Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels (d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language. / Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.

Thesis (M. Ed.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 65-74).

Thesis (M. Ed.)--University of Hong Kong, 1984. / Includes bibliographical references.

Thesis (M.Ed.)--University of Hong Kong, 1984. / Includes bibliographical references. Also available in print.

Thesis (M.Ed.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 65-74). Also available in print.

Thesis (Ph.D.)--Mississippi State University. Department of Leadership and Foundations. / Title from title screen. Includes bibliographical references.

Orientador: Angela B. Kleiman / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Estudos da Linguagem / Made available in DSpace on 2018-08-06T06:00:28Z (GMT). No. of bitstreams: 1 Valverde_ReginaMariaSecodeMiranda_M.pdf: 826979 bytes, checksum: 4b355cd2cc72ded8306f3b6007efa89a (MD5) Previous issue date: 2006 / Resumo: Este trabalho descreve a interação professor-aluno na aula de matemática para a educação de jovens e adultos. Com o intuito de compreender o contexto do ensino de matemática, partimos de uma perspectiva interdisciplinar, para investigar as relações entre a linguagem matemática e a linguagem natural e a importância da análise da interação para o ensino. Com base nas contribuições da sociolingüística interacional para os estudos da interação Gumperz (1972 & 1982), Goffman (1998) e Brown e Levinson (1995), analisamos pistas contextualizadoras diversas e suas funções na promoção de situações de aprendizagem. Verificamos a utilização de mecanismos verbais para a construção de conceitos matemáticos e apresentamos as relações entre o objetivo da aula e o tipo de interação estabelecida. A análise das situações observadas, em 2000, permitiu que se refletisse sobre o papel do professor na escolha de atividades significativas no processo de ensino e aprendizagem e a necessidade do estudo da interação em sala de aula na formação de professores de matemática / Abstract: This study describes teacher-student interaction in mathematics classes for young and adult education. In order to understand the teaching of mathematics, we investigate the relationship between mathematics language and natural language and show the importance of the analysis of interaction for teaching Mathematics. Based on the contribution of interactional sociolinguistics (GUMPERZ, 1972 & 1982; GOFFMAN,1998 e BROWN e LEVINSON,1995), we observe the verbal mechanisms utilized for the introduction of mathematical concepts and establish types of interaction observed. The analysis permits us to reflect on the role of the teacher in choosing significant activities to facilitate the learning processes / Mestrado / Lingua Materna / Mestre em Linguística Aplicada

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.

Learners in South Africa underachieve in Mathematics. Amidst many other factors that influence the Mathematics scenario in South African schools, one major aspect of the Mathematics classroom culture is the Language of Learning and Teaching (LoLT). For many learners the LoLT, namely English, is not their main language. The question arises of whether Setswana learners with Limited English Proficiency (LEP) are disadvantaged because the LoLT is English and if so, what could be done about it. The interaction between language and thought is discussed against the background of the learning theories of Piaget, Vygotsky and van Hiele, as well as the Network Theory of Learning. From this study the importance of language for conceptualisation becomes clear, especially that of the mother tongue. The circle is then narrowed down to take a look at the vital part that language plays in Mathematics and the problems that exist for the learner when negotiating meaning during the journey between natural language and the mathematical register. Focusing on the situation of the Setswana Mathematics learner with English as LoLT, the views of parents and teachers come under scrutiny as well as government policies regarding the LoLT. The techniques and strategies of teachers in the English Second Language Mathematics classrooms (ESL-classrooms) are investigated. In this regard code-switching is of importance and is discussed extensively. These theoretical investigations led to an empirical study. Firstly, a quantitative study was undertaken by means of a survey to investigate the language situation in schools where Setswana is the main language. Furthermore, the views of those teachers, who teach Setswana learners with English as LoLT, on how English as LoLT influences Setswana Mathematics learners' conceptualisation were investigated. A sample of 218 teachers in the North-West Province of South Africa was used in this survey. A complex language situation crystallises where no one-dimensional answer can be recommended. Code-switching has clearly made large inroads into the Mathematics classroom, but teachers' views on the expediency of using Setswana, especially for formal notes, terminology and tests, vary considerably. Secondly, a qualitative study was undertaken in two schools. The study investigated the possibility that notes in Setswana as well as in English, and the aid of an English/Setswana glossary of Mathematical terminology in daily tasks as well as in tests, would be of value to learners. It was clear from the sample that the new terminology is difficult for the teachers in question because they are used to the English terminology. Some learners also find the Setswana terminology difficult. However, the learners experience the use of the Setswana in the notes positively. It was clear from the interviews with the learners that by far the most of the learners in the sample felt that the Setswana/English notes as well as the glossary helped them to understand better. The learners oscillate between English and Setswana to understand the explanation given or the question asked. Most of the learners are of opinion that tests where questions are asked in both languages contribute to a better comprehension of what is asked. They also experience the glossary of English/Setswana terminology supplied in the test as an important aid. Recommendations comprise that the Setswana Mathematics register should be expanded and final examinations set in both Setswana and English. Furthermore, teachers should be educated to use new terminology effectively as a scaffold to ensure adequate conceptualisation, as well as to manage code-switching in a structured way. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.

