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Macmillan, Emily. "Argumentation and Proof : Investigating the Effect of Teaching Mathematical Proof on Students' Argumentation Skills." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517230.
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Brinkerhoff, Jennifer Alder. "Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1960.pdf.
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Vincent, Jill. "Mechanical linkages, dynamic geometry software, and argumentation : supporting a classroom culture of mathematical proof /." Connect to thesis, 2002. http://eprints.unimelb.edu.au/archive/00001399.
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Stoyle, Keri L. "SUPPORTING MATHEMATICAL EXPLANATION, JUSTIFICATION, AND ARGUMENTATION, THROUGH MULTIMEDIA: A QUANTITATIVE STUDY OF STUDENT PERFORMANCE." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460722361.
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Kellen, Matthew. "Observing and evaluating creative mathematical reasoning through selected VITALmaths video clips and collaborative argumentation." Thesis, Rhodes University, 2017. http://hdl.handle.net/10962/6107.
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Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.
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Nordin, Anna-Karin. "Matematiska argument i helklassdiskussioner : En studie av elevers och lärares multimodala kommunikation i matematik i åk 3-5." Licentiate thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-136495.
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This study aimed at investigating and analysing the communication occurring during whole class discussions, with a specific focus on the nature of the mathematical arguments. The investigation was a qualitative case study where the communication during eight whole class discussions in grade 3-5 were analysed. Three types of arguments, wich are functional in the communication and convey different aspects of mathematics, were identified in the study. The types are (a) argument conveying a solution to a task/ a problem (b) argument conveying conceptual properties, and (c) argument conveying a mathematical relationship. The arguments types explain why an answer to a task is correct (type a), illuminate properties of a mathematical object (b), and clarify a mathematical relationship (c). The findings also reveal that arguments may be expressed through the use of a broad range of communicative resources, such as spoken language, written language, symbols, drawings, the use of manipulatives, and gestures. This highlights the importance of taking into account more than speech when construing arguments/reasoning communicated in mathematics classroom. The study also points to the importance of paying attention to arguments/reasoning that are created during other occasions than during task work or problem solving, and that arguments can enable the discerning of mathematical aspects for learners.
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Pugalee, David K. "Plenary Address: Language and Mathematics, A Model for Mathematics in the 21st Century." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79258.
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Sommerhoff, Daniel [Verfasser], and Stefan [Akademischer Betreuer] Ufer. "The individual cognitive resources underlying students' mathematical argumentation and proof skills : from theory to intervention / Daniel Sommerhoff ; Betreuer: Stefan Ufer." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1163949361/34.
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Nnanyereugo, Iwuanyanwu Paul. "An analysis of pre-service teachers' ability to use a dialogical argumentation instructional model to solve mathematical problems in physics." University of the Western Cape, 2017. http://hdl.handle.net/11394/6252.
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Philosophiae Doctor - PhD (Education)This study chronicles a teacher training education programme. The findings emerged from the observation of argumentation skills employed by students in a physical science education classroom for pre-service high school teachers. Their task was to use the nature of arguments to solve mathematical problems of mechanics in a physics classroom. Forty first-year students were examined on how they used a dialogical argumentation instructional model (DAIM) based on Toulmin's (1958/2003) Argument Pattern (TAP), Downing's (2007) Analytical Model (DAM) and Ogunniyi's (2007a & b) Contiguity Argumentation Theory (CAT) to solve mathematical problems in physics. Thus efforts to judge the pre-service teachers' capability to solve mathematical problems in physics with respect to mechanics were compounded by the demand for the inclusion of a self-efficacy framework. According to Bandura (2006) self-efficacy is the judgment of capability. Selfefficacy plays a key role in human functioning in that it affects not only people's behaviour but other issues such as goals and aspirations, outcome expectations, affective proclivities and perception of impediments and opportunities in the social environment (Bandura, 1995, 1997 & 2006).
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Sommerhoff, Daniel Verfasser], and Stefan [Akademischer Betreuer] [Ufer. "The individual cognitive resources underlying students' mathematical argumentation and proof skills : from theory to intervention / Daniel Sommerhoff ; Betreuer: Stefan Ufer." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://nbn-resolving.de/urn:nbn:de:bvb:19-226879.
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Goodman, Lynn. "Effects of a dialogical argumentation instructional model on science teachers’ understanding of capacitors in selected Western Cape schools." University of the Western Cape, 2015. http://hdl.handle.net/11394/5062.
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Magister Educationis - MEdThis study investigated 1) the conceptions on capacitors held by a group teachers in the Western Cape; 2) the effect of a dialogical argumentation instructional model on the teachers’ conceptions on the capacitor; and 3) the teachers’ perceptions on the implementation of this instructional model. The theoretical framework of the study was based on Toulmin’s Argumentation Pattern (TAP) and Ogunniyi’s Contiguity Argumentation Theory (CAT). The objective was to retrain science teachers in their awareness and understanding of the Nature of Science and Indigenous Knowledge Systems thereby enhancing their ability and efficacy in integrating science and Indigenous Knowledge Systems. The study involved workshop activities that included the teachers’ Reflective Diary, interview sessions, and video-taped lesson observations. The study adopted a Case Study approach and the data was analysed both quantitatively and qualitatively. The findings of the study showed that: 1) the teachers held varying conceptions of the capacitor; 2) the teachers’ conceptions of the capacitor improved after being exposed to the Dialogical Argumentation Instructional Model and 3) the teachers were dominantly in favour of the Dialogical Argumentation Instruction Model as a teaching method to be introduced at schools. The implications of the findings for school science and pedagogy were highlighted for closer observation.
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Larsson, Maria. "Orchestrating mathematical whole-class discussions in the problem-solving classroom : Theorizing challenges and support for teachers." Doctoral thesis, Mälardalens högskola, Utbildningsvetenskap och Matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-29409.
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Promising teaching approaches for developing students’ mathematical competencies include the approach of teaching mathematics through problem solving. Orchestrating a whole-class discussion of students’ ideas is an important aspect of teaching through problem solving. There is a wide consensus within the field that it is very challenging for the teacher to conduct class discussions that both build on student ideas and highlight key mathematical ideas and relationships. Further, fostering argumentation in the class, which is important for students’ participation, is also a grand challenge. Teachers need support in these challenges. The aim of the thesis is to characterize challenges and support for mathematics teachers in orchestrating productive problem-solving whole-class discussions that focus on both mathematical connection-making and argumentation. In particular, it is investigated how Stein et al.’s (2008) model with five practices – anticipating, monitoring, selecting, sequencing and connecting student solutions – can support teachers to handle the challenges and what constitutes the limitations of the research-based and widely-used model. This thesis builds on six papers. The papers are based on three intervention studies and on one study of a mathematics teacher proficient in conducting problem-solving class discussions. Video recordings of observed whole-class discussions as well as audio-recorded teacher interviews and teacher meetings constitute the data that are analyzed. It is concluded in the thesis that the five practices model supports teachers’ preparation before the lesson by the practice of anticipating. However, making detailed anticipations, which is shown to be both challenging and important to foster argumentation in the class, is not explicitly supported by the model. Further, the practice of monitoring supports teachers in using the variety of student solutions to highlight key mathematical ideas and connections. Challenging aspects not supported by the monitoring practice are, however, how to interact with students during their exploration to actually get a variety of different solutions as a basis for argumentation. The challenge of selecting and sequencing student solutions is supported for the purpose of connection-making, but not for the purpose of argumentation. Making mathematical connections can be facilitated by the last practice of connecting, with the help of the previous practices. However, support for distinguishing between different kinds of connections is lacking, as well as support for creating an argumentative classroom culture. Since it is a great challenge to promote argumentation among students, support is needed for this throughout the model. Lastly, despite the importance and challenge of launching a problem productively, it is not supported by the model. Based on the conclusions on challenges and support, developments to the five practices model are suggested. The thesis contributes to research on the theoretical development of tools that support teachers in the challenges of orchestrating productive problem-solving whole-class discussions.
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Pease, Alison. "A computational model of Lakatos-style reasoning." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/2113.
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Lakatos outlined a theory of mathematical discovery and justification, which suggests ways in which concepts, conjectures and proofs gradually evolve via interaction between mathematicians. Different mathematicians may have different interpretations of a conjecture, examples or counterexamples of it, and beliefs regarding its value or theoremhood. Through discussion, concepts are refined and conjectures and proofs modified. We hypothesise that: (i) it is possible to computationally represent Lakatos's theory, and (ii) it is useful to do so. In order to test our hypotheses we have developed a computational model of his theory. Our model is a multiagent dialogue system. Each agent has a copy of a pre-existing theory formation system, which can form concepts and make conjectures which empirically hold for the objects of interest supplied. Distributing the objects of interest between agents means that they form different theories, which they communicate to each other. Agents then find counterexamples and use methods identified by Lakatos to suggest modifications to conjectures, concept definitions and proofs. Our main aim is to provide a computational reading of Lakatos's theory, by interpreting it as a series of algorithms and implementing these algorithms as a computer program. This is the first systematic automated realisation of Lakatos's theory. We contribute to the computational philosophy of science by interpreting, clarifying and extending his theory. We also contribute by evaluating his theory, using our model to test hypotheses about it, and evaluating our extended computational theory on the basis of criteria proposed by several theorists. A further contribution is to automated theory formation and automated theorem proving. The process of refining conjectures, proofs and concept definitions requires a flexibility which is inherently useful in fields which handle ill-specified problems, such as theory formation. Similarly, the ability to automatically modify an open conjecture into one which can be proved, is a valuable contribution to automated theorem proving.
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Zulatto, Rúbia Barcelos Amaral. "A natureza da aprendizagem matemática em um ambiente online de formação continuada de professores /." Rio Claro : [s.n.], 2007. http://hdl.handle.net/11449/102133.
