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by Lee Fong-lok. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 309-323). / Questionnaires and some appendixes in Chinese. / TABLE OF CONTENTS --- p.ii / TABLES --- p.vii / FIGURES --- p.viii / ACKNOWLEDGMENTS --- p.ix / ABSTRACT --- p.xi / Chapter 1 --- INTRODUCTION --- p.1 / HOW COMPUTERS CAN HELP OUR CHILDREN --- p.2 / How Human Tutors Tutor --- p.7 / "Can Computers "" Think""?" --- p.11 / Intelligent Tutoring Systems --- p.17 / ELECTRONIC HOMEWORK --- p.18 / A Personal Tutor to Students --- p.18 / The Present Study 226}0ؤ An Investigation into Electronic Homework --- p.23 / How to Build up Electronic Homework --- p.25 / Effect of using Electronic Homework --- p.29 / The Future of Electronic Homework --- p.29 / CHAPTER SUMMARY --- p.30 / Chapter 2 --- REPRESENTATION OF KNOWLEDGE --- p.32 / OVERVIEW --- p.32 / HOW KNOWLEDGE IS REPRESENTED --- p.33 / SYMBOLIC EXPRESSIONS OR NEURAL NETWORKS --- p.36 / PROCEDURAL AND DECLARATIVE KNOWLEDGE --- p.37 / On Evidence Supporting the Procedural- Declarative Knowledge Distinction --- p.39 / Distinction of Knowledge --- p.49 / EXPLICIT VERSUS IMPLICIT KNOWLEDGE --- p.52 / DEGREE OF SOPHISTICATION VERSUS PROCEDURALIZATION --- p.53 / NOTATION OF KNOWLEDGE --- p.59 / What Should Be Done But Not What Is Actually Done --- p.62 / CHAPTER SUMMARY --- p.63 / Chapter 3 --- WHAT KNOWLEDGE TO INCORPORATE AND HOW --- p.67 / OVERVIEW --- p.67 / SEPARATE STORAGE FOR DIFFERENT TYPES OF KNOWLEDGE --- p.69 / DIFFERENT TYPES OF KNOWLEDGE --- p.70 / The Expert module --- p.71 / The Student Module --- p.78 / The Tutoring Module --- p.85 / The Communication Module --- p.121 / CHAPTER SUMMARY --- p.124 / Chapter 4 --- PROBLEM COMPLEXITY AND INDIVIDUAL DIFFERENCES --- p.127 / OVERVIEW --- p.127 / COGNITIVE DIFFICULTY OR SIMPLE ITEM DIFFICULTY RATIO --- p.129 / DIFFICULTY LEVEL OBTAINED BEFORE TEST ADMINISTRATION --- p.130 / OTHER MEASURES OF PROBLEM DIFFICULTY --- p.131 / Complexity of Problems --- p.132 / Problem Complexity Level --- p.133 / INDIVIDUAL DIFFERENCES --- p.133 / Chapter 5 --- HOW TO IMPLEMENT AND EVALUATE THE SYSTEM…… --- p.136 / OVERVIEW --- p.136 / KNOWLEDGE ACQUISITION --- p.140 / Expert Module --- p.141 / Student Module --- p.142 / Tutoring Module --- p.149 / Problem Difficulty --- p.155 / IMPLEMENTATION --- p.161 / Implementation of Knowledge into Computer Tutor --- p.161 / EVALUATION --- p.162 / Formative Evaluation --- p.162 / Summative Evaluation --- p.163 / CHAPTER SUMMARY --- p.167 / Chapter 6 --- KNOWLEDGE ACQUIRED --- p.169 / OVERVIEW --- p.169 / EXPERT MODULE --- p.170 / STUDENT MODULE --- p.172 / Mal-rules --- p.172 / Strategies for Handling Mal-rules --- p.176 / Understanding the Errors --- p.177 / Section Summary --- p.209 / TUTORING MODULE --- p.210 / Effects of tutoring --- p.210 / Scores in Posttest and Ceiling Effect --- p.214 / Effects of Practice and Tutoring Methods on Retention test --- p.214 / How Experienced Teachers Perceive --- p.221 / CHAPTER SUMMARY --- p.228 / Chapter 7 --- PROBLEM DIFFICULTY --- p.230 / OVERVIEW --- p.230 / RESULTS OF DIFFERENT MEASURES OF PROBLEM DIFFICULTY --- p.231 / Students' estimation of Item Difficulty --- p.232 / Item Difficulty Ratio --- p.234 / Teachers' Estimation of Problem Difficulty --- p.234 / Predicted Complexity --- p.237 / CORRELATION AMONG THE VARIOUS MEASURES OF PROBLEM DIFFICULTY --- p.243 / How students rate the problems --- p.245 / PREDICTING THE PROBLEM DIFFICULTY MEASURES --- p.246 / About the Three Measures --- p.249 / Practical Considerations --- p.252 / PROBLEM COMPLEXITY --- p.254 / USING PROBLEM COMPLEXITY IN ELECTRONIC HOMEWORK --- p.258 / CHAPTER SUMMARY --- p.258 / Chapter 8 --- SYSTEM EVALUATION --- p.259 / OVERVIEW --- p.259 / THE EVALUATION --- p.260 / Formative Evaluation --- p.260 / Summative Evaluation --- p.270 / DISCUSSION --- p.288 / Who Benefit From Using The System --- p.288 / Hardware Constraints --- p.289 / Human-computer interface --- p.289 / Effect on the use of Electronic Homework --- p.290 / Expert-Novice Differences --- p.292 / CHAPTER SUMMARY --- p.293 / Chapter 9 --- CONCLUSIONS AND DISCUSSION --- p.294 / OVERVIEW --- p.294 / THEORETICAL ASPECTS --- p.295 / Why and how do students make errors? --- p.296 / What makes an expert tutor? --- p.302 / KNOWLEDGE OBTAINED --- p.304 / CAN ELECTRONIC HOMEWORK HELP STUDENTS AND TEACHERS? --- p.305 / Purposes of the Evaluation --- p.305 / Results of The Evaluation --- p.306 / SUGGESTIONS --- p.306 / Machine Learning --- p.307 / Input Systems --- p.307 / Better understanding of Human Problem Solving Process --- p.307 / REFERENCES --- p.309 / Appendix A: Mal-rule Collecting Tests ……… --- p.324 / Appendix B: Test on Solving Algebraic Equations --- p.334 / Appendix C: Tutoring Scripts --- p.336 / Appendix D: Manipulative Rules Used In Solving Algebraic Equations --- p.338 / Appendix E: Remediation Rules Used In Solving Algebraic Equations --- p.339 / Appendix F: List of Mal-rules --- p.341 / Appendix G: Teachers' Estimation of Problem Difficulty --- p.344 / Appendix H: Learning Process Questionnaire --- p.349 / Appendix I: Questionnaire on the Use of Electronic Homework --- p.344 / Appendix J: Teachers' Perception on Electronic Homework --- p.347 / Appendix K: Students' Perception on the Use of Electronic Homework in Formative Evaluation --- p.346 / Appendix L: Results of Students' Perception on Electronic Homework --- p.347 / Appendix M: Students' Scores in Learning Process Questionnaire --- p.349 / Appendix N: Homework 1 --- p.355 / Appendix O: Homework 2 --- p.358 / Appendix P: Students' Retention Test Scores --- p.361 / Appendix Q: Results of Teachers' Perception on Electronic Homework --- p.366 / Appendix R: Transcript of Students' Interview --- p.368 / Appendix S: Installation and Source Code --- p.404

Orientador: Marcus Vinicius Maltempi / Banca: César Sonizeti Pereira Leite / Banca: Marcio Antônio da Silva / Banca: Roger Miarka / Banca: Sônia Maria Clareto / Resumo: A presente pesquisa de doutorado diz respeito ao ensino e a aprendizagem em matemática com vistas nas "experiências" em uma disciplina de introdução ao Cálculo Diferencial e Integral e suas aplicações ofertada aos alunos do curso de Ciências Biológicas da Universidade Estadual Paulista - Campus Rio Claro. Para subsidiar as aulas desta disciplina o pesquisador desenvolveu um site com o conteúdo da ementa e o mesmo foi amplamente utilizado durante as aulas. A pesquisa supostamente nasceu qualitativa, com o foco nas potencialidades das tecnologias digitais na educação escolar. Mas, ao longo de seu desenvolvimento, foi se constituindo a partir de pistas da cartografia e a tecnologia digital foi deixando de ser o foco da pesquisa, dando lugar às problematizações acerca do ensinar e do aprender matemática. Neste trabalho, professores e alunos são compreendidos não como sujeitos ativos e responsáveis pelo processo educativo, mas como sujeitos da experiência. Sujeitos que padecem e expõem os próprios corpos aos encontros. Deste modo, o aprender e o ensinar que se refere aqui estão mais próximos do exercício de potencializar a capacidade de afetar e ser afetado a cada encontro. Trata-se, portanto, de um aprender que nada tem a ver com desenvolver competências ou adquirir conhecimento. De modo similar, um ensinar que nada tem a ver com transmitir, mediar, facilitar ou compartilhar conhecimentos. Trata-se de um ensinar e um aprender que não são propriedades de ninguém e só têm sentido na atualidade dos acontecimentos / Abstract: This PhD research is related to teaching and learning mathematics with a view in "experiences" in an introduction to Differential and Integral Calculus and its applications course offered to the Biological Sciences undergraduate course of Universidade Estadual Paulista - Rio Claro Campus. As a support to the classes, the researcher developed a website with the content of the syllabus which was widely used during the classes. The research started qualitative, focusing on the potential of digital technologies in school education. But in the progress of its development, it was building up from the clues of cartography, and therefore digital technology was no longer the focus of research, giving rise to questioning teaching and learning mathematics. In this work, teachers and students are understood not as active subjects and responsible for the educational process, but as subjects of experience. Subjects who suffer and expose their bodies to meetings. In this way, the learning and teaching referred here are closer to the exercise of potentiate the ability to affect and be affected by each encounter. It is, therefore, a learning that has nothing to do with developing skills or acquiring knowledge. Similarly, a teaching that has nothing to do with transmitting, mediating, facilitating or sharing knowledge. It is a teaching and a learning that are not owned by anyone and only make sense in the current events / Doutor