Learners in South Africa underachieve in Mathematics. Amidst many other factors that influence the Mathematics scenario in South African schools, one major aspect of the Mathematics classroom culture is the Language of Learning and Teaching (LoLT). For many learners the LoLT, namely English, is not their main language. The question arises of whether Setswana learners with Limited English Proficiency (LEP) are disadvantaged because the LoLT is English and if so, what could be done about it. The interaction between language and thought is discussed against the background of the learning theories of Piaget, Vygotsky and van Hiele, as well as the Network Theory of Learning. From this study the importance of language for conceptualisation becomes clear, especially that of the mother tongue. The circle is then narrowed down to take a look at the vital part that language plays in Mathematics and the problems that exist for the learner when negotiating meaning during the journey between natural language and the mathematical register. Focusing on the situation of the Setswana Mathematics learner with English as LoLT, the views of parents and teachers come under scrutiny as well as government policies regarding the LoLT. The techniques and strategies of teachers in the English Second Language Mathematics classrooms (ESL-classrooms) are investigated. In this regard code-switching is of importance and is discussed extensively. These theoretical investigations led to an empirical study. Firstly, a quantitative study was undertaken by means of a survey to investigate the language situation in schools where Setswana is the main language. Furthermore, the views of those teachers, who teach Setswana learners with English as LoLT, on how English as LoLT influences Setswana Mathematics learners' conceptualisation were investigated. A sample of 218 teachers in the North-West Province of South Africa was used in this survey. A complex language situation crystallises where no one-dimensional answer can be recommended. Code-switching has clearly made large inroads into the Mathematics classroom, but teachers' views on the expediency of using Setswana, especially for formal notes, terminology and tests, vary considerably. Secondly, a qualitative study was undertaken in two schools. The study investigated the possibility that notes in Setswana as well as in English, and the aid of an English/Setswana glossary of Mathematical terminology in daily tasks as well as in tests, would be of value to learners. It was clear from the sample that the new terminology is difficult for the teachers in question because they are used to the English terminology. Some learners also find the Setswana terminology difficult. However, the learners experience the use of the Setswana in the notes positively. It was clear from the interviews with the learners that by far the most of the learners in the sample felt that the Setswana/English notes as well as the glossary helped them to understand better. The learners oscillate between English and Setswana to understand the explanation given or the question asked. Most of the learners are of opinion that tests where questions are asked in both languages contribute to a better comprehension of what is asked. They also experience the glossary of English/Setswana terminology supplied in the test as an important aid. Recommendations comprise that the Setswana Mathematics register should be expanded and final examinations set in both Setswana and English. Furthermore, teachers should be educated to use new terminology effectively as a scaffold to ensure adequate conceptualisation, as well as to manage code-switching in a structured way. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.