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Orientador: Miriam Godoy PenteadoBanca: João Pedro Mendes da Ponte
Banca: Marcelo de Carvalho Borba
Banca: Maria Elizabeth Bianconcini Trindade Morato Pinto de Almeida
Banca: Vani Moreira Kenski
Resumo: A presente pesquisa analisa a natureza da aprendizagem matemática em um curso online de formação continuada de professores, denominado Geometria com Geometricks. Nele, alunos-professores de uma mesma rede de escolas, situadas em diferentes localidades do país, desenvolveram atividades de Geometria utilizando-se do software Geometricks, e se encontravam para discuti-las. Esses encontros aconteceram a distância, em tempo real, por chat ou videoconferência. Nessa proposta pedagógica, a telepresença condicionou a comunicação e oportunizou o estar-junto-virtual-com-mídias. De modo singular, os recursos da videoconferência permitiram que construções geométricas fossem compartilhadas visualmente e realizadas por todos os envolvidos, fomentando a interação e a participação ativa, constituindo, por meio do diálogo, uma comunidade virtual de aprendizagem. Os resultados levam a inferir que, nesse contexto, a aprendizagem matemática teve natureza colaborativa, na virtualidade das discussões, tecidas a partir das contribuições de todos os participantes; coletiva, na medida em que a produção matemática era condicionada pelo coletivo pensante de seres-humanos-com-mídias; e argumentativa, uma vez que conjecturas e justificativas matemáticas se desenvolveram intensamente do decorrer do processo, contando para isso com as tecnologias presentes na interação ocorrida de forma constante e colaborativa.
Abstract: This study was conducted to analyze the nature of mathematical learning in an online continuing education course for teachers entitled Geometry with Geometricks. Teachers employed in a nation-wide network of privately-supported schools developed geometry activities using the software Geometricks and discussed them in virtual meetings, in real time, via chat or video-conference. In this pedagogical proposal, tele-presence conditioned the communication and provided the opportunity for virtual-togetherness-with-media. In a unique way, the resources of the videoconference made it possible for everyone to participate in and visually share geometrical constructions, encouraging interaction and active participation and constituting a virtual learning community through dialogue. The results indicate that, in this context, mathematical learning nature was characterized by: collaboration, in the virtual discussions that were woven from the contributions of all the participants; collectivity, to the degree to which mathematical production was conditioned by the humans-with-media thinking collective; and argumentation, as the development of mathematical conjectures and justifications was intense throughout the process, aided by the technologies that were present in the constant, collaborative interaction.
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Zulatto, Rúbia Barcelos Amaral [UNESP]. "A natureza da aprendizagem matemática em um ambiente online de formação continuada de professores." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/102133.
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A presente pesquisa analisa a natureza da aprendizagem matemática em um curso online de formação continuada de professores, denominado Geometria com Geometricks. Nele, alunos-professores de uma mesma rede de escolas, situadas em diferentes localidades do país, desenvolveram atividades de Geometria utilizando-se do software Geometricks, e se encontravam para discuti-las. Esses encontros aconteceram a distância, em tempo real, por chat ou videoconferência. Nessa proposta pedagógica, a telepresença condicionou a comunicação e oportunizou o estar-junto-virtual-com-mídias. De modo singular, os recursos da videoconferência permitiram que construções geométricas fossem compartilhadas visualmente e realizadas por todos os envolvidos, fomentando a interação e a participação ativa, constituindo, por meio do diálogo, uma comunidade virtual de aprendizagem. Os resultados levam a inferir que, nesse contexto, a aprendizagem matemática teve natureza colaborativa, na virtualidade das discussões, tecidas a partir das contribuições de todos os participantes; coletiva, na medida em que a produção matemática era condicionada pelo coletivo pensante de seres-humanos-com-mídias; e argumentativa, uma vez que conjecturas e justificativas matemáticas se desenvolveram intensamente do decorrer do processo, contando para isso com as tecnologias presentes na interação ocorrida de forma constante e colaborativa.
This study was conducted to analyze the nature of mathematical learning in an online continuing education course for teachers entitled Geometry with Geometricks. Teachers employed in a nation-wide network of privately-supported schools developed geometry activities using the software Geometricks and discussed them in virtual meetings, in real time, via chat or video-conference. In this pedagogical proposal, tele-presence conditioned the communication and provided the opportunity for virtual-togetherness-with-media. In a unique way, the resources of the videoconference made it possible for everyone to participate in and visually share geometrical constructions, encouraging interaction and active participation and constituting a virtual learning community through dialogue. The results indicate that, in this context, mathematical learning nature was characterized by: collaboration, in the virtual discussions that were woven from the contributions of all the participants; collectivity, to the degree to which mathematical production was conditioned by the humans-with-media thinking collective; and argumentation, as the development of mathematical conjectures and justifications was intense throughout the process, aided by the technologies that were present in the constant, collaborative interaction.
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Boudjani, Nadira. "Aide à la construction et l'évaluation des preuves mathématiques déductives par les systèmes d'argumentation." Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS060/document.
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L'apprentissage des preuves mathématiques déductives est fondamental dans l'enseignement des mathématiques. Pourtant, la dernière enquête TIMSS (Trends in International Mathematics and Science Study) menée par l'IEA ("International Association for the Evaluation of Educational Achievement") en mars 2015, le niveau général des étudiants en mathématiques est en baisse et les étudiants éprouvent de plus en plus de difficultés pour comprendre et écrire les preuves mathématiques déductives.Pour aborder ce problème, plusieurs travaux en didactique des mathématiques utilisent l’apprentissage collaboratif en classe.L'apprentissage collaboratif consiste à regrouper des étudiants pour travailler ensemble dans le but d'atteindre un objectif commun. Il repose sur le débat et l'argumentation. Les étudiants s'engagent dans des discussions pour exprimer leurs points de vue sous forme d'arguments et de contre-arguments dans le but de résoudre un problème posé.L’argumentation utilisée dans ces approches est basée sur des discussions informelles qui permettent aux étudiants d'exprimer publiquement leurs déclarations et de les justifier pour construire des preuves déductives. Ces travaux ont montré que l’argumentation est une méthode efficace pour l’apprentissage des preuves mathématiques : (i) elle améliore la pensée critique et les compétences métacognitives telles que l'auto-surveillance et l'auto-évaluation (ii) augmente la motivation des étudiants par les interactions sociales et (iii) favorise l'apprentissage entre les étudiants. Du point de vuedes enseignants, certaines difficultés surgissent avec ces approches pour l'évaluation des preuves déductives. En particulier, l'évaluation des résultats, qui comprend non seulement la preuve finale mais aussi les étapes intermédiaires, les discussions, les conflits qui peuvent exister entre les étudiants durant le débat. En effet, cette évaluation introduit une charge de travail importante pour les enseignants.Dans cette thèse, nous proposons un système pour la construction et l'évaluation des preuves mathématiques déductives. Ce système a un double objectif : (i) permettre aux étudiants de construire des preuves mathématiques déductives à partir un débat argumentatif structuré (ii) aider les enseignants à évaluer ces preuves et toutes les étapes intermédiaires afin d'identifier les erreurs et les lacunes et de fournir un retour constructif aux étudiants.Le système offre aux étudiants un cadre structuré pour débattre durant la construction de la preuve en utilisant les cadres d'argumentation proposés en intelligente artificielle. Ces cadres d’argumentation sont utilisés aussi dans l’analyse du débat qui servira pour représenter le résultat sous différentes formes afin de faciliter l’évaluation aux enseignants. Dans un second temps, nous avons implanté et validé le système par une étude expérimentale pour évaluer son acceptabilité dans la construction collaborative des preuves déductives par les étudiants et dans l’évaluation de ces preuves par les enseignantsLearning deductive proofs is fundamental for mathematics education. Yet, many students have difficulties to understand and write deductive mathematical proofs which has severe consequences for problem solving as highlighted by several studies. According to the recent study of TIMSS (Trends in International Mathematics and Science Study), the level of students in mathematics is falling. students have difficulties to understand mathematics and more precisely to build and structure mathematical proofs.To tackle this problem, several approaches in mathematical didactics have used a social approach in classrooms where students are engaged in a debate and use argumentation in order to build proofs.The term "argumentation" in this context refers to the use of informal discussions in classrooms to allow students to publicly express claims and justify them to build proofs for a given problem. The underlying hypotheses are that argumentation: (i) enhances critical thinking and meta-cognitive skills such as self monitoring and self assessment; (ii) increases student's motivation by social interactions; and (iii) allows learning among students. From instructors' point of view, some difficulties arise with these approaches for assessment. In fact, the evaluation of outcomes -- that includes not only the final proof but also all intermediary steps and aborted attempts -- introduces an important work overhead.In this thesis, we propose a system for constructing and evaluating deductive mathematical proofs. The system has a twofold objective: (i) allow students to build deductive mathematical proofs using structured argumentative debate; (ii) help the instructors to evaluate these proofs and assess all intermediary steps in order to identify misconceptions and provide a constructive feedback to students. The system provides students with a structured framework to debate during construction of proofs using the proposed argumentation frameworks in artificial intelligence. These argumentation frameworks are also used in the analysis of the debate which will be used to represent the result in different forms in order to facilitate the evaluation to the instructors. The system has been implemented and evaluated experimentally by students in the construction of deductive proofs and instructors in the evaluation of these proofs
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Manrique, Ortega Ana María. "Trabajo en pareja y construcción de conocimiento matemático en un aula de matemáticas de sexto de primaria." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/285461.
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El treball de tesis doctoral Treball en parella i construcció de coneixement matemàtic a l’aula de matemàtiques de sisè de primària constitueix una aportació a la investigació en Educació Matemàtica emmarcada en les teories socio-cognitives sobre la construcció de coneixement matemàtic. Per a l’anàlisi de processos de construcció compartida de coneixement matemàtic a l’aula de primària, considerem usos de la fracció, estructures dels arguments i tipus d’interacció en discussions en parella.
La pregunta de recerca és: Com influeix la resolució en parella de problemes contextualitzats en la construcció del concepte de fracció en una aula de primària? Per respondre a aquesta qüestió, plantegem tres objectius consecutius de caracterització de: 1) les produccions escrites individuals inicials dels alumnes en la resolució de problemes; 2) la posterior interacció oral i escrita en parella; i 3) les produccions escrites individuals de revisió. Dissenyem una situació d'investigació en una classe de primària d'un centre de la província de Barcelona amb alumnat de 11 i 12 anys.
