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Using erroneous examples to improve mathematics learning with a web-based tutoring system

Adams, Deanne M; McLaren, Bruce M; Durkin, Kelley; Mayer, Richard E; Rittle-Johnson, Bethany; Isotani, Seiji; Velsen, Martin van
Fonte: Amsterdam Publicador: Amsterdam
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
55.88%
This study examines whether asking students to critique incorrect solutions to decimal problems based on common misconceptions can help them learn about decimals better than asking them to solve the same problems and receive feedback. In a web-based tutoring system, 208 middle school students either had to identify, explain, and correct errors made by a fictional student (erroneous examples group) or solve isomorphic versions of the problems with feedback (problem-solving group). Although the two groups did not differ significantly on an immediate posttest, students in the erroneous examples group performed significantly better on a delayed posttest administered one week later (d = .62). Students in the erroneous examples group also were more accurate at judging whether their posttest answers were correct (d = .49). Students in the problem-solving group reported higher satisfaction with the materials than those in the erroneous examples group, indicating that liking instructional materials does not equate to learning from them. Overall, practice in identifying, explaining, and correcting errors may help students process decimal problems at a deeper level, and thereby help them overcome misconceptions and build a lasting understanding of decimals.; Pittsburgh Science of Learning Center (NSF Grant 0354420)

Construção de conceitos de matemática via projetos de aprendizagem

Mattos, Eduardo Britto Velho de
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
46.12%
Nesta dissertação desenvolvemos e analisamos uma proposta de ensino-aprendizagem de matemática para alunos de sexta série do ensino fundamental, com base nas pesquisas e inovações realizadas no Laboratório de Estudos Cognitivos da Universidade Federal do Rio Grande do Sul (LEC/UFRGS) – com a coordenação da professora Léa da Cruz Fagundes – e nas experiências desenvolvidas no Projeto Amora do Colégio de Aplicação dessa universidade (Projeto Amora/CAp/UFRGS), todas focadas no desenvolvimento de Projetos de Aprendizagem com uso dos recursos digitais oferecidos pelas novas tecnologias de informação e comunicação e à luz da teoria psicogenética de Jean Piaget. Na proposta, alunos da sexta série do ensino fundamental desenvolvem Projetos de Aprendizagem como estratégia pedagógica das aulas de matemática e, com eles, constroem as suas aprendizagens de matemática. Por consequência, o currículo de matemática desses alunos é constituído pelas construções conceituais de matemática impulsionadas pelo desenvolvimento dos seus Projetos de Aprendizagem. Analisamos as aprendizagens de matemática dos alunos envolvidos nesta investigação e comparamos com as sequências curriculares tradicionalmente propostas para a mesma etapa escolar...

Dificuldades de aprendizagem na matemática : um estudo de intervenção pedagógica com alunos do 4º ano do ensino fundamental

Müller, Gessilda Cavalheiro
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Tese de Doutorado Formato: application/pdf
POR
Relevância na Pesquisa
45.97%
O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa...

Engineering students and mathematics achievement : a portuguese case study

Alves, M.; Rodrigues, Cristina S.; Rocha, Ana Maria A. C.
Fonte: Newswood Limited Publisher Publicador: Newswood Limited Publisher
Tipo: Conferência ou Objeto de Conferência
Publicado em //2012 ENG
Relevância na Pesquisa
45.97%
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)

Promoting the power of mathematics : children learning fractions with understanding

Mamede, Ema; Oliveira, Manuela
Fonte: GRIM Publicador: GRIM
Tipo: Artigo de Revista Científica
Publicado em //2012 ENG
Relevância na Pesquisa
45.91%
This paper focuses on a teaching experiment that helps second grade students to discover the power of mathematics by building on their informal knowledge of fractions with understanding. It describes a study on children’s understanding of fractions when the quotient interpretation of fractions is used to introduce them this concept, after a contact with partitioning and equal sharing activities. The study tries to address two questions: How do children understand ordering of fractions when introduced to this concept using the quotient interpretation? How do children understand the equivalence of fractions in this interpretation? An intervention program comprising 7 sessions was conducted in a 2nd-grade classroom, with 7-years-old children, from a public primary school, in Portugal. The findings of this study suggest that to solve ordering problems of fractions using the quotient interpretation can help children to easily understand the inverse relation between the divisor and the quotient, when the dividend is the same; the equivalence problems presented in quotient interpretation can give the children an opportunity to promote their proportional reasoning. Issues on their learning process are analyzed and discussed here.; CIEC – Research Centre on Child studies...

