Data were examined in this study from student records in a large North Texas urban school district who were taught with two different mathematics curricula to determine whether or not they had different effects on student achievement. One of the mathematics curricula, Everyday Mathematics, was developed upon national mathematic standards, written by the National Council of Teachers of Mathematics. The other mathematics curriculum was district-approved, using a textbook from a large publisher, with a more traditional approach. The students selected for the experimental group came from six schools that had implemented the Everyday Mathematics curriculum for the 1998-99 school year. An experimental group was formed from these students. Twelve schools with similar socioeconomic ratios, ethnic makeup and 1998 Iowa Test of Basic Skills mathematic score profiles were selected. A control group was formed from this population of students that was similar to the experimental group with the exception of having been taught using the district-approved mathematics curriculum. These two groups were very similar in socioeconomic, ethnic, gender, and grade level makeup. Most importantly, the experimental group and control group were almost identical (there was no statistically significant difference) in their 1998 Iowa Test of Basic Skills mathematics scores, a gauge used to demonstrate that prior mathematics ability was equal going into the 1998-99 school year. In the statistical analysis, almost all comparisons showed that the experimental group taught with the Everyday Mathematics curriculum had higher scores on the 1999 Texas Assessment of Academic Skills mathematics test. When compared to children with similar mathematics ability at the beginning of the 1998-99 school year, the students in this study who were taught using Everyday Mathematics showed greater achievement gains than students in classes that used the district-approved curriculum.

M.Ed. / It has become quite clear in recent times that media is expected to play an active role in improving the learning - teaching process in school. When the media is intergrated into a school lesson, the expectation is created that it would bring about a renewal and improvement in the teaching - learning process. A geometrical problem can be solved in a logical manner, helping to expand and enrich the pupils point of reference in Geometry. In the learning process the teacher, pupil and learning content are inextricably linked. It is in this process where media can, playing a very important role, act as intermediate link between the elementary and the fundamental. Furthermore, the media can be used to solve various geometrical theorems and problems making it accessible, visual and concrete. This would greatly benefit the Standard eight pupil. There are specific problems which arise in Geometry. These problems relate to certain skills, for example, discovery method, observation, direct experience and verification. It is in this regard that the teacher needs to be very selective in the choice of media, so that it encourages the mastering of the content. Media promotes learning by involving both hemispheres of the brain. By virtue of the subject, visual presentation in Geometry makes learning easier. It is in this regard that models are the most suitable medium due to the characteristics they posses. A number of guidelines for planning a Geometry lesson for Standard eight are suggested in this study. Recommendations are made regarding the content of a lesson, the production of suitable models to provide for the needs of teachers and pupils as well as the active involvement of pupils in the production of models for Geometry. The empirical reseach has shown that models can serve as a medium to unlock the learning content of Geometry to the pupil. This can be done by concretising and presenting Geometry on a level which enables the pupil to experience it's simplicity with optimal learning. The important role of models in the daily life of every person makes further reseach into the nature of symbol systems and how they influence learning essential, so that every pupil may fully benefit from the potential of models.