El marc teòric s'organitza mitjançant tres eixos. En primer lloc, l'eix conceptual tracta el concepte de fracció des de la perspectiva dels seus usos. En segon lloc, l'eix estructural tracta l'argumentació a la classe de matemàtiques com un component essencial de la comunicació i com a eina del procés d'organització del raonament. Finalment, l'eix interaccional tracta els processos d'interacció que tenen lloc en situacions escolars d'ensenyament i aprenentatge de les matemàtiques.
D'acord amb la pregunta, els objectius i els eixos teòrics, proposem el disseny i els mètodes d'anàlisi. Elaborem una seqüència de tasques aritmètiques de repartiment sense incloure els significats de mesura i operador de la fracció, pensada per ser gestionades en un ambient de resolució de problemes en parella. En la implementació considerem una dinàmica basada en treball individual seguit de discussió en parella i la seva posterior reconstrucció de nou individual. Les dades són escrites i orals, relatives als moments de resolució individual i en parella.
Creem quatre instruments per a l'estudi combinat dels diferents eixos. Per a cada eix, definim codis que permeten reduir la informació oral i escrita més rellevant. Els instruments d'anàlisi constitueixen una aportació original de la investigació. L'aplicació dels instruments porta a caracteritzar les produccions escrites inicials i de revisió dels alumnes, així com les produccions orals en parella, atenent a la coordinació dels eixos conceptual, estructural i interaccional.
De l'estudi es desprèn que la interacció alumne-alumne afavoreix la construcció del concepte de fracció durant la resolució de problemes aritmètics de repartiment. La implementació de la seqüència de problemes ha generat progressos en el coneixement matemàtic. Establim una connexió entre l'argumentació matemàtica i els processos d'interacció. També vam detectar situacions sense millora o retrocés en la construcció compartida de coneixement ni en l'elaboració d'argumentació col·lectiva.
Hi ha avenços en la construcció de coneixement matemàtic quan els alumnes resolen situacions que impliquen la identificació de la fracció com a part-tot en context continu, la identificació de la fracció com a part-tot en context discret i la identificació de la fracció com a quocient. No hi ha avenços en la construcció de coneixement matemàtic quan els alumnes resolen situacions que impliquen la identificació de la fracció com a part-tot en context discret, com a quocient quan no es reparteixen totes les unitats disponibles i en la identificació de la fracció com a raó. En aquests significats de la fracció, les reconstruccions no milloren i fins i tot apareixen canvis en respostes que reflecteixen retrocessos matemàtics i argumentatius.
Quant a l'activitat argumentativa, els alumnes avancen en la reconstrucció dels seus arguments quan desestimen desajustos per donar garanties o suports, o quan amplien explicacions o justificacions elaborades, millorant l'ús del llenguatge i connexions. Aquestes millores poden ser degudes a la influència del context en la resolució, al domini del significat de la fracció, o bé al paper de l'alumne en la resolució en parella i en l'elaboració de respostes.
Finalment, concloem sobre la rellevància de les interaccions atenent al paper dels alumnes en elles. De vegades, es donen interaccions satisfactòries en termes d'argumentació col·lectiva i de construcció de coneixement matemàtic, on un dels alumnes s'imposa sense discussió els seus arguments. Així, l'elaboració d'aclariments, imposicions, revisions i ampliacions emergeixen d'aquestes actuacions, provocant o no, avenços matemàtics. Hem detectat abundants interaccions en parella orientades al desenvolupament d'argumentació col·lectiva i consens de significats. Es donen intervencions i intercanvis que mostren que, en el procés de resolució en parella, predominen acords, ampliacions i síntesi. Observem a més que alumnes involucrats en una discussió produeixen desacords que permeten avançar, de manera conjunta, en continguts matemàtics o en argumentacions.The doctoral work Pair work and construction of mathematical knowledge in the grade 6 mathematics classroom constitutes a progress in mathematics education research under the tradition of socio-cognitive approaches about the construction of mathematical knowledge. For the analysis of processes of shared construction of mathematical knowledge in a primary school classroom, we consider the uses of fractions, the structures of arguments and the discussions in pairs. The research question is: How does the resolution in pairs of contextualized problems influence on the construction of the fraction concept in a primary school class? To answer this question we take three consecutive goals aimed at characterizing: 1) the initial individual written productions of the students’ solutions to the problems; 2) the follow-up oral and written interactions among students; and 3) the revised individual written productions. We desing a scientific situation with 11-and-12-year-old students in a class of Barcelona province. The theoretical framework is organized around three axes. First, the conceptual axis deals with is the concept of fraction from the perspective of its uses. Second, the structural axis deals with argumentation in the mathematics classroom as an essential component of communication and as a tool of the process of organizing reasoning. Finally, the interactional axis deals with the interaction processes that take place in school settings of teaching and learning mathematics. According to the question, the goals and theoretical axes, we propose the experimental design and methods of analysis. We create a sequence of arithmetic problems on distribution excluding the meanings of measurement and operator for fraction, planned to be orquestrated in a problem-solving environment with pair work. For the implementation, we consider a lesson dynamics with individual work followed by pair discussion and subsequent individual reconstructions. Our data set is written and oral, in relation to the moments for individual and pair resolution. We create four analytical tools for the combined study of the different axes. For each axis, we define codes that lead to reduce oral and written relevant data. The analytical tools are themselves an original contribution of the research. Through the application of the tools we characterize the initial and revised individual written productions of the students and their oral productions in pairs. The coordination of the conceptual, structural and interactional axes is key to this stage of the study. It can be inferred from the analysis that student-student interaction facilitates the construction of the concept of fraction during the resolution of arithmetic problems of distribution. The implementation of the sequence of problems has been proved to generate progress in the students’ mathematical knowledge. We establish a connection between the mathematical argumentation and the interaction processes. Also, we detect situations without either improvement or regression in the shared construction of knowledge and the development of collective argumentation. There are progresses in the construction of mathematical knowledge when the students solve situations involving identification of the fraction as part-whole in a continuous context, the identification of the fraction as part-whole in a discrete context, and the identification of the fraction as quotient. Nevertheless, there is no progress detected in the construction of mathematical knowledge when the students solve situations involving the identification of the fraction as part-whole in a discrete context, as quotient when all available units are not distributed, and as ratio. Under these meanings of the fraction, the reconstructions do not improve and may reflect changes in responses that point to mathematical and argumentative misunderstandings. As for the argumentative activity, students progress in the reconstruction of their arguments when rejecting mismatches to provide guarantees or endorsements, or when extending explanations or justifications, while improving the use of language and connections. These improvements may be due to the influence of the context in the resolution, the domain of the meaning of the fraction, or the role of the student in pair work during the resolution and the elaboration of responses. Finally, we conclude on the relevance of interactions by paying attention to the roles of the students. Sometimes satisfying interactions are reached in terms of collective reasoning and mathematical knowledge construction, where one of the students imposes without discussion her/his arguments. Thus, the development of clarification, enforcement, revision and expansion emerge from these actions, causing or not, mathematical advances. We have detected many pair work interactions oriented toward collective argumentation and meaning consensus. Various interventions and exchanges show that in pair work resolutions agreements, extensions and synthesis are dominant. We further note that students involved in a discussion, tend to produce disagreements that have the effect to facilitate joint progress in mathematical contents or in argumentations.
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Willard, Catherine. "Effects of Collaborative Reasoning on Students' Mathematics Performance and Numerical Reasoning Abilities." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/328799.
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Math & Science EducationPh.D.
Current reform efforts, which aim to improve the mathematics abilities of American citizens, call for mathematics instruction that emphasizes sense making, reasoning and argumentation. This study was conducted to understand the outcomes of Collaborative Reasoning, a reform-oriented instructional strategy, in seventh and eighth grade mathematics classrooms. An embedded, quasi-experimental, mixed-methods design was used to investigate: the effects of Collaborative Reasoning on students' mathematics performance, and the ways in which students' reasoning abilities change as a result of participating in Collaborative Reasoning. The quantitative results revealed statistically significant changes in mathematics performance from pre-test to post-test. Post-test analysis showed a statistically significant difference in assessment scores, with the treatment group out-performing their comparison group peers. The qualitative results of the study show that as a result of participating in Collaborative Reasoning sessions, students were choosing reasoning strategies that were more appropriate, were using appropriate reasoning strategies more consistently, and were better able to verbally explain their reasoning. Finally, it was found that as students participate in Collaborative Reasoning their discourse becomes less calculational and more conceptual in nature, and more students become active participants within small group discussions.
Temple University--Theses
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Santos, Jonas Borsetti Silva. "Argumantação e prova: análise de argumentos algébricos de alunos da educação básica." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11491.
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Secretaria da Educação do Estado de São Paulo
The present work focuses questions presented in the questionnaire of Algebra of the AProvaME project (Argumentation and Proof in the School Mathematics), of the PUC-SP. One of the goals of the project is to raise a map on the conceptions of argument and proof of the Brazilian pupils, more necessarily of the pupils of the State of São Paulo. Two questionnaires, one of Algebra and one of Geometry, had been elaborated for this survey, applied for a composed sample of 1998 pupils in the band of 14 the 16 years, registered in 8th series of Basic School and 1° year of Average School. After descriptive analysis of the collected data, we could verify that the creation of argumentation and proof for the pupils is defective, since many of them had never seen any type of argumentation or proof in its school life. Made the descriptive analysis, we carry through a multidimensional analysis, with the aid of the software C.H.I.C. that also assisted us in the choice of the pupils who would be interviewed. Still, for one better analysis, we carry through interviews with some teachers, concerning the questions that are object of our study, as also on the use of argumentations and proofs in classroom. The same ones are little used in their classes. In general, our analyses, in such a way quantitative how much qualitative, they suggest that the processes of argumentation and proofs are not being contemplated with these pupils. The pupils who had answered to the questions had presented, in the majority of the times, empirical arguments. The ones that had tried to evidence some property or some structure for the argumentations and proofs had used many times the narrative form. Moreover, the use of the algebraic language is little spread out in the schools, fact evidenced for the arguments presented for the pupils
O presente trabalho trata de questões apresentadas no questionário de álgebra do projeto AprovaME (Argumentação e Prova na Matemática Escolar), da PUC-SP. Uma das metas do projeto é levantar um mapa sobre as concepções de argumentação e prova dos alunos brasileiros, mais precisamente dos alunos do Estado de São Paulo. Foram elaborados dois questionários, um de Álgebra e um de Geometria para esse levantamento, aplicados para uma amostra composta de 1998 alunos na faixa de 14 a 16 anos, matriculados na 8ª série do Ensino Fundamental e 1º ano do Ensino Médio. Após a análise descritiva dos dados coletados, pudemos verificar que a criação de argumentação e prova pelos alunos é falho, visto que muitos deles sequer viram qualquer tipo de argumentação ou prova em sua vida estudantil. Feita a análise descritiva, realizamos uma análise multidimensional, com o auxílio do software C.H.I.C. que também nos auxiliou na escolha dos alunos que seriam entrevistados. Ainda, para uma melhor análise, realizamos entrevistas com alguns professores acerca das questões que são objeto de nosso estudo, como também sobre o uso de argumentações e provas em sala de aula. Os mesmos valem-se muito pouco desse recurso. Em geral, nossas análises, tanto quantitativas quanto qualitativas, sugerem que os processos de argumentação e provas não estão sendo contemplados com esses alunos. Os alunos que responderam às questões apresentaram, na maioria das vezes, argumentos empíricos. Os que tentaram evidenciar alguma propriedade ou alguma estrutura para a argumentação e prova valeram-se muitas vezes da língua materna. Além disso, o uso da linguagem algébrica é pouco difundida nas escolas, fato evidenciado pelas argumentações apresentadas pelos alunos
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Persson, Helén. "Matematikdidaktiska val En argumentationsanalys av det lustfyllda lärandet Mathematics education choice An argumentation analysis of a zestful learning." Thesis, Malmö högskola, Fakulteten för lärande och samhälle (LS), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-35502.