Um estudo comparativo sobre o uso das TIC na aprendizagem de matemática do ensino secundário/médio em Portugal e no Brasil; A comparative study on the use of ICT for learning in secondary school mathematics in Portugal and in Brazil school

Viseu, Floriano; Lima, Antonia Jacinta Barbosa; Fernandes, José António
Fonte: Programa de Estudos Pós-Graduados em Educação Matemática da PUC-SP Publicador: Programa de Estudos Pós-Graduados em Educação Matemática da PUC-SP
Tipo: Artigo de Revista Científica
Publicado em //2013 POR
Relevância na Pesquisa
45.95%
A crescente utilização de recursos tecnológicos na sociedade encontra abertura da escola para os integrar nas atividades de ensino e de aprendizagem. Na disciplina de matemática, muito contribuem para essa abertura as recomendações dos programas escolares ao preconizarem o uso desses recursos. Como o que é prescrito nem sempre é concretizado, procuramos averiguar como alunos do ensino médio, do Brasil, e do ensino secundário, de Portugal, utilizam os recursos tecnológicos nas suas atividades de aprendizagem nesta disciplina. O estudo seguiu uma abordagem quantitativa e a recolha de dados foi efetuada através de um questionário. Em termos de resultados, dos recursos tecnológicos, o mais utilizado pelos alunos nas suas atividades de estudo de matemática é a calculadora. O computador, a Internet e, sobretudo, o Quadro Interativo e o Moodle são ainda pouco explorados pelos alunos de ambos os países nas atividades que realizam na sala de aula e fora dela.; The increasing use of technology resources in society is having an impact in the school in what regards their integration in teaching and learning processes. In the Mathematics, the school curriculum is also advocating the use of these resources. However, as what is prescribed is not always implemented...

Relatório Final da Prática de Ensino Supervisionada O dia-a-dia da Matemática: A importância dos materiais manipuláveis em sala de aula

Duarte, Madalena Filipa Garrido
Fonte: Repositório Comum de Portugal Publicador: Repositório Comum de Portugal
Tipo: Dissertação de Mestrado
Publicado em 22/04/2015 POR
Relevância na Pesquisa
46.05%
O presente relatório insere-se no âmbito da Prática Pedagógica Supervisionada do Mestrado de Qualificação para a Docência em Educação Pré-Escolar e Ensino do 1.º Ciclo do Ensino Básico, e pretende refletir sobre a prática desenvolvida ao longo da prática pedagógica decorrida em três semestres, assim como analisar a evolução dos grupos perante a temática abordada. A matemática ao assumir um papel importante no percurso escolar de cada aluno, permite desenvolver capacidades e competências que lhe serão úteis no futuro. Contudo, as crianças e alunos tendem a rejeitar a matemática, o que condiciona o seu envolvimento nas atividades matemáticas e na atribuição de sentidos às aprendizagens matemáticas. Desta forma, o recurso a materiais manipuláveis, estruturados e não estruturados, poderá ser um facilitador na apropriação de conhecimentos matemáticos e no desenvolvimento de capacidades e competências (matemáticas). Esta investigação encontra-se sustentada por um design de investigação-ação, do paradigma interpretativo, através da qual se pretende observar, planificar, refletir, intervir e voltar a refletir consoante os objetivos a alcançar. Deste modo, os instrumentos utilizados são diversos como sejam a observação...

Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

Haase, Vitor G.; Júlio-Costa, Annelise; Lopes-Silva, Júlia B.; Starling-Alves, Isabella; Antunes, Andressa M.; Pinheiro-Chagas, Pedro; Wood, Guilherme
Fonte: Frontiers Media S.A. Publicador: Frontiers Media S.A.
Tipo: Artigo de Revista Científica
Publicado em 13/02/2014 EN
Relevância na Pesquisa
45.95%
Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast...

