaching environment within textbooks. To investigate a part of the linguistic structure of this literature, this study reports on the main features that characterize the word class known as verbs due to their presence throughout a series of textbooks designed for the stages 1 to 3 in Sweden. The goal was to make common claims about frequency, tense and processes due to these verbs. By creating a specialized corpus, these verbs were catalogued and marked in comparison to two larger corpora and to GERS-levels. A process analysis was then done based on a systemic-functional linguistic tool. The results show a vast difference between the low- and the high frequency verbs. Analysis showed that present tense held the highest frequency by over 50%. Results also showed presence of the formal passive voice. Furthermore, the material processes were in a large majority in contrast to others present. Other indications of the analysis showed poor conditions for development of relational understanding in contrast to emphasis made in the national curriculum. Conclusions involve statements regarding textbook teaching methods not providing sufficient environments for language development. The characters of the verb corpus might place demands on students’ lexical knowledge and language proficiency level on forehand, which might induce a language-related knowledge barrier against the mathematical communication provided through the textbook.
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Wolska, Magdalena, and Ivana Kruijff-Korbayová. "Modeling anaphora in informal mathematical dialogue." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2006/1045/.
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We analyze anaphoric phenomena in
the context of building an input understanding
component for a conversational
system for tutoring mathematics.In this paper, we report the results of data analysis of two sets of corpora of dialogs on mathematical theorem proving. We exemplify anaphoric phenomena, identify factors relevant to anaphora resolution in our domain and extensions to the input interpretation component to support it.
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Grefenstette, Edward Thomas. "Category-theoretic quantitative compositional distributional models of natural language semantics." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d7f9433b-24c0-4fb5-925b-d8b3744b7012.
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This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over these contexts and represents them as vectors in high dimensional spaces. The problem of compositionality for such models concerns itself with how to produce distributional representations for larger units of text (such as a verb and its arguments) by composing the distributional representations of smaller units of text (such as individual words). This thesis focuses on a particular approach to this compositionality problem, namely using the categorical framework developed by Coecke, Sadrzadeh, and Clark, which combines syntactic analysis formalisms with distributional semantic representations of meaning to produce syntactically motivated composition operations. This thesis shows how this approach can be theoretically extended and practically implemented to produce concrete compositional distributional models of natural language semantics. It furthermore demonstrates that such models can perform on par with, or better than, other competing approaches in the field of natural language processing. There are three principal contributions to computational linguistics in this thesis. The first is to extend the DisCoCat framework on the syntactic front and semantic front, incorporating a number of syntactic analysis formalisms and providing learning procedures allowing for the generation of concrete compositional distributional models. The second contribution is to evaluate the models developed from the procedures presented here, showing that they outperform other compositional distributional models present in the literature. The third contribution is to show how using category theory to solve linguistic problems forms a sound basis for research, illustrated by examples of work on this topic, that also suggest directions for future research.
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Kartsaklis, Dimitrios. "Compositional distributional semantics with compact closed categories and Frobenius algebras." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1f6647ef-4606-4b85-8f3b-c501818780f2.
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The provision of compositionality in distributional models of meaning, where a word is represented as a vector of co-occurrence counts with every other word in the vocabulary, offers a solution to the fact that no text corpus, regardless of its size, is capable of providing reliable co-occurrence statistics for anything but very short text constituents. The purpose of a compositional distributional model is to provide a function that composes the vectors for the words within a sentence, in order to create a vectorial representation that re ects its meaning. Using the abstract mathematical framework of category theory, Coecke, Sadrzadeh and Clark showed that this function can directly depend on the grammatical structure of the sentence, providing an elegant mathematical counterpart of the formal semantics view. The framework is general and compositional but stays abstract to a large extent. This thesis contributes to ongoing research related to the above categorical model in three ways: Firstly, I propose a concrete instantiation of the abstract framework based on Frobenius algebras (joint work with Sadrzadeh). The theory improves shortcomings of previous proposals, extends the coverage of the language, and is supported by experimental work that improves existing results. The proposed framework describes a new class of compositional models thatfind intuitive interpretations for a number of linguistic phenomena. Secondly, I propose and evaluate in practice a new compositional methodology which explicitly deals with the different levels of lexical ambiguity (joint work with Pulman). A concrete algorithm is presented, based on the separation of vector disambiguation from composition in an explicit prior step. Extensive experimental work shows that the proposed methodology indeed results in more accurate composite representations for the framework of Coecke et al. in particular and every other class of compositional models in general. As a last contribution, I formalize the explicit treatment of lexical ambiguity in the context of the categorical framework by resorting to categorical quantum mechanics (joint work with Coecke). In the proposed extension, the concept of a distributional vector is replaced with that of a density matrix, which compactly represents a probability distribution over the potential different meanings of the specific word. Composition takes the form of quantum measurements, leading to interesting analogies between quantum physics and linguistics.