M.A. (Psychology) / Please refer to full text to view abstract

Orientador: Marcus Vinicius Maltempi / Banca: Jonei Cerqueira Barbosa / Banca: Maurício Rosa / Banca: Marcelo de Carvalho Borba / Banca: Maria Aparecida Viggianni Bicudo / Resumo: Este trabalho investiga a Modelagem Matemática com o mundo cibernético, aqui entendido como qualquer ambiente produzido com as Tecnologias Digitais. Para tanto, percorre-se um caminho que procura sustentação teórica tanto em aspectos discutidos no âmbito da Modelagem Matemática, quanto em campos que não necessariamente dizem respeito a essa região de inquérito. Como desdobramento desse caminho, tem-se a construção de uma visão teórica de Modelagem Matemática que, além de potencialmente sustentar o mundo cibernético como dimensão de abrangência, permite compreender as ações dos sujeitos quando estão construindo modelos que se atualizam nesse espaço específico. O estudo, desenvolvido sob uma perspectiva qualitativa, é resultado não somente do entrelaçamento teórico, como também dos dados produzidos no decorrer da pesquisa, os quais provieram da construção de jogos eletrônicos feitos por oito estudantes do curso de graduação em Licenciatura Matemática. O principal software utilizado nas construções dos jogos eletrônicos foi o Scratch, que é uma linguagem de programação desenvolvida pelo Massachusetts Institute of Technology. A presente pesquisa, além de permitir uma atualização da visão teórica construída, apresenta a Modelagem Matemática como fluida, isto é, que se mostra em constante movimento e que perpassa: (i) o objetivo pedagógico, que na particularidade da tese focou as ações de aprendizagem abarcadas pelas ideias construcionistas; (ii) a linguagem específica utilizada, a qual possibilitou a construção de modelos que trazem em sua estrutura aspectos matemáticos e aspectos estéticos e interativos possibilitados pelas tecnologias, constituindo o que foi denotado modelo matemático/tecnológico; (iii) o modo como o problema é determinado pelos participantes, o qual norteou o encaminhamento... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This study investigates Mathematical Modeling with the cyber world, herein understood as any environment produced based on Digital Technologies. In this sense, the research line followed aimed at a theoretical framework both in the aspects addressed in the scope of Mathematical Modeling and in fields not necessarily covered by this area of investigation. As this line unfolded, a theoretical view of Mathematical Modeling is constructed that, apart from being able to potentially sustain the cyber world as a dimension, it allows understanding the actions of subjects when they are building models that update within this specific space. This study, carried out from a qualitative perspective, is the result not only of the theoretical intertwining, but also the data collected throughout the research, obtaining during the development of electronic games by eight students of the Bachelor of Mathematical Education course. The main software used was Scratch, a programming language developed by the Massachusetts Institute of Technology. This study, apart from allowing updating the theoretical view constructed, presents a fluid Mathematical Modeling, that is, one that is constantly moving and that includes (i) the pedagogical objective, which in the scope of the thesis focused on learning actions embraced by constructionist ideas; (ii) the specific language used, which afforded the construction of models that carry mathematical and esthetical and interactive aspects these technologies enable, constituting what was called mathematical/technological model; (iii) the mode the problem is determined by participants, which has directed the conduction and search for solutions, and (iv) the specific aspects of reality of the cyber world, which allow the construction of... (Complete abstract click electronic access below) / Doutor

M.Sc., Faculty of Science, University of the Witwatersrand, 2011 / This study serves to explore the notion of context familiarity and how it affects the way learners perform in closed and open-ended problems in Mathematical Literacy (ML). The learners’ performances in this study are based on how well they were able to do the following: select the relevant data from the given tables; select the appropriate mathematics and execute them with precision; relate the mathematical solution back to the context in order to understand the problem better. The key findings indicate that more familiar contexts provide better opportunities for learners to: select the relevant data from given tables; select and execute the relevant mathematical tools; and relate the mathematical solution back to the context.

A thesis submitted to the Wits school of Education, Faculty of Humanities, University of the Witwatersrand in fulfillment of the requirements for the degree of Doctor of Philosophy Johannesburg 2017 / MT2017

This study explores the nature of pre-service Mathematical Literacy teachers' problem solving with a focus on intra-mathematics and extra-mathematics connections, across two years (2011-2012). The pre-service teachers were enrolled into a new three-year Bachelor of Education course, Concepts and literacy in mathematics (CLM), at a large urban University in South Africa. The CLM course aimed specifically at developing the teachers' fundamental mathematical knowledge as well as contextual knowledge, which were believed to be key components in ML teaching. The fact that the course offered a new approach to professional teacher development in ML (pre-service), contrasting the old model (in-service) reported in ML-related literature in South Africa, where qualified teachers from other subjects were reskilled, coupled with the need to grow the pool of qualified ML teachers, provided a rationale for conducting this study. Data relating to the pre-service teachers' responses to assessment tasks within the course, and their school practicum periods focusing on classroom mathematical working, combined with pedagogical orientations, was collected. PISA's (OECD, 2010, 2013) dimensions of the mathematisation process provided the theoretical framework while Graven and Venkat's (2007a) pedagogic agendas were used to make sense of the pedagogic orientations in practice. The results relating to both learning and practice suggest that the teachers' knowledge relating to model formulation, an aspect of extramathematics connections, was weak across the two years. Nevertheless, improvements in ways in which the dimensions ofthe mathematisation process occurred were noted across the two years, with localised errors. In terms of pedagogic agendas foregrounded by the teachers in ML classrooms, results indicate that agenda 2 (content and context driven) and agenda 3 (mainly content driven) featured more than agenda 1 (context driven) which supports the rhetoric in the ML curriculum. Two implications to teacher training have been noted; first the need for a focus on correctly translating quantities from problem situations into mathematical models, and secondly, the need for promotion of provision of solution procedures with pedagogic links. This study offers two key contributions namely; extending knowledge relating to pre-service ML teacher training, and extending theory for understanding steps in problem solving to incorporate aspects of pedagogy.