A complexity theoretic approach to learning

Klivans, Adam R
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 138 leaves; 9348960 bytes; 9348716 bytes; application/pdf; application/pdf
ENG
Relevância na Pesquisa
45.99%
This thesis details a new vantage point for attacking longstanding problems in machine learning. We use tools from computational complexity theory to make progress on problems from computational learning theory. Our methods yield the fastest and most expressive algorithms to date for learning several fundamental concept classes: * We show that any s-term DNF over n variables can be computed by a polynomial threshold function of order O(n1/3 log s). As an immediate consequence we obtain the fastest known DNF learning algorithm which runs in time 2O(n1/3). * We give the first polynomial time algorithm to learn an intersection of a constant number of halfspaces under the uniform distribution to within any constant error parameter. We also give the first quasipolynomial time algorithm for learning any function of a constant number of halfspaces with polynomial bounded weights under any distribution. * We give an algorithm to learn constant-depth polynomial-size circuits augmented with majority gates under the uniform distribution using random examples only. For circuits which contain a polylogarithmic number of majority gates the algorithm runs in quasipolynomial time. Under a suitable cryptographic assumption we show that these are the most expressive circuits which will admit a non-trivial learning algorithm. Our approach relies heavily on giving novel representations of well known concept classes via complexity theoretic reductions. We exploit the fact that many results in computational learning theory have a complexity theoretic analogue or implication. As such...

Ensino de Matemática com o apoio do TelEduc: experiência etnográfica em um curso de Administração; Mathematics Teaching with TelEduc support: an ethnographic experience on an Administration Course

SOUZA, Renato Sardinha de
Fonte: Universidade Federal de Goiás; BR; UFG; Mestrado em Educação em Ciências e Matemática; Ciências Exatas e da Terra Publicador: Universidade Federal de Goiás; BR; UFG; Mestrado em Educação em Ciências e Matemática; Ciências Exatas e da Terra
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
46.14%
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...

Matemática financeira: aprendendo a usar essa poderosa ferramenta no dia a dia; Financial mathematics: learning to use this powerfull tool in day to day

Pedro Jr, Simão
Fonte: Universidade Federal de Goiás; Brasil; UFG; Programa de Pós-graduação em Matemática (IME); Instituto de Matemática e Estatística - IME (RG) Publicador: Universidade Federal de Goiás; Brasil; UFG; Programa de Pós-graduação em Matemática (IME); Instituto de Matemática e Estatística - IME (RG)
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
45.92%
The goal of this work is to serve as a guide so that teachers can orientate and enrich their pedagogical practice in an appropriate manner as well as to enable readers to solve problems of their daily lives, such as: evaluating loans, understand and decide on investments, among other similar. With this, emphasize the importance of processing your teaching and learning. We believe that this is a matter of great importance in the daily lives of people, especially after the stabilization of the Brazilian economy because the real plan, where people now have easier access to credit, acquiring Financing and loans with higher frequency. This justi es a solid learning and future application of Financial Mathematics. Through their study, students can be prepared to perform commercial and nancial transactions that occur in your daily life, such as choosing the best form of payment, cash or term, analyzing investment alternatives, understand the functioning of nancial markets organize your personal nances etc.; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES; O objetivo deste trabalho é servir de guia para que os professores possam orientar e enriquecer sua prática pedagógica de maneira adequada, além de capacitar o leitor para resolver problemas do cotidiano...

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

Ailles, Douglas S.
Fonte: Brock University Publicador: Brock University
Tipo: Electronic Thesis or Dissertation
ENG
Relevância na Pesquisa
45.92%
This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly...