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Muhammad, Humayoun. "Développement du système MathNat pour la formalisation automatique des textes mathématiques." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00680095.
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Le langage mathématique courant et les langages mathématiques formelssont très éloignés. Par <> nousentendons la prose que le mathématicien utilise tous les jours dansses articles et ses livres. C'est une langue naturelle avec desexpressions symboliques et des notations spécifiques. Cette langue està la fois flexible et structurée mais reste sémantiquementintelligible par tous les mathématiciens.Cependant, il est très difficile de formaliser automatiquement cettelangue. Les raisons principales sont: la complexité et l'ambiguïté deslangues naturelles en général, le mélange inhabituel entre languenaturelle et notations symboliques tout aussi ambiguë et les sautsdans le raisonnement qui sont pour l'instant bien au-delà descapacités des prouveurs de théorèmes automatiques ou interactifs.Pour contourner ce problème, les assistants de preuves actuelsutilisent des langages formels précis dans un système logique biendéterminé, imposant ainsi de fortes restrictions par rapport auxlangues naturelles. En général ces langages ressemblent à des langagesde programmation avec un nombre limité de constructions possibles etune absence d'ambiguïté.Ainsi, le monde des mathématiques est séparé en deux, la vastemajorité qui utilise la langue naturelle et un petit nombre utilisantaussi des méthodes formelles. Cette seconde communauté est elle-mêmesubdivisée en autant de groupes qu'il y a d'assistants de preuves. Onperd alors l'intelligibilité des preuves pour tous les mathématiciens.Pour résoudre ce problème, on peut se demander:est-il possible d'écrire un programme qui comprend la langue naturellemathématique et qui la traduit vers un langage formel afin depermettre sa validation?Ce problème se subdivise naturellement en deux sous-problèmes tous lesdeux très difficiles:1. l'analyse grammaticale des textes mathématiques et leur traductiondans un langage formel,2. la validation des preuves écrites dans ce langage formel.Le but du projet MathNat (Mathematics in controlled Natural languages)est de faire un premier pas pour répondre à cette question trèsdifficile, en se concentrant essentiellement sur la première question.Pour cela, nous développons CLM (Controlled Language for Mathematics)qui est un sous-ensemble de l'anglais avec une grammaire et un lexiquerestreint, mais qui inclut tout de même quelques ingrédientsimportants des langues naturelles comme les pronoms anaphoriques, lesréférences, la possibilité d'écrire la même chose de plusieursmanières, des adjectifs distributifs ou non, ...Le second composant de MathNath est MathAbs (Mathematical Abstractlanguage). C'est un langage formel, indépendant du choix d'un systèmelogique permettant de représenter la sémantique des textes enpréservant leur structure et le fil du raisonnement. MathAbs est conçucomme un langage intermédiaire entre CLM et un système logique formelpermettant la vérification des preuves.Nous proposons un système qui permet de traduire CLM vers MathAbsdonnant ainsi une sémantique précise à CLM. Nous considèrons que cetravail est déjà un progrès notable, même si pour l'instant on estloin de pouvoir vérifier formellement toutes les preuves en MathAbsainsi générées.Pour le second problème, nous avons réalisé une petite expérience entraduisant MathAbs vers une liste de formules en logique du premierordre dont la validité garantit la correction de la preuve. Nous avonsensuite essayé de vérifier ces formules avec des prouveurs dethéorèmes automatiques validant ainsi quelques exemples.
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Womack, Catherine A. "The crucial role of proof--a classical defense against mathematical empiricism." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12678.
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Hunsader, Patricia D. "Lessons learned about boys' and girls' mathematical problem solving : the solution processes, performance, linguistic explanations, self-efficacy, and self-assessment of fifth-grade students of varying reading and mathematics abilities." [Tampa, Fla] : University of South Florida, 2005. http://purl.fcla.edu/usf/dc/et/SFE0001185.
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Stroinska, Maria Magdalena. "Indirect reference in German mathematical discourse." Thesis, University of Edinburgh, 1987. http://hdl.handle.net/1842/24351.
