Based on a survey of summaries of courses on the Foundations of Mathematics, from Mathematics Teacher Education programs in the southern part of Brazil, and some remarks on the legislation related to the course syllabuses, we discuss the meaning of the word ""Foundations"" in order to reflect on the proposals of these issues in the courses, which will be undergoing reformulation. The opinions of students in one of these courses regarding the meaning of the term ""foundations"", as well as the data obtained from the survey and the remarks regarding legislation, may lead to considerations about the possibilities for a better qualification of the initial education of Mathematics teachers.

O objetivo deste trabalho é investigar as modalidades de recuperação, bem como apresentar e discutir os esforços realizados no âmbito das políticas públicas no sentido de minimizar o fracasso do aluno, sobretudo na disciplina de Matemática. Para isso, são analisadas diferentes concepções de avaliação produzidas ao longo do tempo, assimiladas em currículos e documentos oficiais e que se manifestam no cotidiano escolar, pois são os resultados das avaliações realizadas pelos professores em sala de aula que sinalizam e, em muitos casos definem os rumos das trajetórias escolares dos alunos. São apresentadas diversas concepções, desde a mensuradora, classificatória e seletiva, centradas mais no cumprimento dos objetivos educacionais, até as abordagens mais recentes, que evidenciam uma preocupação maior com a reorientação do processo de ensino e aprendizagem, centrada nos atores desse processo. Tomando como base o desenvolvimento do ensino da disciplina de Matemática praticado nas escolas, essas concepções são analisadas do ponto de vista da produção bibliográfica e acadêmica, além de contemplar também o discurso presente nos documentos oficiais. Ao lado da avaliação empreendida pelos professores no cotidiano da escola foram criados sistemas de avaliação pelos órgãos públicos da Educação intensificando a aplicação de testes e provas...

Como o termo matemática vem sendo usado na literatura acadêmica da Educação Matemática? Esta é a questão inicial que orienta este estudo investigativo realizado com base em publicações e pesquisas acadêmicas recentes em Educação Matemática. Com base nesses documentos, verificou-se a ocorrência, em freqüência significativa, de diversas adjetivações do termo matemática tais como: matemática escolar, matemática da rua, matemática acadêmica, matemática popular, matemática do cotidiano, etc. A partir da análise de alguns desses textos, constatou-se que as adjetivações, que ocorrem geralmente aos pares, apontam especificidades das matemáticas, tais como, diferenças em resultados, processos, valores, significados, conceitos, etc. A partir de uma visão de conjunto das especificidades apontadas nos textos pesquisados, as diversas adjetivações são interpretadas como jogos de linguagem que não possuiriam uma essência, mas apresentariam semelhanças de famílias, no sentido dado por Wittgenstein a este conceito. Para formular a questão acima, inspiramo-nos nos conceitos desse filósofo, bem como em sua concepção de filosofia, que possui uma perspectiva de ampliação dos significados alcançada mediante as descrições dos usos de um conceito...

Mathematics is a discipline that appears on the syllabus of many courses, including courses in engineering, where it is an essential discipline to the formation of all future engineers, whatever their field of study and work. Despite that, engineering students tend to reveal difficulties with courses based on mathematics. The factors that influence learning mathematics have been the subject of study for several researchers around the world. Researchers attempt to identify variables that explain mathematics achievement, but fail to address university students. In this paper, we present the results of an exploratory study based on industrial engineering students of University of Minho, concerning their grades in the courses of statistics and numerical methods. The preliminary results show that gender is an unexpected and significant factor.; Fundação para a Ciência e a Tecnologia (FCT)

Mathematics is a discipline that appears on the syllabus of many courses, including courses in engineering, where it is essential to the formation of all future engineers, whatever their field of study and work. Despite that, engineering students tend to reveal difficulties with course units based on mathematics. The factors that influence learning mathematics have been the subject of study for several researchers around the world. Researchers attempt to identify variables that explain mathematics achievement, but fail to address university students. In this paper, an exploratory study based on engineering students of University of Minho, concerning their grades in statistics and numerical methods curricular units is presented. The aim of this study is to explore the mathematics achievement in the process of learning mathematical concepts. The preliminary results show that gender is an unexpected and significant factor.; Fundação para a Ciência e a Tecnologia (FCT)

Copyright © 2012 World Economics Association.; In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced by the Newtonian approach that still characterised many aspects of the Cambridge Mathematical Tripos, where the emphasis was on geometrical and mechanical examples rather than on symbolic (Cartesian) mathematics. Keynes, who criticised (Cartesian) symbolic mathematics, was indeed an admirer of Newton and of his method. Sraffa’s mathematical constructions are also in line with the Newtonian approach where arithmetic and geometry were strictly separated, since Sraffa’s mathematical constructions typically use arithmetic without engaging in the mixture between geometry and arithmetic that occurs in the Cartesian approach.