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The purpose of this study is to present arguments concerning a zestful learning for children ages 6-9 in mathematics. Four books in mathematics has specifically been analyzed to investigate what is written concerning a zestful learning. By means of an argumentation analysis within a qualitative text analysis the arguments are put forth. The didactic choices of the chosen literature are analyzed in a subject-matter didactic context. The result implicates a multitude of arguments and didactic choices supporting a zestful learning. The most prominent one is that teaching should presuppose the every-day life of the students, be varied concerning both education and environment and promote communication. Education should relate to joint experiences and clarify the already gained knowledge in math’s of the students, thus enhancing the students’ self-esteem within mathematical contexts: in addition, if students experience the usability of math’s and are given the opportunity to apply their body and senses in gaining this knowledge this is beneficial for zestful learning. To feel a desire to learn engages the students and motivates them to learn. As a conclusion there are many opportunities in creating zestful learning possibilities, prior research shows the importance of making the experience of learning enjoyable to promote a lifelong lust to learn, which is one of the assignments of school according to Läroplan för grundskolan, förskoleklass och fritidshemmet 2011 (Skolverket 2011).
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Moran, Renee Rice. "Applying Argumentation in the Middle School and High School ELA Classroom." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etsu-works/3624.
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Eduardo, Antonio Carlos. "Contextos para argumentar: uma abordagem para iniciacao a prova no EM utilizando P.A." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11253.
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Previous issue date: 2007-10-15Secretaria da Educação do Estado de São Paulo
This research invests in the conception of learning environments aimed to contribute to the creation of a culture of argumentation, proving and proof in mathematics classrooms. It developed within the context of the project AProvaME as part of the exploration of how to initiate students into aspects of the proving process in relation to the topic of Arithmetic Progressions. In designing this learning environment, we sought contributions from the studies of Bordenave from the areas of the Communication Science and in the field of Mathematics Education, from research relatied to argumentation and in particular the work of Bolite Frant and Castro and of Maher. These contributions enabled the elaboration of an interactive environment for the mediation of mathematical ideas. One of the roles of mediation within the study focuses, in the light of Communication, on the action of the teacher during the negotiation of the mathematics presented in the classroom. Aspects related to socialisation, interaction and mediation were inspired by the constructionist proposal of Papert and other constructionist thinkers. On the basis of these studies, an approach was adopted to the use of technology involving the conception of visual objects embedded within activities aiming to support the development of certain habits of mathematical thinking delineated by Goldenberg. This qualitative study made use of didactic resources such as as the dynamic of games and the use of the computer to promote interaction and the emergence of scenarios for medication. The instruments used in the collection of data Blogs and video recordings valorised the interpretation of the dialogs which occurred within these scenarios. The use of Blogs, still not well documented in research in Mathematics Education, served to show the evolution of mathematical fluency in the arguments produced by the students and also acted as a parameter on the practice of the educator. Editing of the videos collected, permitted the formatting of fragments of registers from the dialogs in the form of cartoon strips, which came to represent a product with a wide range of possible uses both in the interpretation of dialogs and in reflections about the role of the teacher. The results obtained in this study led to recommendations for the creation of new contexts for argumentation
Esta pesquisa investe na proposição de ambiente de aprendizagem como possibilidade de criar uma cultura na sala de aula que promova / favoreça a argumentação. No transcorrer do projeto APROVAME1 surgiu a opção em explorar tópicos do conceito Progressão Aritmética para auxiliar no desenvolvimento de processos de iniciação à prova. Na implementação deste ambiente de aprendizagem buscamos contribuições advindas dos estudos de Ciência da Comunicação através de Bordenave, da Educação Matemática pelos estudos de alguns pesquisadores voltados à argumentação, dentre os quais: Bolite Frant e Castro, e estudos sobre desenvolvimento de provas de Maher. Estas contribuições possibilitaram a elaboração de um ambiente interativo e propício à prática da mediação. Um dos papéis de mediação exercido durante este estudo é apresentado à luz da Comunicação, focando na ação do professor durante a negociação matemática que se apresenta em sala de aula. Corroboram para estes aspectos socializáveis do ambiente, interação e mediação, a proposta construcionista de Papert, valorizada pela contribuição de outros estudiosos do construcionismo. Através desses estudos, um dos usos da tecnologia nesta pesquisa volta-se à elaboração de objetos visuais e possibilita o design das atividades sob a ótica do desenvolvimento de alguns hábitos de pensamento matemáticos, segundo Goldenberg. Este estudo qualitativo, emprega recursos didáticos como a dinâmica do jogo e o uso do computador, para promover a interação e o surgimento de cenários de mediação. Os instrumentos de coleta de dados vídeo e blog valorizam a interpretação dos diálogos surgidos nesses cenários. O uso do blog, ainda pouco difundido entre pesquisas da Educação Matemática, serve para mostrar a evolução da fluência matemática na argumentação dos alunos, e também atua como parâmetro da prática do educador. A edição do vídeo permitiu a formatação dos registros de fragmentos dos diálogos na forma de quadrinhos, o que veio a se constituir num produto com amplas possibilidades de uso, tanto no tocante à interpretação dos diálogos, quanto na reflexão sobre a postura do educador. Os resultados obtidos por este estudo recomendam a criação de novos Contextos para Argumentar
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Chen, Ying-Chih. "Examining the integration of talk and writing for student knowledge construction through argumentation." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1129.
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The purpose of this study was to examine students' understanding of argumentation when talk and writing were provided as learning tools, as well as to explore how talk and writing can best support students' construction of scientific knowledge. Most current studies have examined discourse patterns over a short interval of only a few class periods or compared only the students' initial and final products to assess the quality of their argument structure. Few studies have examined how students develop their understanding of argumentation over time and how their understanding might result in overcoming those challenges. Moreover, talk and writing have been offered as two critical learning tools to support students' argumentative practice. So far, few studies have explored how those two learning tools could be combined to better support students in constructing scientific knowledge. The research questions that guided this study were: (1) How do students develop an understanding of the components of argumentation for public negotiations over time when participating in an argument-based inquiry classroom? (2) In what ways do talk and writing support scientific knowledge construction in an argument-based inquiry classroom?
This sixteen-week study was grounded in interactive constructivism and utilized qualitative design to identify students' understanding of argumentation, trace their learning trajectories, examine potential use of the combination of talk and writing, and analyze the cognitive processes involved when talk and writing were used as learning tools. Due to the lack of studies that focus on the elementary level, this study was conducted in a fifth-grade classroom that used the Science Writing Heuristic (SWH) approach with 22 students participating. Six students were selected for interviewing intensively. Multiple sources of data were collected, including classroom observations, semi-structured interviews, students' writing samples, and the researcher's field notes. To strengthen the interpretations, data analysis was conducted using three different approaches: (1) the constant comparative method, (2) the enumerative approach, and (3) in-depth analysis of knowledge construction trajectory (KCT) episodes.
The results showed that as fifth-grade students had more opportunities to practice, they could develop a more sophisticated understanding of argumentation, use talk and writing as learning tools to negotiate their ideas with peers, engage in more complex cognitive processes, and take ownership for their learning in science. Three major findings are discussed: (1) increased understanding of argumentative components in public negotiations, (2) increased ability to craft written arguments, and (3) five patterns in the use of talk and writing for knowledge construction and cognitive processes.
The findings have informed theories about argumentative practice, the use of language as a learning tool, and science learning from six aspects: (1) understanding of argumentation, (2) ability to craft written arguments, (3) use of talk and writing, (4) cognitive processes, (5) meaning of negotiation, and (6) methodology consideration. This study provides insights into the design of an argument-based environment in which students can develop successful argumentative practices. A long-term professional development program in the support of teachers implementing argument-based inquiry is suggested.
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Wessels, Helena. "Using a modelling task to Elicit Reasoning about data." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-83189.
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Taneja, Anju. "Argumentation in Science Class| Its Planning, Practice, and Effect on Student Motivation." Thesis, Walden University, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10133198.
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Studies have shown an association between argumentative discourse in science class, better understanding of science concepts, and improved academic performance. However, there is lack of research on how argumentation can increase student motivation. This mixed methods concurrent nested study uses Bandura’s construct of motivation and concepts of argumentation and formative feedback to understand how teachers orchestrate argumentation in science class and how it affects motivation. Qualitative data was collected through interviews of 4 grade-9 science teachers and through observing teacher-directed classroom discourse. Classroom observations allowed the researcher to record the rhythm of discourse by characterizing teacher and student speech as teacher presentation (TP), teacher guided authoritative discussion (AD), teacher guided dialogic discussion (DD), and student initiation (SI). The Student Motivation Towards Science Learning survey was administered to 67 students before and after a class in which argumentation was used. Analysis of interviews showed teachers collaborated to plan argumentation. Analysis of discourse identified the characteristics of argumentation and provided evidence of students’ engagement in argumentation in a range of contexts. Student motivation scores were tested using Wilcoxon signed rank tests and Mann-Whitney U-tests, which showed no significant change. However, one construct of motivation—active learning strategy—significantly increased. Quantitative findings also indicate that teachers’ use of multiple methods in teaching science can affect various constructs of students’ motivation. This study promotes social change by providing teachers with insight about how to engage all students in argumentation.