Orientador: Rodney Carlos Bassanezi / Banca: Ubiratan DþAmbrosio / Banca: Geraldo Pompeu Junior / Resumo: Partindo do pressuposto de que o Cálculo Diferencial e Integral (CDI) é de vital importância para a formação cultural e intelectual do educando no Ensino Médio, o trabalho aborda as razões de não mais se ensinar o CDI neste nível, contemplando e envolvendo a descrição e análise da metodologia do ensino do CDI., procurando demonstrar, por meio de uma experiência prática com abelhas, efetuada com alunos dos 1º, 2º e 3º anos do Ensino Médio, como a Modelagem Matemática pode ser eficiente veículo de transmissão de conceitos do CDI de uma forma atraente e motivadora. Por estas razões, elegemos como proposta central do presente trabalho a inclusão de conceitos (idéias) do Cálculo Diferencial e Integral no Ensino Médio com estratégia que contempla e atende à interdisciplinaridade e facilita a resolução de problemas significativos do mundo real. Nosso problema consiste em apontar uma boa metodologia para transmissão integral e integrada dos conteúdos matemáticos, em sintonia com a realidade em contínua mutação, a fim de criar condições para que o educando possa ampliar sua própria cosmovisão. Este trabalho parte da hipótese de que devemos mudar nossa abordagem, trabalhando os conteúdos vigentes de uma maneira diferente, no contexto do Cálculo Diferencial e Integral e utilizando uma estratégia de ensino interdisciplinar - a Modelagem Matemática. / Abstract: Leaving of the presupposition that Diferential and Integral Calculus (DIC) is of vital importance for the student's cultural and intellectual formation in the Medium Teaching, the work approaches the reasons of not more to become trained DCI in this level, by the description and analysis of the methodology of the teaching of DCI, trying to demonstrate, through a practical experience with bees, made with students of the 1st, 2nd and 3rd years of the Medium Teaching, as the Mathematical Modelling can be efficient vehicle of transmission of concepts of Diferential and Integral Calculus in an attractive way. For these reasons, we chose as proposal headquarters of the present work the inclusion of concepts of DCI in the Medium Teaching as strategy that assists to the interdisciplinarity and facilitates the resolution of significant problems of the real world. Our problem consists of pointing a good methodology for integral and integrated transmission of the mathematical contents, in syntony with the reality in continuous mutation, in order to create conditions so that the student can enlarge your own world conception. This work part of the hypothesis that we should change our approach, working the effective contents in a different way, in the context of Diferential and Integral Calculus and using a strategy of interdisciplinar teaching - the Mathematical Modelling. / Mestre

Thesis (M.Ed.) -- University of the North, 1983 / Refer to the document

Orientador: Ole Skovsmose / Banca: Jackeline Rodrigues Mendes / Banca: Patrícia Rosana Linardi / Banca: Raquel Milani / Banca: Roger Miarka / Resumo: Esta pesquisa tem como objetivo compreender como as professoras e os estudantes colocam o diálogo em ação nas aulas de matemática dos anos iniciais do Ensino Fundamental, buscando, assim, identificar elementos que favorecem a construção de uma aula de matemática dialógica. A questão norteadora da pesquisa traduz-se por: "De que modo o diálogo é colocado em ação nas aulas de matemática dos anos iniciais do Ensino Fundamental?". O referencial teórico para esta pesquisa se pautou nas perspectivas de