The National Curriculum statement, or NCS for short, proposes significant shifts in the way that teachers carry out their work. Strategies, such as investigation and collaborative work were promoted as a reform model for effective teaching and learning. Thus, the intention of this research project is to determine how mathematics teachers are implementing the new reform in South Africa. Based on Sfard’s theory of commognitive development, a theoretical framework has been established and the focus specified in the following research questions: 1. How does a teacher mediate instruction during object-level & meta-level learning? 2. What enables and constrains her/his facilitative mediation in the case of Congruency in Grade 9? 3. What can we learn about the practical efficacy of Sfard’s discourse theory? In order to explore the actual teaching process the research project presents a case study constituted from two teaching practices on one topic, Congruency, at a College in Johannesburg. The purpose of observing and interviewing two teachers on the same lessons is to get a greater variety of conversation on object-level and meta-level learning. At the same time analysing their teaching process in-depth creates an opportunity to have different possibilities of mediating collaborative learning. The study addresses the three research questions through two related activities – non-participant observation and semi-structural interviews with teachers (in order to provide an opportunity for teachers to express their opinion). Two main findings can be summarized: Firstly, the way the teacher manages instruction originates from her/his teaching style. The data analysis clearly confirms that mediation of the two teachers on the topic Congruency does not differ according object-level and meta-level learning, but according to the teachers. The second finding is related with Sfard’s theoretical perspective: on the one hand the Department recommends investigative activities, whilst, on the other hand, Sfards’ theory states that reinvention by the learner is highly unlikely. Therefore the practical efficacy of Sfard’s theory is that in meta-level learning investigative activities are not appropriate and the role of the teacher should be dominant, not necessarily as facilitator. This research study is an empirical proof of the validity of Sfard’s theory and unspecified requirements of the Department of Education. KEYWORDS: object-level learning, meta-level learning, Congruency, Commognitive theory.

Orientador: Romulo Campos Lins / Orientador: Heloisa da Silva / Banca: João Ricardo Viola dos Santos / Banca: Jorge Tarcísio da Rocha Falcão / Banca: Marcus Vinicius Maltempi / Banca: Regina Luzia Corio de Buriasco / Resumo: Este estudo encontra sua justificação no cenário mais amplo de uma pesquisa bibliográfica sobre teorias de educação matemática como as postuladas em Lins, Freudenthal, Davidov, Brosseau, etc., no qual procuramos por desenvolvimento teórico na perspectiva do Modelo dos Campos Semânticos (LINS, 1999, 2004, 2008, 2012), a propósito de gerar meios a caracterizar "ação didática" quando fundamentada em diferentes teorias de educação matemática. A intenção é alcançar dizer de modelo didático a partir do ponto de vista teórico de diferentes constructos de educação matemática. Neste largo cenário, a ideia de caracterizar "ação didática" em diferentes teorias para então oferecer delas uma leitura em paralelo, nos trouxe diante de uma questão central que a precede: a de buscar uma forma de abordar diferença para tecer um contexto em que "ação didática" no escopo de uma teoria não fosse lida por falta no escopo de outra, nem em discursos sobre "melhoria" do ensino de matemática. Este foi o objetivo central desta tese que se caracteriza, então, na produção de um conjunto de ensaios em cuja forma buscamos abordar diferença como experiência necessária e anterior para um modo de ler modelos didático-teóricos e dizer de "ação didática" em educação matemática. Neste intento, a teoria epistemológica do conhecimento elaborada por Romulo Campos Lins, o Modelo dos Campos Semânticos (MCS), comparece tanto como metodologia de pesquisa à produção da forma dos ensaios, quanto como uma das teorias de e... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This study finds its justification in the broader scenario of one bibliographical research on mathematical education theories such as those postulated by Lins, Freudenthal, Davidov, Brosseau, etc. In it, we seek theoretical development from the perspective of the Model of Semantic Fields (LINS, 1999, 2004, 2008, 2012) in order to generate means to characterize "didactical action" when based on different theories of mathematical education. The intention is to talk about a didactical model from theoretical points of view of mathematical education constructs. In this scenario, the idea of characterizing "didactical action" in different theories, to offer from them a parallel reading, brought us to a central question that precedes it. The question is to seek a way of approaching difference to produce a context in which "didactical action", in the scope of one theory, would not be read in the scope of another one through a deficit reading and nor in discourses on "improvement" of mathematics teaching. This was the central aim of this dissertation. It is characterized as a cluster essays production, in which form we search a way of approaching difference as a necessary and previous experience to a mean of reading "didactical action" and saying of didactical models in mathematical education. In this attempt, the epistemological theory of knowledge elaborated by Romulo Campos Lins, the Model of Semantic Fields, appears on one side, as a research methodology to the production of the e... (Complete abstract click electronic access below) / Resumen: Este estudio encuentra su justificación en el escenario más amplio de una investigación bibliográfica sobre teorías de educación matemática como las postuladas en Lins, Freudenthal, Davidov, Brosseau, etc., en el cual buscamos por desarrollo teórico en la perspectiva del Modelo de los Campos Semánticos (LINS, 1999, 2004, 2008, 2012), a propósito de generar medios para caracterizar "acción didáctica" cuando está fundamentada en diferentes teorías de educación matemática. La intención es llegar a decir de modelo didáctico desde el punto de vista teórico de diferentes constructos de educación matemática. En este escenario, la idea de caracterizar "acción didáctica" en diferentes teorías para entonces ofrecer de ellas una lectura en paralelo, nos trajo ante una cuestión central que la precede: la de buscar una forma de abordar diferencia para tejer un contexto en que "acción "didáctica" en el alcance de una teoría no fuera leída por falta en el ámbito de otra, ni en discursos sobre "mejora" de la enseñanza de matemáticas. Este fue el objetivo central de esta tesis que se caracteriza entonces, en la producción de un conjunto de ensayos en cuya forma busco abordar diferencia como experiencia necesaria y anterior para un modo de leer "acción didáctica" y decir de modelos didácticos en educación matemática. En este intento, la teoría epistemológica del conocimiento elaborada por Romulo Campos Lins, el Modelo de los Campos Semánticos (MCS), aparece tanto como metodología de investigac... (Resumen completo clicar acceso eletrônico abajo) / Doutor