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Ohman, Jonny. "Ett annorlunda matematikprov : – med fokus på textförklaring, stilpoäng samt grupparbete." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-615.
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Matematikundervisning kan se ut på en mängd olika sätt. Strävandemålen i Läroplanerna beskriver att läraren skall sträva efter att eleverna både skriftligt och muntligt bör redovisa och argumentera för sina lösningar samt lära sig hantera olika matematiska hjälpmedel. Tanken är att läraren skall planera för en undervisningsform som innehåller dessa strävandemål.
Utifrån ovanstående har jag gjort en kvalitativ studie med hjälp av ett laborativt grupprov. Studien bygger på att undersöka om man med hjälp av prov kan stärka elevernas motivation där de tränar sig i att få en bra lösningsstrategi genom att ge dem poäng för detta. Provet bygger på att eleverna arbetar två och två där de i text ska redovisa och argumentera för sina uträkningar.
Min samlade bild av elevernas förmåga att strukturera uppgifterna på ett bra och tydligt sätt samt i text förklara hur de löst uppgifterna blev inte riktigt vad jag väntat mig. Över lag tror jag att eleverna har för lite rutin kring detta. Dock fick jag en del positiva reaktioner från eleverna kring detta arbetssätt och att det är något de vill ha mer av.
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Pedemonte, Bettina. "Etude didactique et cognitive des rapports de l'argumentation et de la démonstration dans l'apprentissage des mathématiques." Université Joseph Fourier (Grenoble), 2002. http://tel.archives-ouvertes.fr/tel-00004579.
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Ce travail présente une analyse cognitive sur les rapports entre argumentation et démonstration. L'hypothèse de départ est que la recherche en didactique sur la démonstration a besoin, pour progresser, de comprendre la nature et la complexité de cette notion en la replaçant dans le référentiel de l'activité rationnelle de l'élève : comment il décide, fait des choix, valide. Nous commençons par proposer une caractérisation de l'argumentation et de la démonstration en mathématiques. Les théories linguistiques contemporaines nous permettent d'avancer l'hypothèse que la démonstration est une argumentation particulière et nous a conduite à proposer le modèle de Toulmin comme outil méthodologique pour leur comparaison. Cette comparaison est faite selon deux points de vue : la structure, et le système de référence. D'une part, une analyse structurelle de l'argumentation et de la démonstration permet de rendre compte de certaines continuités ou écarts nécessaires pour passer d'une argumentation à une démonstration (d'une argumentation abductive à une démonstration déductive, d'une argumentation inductive à une démonstration par récurrence, etc. ). D'autre part, il est possible, au moyen de ce modèle, de prendre en compte les énoncés mobilisés par les élèves pendant l'argumentation pour les comparer avec les théorèmes utilisés pendant la démonstration. La continuité ou l'écart du système de référence, conception ou théorie, s'appuie sur cette comparaison. Nous avons mis en place un dispositif expérimental afin de montrer comment analyser les productions des élèves avec le modèle de Toulmin, et afin d'éclairer et de comprendre les rapports cognitifs entre argumentation et démonstration. Nous avons proposé trois problèmes de géométrie demandant la construction d'une démonstration. Les résultats obtenus permettent de proposer une analyse cognitive de l'argumentation et de la démonstration à partir de l'analyse structurelle et celle du système de référenceThe purpose of this research is to analyze some aspects of the relationships between argumentation and proof. Our assumption is that a didactical research on the learning of proof needs to understand the nature and the complexity of the notions of argumentation and proof in the referential of the student rational activity: how he decides, he chooses and he proves. At the beginning, we characterize argumentation and proof in mathematics. On the base of the contemporary linguistics theory, we put forward the hypothesis that proof is a particular mathematical argumentation and we propose Toulmin's model as a methodological tool to compare them. Argumentation and proof can be compared from two points of view: structure and referential system. First, besides clear cases of continuity, our structural analysis highlights the distance distances between the argumentation supporting the conjecture and its proof (from an abductive argumentation to a deductive proof, from a inductive argumentation to a deductive proof and so on). Then it is possible, by means of Toulmin's model, to compare the statements mobilized by student during the argumentation with the theorems used in the proof. This comparison constitutes the basis of the analysis concerning the continuity or the distance between conceptions and theory in the referential system. An experimental design was carried out. We proposed three geometric problems requiring the production of conjectures and the related proofs. The students' productions were analysed according to Toulmin's model in order to highlight and to understand the cognitive relation between argumentation and proof. Our results show the potentialities of our cognitive analysis in order to interpret and foresee students' difficulties related to the passage from argumentation to proof
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Diaz, Juan Francisco Jr. "Examining student-generated questions in an elementary science classroom." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/946.
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This study was conducted to better understand how teachers use an argument-based inquiry technique known as the Science Writing Heuristic (SWH) approach to address issues on teaching, learning, negotiation, argumentation, and elaboration in an elementary science classroom. Within the SWH framework, this study traced the progress of promoting argumentation and negotiation (which led to student-generated questions) during a discussion in an elementary science classroom. Speech patterns during various classroom scenarios were analyzed to understand how teacher-student interactions influence learning.
This study uses a mixture of qualitative and quantitative methods. The qualitative aspect of the study is an analysis of teacher-student interactions in the classroom using video recordings. The quantitative aspect uses descriptive statistics, tables, and plots to analyze the data. The subjects in this study were fifth grade students and teachers from an elementary school in the Midwest, during the academic years 2007/2008 and 2008/2009. The three teachers selected for this study teach at the same Midwestern elementary school. These teachers were purposely selected because they were using the SWH approach during the two years of the study.
The results of this study suggest that all three teachers moved from using teacher-generated questions to student-generated questions as they became more familiar with the SWH approach. In addition, all three promoted the use of the components of arguments in their dialogs and discussions and encouraged students to elaborate, challenge, and rebut each other's ideas in a non-threatening environment. This research suggests that even young students, when actively participating in class discussions, are capable of connecting their claims and evidence and generating questions of a higher-order cognitive level. These findings demand the implementation of more professional development programs and the improvement in teacher education to help teachers confidently implement argumentative practices and develop pedagogical strategies to help students use them.
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Pinzino, Dean William. "Socioscientific Issues: A Path Towards Advanced ScientificLiteracy and Improved Conceptual Understanding of Socially Controversial Scientific Theories." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4387.
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This thesis investigates the use of socioscientific issues (SSI) in the high school science classroom as an introduction to argumentation and socioscientific reasoning, with the goal of improving students' scientific literacy (SL). Current research is reviewed that supports the likelihood of students developing a greater conceptual understanding of scientific theories as well as a deeper understanding of the nature of science (NOS), through participation in informal and formal forms of argumentation in the context of SSI. Significant gains in such understanding may improve a student's ability to recognize the rigor, legitimacy, and veracity of scientific claims and better discern science from pseudoscience. Furthermore, students that participate in significant SSI instruction by negotiating a range of science-related social issues can make significant gains in content knowledge and develop the life-long skills of argumentation and evidence-based reasoning, goals not possible in traditional lecture-based science instruction. SSI-based instruction may therefore help students become responsible citizens. This synthesis also suggests that that the improvements in science literacy and NOS understanding that develop from sustained engagement in SSI-based instruction will better prepare students to examine and scrutinize socially controversial scientific theories (i.e., evolution, global warming, and the Big Bang).
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Yarker, Morgan Brown. "Teacher Challenges, Perceptions, and Use of Science Models in Middle School Classrooms about Climate, Weather, and Energy Concepts." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4929.
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Research suggests that scientific models and modeling should be topics covered in K-12 classrooms as part of a comprehensive science curriculum. It is especially important when talking about topics in weather and climate, where computer and forecast models are the center of attention. There are several approaches to model based inquiry, but it can be argued, theoretically, that science models can be effectively implemented into any approach to inquiry if they are utilized appropriately. Yet, it remains to be explored how science models are actually implemented in classrooms. This study qualitatively looks at three middle school science teachers' use of science models with various approaches to inquiry during their weather and climate units. Results indicate that the teacher who used the most elements of inquiry used models in a way that aligned best with the theoretical framework than the teachers who used fewer elements of inquiry. The theoretical framework compares an approach to argument-based inquiry to model-based inquiry, which argues that the approaches are essentially identical, so teachers who use inquiry should be able to apply model-based inquiry using the same approach. However, none of the teachers in this study had a complete understanding of the role models play in authentic science inquiry, therefore students were not explicitly exposed to the ideas that models can be used to make predictions about, and are representations of, a natural phenomenon. Rather, models were explicitly used to explain concepts to students or have students explain concepts to the teacher or to each other. Additionally, models were used as a focal point for conversation between students, usually as they were creating, modifying, or using models. Teachers were not observed asking students to evaluate models. Since science models are an important aspect of understanding science, it is important that teachers not only know how to implement models into an inquiry environment, but also understand the characteristics of science models so that they can explicitly teach the concept of modeling to students. This study suggests that better pre-service and in-service teacher education is needed to prepare students to teach about science models effectively.
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Carmo, Alex Bellucco do. "Argumentação matemática em aulas investigativas de física." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-12052015-135710/.