This study aims to provide new evidence from Turkish pre-service elementary school (PES) teachers and to identify some correlations and factors associated with mathematics anxiety (MA). 480 Turkish PES teachers participated in this study. Data was collected using a Personal Information Form, Mathematics Anxiety Scale, and Mathematics Attitude Scale. Data was analyzed using the SPSS 17.0 statistics program. It was revealed that the MA level of the participants was low, and the difference based on gender was not significant. Cross-sectional comparison indicated that freshmen were more inclined to have MA than the seniors. Based on self-reported perceptions, we found that there were significant differences related to mathematics. There was a tendency for participants with negative attitudes towards mathematics and low achievers to possess higher levels of MA. It was also found that there was a significant correlation among mathematics anxiety, mathematics achievement, and mathematics attitudes. This study will provide some guidance for the revision of course requirements and teaching strategies, and promotes collaboration between mathematics educators and counselors.

This research subject is about the continuing education proposals of Mathematics teachers of Colmeia and Revivenciando o Colmeia projects in Goiânia, State of Goiás. Such research, of historical nature, has as goals understanding the relation on both proposals, in order to identify the ruptures and continuities and the transformations in these continuing education projects, and whether they show the appearance of a school culture of Mathematics teachers continuous formation at the Federal University of Goias. For the research development, the studies of Michael and Miorim, Valente, and Chartier Certeau were used. Those authors discuss the historical making meaning as production. Theoretical frameworks of different areas were considered once they address issues concerning to the researched topic, as some concepts of Bourdieu, Geertz, Chervel, Frago, Julia and Freire. Based on Chen, Meihy, Nóvoa and Finger, Nóvoa and Fiorentini and Lorenzato reflections, we chose a planning using the biographical method. The data collecting, obtained through written and oral narratives, was done from the reading of various documents that make part of the collection of projects Colmeia and Revivenciando o Colmeia projects, of the meetings observations and an open questionnaire applied to Colmeia project coordinator and an interview with the Colmeia project coordinator. From this research it was possible to identify ruptures and what has remained on the Mathematic teachers continuing education proposals of the projects mentioned above. We noticed...

The investigation presented here is based on the scoop of the Teaching and Learning of Science and Mathematics, from the Post-Graduation program in Education in Science and Mathematics, from the Federal University of Goiás and its main goal is to study a group of second-year students from the Administration Course, evening-course, from a private college, located in Goiânia, state of Goiás, Brazil. This study relates to the Learning of Mathematics applied to administration, to Internet usage and to a free virtual learning ambience which is used as a support to face-to-face teaching - the TelEduc. Besides, the contribution given by the students presently called Monitors of applied Mathematics, Applied Mathematics: virtual resources, offered on the TelEduc ambience were also studied. Throughout the pages on this dissertation, there is a feedback , a kind of descriptive memorial of the academic life of the researcher, exploring his initial contacts with the Mathematics Learning Process and also his contacts with Educational Technology. Lately, the choice of this work methodology is justified, inspired by the principle of the utility for the research reflection, in Edgard Morin. In order to offer theoretical support, the methodology of ethnographic type research was adopted...

Students’ attitudes toward mathematics have been known to influence students’ participation, engagement, and achievement in mathematics. A variety of instruments have been developed to measure students’ attitudes toward mathematics for example Mathematics Attitude Scale (Aiken, 1974), Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976), and Attitudes Toward Mathematics Inventory (ATMI) (Tapia & Marsh, 1996). The purpose of this paper is to report the validation of the ATMI instrument. It was administered to 699 Year 7 and 8 students in 14 schools in South Australia. The students responded on a five-point Likert scale. Confirmatory factor analysis (CFA) supported the original four-factor correlated structure based on several fit indices. The validation provided evidence that ATMI can be a viable scale to measure students’ attitudes toward mathematics in a South Australian context; Aysha Abdul Majeed, I Gusti Ngurah Darmawan, Peggy Lynch

The Department of Applied Mathematics has a multi-faceted mission to provide an exceptional mathematical education focused on the unique needs of NPS students, to conduct relevant research, and to provide service to the broader community. A strong and vibrant Department of Applied Mathematics is essential to the university's goal of becoming a premiere research university. Because research in mathematics often impacts science and engineering in surprising ways, the department encourages mathematical explorations in a broad range of areas in applied mathematics with specific thrust areas that support the mission of the school.