Aprendizaje de las matemáticas mediante el ordenador en Educación Primaria; Computer-assisted learning of mathematics in Primary Education

Santiago Etxeberría, Karlos; Etxeberria Murgiondo, Juan; Lukas Mujika, Jose Francisco
Fonte: Universidade de Múrcia Publicador: Universidade de Múrcia
Tipo: Artigo de Revista Científica Formato: application/pdf
SPA
Relevância na Pesquisa
56%
This article is about the implementation and use of ICT as a means of learning in Primary Education. In order to enhance mathematics learning, the Ikastolas organism from the Basque Country (cooperative of private and state-subsidised schools) developed the Ikasys Programme with the purpose of integrating computers in the learning of mathematics. This paper briefly describes the contents of the Ikasys Programme, and outlines the results of research undertaken to date on this area. Methodological complementarity with quantitative and qualitative procedures was used to assess the programme. Students in all levels participating in the programme (2nd, 4th and 6th grade) achieved better results that those not involved in the programme. There was, however, variation in terms of the competencies assessed.; El presente artículo se inserta dentro del campo de implantación y uso de las TIC como medio de aprendizaje en la Educación Primaria. Con objeto de mejorar el aprendizaje de las matemáticas por parte del alumnado, las Federación de Ikastolas del País Vasco (Cooperativa de centros privados concertados con el Gobierno Vasco) crearon el Programa Ikasys para introducir el ordenador en el aprendizaje de las matemáticas y desde entonces se está implantando...

Designing professional learning tasks for mathematics learning trajectories

Wilson, P. Holt; Sztajn, Paola; Edgington, Cyndi
Fonte: Grupo de Investigaci??n Did??ctica de la Matem??tica: Pensamiento Num??rico (FQM-193) Publicador: Grupo de Investigaci??n Did??ctica de la Matem??tica: Pensamiento Num??rico (FQM-193)
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.03%
In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers??? learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project.; En este art??culo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de dise??o para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matem??ticas de maestros de primaria. Describimos brevemente nuestra perspectiva te??rica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el dise??o de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigaci??n actual.

A Case Study of Social Justice Mathematics: The Experiences of Secondary Students and Preservice Teachers in Mathematics Teaching and Learning

Lam, MANDY
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado
EN; EN
Relevância na Pesquisa
46.09%
This case study described the experiences of secondary students and preservice mathematics teachers in the teaching and learning of social justice mathematics (SJM). Specifically, participants’ experiences in making connections among the mathematics curricula and the real world, perceptions about mathematics, and responses to an integrated curriculum approach were described. Students participated in SJM activities designed by preservice teacher participants: one component of a pre-existing extracurricular Social Issues Club at a high school in Southeastern Ontario. Mathematics activities, led by the researcher or one of the preservice teacher participants, were designed to complement the social justice issues that were being explored by the members of the Social Issues Club. Data were obtained through observations, questionnaires, focus group, individual interviews, written reflections, and artifacts. Results demonstrated that preservice teacher participants had unique professional and educational encounters prior to SJM that they connected to their SJM experience. Subsequent to this experience, preservice teachers suggested limited ideas about integrating curriculum into their future teaching practice beyond the content and contexts made familiar to them through SJM. With limited exposure to examples of curriculum integration identified by preservice teachers as a barrier...

One Teacher’s Focus on Reading in a Grade 9 Mathematics Classroom: A case study

Voytsekhovska, SVITLANA
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado Formato: 1862843 bytes; application/pdf
EN; EN
Relevância na Pesquisa
45.93%
This thesis reports on a qualitative study that documented one teacher’s research-based practice of teaching students to read in a Grade 9 ESL Academic mathematics course. Specifically, this thesis focuses on the description of the range of strategies and reading-based activities that the teacher used; the experiences and influences that led him to include reading strategies in his regular instructional practice; and, the challenges that he faced when integrating these strategies routinely as part of his daily mathematics program. The complexity of simultaneously teaching mathematics and reading strategies in the context of a Grade 9 ESL Academic course is also discussed. The study was conducted early in the second semester of the 2007-2008 school year. A variety of data collection methods were used: interview, classroom observation, and document collection. The findings of the study provide concrete examples of designing lessons that embed the use of reading strategies (e.g., vocabulary development, reading supplementary text, and reflection) to teach or inform mathematics concepts. The large number of ESL students in the observed class underscored the importance of incorporating reading strategies into the mathematics program in order to facilitate ESL students’ language learning processes. The teacher under study focused on using additional literature as an aid to develop students’ deeper understanding of mathematics concepts and introduced reading strategies as a means to improve students’ reading comprehension of supplementary text; however...