diálogo de Paulo Freire, no campo da Educação, e de Helle Alrø e Ole Skovsmose, no campo da Educação Matemática. Centrada em uma abordagem qualitativa, esta pesquisa teve como contexto de produção dos dados duas salas de aula dos anos iniciais do Ensino Fundamental de uma escola pública do interior de São Paulo, mais especificamente uma sala do terceiro ano e uma do quinto ano. Os participantes da pesquisa são as professoras em interação com os estudantes. A turma do terceiro ano era composta por 28 crianças entre oito e nove anos de idade. O quinto ano possuía 26 crianças entre nove e onze anos de idade. O critério inicial de escolha das professoras participantes da pesquisa foi a disponibilidade de ambas em discutir os textos e desenvolver as atividades na sala de aula, e, com este propósito, suas aulas foram acompanhadas durante um semestre, considerando-se também a disponibilidade da escola. Os dados foram produzidos com a utilização do diário de campo, de audiogravações e de vid... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The research herein aims to understand how teachers and students put dialogue into action in the mathematics classes of the early years of Elementary School in order to identify elements that favor the construction of a dialogic mathematics class. The guiding question of the research is: "How is dialogue put into action in the mathematics classes of the early years of Elementary School?" The theoretical reference for this research is based on both Paulo Freire's dialogue perspectives in the field of Education and Helle Alrø and Ole Skovsmose's perspectives in the field of Mathematics Education. As it is focused on a qualitative approach, the research had two classrooms of the early years of the Elementary School of a public school in the countryside of Sao Paulo as the context for data production, more specifically a third-year group and a fifth-year group. The participants in the research are the teachers in interaction with the students. The third-year group consisted of 28 children who are between eight and nine years old. The fifth-year group had 26 children between nine and eleven years old. The first criterion in the choice of the teachers who participated in the research was their availability to discuss the texts and to develop the activities in the classroom. In this sense, also considering the availability of the school, their classes were observed during a whole semester. The data were collected by using a field diary as well as audio recordings and video recording... (Complete abstract click electronic access below) / Doutor

Thesis (M.A.)(Mathematics Education) -- University of Limpopo, 2010. / Culture has become a household name in research circles mainly due to different interpretations that people come up with. How one defines it is relative to the discipline from which one is reasoning from. My engagement with literature in trying to define culture was limited to what happens in the mathematics classroom. What comes out as the operating definition in this study is that culture evolves. Classroom is about learning. As with culture, there are different interpretations of what it means. In this study my discussions on this issue were limited to those that use constructivism as a referent to learning. However, there are still a lot of debates within constructivism in terms of what it means to learn. My discussions were then confined to what it means to learn from a sociocultural perspective. From this perspective learning is accounted for on social and cultural processes. In contrast from a constructivist perspective the individual’s cognitive processes and the classroom culture are reflexively related. The evolving classroom culture does not exist apart from the teacher’s and students’ attempt to coordinate their individual activities (Cobb and Yackel, 1998). Initially the study was aimed at collaborating with an intermediate mathematics teacher in creating a constructivist classroom learning environment. However, the nature of data I had was such that I developed interest in what constitute enculturation process. I had moved between my classroom experiences and experiences with literature to establish what constitute enculturation process. The following constructs emerged as attributes of what enculturation process for both classroom and mathematics culture entails: language, learning, and negotiation of meaning. / N/A