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Kneißl, Fabian. "Crowdsourcing for linguistic field research and e-learning." Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-168412.
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Crowdsourcing denotes the transfer of work commonly carried out by single humans to a large group of people. Nowadays, crowdsourcing is employed for many purposes, like people contributing their knowledge to Wikipedia, researchers predicting diseases from data on Twitter, or players solving protein folding problems in games. Still, there are areas for which the application of crowdsourcing has not yet been investigated thoroughly. This thesis examines crowdsourcing for two such areas: for empirical research in sciences oriented on humans -focusing on linguistic field research- and for e-learning.
Sciences oriented on humans -like linguistics, sociology, or art history- depend on empirical research. For example, in traditional linguistic field research researchers ask questions and fill in forms. Such methods are time-consuming, costly, and not free of biases. This thesis proposes the application of crowdsourcing techniques to overcome these disadvantages and to support empirical research in getting more efficient. Therefore, the concept of a generic market for trading with symbolic goods and speculating on their characteristics in a playful manner, called Agora is introduced. Agora aims to be an "operating system" for social media applications gathering data. Furthermore, the Web-based crowdsourcing platform metropolitalia has been established for hosting two social media applications based upon Agora: Mercato Linguistico and Poker Parole. These applications have been conceived as part of this thesis for gathering complementary data and meta-data on Italian language varieties. Mercato Linguistico incites players to express their own knowledge or beliefs, Poker Parole incites players to make conjectures on the contributions of others. Thereby the primary meta-data collected with Mercato Linguistico are enriched with secondary, reflexive meta-data from Poker Parole, which are needed for studies on the perception of languages. An evaluation of the data gathered on metropolitalia exhibits the viability of the market-based approach of Agora and highlights its strengths.
E-learning is concerned with the use of digital technology for learning, nowadays especially via the Internet. This thesis investigates how e-learning applications can support students with association-based learning and lecturers with teaching. For that, a game-like e-learning tool named Termina is proposed in this thesis. From the data collected with Termina association maps are constructed. An association map is a simplified version of a concept map, in which concepts are represented as rectangles and relationships between concepts as links. They constitute an abstract comprehension of a topic. Students profit from the association maps' availability, learn from other participating students, and can track their own learning progress. Lecturers gain insights into the knowledge and into potential misunderstandings of their students. An evaluation of Termina and the collected data along a university course exhibits Termina's usefulness for both students and lecturers.
The main contributions of this thesis are (1) a literature review over collective intelligence, crowdsourcing, and related fields, (2) a model of a generic market for gathering data for empirical research efficiently, (3) two applications based on this model and results of an evaluation of the data gathered with them, (4) the game-like e-learning tool Termina together with insights from its evaluation, and (5) a generic software architecture for all aforementioned applications.Crowdsourcing bezeichnet die Auslagerung von Arbeit an eine Gruppe von Menschen zur Lösung eines Problems. Heutzutage wird Crowdsourcing für viele Zwecke verwendet, zum Beispiel tragen Leute ihr Wissen zu Wikipedia bei, Wissenschaftler sagen Krankheiten anhand von Twitter-Daten vorher oder Spieler lösen Proteinfaltungsprobleme in Spielen. Es gibt dennoch Gebiete, für die der Einsatz von Crowdsourcing noch nicht gründlich untersucht wurde. Diese Arbeit untersucht Crowdsourcing für zwei solche Gebiete: für empirische Forschung in auf den Menschen bezogenen Wissenschaften mit Fokus auf linguistischer Feldforschung sowie für E-Learning. Auf den Menschen bezogene Wissenschaften wie Linguistik, Soziologie oder Kunstgeschichte beruhen auf empirischer Forschung. In traditioneller linguistischer Feldforschung zum Beispiel stellen Wissenschaftler Fragen und füllen Fragebögen aus. Solche Methoden sind zeitaufwändig, teuer und nicht unbefangen. Diese Arbeit schlägt vor, Crowdsourcing-Techniken anzuwenden, um diese Nachteile zu überwinden und um empirische Forschung effizienter zu gestalten. Dazu wird das Konzept eines generischen Marktes namens Agora für den Handel mit symbolischen