The following report is the first of a two-stage video study to examine teaching practices and activities in Indonesian classrooms. The first stage is linked to results of the 2007 Trends in International Mathematics and Science Study (TIMSS) where 100 of the 150 classes that participated in the TIMSS examination also participated in this additional video study component. The second stage will also involve 100 classes that will participate in the 2011 exam. The second phase will follow the same methodology, allowing for comparison across years, but will also involve more in-depth analysis of the links between teaching practices and student outcomes and how teaching practices are influenced by teachers' belief systems and subject content knowledge. Indonesia has been a committed participant in the TIMSS, Program for International Student Assessment (PISA) and the Progress in International Reading Literacy Study (PIRLS) international standardized student examinations for many years and is one of the few non-OECD (Organization for Economic Cooperation and Development) countries to participate so fully. Indonesian student performance in these examinations has been relatively low...

This qualitative case study examined a cohort of prospective teachers who completed a university mathematics course during which they were given the opportunity to relearn geometry conceptually and gain experience teaching using contemporary approaches. The course embedded mathematics content using the context of (a) problem solving in university-based seminar classes and (b) a concurrent Grade 7 and 8 teaching placement. Questionnaires, administered at the beginning and end of the semester, and individual interviews were used to obtain data about the prospective teachers’ beliefs about the nature of mathematics and its teaching, and about their pedagogical content knowledge. The pre-course profile was that of a group who held comparable views about mathematics teaching as passive, learning as procedural, and mathematics itself as instrumental. The post-course profile, however, was of a radically different group who once again claimed to hold comparable beliefs about reform-based teaching methods, conceptual learning, and a dynamic view of the utility of mathematics. There are five findings from this study with import for preservice mathematics teacher education. First, learning best occurs within a community. Second, an inquiry-based approach to mathematics provides a rich learning opportunity for students. Third...

Research on English Language Learners’ (ELL) test performance in relation to their language use at home and attitudes towards mathematics have rarely been investigated. This study examines the effects of different test formats and constructs, learner characteristics, and attitudes towards mathematics on ELLs’ performance in the Education Quality Accountability Office (EQAO) Grade 9 mathematics test. The participants include a total of 2867 ELLs in Grade 9 who participated in the EQAO Grade 9 mathematics test (1887 from the academic course and 980 from the applied course). The overall results of the study supported the following conclusions. First, ELLs tend to score better in Multiple Choice Questions (MCQ) over Open Response Questions (ORQ), and language use at home has interaction effects on their performances on various test formats and constructs. Secondly, significant interactions occurred between language use at home and ELLs’ performance of test formats and constructs. In addition, ELLs who speak another language (only another language) scored higher in performance in both test formats and constructs than ELLs who spoke only English at home. From the ELLs’ questionnaire responses at both the academic and applied levels...

This qualitative case study describes how two teachers translate communication messages from curriculum statements into classroom practice. These illuminative cases illustrate the perspectives and practices of two teachers who support the spirit of the Ontario Mathematics Curriculum by working to implement communication in the Foundations of Mathematics (MFM1P), Grade 9, Applied course (Ontario Ministry of Education, 2005). Data for this study were collected from individual interviews with teachers, classroom observations, and document analysis. Grade 9 Applied mathematics teachers across Ontario indicate on surveys that they support communication in the mathematics classroom (Education Quality and Accountability Office, 2007; Suurtamm & Graves, in press). Despite evidence of support for this aspect of the curriculum, findings from this study point to a need for finer analysis of teachers’ perspectives and practices when it comes to communication in mathematics. The cases presented in this thesis illustrate different images, or meanings, associated with communication in mathematics. Furthermore, even in unique cases where the gap between curriculum developers and teachers images is minimal, the idealized vision of communication may not be realized in classroom practice since teachers may face challenges in implementation. The teachers report that despite additional challenges involved with implementing communication in Grade 9 Applied mathematics...

Preservice teachers bring to their studies a host of beliefs concerning the nature of mathematics. These mathematical beliefs have been shown to influence teachers’ instructional practices. Research that examines the alignment of beliefs about the nature of mathematics and beliefs about effective instructional practices have left many unanswered questions including, do beliefs concerning the nature of mathematics held by preservice primary-junior mathematics teachers align with beliefs concerning effective mathematics instruction at the beginning of teacher education programs? In this study, the beliefs Ontario preservice primary-junior (grades JK-6) teachers bring to their teacher preparation programs were examined and the alignment of beliefs concerning the nature of mathematics and the teaching and learning of mathematics was explored. Specifically, I investigated the beliefs of preservice teachers who displayed contradictory views on the nature of mathematics and effective instructional practice; preservice teachers who held absolutist beliefs about mathematics but intended to teach using a constructivist approach. A questionnaire was used to identify participants with misaligned beliefs, and interviews, with a focus on manipulative use...