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No trabalho a seguir buscamos compreender o papel da matemática na construção dos argumentos dos estudantes em atividades de ensino investigativas. Para o encaminhamento dessa pesquisa, realizamos uma revisão sobre argumentação e argumentação matemática com o intuito de obter elementos para a construção de um instrumento de análise de situações de ensino e aprendizagem. A partir desse estudo emergiu também a necessidade da consideração das diferentes linguagens usadas na comunicação e de observar a qualidade do processo argumentativo em termos de sua forma e conteúdo. Com a estruturação desse quadro teórico, elaboramos uma sequência de ensino investigativa (SEI) sobre quantidade de movimento, sua conservação e as leis de Newton, que agrupa as características encontradas, tal como a abdução, isto é, o uso de uma regra ou lei como hipótese que auxilia na explicação de um fato novo. Para alcançar nossos objetivos, analisamos a gravação em vídeo da aplicação dessa sequência em uma turma do primeiro ano do ensino médio, de uma escola pública do estado de Santa Catarina, com o auxílio do software Videograph, que facilita visualizar a ocorrência das categorias propostas em um gráfico temporal. Verificamos a intensa frequência das propriedades da argumentação destacadas, com um grande movimento das diferentes linguagens na construção dos significados, em especial a algébrica no processo de estimativas. Por outro lado, ficou explícita a desconexão entre fenômenos e suas representações, à medida que os estudantes se distanciaram do problema experimental do início da SEI e se envolveram no processo de resolução de problemas isso demanda o planejamento de atividades específicas para estimular a reflexão sobre essas situações.In the following work we seek to understand the role of mathematics in the construction of the arguments of students in inquiry teaching activities. For forwarding this research, we conducted a review about argumentation and mathematical argumentation with the purpose to provide elements for the construction of an analytical tool for teaching and learning situations. From this study also emerged the need for consideration of the different languages used for communication and observe the quality of the argumentative process in terms of its form and content. With the structuration of this theoretical framework, we developed an Inquiry-Based Teaching Sequence (IBTS) about momentum, its conservation and Newton\'s laws, which brings together the features found, such as abduction, i.e. the use of a rule or law as hypothesis that helps to explain a new fact. To achieve our goals, we analyze the video recording of the application of this sequence in a first year high school class in a public school in the state of Santa Catarina, with the help of Videograph software that makes easy to observe the occurrence of the categories proposed in a temporal graph. We verified the intense frequency of the argument properties highlighted, with a large movement of the different languages in the construction of the meanings, especially the algebraic one on the estimation process. On the other hand, was explicit the disconnection between phenomena and their representations, as students distanced themselves from the experimental problem of the beginning of IBTS and became involved in the problem-solving process - that demand the planning of specific activities to stimulate reflection about these situations.
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Benus, Matthew J. "The teacher's role in the establishment of whole-class dialogue in a fifth grade science classroom using argument-based inquiry." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/2673.
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The purpose of this study was to examine the patterns of dialogue that were established and emerged in one experienced fifth-grade science teacher's classroom that used the argument-based inquiry (ABI) and the ways in which these patterns of dialogue and consensus-making were used toward the establishment of a grasp of science practice. Most current studies on ABI agree that it does not come naturally and is only acquired through practice. Additionally, the quality of dialogue is also understood to be an important link in support of student learning. Few studies have examined the ways in which a teacher develops whole-class dialogue over time and the ways in which patterns of dialogue shift over time. The research questions that guided this study were: (1) What were the initial whole-class dialogue patterns established by a fifth-grade science teacher who engaged in ABI? (2) How did the science teacher help to refine whole-class dialogue to support the agreeability of ideas constructed over time?
This eighteen week study that took place in a small city of less than 15,000 in Midwestern United States was grounded in interactive constructivism, and utilized a qualitative design method to identify the ways in which an experienced fifth-grade science teacher developed whole-class dialogue and used consensus-making activities to develop the practice of ABI with his students. The teacher in this study used the Science Writing Heuristic (SWH) approach to ABI with twenty-one students who had no previous experience engaging in ABI. This teacher with 10 of years teaching experience was purposefully selected because he was proficient and experienced in practicing ABI. Multiple sources of data were collected, including classroom video with transcriptions, semi-structured interviews, after lesson conversations, and researcher's field notes. Data analysis used a basic qualitative approach.
The results showed (1) that the teacher principally engaged in three forms of whole-class dialogue with students; talking to, talking with, and thinking through ideas with students. As time went on, the teacher's interactions in whole-class dialogue became increasingly focused on thinking through ideas with students, while at the same time students also dialogued more as each unit progressed. (2) This teacher persistently engaged with students in consensus-making activities during whole-class dialogue.These efforts toward consensus-making over time became part of the students' own as each unit progressed. (3) The classroom did not engage in critique and construction of knowledge necessarily like the community of science but rather used agreeing and disagreeing and explaining why through purposeful dialogic interactions to construct a grasp of science classroom practice.
The findings have informed theory and practice about science argumentation, the practice of whole-class dialogue, and grasp of science practice along four aspects: (1) patterns of dialogue within a unit of instruction and across units of instruction, (2) the teacher's ability to follow and develop students' ideas, (3) the role of early and persistent opportunities to engage novice students in consensus-making, and (4) the meaning of grasp of science practice in classroom. This study provides insight into the importance of prolonged and persistent engagement with ABI in classroom practice.
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Karlström, Gustaf. "Förstaklasselevers kollektiva algebraiska resonemang om funktioner." Thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-194469.
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Hur elever utvecklar algebraiska resonemang är inte så välförstått, vilket i kombination med svenska elevers låga resultat vid algebraiska uppgifter på internationella mätningar utgör en problematik. Denna problematik syftar studien att minska genom att undersöka förstaklasselevers kollektiva algebraiska resonemang om funktioner, för att identifiera vilka typer av algebraiskt tänkande som ges uttryck. För att undersöka detta observerades nio grupper av förstaklasselever i deras möte med tre uppgifter om funktioner som sedan kodades efter resonemang, argument, algebraiska aspekter, generalisering, och funktionellt tänkande. Resultatet visar att förstaklasselever är kapabla att resonera kring algebra och närma sig intern säkerhet på sina svar. Elevernas resonemang visade också tecken på alla algebraiska aspekter, relaterande och sökande men inte utökande generaliseringar, och alla kategorier av funktionellt tänkande. Den rekursiva kategorin av funktionellt tänkande kopplades endast till den första uppgiften, vilken var av en dynamisk karaktär vilket är intressant för verksamma lärare då det har implikationen att introducera funktioner med två objekt som variabler.
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Campos, Rodrigo Ruiz. "Argumentação e demonstração dos alunos do Ensino Médio: uma proposta de investigação matemática sobre crescimento e decrescimento de funções afins." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45135/tde-13062018-213641/.
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O presente trabalho tem como objetivo estudar se atividades de investigação matemática podem ajudar a desenvolver a capacidade de argumentação e demonstração matemática nos alunos do Ensino Médio, abordando o tema do crescimento e decrescimento de funções afins. Para isso, propõe uma reflexão sobre o papel da argumentação e da demonstração na formação integral do aluno do ensino médio. Enfoca, em particular, a transição entre o ensino básico e o superior, estudando algumas de suas dificuldades. O trabalho explora a diferença entre esses níveis de ensino, considerando que, enquanto a escola básica trata a matemática baseada em procedimentos aritméticos e algébricos, do ponto de vista prático tais como contas, medições, equações, análise de dados , o ensino superior exige mais abstração por parte do aluno onde a argumentação, o raciocínio lógico (dedutivo e indutivo) e as demonstrações são condições necessárias para a produção do conhecimento. Ao final, faremos uma proposta de atividade matemática através de uma abordagem investigativa, refletindo sobre como a demonstração, abordada dessa forma, pode contribuir para a formação integral do aluno e criar aproximações entre a forma como a matemática é tratada na escola básica e no ensino superior.This present work aims to study if mathematical research activities can help to develop mathematical argumentation and demonstration capacity in high school students, addressing the theme of growth and decrease of linear functions. For this, it proposes a reflection about the role of argumentation and demonstration in the integral formation of the high school student. It focuses on the transition between basic and higher education, studying some of its difficulties. The study explores the difference between these levels of education, whereas, while the basic school treats mathematics based on arithmetic and algebraic procedures from a practical point of view - such as arithmetic, measurements, equations, data analysis -, higher education demands from the student a greater abstraction level, where argumentation, logical reasoning (deductive and inductive) and demonstrations are necessary conditions to knowledge construction. In the end, we will propose a mathematical activity through an investigative approach, reflecting on how the demonstration, addressed in this way, can contribute to the integral formation of the student and create approximations between the way mathematics is treated in elementary school and in higher education.
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Miyakawa, Takeshi. "Une étude du rapport entre connaissance et preuve : le cas de la notion de symétrie orthogonale." Phd thesis, Université Joseph Fourier (Grenoble), 2005. http://tel.archives-ouvertes.fr/tel-00076565.
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Ce travail présente une analyse des rapports entre connaissance et preuve à travers une notion mathématique : La symétrie orthogonale (abordée dans une situation de construction d'une preuve). Nous nous proposons d'éclairer la distance cognitive qui puisse exister chez les élèves, entre la construction géométrique et la géométrie théorique à partir de la spécification des connaissances.Des outils d'analyse (conception, règle, support, etc.) sont adoptés et développés à partir du modèle de connaissance (modèle cK¢) de Balacheff et d'autres modèles de raisonnement et d'argumentation (modèle de Toulmin, etc.), afin d'établir la relation comparative entre le problème de preuve et les autres problèmes (construction géométrique, reconnaissance de figures) en termes de connaissance engagée.
Pour tenter d'identifier les connaissances effectives mobilisées par les élèves dans une situation de construction de preuve, une expérimentation est réalisée au collège en classe de 3e en France. Cette expérimentation vient à la suite d'une analyse théorique de certains types de problèmes permettant de mettre en évidence les différents fonctionnements de composants de conception au sens de Balacheff. Les problèmes de construction et de preuve y sont proposés. L'analyse des données met en évidence un écart sur l'état de connaissance des élèves. En effet, ces derniers réussissent bien le problème de construction des figures symétriques, cependant, ils échouent sur un problème analogue (exigeant la même règle), où la preuve est exigée. L'absence d'un « contrôle » organisé dans la construction qui est exigé dans la preuve est identifié.
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Goizueta, Manuel. "Aspectos epistemológicos de la argumentación en el aula de matemáticas." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/299192.
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Este trabajo de tesis doctoral “Aspectos epistemológicos de la argumentación en el aula de matemáticas” se inscribe en el área de estudio de la argumentación en clase de matemáticas. En él se aborda la cuestión de investigación: ¿Cómo se construye la validez de la producción matemática cuando se resuelven problemas en aulas de matemáticas? Para acercarse a esta cuestión se plantean tres objetivos:
Primer objetivo: Caracterizar procesos de construcción de la validez de la producción matemática en el trabajo en grupo de alumnos.