Gütern und für die Spekulation über deren Charakteristika eingeführt. Agora ist ein generisches "Betriebssystem" für Social Media Anwendungen. Außerdem wurde die Internet-basierte Crowdsourcing-Plattform metropolitalia eingerichtet, um zwei dieser Social Media Anwendungen, die auf Agora basieren, bereitzustellen: Mercato Linguistico und Poker Parole. Diese Anwendungen wurden als Teil dieser Arbeit entwickelt, um komplementäre Daten und Metadaten über italienische Sprachvarietäten zu sammeln. Mercato Linguistico regt Spieler dazu an, ihr eigenes Wissen und ihre Überzeugungen auszudrücken. Poker Parole regt Spieler dazu an, Vermutungen über die Beiträge anderer Spieler anzustellen. Damit werden die mit Mercato Linguistico gesammelten primären Metadaten mit reflexiven sekundären Metadaten aus Poker Parole, die für Studien über die Wahrnehmung von Sprachen notwendig sind, bereichert. Eine Auswertung der auf metropolitalia gesammelten Daten zeigt die Zweckmäßigkeit des marktbasierten Ansatzes von Agora und unterstreicht dessen Stärken. E-Learning befasst sich mit der Verwendung von digitalen Technologien für das Lernen, heutzutage vor allem über das Internet. Diese Arbeit untersucht, wie E-Learning-Anwendungen Studenten bei assoziationsbasiertem Lernen und Dozenten bei der Lehre unterstützen können. Dafür wird eine Spiel-ähnliche Anwendung namens Termina in dieser Arbeit eingeführt. Mit den über Termina gesammelten Daten werden Association-Maps konstruiert. Eine Association-Map ist eine vereinfachte Variante einer Concept-Map, in der Begriffe als Rechtecke und Beziehungen zwischen Begriffen als Verbindungslinien dargestellt werden. Sie stellen eine abstrakte Zusammenfassung eines Themas dar. Studenten profitieren von der Verfügbarkeit der Association-Maps, lernen von anderen Studenten und können ihren eigenen Lernprozess verfolgen. Dozenten bekommen Einblicke in den Wissensstand und in eventuelle Missverständnisse ihrer Studenten. Eine Evaluation von Termina und der damit gesammelten Daten während eines Universitätskurses bestätigt, dass Termina sowohl für Studenten als auch für Dozenten hilfreich ist. Die Kernbeiträge dieser Arbeit sind (1) eine Literaturrecherche über kollektive Intelligenz, Crowdsourcing und verwandte Gebiete, (2) ein Modell eines generischen Marktes zur effizienten Sammlung von Daten für empirische Forschung, (3) zwei auf diesem Modell basierende Anwendungen und Ergebnisse deren Evaluation, (4) die Spiel-ähnliche E-Learning-Anwendung Termina zusammen mit Einblicken aus dessen Evaluation und (5) eine generische Softwarearchitektur für alle vorgenannten Anwendungen.
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Botha, Jan Abraham. "Probabilistic modelling of morphologically rich languages." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:8df7324f-d3b8-47a1-8b0b-3a6feb5f45c7.
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This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often rely on the simplistic assumption that words are opaque symbols. This assumption does not fit morphologically complex language well, where words can have rich internal structure and sub-word elements are shared across distinct word forms. Our approach is to encode basic notions of morphology into the assumptions of three different types of language models, with the intention that leveraging shared sub-word structure can improve model performance and help overcome data sparsity that arises from morphological processes. In the context of n-gram language modelling, we formulate a new Bayesian model that relies on the decomposition of compound words to attain better smoothing, and we develop a new distributed language model that learns vector representations of morphemes and leverages them to link together morphologically related words. In both cases, we show that accounting for word sub-structure improves the models' intrinsic performance and provides benefits when applied to other tasks, including machine translation. We then shift the focus beyond the modelling of word sequences and consider models that automatically learn what the sub-word elements of a given language are, given an unannotated list of words. We formulate a novel model that can learn discontiguous morphemes in addition to the more conventional contiguous morphemes that most previous models are limited to. This approach is demonstrated on Semitic languages, and we find that modelling discontiguous sub-word structures leads to improvements in the task of segmenting words into their contiguous morphemes.
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Rodriguez, Paul Fabian. "Mathematical foundations of simple recurrent networks /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9935464.
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Jewett, Bethany. "Investigation of optimal dosing strategies for Ertapenem for varying BMI using mathematical modeling." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/honors/500.