Investigar o ensino de matemática por meio do estudo das práticas e do cotidiano da escola salesiana Liceu Coração de Jesus em São Paulo, entre 1885 e 1929, é o objetivo desta pesquisa. Apóia-se em fontes históricas escritas e iconográficas, recolhidas a partir de pesquisas em arquivos escolares, em centros de documentação histórica e em bibliotecas. No cruzamento dessas fontes, busca-se construir uma história tendo presente os pressupostos teóricos de Michel de Certeau, Dominique Juliá e André Chervel, dentre outros autores da história cultural e também da História da Educação e da Educação Matemática no Brasil. Essa história é uma dentre as possíveis. É, principalmente, um exercício de escrita e de reflexão sobre um passado não vivido, mas cuja investigação permite que se (re) construam elementos importantes para a compreensão do desenvolvimento do ensino de matemática no Brasil, por meio de uma instituição católica de ensino, que teve um papel de destaque no cenário brasileiro no período de transição entre o Império e a República. Verifica-se que o ensino de matemática passou por significativas mudanças nesse período, tanto em termos quantitativos como em relação aos objetivos e aos conteúdos ensinados...

Esta tese investiga os propósitos, valores, conflitos e formas diversificadas de representação do social que têm participado da constituição da comunidade de prática científica internacional denominada Mathematics Education and Society (MES), tanto no que se refere ao processo constitutivo de sua identidade, quanto no que diz respeito à realização de suas práticas sócio-culturais e de sua produção científico-cultural. A base documental na qual se assenta o processo de constituição dessa comunidade é composta pelos anais das quatro conferências do MES realizadas até o momento, por mensagens da sua lista de discussão, por entrevistas realizadas com membros do MES e pesquisadores relacionados e por notas de campo obtidas com base em participação pessoal em duas dessas conferências. O referencial metodológico-conceitual subjacente a essa constituição foi construído com base no diálogo com autores como Foucault, Bourdieu, Hall e Wenger.; This thesis focuses on the purposes, values, conflicts and diversified forms of social representation that have comprised the international community of scientific practice named Mathematics Education and Society (MES), not only in terms of the constitution process of its identity...

ensino: (a) textos de aprendizagem, aqueles utilizados, simultaneamente, na sala de aula por professor e alunos, como os livros didáticos e textos alternativos; (b) os textos de apoio e aprofundamento, como Ruiz (2005), Glaeser (1985) e de autores da História da Matemática, como Boyer (1984) e outros e (c) textos oficiais de orientações curriculares e de formação de professores. A questão central de pesquisa consistiu em entender quais as contribuições dos textos impressos na formação dos licenciandos em matemática, para as idéias iniciais do conceito números inteiros. Esse entendimento foi realizado por meio de diálogos ocorridos num grupo de licenciandos ao desenvolver atividades nas aulas de Metodologia e Prática de Ensino de Matemática na Educação Básica, em uma Universidade pública do interior do Estado de São Paulo. Recorremos a Olson (1997) para compreender a constituição do mundo do papel da matemática escolar, a Bohm&Peat (1989) para a compreensão das infraestruturas tácitas do conhecimento, e a Lizcano (1993, 2006), para a compreensão dos imaginários dos números inteiros e as metáforas derivadas desses imaginários, que possibilitam a compreensão do significado de negatividade que precede o significado do número negativo. Como resultados verificamos que os licenciandos interagiram com os autores estudados...

http://dx.doi.org/10.5007/1981-1322.2014v9nespp21Neste artigo apresentamos considerações em relação aos dados que envolvem a categoria: Objetivos que buscam relacionar a Modelagem Matemática com outras teorias, tendências ou tecnologias e seus respectivos resultados revelados nos trabalhos apresentados e constantes nos anais da VI Conferência Nacional de Modelagem em Educação Matemática - VICNMEM. A questão de fundo é: Como se apresentam os objetivos e os resultados dos trabalhos publicados no âmbito da VI CNMEM? A natureza da investigação é predominantemente qualitativa e a análise dos dados se pautou nas orientações de Bardin (2009) para a análise de conteúdo. Foram analisados quinze (15) trabalhos submetidos ao evento, com o auxílio do software Atlas t.i. Alguns resultados mostram o avanço na busca de associar a Modelagem com outras tendências da Educação Matemática, mas também ainda uma pequena contribuição em relação à consolidação do campo da Modelagem na Educação Matemática.; http://dx.doi.org/10.5007/1981-1322.2014v9nespp21This article presents considerations regarding the data involving the category: Objectives that seek association of Modeling Mathematics with other theories, trends or technologies and their results presented and disclosed in constant work in the annals of the Sixth National Conference on Mathematical Modeling in Education - VICNMEM . The question to be answered is: How if show the objectives and results of published works within the VI CNMEM? The nature of research is predominantly qualitative and data analysis was based under the guidelines of Bardin (2009) for content analysis. Were analised 15 papers submitted to the event...