Avaliação do Processo de Ensino e Aprendizagem em Matemática: contribuições da teoria histórico-cultural; Evaluation of the Teaching and Learning Process in Mathematics: contributions from historical-cultural theory

MORAES, Silvia Pereira Gonzaga de; MOURA, Manoel Oriosvaldo de
Fonte: UNESP-DEPT MATHEMATICA Publicador: UNESP-DEPT MATHEMATICA
Tipo: Artigo de Revista Científica
POR
Relevância na Pesquisa
45.97%
This article presents the results of a study that investigated the meaning of evaluation in mathematics from the historical cultural perspective, focusing on activity theory. In order to develop the investigation, a collaborative group was formed from the Oficina Pedagogica de Matematica de Ribeirao Preto - Sao Paulo (Math Pedagogic Workshop of Ribeirao Preto - OPM/RP), constituted of pre-school teachers and early elementary school teachers, who were participants in this research. The main role of the collaborative group was to offer guided development to the teachers about the teaching of mathematics from the historical-cultural perspective, aiming at collecting data on the process of appropriation of mathematical knowledge by the teachers. The syntheses about the teachers' learning process have contributed to systematize the guiding elements of evaluation in mathematics from the historical-cultural perspective.

Algebraic models of conceptual metaphor: contributions to the understanding of mathematics learning processes

Navarrete Ulloa, Jairo Alfredo
Fonte: Universidad de Chile Publicador: Universidad de Chile
Tipo: Tesis
EN
Relevância na Pesquisa
45.98%
Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática; This thesis studies a human cognitive phenomenon called Conceptual Metaphor in the context of mathematics learning and reasoning. Metaphor enables the understanding of an abstract concept called target, e.g. numbers, in terms of a more concrete concept called source, e.g. piles of can-dies. Often, inferences from the source are carried to the target and applied there yielding some conclusions about the target. This is known as reasoning by analogy. Empirical evidence indicates that metaphor enhances learning. Converging evidence is pro-vided by working scientists who report the use of analogies while developing their theories. On the other hand, some people advise against its usage in education. They argue that politicians and communicators often lead people into erroneous conclusions by using metaphor, and then, analo-gies undermine objective reasoning. This discussion highlights the need for research to shed light into the learning mechanics underlying metaphor in order to understand its scope and limitations. This work presents a formal model of metaphor which can be used as a framework to study learning by analogy. Since the model is abstract, we use Chapter 1 to make ideas more concrete: we use our formalism for analize deeply a well known example. Along these lines...

“I’m like the Sherpa guide”: On Learning to Teach Proof in School Mathematics

Cirillo, Michelle
Fonte: The International Group for the Psychology of Mathematics Education Publicador: The International Group for the Psychology of Mathematics Education
Relevância na Pesquisa
45.93%
This article describes the experiences of a beginning mathematics teacher, Matt, across his first three years of teaching proof in a high school geometry course. Matt’s past experiences with mathematics influenced his beliefs about what he could and could not do to help his students learn how to prove. During his first year of teaching proof, Matt claimed that you cannot teach someone to write a proof. Over time, however, Matt eventually developed some strategies for teaching proof to his students. Within this work is an interest in learning more about how a teacher learns to teach proof to students who are just learning how to construct a formal proof. This case highlights the importance of pedagogical content knowledge.; This research was supported, in part, by the National Science Foundation under Grant no. 0347906 (Beth Herbel-Eisenmann, PI).

South African research in mathematical cognition and language in childhood: Towards an expanded theoretical framework

Henning,Elizabeth
Fonte: South African Journal of Childhood Education Publicador: South African Journal of Childhood Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2013 EN
Relevância na Pesquisa
46%
The article proposes that cognitive developmental psychology and cognitive neuroscience theory need to feature more prominently in the theoretical frameworks for South African research on language in mathematics learning in the early years of school. I argue that, considering the state of mathematics learning in the foundation phase and the conundrum around the language of learning and teaching debate in the country, we need more integrated theoretical work for equally integrated analyses of learners and learning, moving beyond the practice of drawing from mostly single theories, such as bilingual education theory, or sociocultural theory. The article explains the reasoning behind the proposition for an expansion of the theoretical work in this field, claiming that policy decisions about language of learning and teaching depend on empirical research that includes theories from the cognitive sciences as framework.