"Exhibits" ([19] leaves) in pocket. Bibliography: leaves 430-440.

Thesis (Ph. D.)--University of Adelaide, 1989. / "Exhibits" ([19] leaves) in pocket. Includes bibliographical references (leaves 430-440).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 178-182).

"Exhibits" ([19] leaves) in pocket / Bibliography: leaves 430-440 / 449 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Philosophy, 1989

Thesis (Ph. D.)--Open University. BLDSC no. DXN024722.

Thesis (Ph. D.)--State University of New York at Binghamton, Mathematical Sciences Department, 2007. / Includes bibliographical references.

Thesis (Ph. D.)--University of Michigan, 1935. / Bibliography: p. 79-99.

Introdução: Os Logaritmos, objeto matemático desenvolvido há quatro séculos como uma ferramenta facilitadora de cálculos hoje gozam de uma miríade de outros significados, mas manteve seu signo, sua maneira de representação, estagnado no tempo. A Língua Materna e a Matemática estão entrelaçadas e impregnam uma à outra. Como a Língua Materna é a principal influência na formação do raciocínio, esta enraíza-se e permeia as aulas e o ensino de todas as disciplinas, incluindo as de Matemática. Objetivo: Este trabalho visa propor uma modernização para a notação matemática e modo de se interpretar os logaritmos para uma forma mais concordante com a organização de pensamento dos falantes de Língua Portuguesa do Brasil, haja visto que a leitura e maneira de representar um objeto matemático estão diretamente ligadas com o processo de aprendizagem de um indivíduo. Método: Delineada como pesquisa explicativa de abordagem qualitativa, o estudo utilizou de textos e ideias da Linguística, Educação e Matemática para explicitar os efeitos da notação de representação de um objeto matemático no ensino e aprendizagem, e propor maneiras de como utilizar estes efeitos de maneira positiva para a transposição didática do conhecimento. Conclusões: A maneira como a Língua Materna embasa o raciocínio de seus falantes é um fator importante a se considerar na elaboração de uma notação de representação em Matemática. Como as diferentes representações de um objeto estão diretamente ligadas com a aprendizagem, torna-se essencial buscar uma maior concordância entre a representação, impregnada tanto de Matemática quanto de Língua Materna, e o representado, o conhecimento matemático em questão. / Introduction: The Logarithms, the mathmatical object developed four centuries ago as a tool to facilitate calculations today possesses a myriad of other meanings, but kept its sign, its representation, stagnant in time. The Mother Language and the Mathmatics are entangled and impregnate one another. Since the Mother Language is the main influence in the development of the reasoning, it permeates classes and teaching of all subjects, including the Mathmatical ones. Goal: This paper aims to propose an update to the mathmatical notation and way of rendering the logarithms to a more concordant form with the though organization of the Portuguese speakers of Brazil, since the signs and representation of a mathmatical object are directly connected with the learning process of an individual. Method: Outlined as an qualitative approach and explanatory research, the paper used texts and ideas from Linguistics, Education and Mathmatics to explicit the effects of notation and the representations of a mathmatical object in the learning process while also proposing ways to use this effects in a positive manner to the didactic transposition of the knowledge. Conclusions: The way the Mother Language bases the thought organization is an important factor to consider in the elaboration of a mathmatical notation and representation in Mathmatics. Since a multitude of representations are directly connected with the learning process, its essential to search for a concordance between the representation, impregnated both with Mother Language and Mathmatics, and the represented, the mathmatical object.

Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016. / Numerical and algebraic equations require understanding of the equal sign as an equivalence relation. Teachers and learners, however, often have an operational, rather than a relational, understanding of the equal sign. This conception is viewed as a misconception. This study investigates the extent to which Grade 6 learners at a particular school have this and other misconceptions regarding equality, with the equal sign as focus. It also investigates this school’s Grade 1 to 6 teachers’ specialised content knowledge (SCK) regarding equality, again focusing on the equal sign. Ultimately the study wishes to establish whether there might be a possible relationship between the level of these teachers’ SCK of the equal sign and learners’ misconceptions of the equal sign. In particular, it tries to answer the question whether teachers’ SCK of the equal sign could possibly promote or prevent the forming of such misconceptions in learners, as well as whether teachers’ SCK of the equal sign could possibly help them identify learners’ misconceptions and help learners form the correct conceptions. This research project is framed within an interpretive paradigm. It focuses on one school taking the form of a theory-led case study in which a mixed method approach is used. Data collection methods include teacher questionnaires followed by two focus group interviews with teachers, based on data collected from questionnaires. In addition, data is collected through a series of lesson observations on number concepts and assessment. Grade 6 learners answered a set of questions structured in the form of a test to investigate their understanding of equality and the equal sign. Six learners were purposefully selected, based on their answers to the questions, and interviewed. Although this school is a high-performing academic school, results indicate that few learners have a flexible operational or basic relational view of the equal sign. The same group of learners that struggle with closure seems to struggle with the misconception of using all the numbers in an equation to solve a particular equation. The majority of Grade 6 learners cannot define the equal sign correctly. According to results, the nature of Grade 1- 6 teachers’ SCK of the equal sign shows that teachers lack skills to prevent, reduce or correct misconceptions about the equal sign.

Abstract not available