Orientador: Maria Aparecida Viggiani Bicudo / Coorientador: Adlai Ralph Detoni / Banca: Rúbia Barcelos Amaral Schio / Banca: Verilda Speridião Kluth / Banca: Marli Regina dos Santos / Banca: Mauricio Rosa / Resumo: Esta pesquisa interroga como se dá o movimento e a percepção do movimento quando se está com o computador e alunos realizando atividades em um ambiente de Geometria Dinâmica. Tem-se por objetivo compreender o fenômeno movimento-percepção-conhecimento no processo de constituir sentidos e significados geométricos, indo aos sujeitos que vivenciam modos de estar com o computador, trabalhando com Geometria Dinâmica. Para tanto, um grupo de graduandos em Licenciatura em Matemática foi convidado a desenvolver atividades junto aos demais cossujeitos de aprendizagem, aos recursos didáticos e ao ambiente de Geometria Dinâmica. As experiências assim vivenciadas são dadas ao conhecimento mediante descrições realizadas por nossos sujeitos de pesquisa. Essas descrições foram analisadas mediante o movimento de voltar-se à interrogação da pesquisa aqui apresentada e de constituir sentidos do que o dito pelo sujeito faz para o pesquisador. Nesse movimento, foram destacadas nas descrições Unidades de Sentido, com as quais tecemos as Unidades Significativas, compreendidas como o dito nas Unidades de Sentido. Atentos às individualidades de cada Unidade Significativa, mas pensando-as com cada uma das outras, vimos possibilidades de convergências, que ao serem atualizadas evidenciaram grupos que explicitaram ideias abrangentes. Mediante três movimentos de convergência, nos quais foi se ampliando cada vez mais um pensar articulador sobre o fenômeno interrogado, foram constituídos quatro núcleos est... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research inquires how the movement and the perception of the movement take place when one is with the computer, and students performing activities in a Dynamic Geometry environment. It aims to understand the movement - perception - knowledge phenomenon in the process of to constitute geometric senses and meanings up, going to the subjects who experience ways of being with the computer, working with Dynamic Geometry. In order to do so, a group of undergraduate students in teacher training in mathematics wer e invited to develop activities enjoyed with other learning co - subjects, with teaching resources, and with the dynamic geometry environment. The experiences thus experienced are given to knowledge through descriptions made by our research subjects up. Thes e descriptions were analyzed by means of the movement to return to the interrogation of the research presented here and to constitute sense of what the said by the subject brings to the researcher. In this movement, they were highlighted out in the descrip tions Units of Sense, with which we weave the Significant Units, understood as the said in Units of Sense. Attentive to the individualities of each Significant Units, but considering them with each other, we saw possibilities of convergence, which when upd ated revealed groups that made explicit ideas. By means of three convergence movements, in which an articulating thinking about the inquired phenomenon was increasingly extended, four structuring nuclei of the ... (Complete abstract click electronic access below) / Doutor