Thesis (M.ED. (Mathematics Education)) -- University of Limpopo, 2012 / This study investigated Mathematics teachers’ beliefs about the nature of Mathematics and their impact on classroom practices. It was conducted in a public semi-urban school in the Capricorn District-Limpopo Province. It was a case study targeting two FET teachers with teaching experiences of 15 years or more. The central research questions addressed in this study are, namely: What are Mathematics teachers’ beliefs about the nature of Mathematics? And, what is the relationship between teachers’ beliefs and their classroom practices? Data were collected through pre-observation interviews, classroom observation and through post observation interviews. Pre-observation interviews were conducted once before the participants were observed. I was a complete observer during my colleagues’ lessons. Interviews and observations data were analysed using categorisation and interpretation of data in terms of common themes and synthesis into an overall portrait of the case. Each case study teacher’s data were analysed individually (that is within-case analysis) first and thereafter cross-case analysis was done in order to compare the two case studies.

Through a historical perspective, this study highlighted significant events and milestones about multilingualism, cultural identity, and mathematics education in Morocco pre-, during, and post-French Protectorate. Prior research in this area has typically focused on the effect on education of multilingualism and cultural identity in general, involving mathematics education only in passing. This study’s purpose was to explore Morocco’s attempt to restore its cultural identity post-French Protectorate and how that attempt influenced the Moroccan mathematical educational system. In addition, this study focused on the Arabic and indigenous Berber (Tamazight) languages of instruction in mathematics in Morocco to investigate if teaching and learning mathematics in the Arabic and Tamazight languages in secondary schools is preparing students adequately for the tertiary level. Finally, this study attempted to see if multilingualism and cultural identity are at the heart of mathematical educational reform and to offer insight into the state of mathematics education reforms suggested by the Moroccan government to remedy this challenge. In order to develop a comprehensive picture of how multilingualism and cultural identity have historically influenced the mathematics education system in Morocco and answer the research questions of the study, a historical research methodology was employed based on views of numerous scholars about bilingual education, cultural identity, diglossia, and how they affect cognition and learning/teaching of mathematics. Supplementary knowledge about students’ achievements, retention, and dropout rates at the primary, secondary, and tertiary levels by gender and grade were acquired and supported by quantitative available data in the official archives supplied by the Ministry of Education, UNESCO, and other organizations. After independence, the establishment of an educational system that would take into consideration the deeply rooted Arab-Islamic culture and language and, at the same time, make use of the imposed Western system was a priority. Arabisation received more attention, and the selection of Arabic as a national language was a form of countering the colonizer’s language policy. Morocco has a particularly complex language situation, where French predominates in most postsecondary institutions, despite attempts to restore Arabic. The indigenous Berber language also plays a role in local culture and education. This work reveals a great number of attempted reforms by the Moroccan government and also demonstrates serious flaws in recent past attempts to reconcile the language issues, but offer ways forward in relation to mathematics instruction.