Segundo objetivo: Caracterizar procesos de construcción de la validez de la producción matemática en la interacción de grupos de alumnos con el profesor del aula.
Tercer objetivo: Caracterizar la gestión de procesos de construcción de la validez de la producción matemática a cargo de dos profesores en el aula de matemáticas.
Se entiende el conocimiento matemático como producto cultural e histórico, cuya justificación implica la acción humana, por lo que no puede ser reducido a condiciones objetivas. La argumentación se presenta como unidad epistemológica del conocimiento matemático y se enmarca dentro del comportamiento racional de las personas. Describimos la argumentación como una práctica dirigida a justificar, reflexionar y persuadir, que acontece en situaciones de interacción y depende del contexto. Pueden estar implicadas una o varias personas, que se involucran ofreciendo razones para justificar o criticar sus posiciones o las de otros con la intención de modificar el valor epistémico de tales posiciones.
Se sostiene que la epistemología de las matemáticas del aula es investigable a partir del análisis de la interacción entre los participantes del proceso de enseñanza y aprendizaje y, en particular, a partir de las prácticas argumentativas en clase.
Los métodos de investigación en este estudio se inscriben dentro del paradigma investigativo de la teoría fundamentada. El análisis de datos se estructura alrededor del método de comparación constante y se organiza alrededor de la comparación de episodios similares. Para ello se realizan ciclos iterativos de codificación de datos hasta alcanzar el punto de saturación teórica. A partir de este análisis se generan categorías descriptivas y explicativas que dan cuenta de los datos analizados y, mediante un proceso de síntesis, de los objetivos de la investigación. Los resultados se presentan en forma de temas narrativos que dan cuenta de manera articulada de los aspectos más relevantes aparecidos en el análisis.
Los datos de aula se obtuvieron a partir de la resolución de un problema de modelado matemático, ideado para introducir nociones básicas de teoría de la probabilidad, en dos aulas del cuarto curso de secundaria con dos profesores. Además se sostuvieron dos entrevistas semi-estructurada basadas en el visionado de videoclips del trabajo realizado en aula. Los datos de aula y los de entrevista constituyen el cuerpo de datos.
Se pone en evidencia la compleja relación entre la epistemología de las matemáticas del aula y aspectos sociales del contrato didáctico. Se observan así raíces sociales de la construcción de la validez de la producción matemática en el aula y, en particular, la relevancia del papel del profesor y su gestión en estos procesos.
Los resultados obtenidos indican que los alumnos no cuentan con conocimientos meta-matemáticos necesarios para producir y evaluar argumentos de acuerdo con principios disciplinares que se pretenden enseñar y que estas actividades no son centrales en el trabajo matemático del aula. Se concluye que es necesario propiciar la visibilización de aspectos epistemológicamente relevantes de la producción matemática de los alumnos en las interacciones con el profesor. Esto debe permitir la evaluación de la producción matemática por el profesor, así como la emergencia de conocimientos meta-matemáticos como objeto de aprendizaje y discusión en el aula.This doctoral thesis “Epistemological aspects of argumentation in the mathematics classroom” is inscribed in the area of study of argumentation in the mathematics classroom. It tackles the research question: ¿How is the validity of mathematical production constructed while solving problems in mathematics classrooms? To approach this question three objectives are proposed: First objective: To characterize validity construction processes of mathematical production in students’ group work. Second objective: To characterize validity construction processes of mathematical production in the interaction between groups of students and the teacher. Third objective: To characterize the management of validity construction processes of mathematical production by two teachers in the mathematics classroom. Mathematical knowledge is understood as a cultural and historical product, whose justification implies human action, so it cannot be reduced to objective conditions. Argumentation is presented as an epistemic unit of mathematical knowledge and is framed within human rational behavior. We describe argumentation as a practice aimed at justifying, reflecting and persuading, that occurs in interaction situations and depends on the context. One or more participants may be involved, offering reasons to justify or criticize their own or others positions in order to modify, positively or negatively, the epistemic value of such positions. It is argued that mathematics classroom epistemology is researchable based on the analysis of interactions between participants in the teaching and learning process and, particularly, by considering argumentative practices in class. Research methods come from the grounded theory research paradigm. Data analysis is structured around the constant comparative method and interpretive-inductive analysis is organized around comparison of similar episodes. To that purpose, iterative codification cycles are performed until reaching theoretical saturation. Descriptive and explicative categories are generated on the basis of this analysis, which account for the data and, by a process of synthesis, for the research objectives. Results are presented as narrative themes that account in an articulated way for the most relevant aspects of the analysis. Classroom data were gathered from a mathematical modeling, problem solving task, devised to introduce basic notions of probability theory in two middle-school, fourth grade classrooms with two teachers. Two semi-structured, video based interviews were held with two groups of students. Classroom and interview data constitute the corpus of data of the study. The complex relationship between mathematics classroom epistemology and social aspects of the didactical contract is highlighted. The social roots of validity construction of mathematical production in the classroom and the teacher’s role relevance in the management of such processes are pointed out. Results indicate that students lack meta-mathematical knowledge necessary to produce and assess arguments according to disciplinary principles aimed at this level and that these activities are not central to classroom mathematical work. The necessity to propitiate that epistemologically relevant aspects of the mathematical production are made visible in the interactions with the teacher is concluded. This should allow the teacher to assess students’ mathematical production as well as the emergence of meta-mathematical knowledge as a learning object in the classroom.
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Carvalho, Moacir Benvindo de. "Concepções de alunos sobre provas e argumentos matemáticos: análise de questionário no contexto do Projeto AProvaME." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11506.
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This work is inserted in the context of teaching and learning proofs and mathematical arguments in school mathematics and was developed as part of the project AProvaME (Argumentation and Proof in School Mathematics). The main aim of the study relates to the construction of a panorama of students´ conceptions about proof on the basis of the results of a questionnaire applied to nearly 2000 students aged between 14 and 15 years. More specifically, the study centres on the analysis of two questions related to Algebra (A1 and A2), which solicited the selection of arguments by the students and the assessment of these arguments in terms of their validity and generality. The questions from the questionnaire, as well as the discussions of students responses are informed principally by the research studies of Balacheff (1988) and Healy & Hoyles (2000), both of which consider empirical and formal arguments and the complex passage from the production of pragmatic to conceptual proofs. The results show that half of the 1998 subjects who completed the questionnaire had a preference for empirical arguments (verification through some cases) and a quarter chose narrative arguments. With respect to the analysis of the generality of proofs, students responses were generally somewhat inconsistent, with, for example, those who considered the same arguments to be both always true and valid only for some cases . In the group of students under our responsibility, made up of three 8th grade classes (70 students), the same results were observed. Some of the reasons motivating these choices were illuminated in the interviews. In the vision of the students, empirical evidence counts as proof and arguments in natural language are judged as clearer, with a greater explanatory power
Nosso trabalho insere-se no contexto do ensino e aprendizagem de provas e argumentos matemáticos por alunos da Escola Básica e foi desenvolvido no âmbito do Projeto Argumentação e Prova na Matemática Escolar (AProvaME). O principal objetivo de nosso estudo refere-se ao mapeamento das concepções de alunos sobre prova, a partir dos resultados de um questionário aplicado a cerca de 2.000 alunos de 14-15 anos. Mais especificamente, nosso trabalho centrou-se na análise de duas questões de Álgebra (A1 e A2), as quais solicitavam escolhas de argumentos por parte dos alunos e avaliação destes em termos de sua validade e generalidade. A elaboração e discussão das respostas são baseadas principalmente nas pesquisas de Balacheff (1988) e Healy & Hoyles (2000), sobre argumentos empíricos e formais e sobre a complexa passagem da produção de provas pragmáticas para as conceituais. Os resultados mostram que a metade dos sujeitos analisados na amostra total (de 1.998 alunos) tem preferência por argumentos empíricos (verificações para alguns casos) e um quarto escolhe argumentos narrativos. Quanto à avaliação da generalidade de uma prova, verificamos inconsistência nas respostas dos alunos, que consideram um mesmo argumento sempre verdadeiro e, simultaneamente, válido somente para alguns casos . No grupo sob nossa responsabilidade, constituído por três turmas de 8ª série (70 alunos), esses resultados se mantêm. Algumas razões dessas escolhas foram esclarecidas nas entrevistas. Na visão dos alunos, evidências empíricas são provas e os argumentos em língua natural são considerados mais claros, com maior poder de explicação
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Ferreira, Filho José Leôncio. "Um estudo sobre argumentação e prova envolvendo o teorema de Pitágoras." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11279.