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Previous research suggests that the efficacy of Ertapenem, a carbapenem antibiotic administered intravenously, is related to a patient’s body mass index. Using an existing physiologically based pharmacokinetic (PBPK) model for Ertapenem, we constructed a least squares inverse problem to determine an optimal dose for males with varying body weights and heights. The criteria for an optimal dose was based upon pharmacokinetic and pharmacodynamic (PK/PD) parameters calculated for a male with a body height of 175 cm and a weight of 72 kg. We also adjusted dosing intervals to ensure that effective concentration of drug between doses was the same for all males regardless of BMI.
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Farsani, Danyal. "Making multi-modal mathematical meaning in multilingual classrooms." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5752/.
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This thesis investigates communication (verbal and nonverbal) in a bilingual (Farsi-English) complementary school mathematics’ classroom. The study examines gestures were used as a resource for teaching mathematics in a bilingual setting, enabling intercolutors to construct meaning and mediate understanding. That is, the ways in which language and gesture can be seen as resources in supporting and conveying mathematical ideas is described. I investigated a number of verbal and nonverbal resources and show how these are culturally and socially shaped. I also explored how modes of communication are employed in creating mathematical meaning in a bilingual classroom context. A multimodality framework was adopted to analyse data which included audio and video recordings, observations and interviews with teachers and pupils. I found that gestures were employed to convey aspects of the mathematical register and how these were used to amplify what interlocutors were expressing verbally. Furthermore, I identified that different languages activated a different conceptual understanding of the same mathematical concept which was reflected through the students’ and teachers’ gestures.
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Lopez, Jaramillo Maria Gabriela. "Mathematical literacy: A case study of pre-service teachers." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/dissertations/1798.
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This study addresses the question of whether or not pre-service teachers are ready and prepared to use and teach the highly-specialized language of each discipline. The disciplinary languages present teaching and learning challenges due to their lack of parallels in the daily language (Shanahan & Shanahan, 2008). Additionally, the languages of the disciplines are rarely taught and are commonly acquired through an isolated representation of words without a situated meaning within the theory (Gee, 2002). The knowledge of the particular ways of reading, writing, listening to, and talking in the content areas provides opportunities for students’ apprenticeship within the disciplines required for success in higher education contexts (Dobbs, Ippolito, and Charner, 2017). Moreover, this study addresses the question of how future teachers develop disciplinary knowledge and skills. The purpose of this case study was to investigate how mathematical literacy is shaped and defined by the experiences, language, and disciplinary practices of pre-service teachers and experts in mathematics. This overall aim was unfolded by three guiding research questions: 1) What do the Experiences of Pre-Service Teachers and Experts in Mathematics Reveal about their Understanding of Mathematical Literacy? 2) RQ 2. How do pre-service teachers and experts in mathematics use language when solving mathematical problems? and 3) What literacy practices do pre-service teachers and experts in mathematics utilize when presented with modules that require mathematics problem-solving? To structure the elements of analysis for the participants’ responses, I adopted the theoretical support from the emerging disciplinary literacy framework, the novice-expert paradigm, and the tenets of M. K. Halliday’s functional linguistic theory (i.e., Systemic Functional Linguistics; [SFL]). Four faculty in the Department of Mathematics and four pre-service teachers in the Department of Curriculum and Instruction at a large Midwest university agreed to participate in this case study. For the data collection, I asked the participants to participate in two sessions. In the first sessions, the participants responded to a semi-structured interview. Afterward, in a second session, the participants solved modules of mathematical problems following three protocols: a think-aloud, a silent-solving, and an oral-explanatory. The results of the participants’ responses to the semi-structured interview and the three protocols indicated that their experiences as learners and teachers of mathematics are tied to their definitions of literacy and disciplinary literacy. The SFL analysis showed that for the experts of mathematics, mathematical problem-solving is a more abstract and cognitive practice. The pre-service teachers’ registers indicated that mathematical problem-solving is experienced as more concrete and real practice. The unique literacy practices that these participants displayed showed the strong connection between language, literacy, and mathematical thought.The implications of this study are discussed in terms of the importance of language and disciplinary literacy in preparation for future teachers as they progress in their course of study within their teaching education programs.
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Shah, Vijay Pravin. "A wavelet-based approach to primitive feature extraction, region-based segmentation, and identification for image information mining." Diss., Mississippi State : Mississippi State University, 2007. http://library.msstate.edu/etd/show.asp?etd=etd-07062007-134150.
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Amaro-Jimenez, Carla. "Latino Children’s English as a Second Language and Subject-Matter Appropriation through Technology-Mediated Activities: A Cultural Historical Activity Theory Perspective." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1211938498.
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