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The National Curriculum Parameters (Brazil, 1998), acknowledge and recommend that the Mathematics syllabus should necessarily cover activities and experiences which enable learners to develop and effectively communicate with valid mathematical argumentation. However, there is consensus among Mathematics Education researchers, in several countries, as to the inherent difficulties of teaching and learning proof. This research is inserted in the AprovaME project, in the Mathematics Education area at PUC-SP, which has as one of its goals to foster debate over the teaching and learning of proof in Mathematics. The objective of the present study was to investigate the involvement of first-year students at high school in processes of conjecture and proof construction, aiming to answer the following research question: what difficulties do students present when faced with argumentation and proof situations involving the Pythagorean Theorem? In order to answer the research question, we adopted some elements from the didactic engineering as the research methodology. A teaching sequence was then elaborated with questions on argumentation and proof involving the Pythagorean Theorem and applied to students from a private school in a countryside city in the State of Sao Paulo. The work by Robert (1998) and Duval (2002) contributed to the conception of activities, and the ones by Balacheff (1988), to the analysis of the types of proof from the students. The production from the students, at the end of the activities, show that the teaching sequence conceived to produce argumentation and proof advantaged the passing of a step where validations are predominantly empirical into another step, in which validation takes on a deductive character. Other studies approaching different mathematics topics and which treat teaching and learning of proof have become more and more needed for understanding the complexity surrounding this process
Os Parâmetros Curriculares Nacionais (Brasil, 1998) reconhecem e orientam, que o currículo de Matemática deve necessariamente contemplar atividades e experiências que possibilitem aos aprendizes o desenvolvimento e a comunicação efetiva de argumentos matematicamente válidos. Mas há consenso entre os pesquisadores da Educação Matemática, em diversos países, quanto às dificuldades inerentes ao ensino e à aprendizagem de prova. Esta pesquisa está inserida no projeto AprovaME na área da Educação Matemática da PUC-SP, que tem entre seus objetivos, o de contribuir para o debate sobre o ensino e aprendizagem de prova em Matemática. O objetivo do presente trabalho foi investigar o envolvimento de alunos da 1ª.série do Ensino Médio em processos de construção de conjeturas e provas, a fim de responder à seguinte questão de pesquisa: que dificuldades apresentam os alunos diante de situações de argumentação e prova envolvendo o teorema de Pitágoras? Para responder à questão de pesquisa, adotamos como metodologia de pesquisa alguns elementos da engenharia didática. Uma seqüência de ensino foi elaborada com questões sobre argumentação e prova, envolvendo o teorema de Pitágoras e aplicada a alunos de uma escola particular do interior do Estado de São Paulo. Os trabalhos de Robert (1998) e Duval (2002) contribuíram para a concepção das atividades e os de Balacheff (1988) para a análise dos tipos de provas dos alunos. As produções dos alunos ao final das atividades mostram que uma seqüência de ensino concebida para produzir argumentações e provas favoreceu a passagem de uma etapa onde as validações são predominantemente empíricas para uma outra etapa onde as validações são dedutivas. Outros trabalhos abordando diferentes tópicos de matemática e que tratem do ensino e aprendizagem da prova tornam-se cada vez mais necessários para compreender a complexidade desse processo
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Mendes, Lourival Junior. "Uma análise da abordagem sobre argumentações e provas numa coleção do ensino médio." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11492.
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Secretaria da Educação do Estado de São Paulo
The purpose of this study was to investigate the role of proofs and demonstration on textbooks of high school. This work contributes with APROVA ME, a project that aims to investigate, analyze and propose activities for the learning of proofs and demonstration in school mathematics. The text books from Manoel Paiva was analyzed; three volumes constituted his collection and it was approved by the National Program that evaluate high school text books. It was distributed among public schools in the state of Sao Paulo, including the one I teach. Since text books are, in general, the solely source for classroom teachers, and many studies point out the impact of text books on teacher s way of teaching and consequently impact on students learning, to investigate how it deals with proofs and demonstration may help to show new ways of teaching proofs in schools. Our investigation focused on the topics: Number sets; functions; arithmetic and geometric progressions; parallelism and perpendiculars. After analyzing the three volumes, based on Balacheff, Villiers and IREM group, it was possible to classify the proofs that were privileged by the author. I discuss and present suggestions to enhance the teaching of proofs related to the analyzed topics
O objetivo deste trabalho foi investigar o papel que assume as provas e demonstrações no livro didático de matemática do Ensino Médio. O trabalho contribui com o projeto AProvaME1 cujo objetivo é investigar, analisar e propor atividades para a aprendizagem de provas e demonstrações na matemática escolar. Minha investigação se pautou na coleção de Manoel Paiva aprovada pelo PNLEM/20052 e distribuída para as escolas públicas de Ensino Médio do estado de São Paulo que optaram por adotá-la, entre elas a que leciono. Uma vez que o livro didático é uma fonte quase que única para o apoio do professor, vários estudos apontam a influência do mesmo no ensino do professor e consequentemente influencia a aprendizagem dos alunos, investigar se existe e de que modo trata provas e demonstrações em sua coleção contribui para apontar novos caminhos para tal ensino. Os temas investigados foram: Conjuntos Numéricos, Funções, Progressões Aritméticas e Geométricas, Paralelismo e Perpendicularismo. Analisando os três volumes, relativos às três séries do Ensino Médio, segundo Balacheff, Villiers e do grupo IREM, foi possível classificar os tipos de provas que são privilegiados na coleção. Discuto e apresento algumas sugestões para complementar o ensino de provas relativas aos tópicos analisados
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Signorelli, Shirley Ferreira. "Um ambiente virtual para o ensino semipresencial de funções de uma variável real: design e análise." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11284.
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Previous issue date: 2007-10-31Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The purpose of this investigation was the elaboration and implementation of a virtual environment for a part time distance course for students of the Computer Science and Systems of Information. The students failed in a former discipline that approaches topics of elementary Mathematics. It happened in a particular university in the city of São Paulo. Our focus was on analyzing this environment, the tools and interactions that happened on distance mode, about the content of real function of one variable. The methodology used, design-based research, favored proposing and analyzing the activities about this topic, as well as their reorganization and, the re design of the environment. The Blackboard platform and the used tools were analyzed based on Chaves (2000) criteria, and it seemed efficient as a virtual environment for the learning in our course. However, we leaved some critical and suggestions for future works, mainly about the role of the tools for communication within part time distance courses. The analysis of the students and teacher speeches' was based on the Model of Argumentative Strategy (CASTRO et al, 2004) and allowed to raise some aspects on the understanding of Real Functions of one variable, as they were privileged in the different interactive spaces such as forum, chat, email and daily log. Aspects like the meaning production in Mathematics can be produced due to the authority of a teacher or of another student who is considered good by the classroom peers, or based on everyday language usage or on cultural characteristics. Moreover, we found that besides the students lack of prerequisite elementary mathematics, there is a lack of a culture for on-line courses
Nesta pesquisa objetivamos a elaboração e implementação de um ambiente virtual para um curso semipresencial, para estudantes dos cursos de Bacharelado em Ciência da Computação e Sistemas de Informação de uma instituição particular na cidade de São Paulo, dependentes na disciplina que aborda tópicos de pré-calculo. Nosso foco recaiu na análise do ambiente, da viabilidade das ferramentas e das interações que ocorreram a distância, no que tange o conteúdo de Funções de uma Variável Real. A metodologia utilizada, design research, permitiu propor e analisar as atividades sobre este tópico, incluindo a reestruturação e complementação deste ambiente. A plataforma Blackboard e as ferramentas foram analisadas segundo critérios definidos por Chaves (2000) e se mostraram eficazes como ambiente virtual de aprendizagem atendendo, para nosso curso, os critérios necessários. Entretanto, deixamos algumas críticas e sugestões para trabalhos futuros, principalmente quanto o papel do uso de ferramentas de comunicação em cursos semipresenciais. A análise dos discursos dos alunos e docente baseados no Modelo de Estratégia Argumentativa (CASTRO et al, 2004) permitiu levantar alguns aspectos sobre a compreensão de Funções de uma Variável Real que foram privilegiados nos diferentes espaços interativos como fórum, chat, e-mail e diário de rotina, tais como o fato de que a produção de significados em Matemática pode estar apoiada na autoridade do professor ou alunos bem vistos pela classe, na linguagem cotidiana e no aspecto cultural. Observamos ainda que além da falta de pré-requisitos de matemática básica, ainda há falta de cultura de trabalhos on-line
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Nunes, José Messildo Viana. "A prática da argumentação como método de ensino: o caso dos conceitos de área e perímetro de figuras planas." Pontifícia Universidade Católica de São Paulo, 2011. https://tede2.pucsp.br/handle/handle/10891.
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Previous issue date: 2011-10-28This research treats the practice of the argumentation as teaching method, focusing the concepts of area perimeter of plane figures. Studies in national and international levels have already broached the subject, many times using the practice of the argumentation as method, not proposing, however, ways that demonstrate the functionality of that method. So this work answers the following question: in what measure the practice of the argumentation can present itself as method that contributes to the comprehension of concepts in mathematics taking as reference the case of the area and the perimeter of plane figures? To answer our question, we propose a didactic sequence modeled and analyzed with basis in the phases that compose the argumentative process, according to Toulmin (1996). The methodology of the study have been supported in Didactic Engineering purposes, the intervention have been effectuated with pupils at the fifth grade in Ensino Fundamental (students aged 10-11), using two argumentative institutions: the classroom and the informatics laboratory where we used the Geogebra software. The theoretical foundation have been based in speculative reflections by Toulmin (1996), in argumentative classification by Pedemonte (2002) and Cabassut (2005) and in the idea of argumentative convergence by Perelman and Olbrechts-Tyteca (2005). The analysis of the activities have evidenced that the practice of the argumentation contribute to the comprehension of the concepts of area and perimeter of plane figures, habilitating this practice as teaching method. The argumentative competences acquired by the pupils through the interactions with their classmates and the researchers about the subject allowed them have more autonomy to communicate and defend their ideas, respecting the opinion of the other classmates during the discussions, pay attention to the functionality and the possible validity of their argument, besides to learn specific symbols and language of mathematics
Esta pesquisa trata da prática da argumentação como método de ensino, focalizando os conceitos de área e perímetro de figuras planas. Estudos em níveis nacionais e internacionais já abordaram o assunto, muitas das vezes utilizando a prática da argumentação como método, sem, no entanto, propor caminhos que demonstrassem a funcionalidade dessa abordagem. Assim, este trabalho responde à seguinte questão: em que medida a prática da argumentação pode se apresentar como método que favoreça a compreensão de conceitos em matemática, tomando como referência o caso da área e perímetro de figuras planas? Como resposta, propomos uma sequência didática modelada e analisada com base nas fases que compõem o processo argumentativo segundo Toulmin (1996). A metodologia do estudo apoiou-se em pressupostos da Engenharia Didática e a intervenção foi efetivada com alunos do quinto ano do Ensino Fundamental (alunos de 10 a 11 anos), utilizando duas instituições argumentativas: a sala de aula e o laboratório de informática, no qual usamos o software Geogebra. A fundamentação teórica baseou-se nas reflexões teóricas de Toulmin (1996), na classificação de argumentos de Pedemonte (2002) e Cabassut (2005) e na idéia de convergência argumentativa de Perelman e Olbrechts-Tyteca (2005). As análises das atividades evidenciaram que a prática da argumentação favoreceu a compreensão dos conceitos de área e perímetro de figuras planas, habilitando essa prática como método de ensino. As competências argumentativas adquiridas pelos discentes, a partir das interações com colegas e pesquisador sobre o assunto em questão, possibilitaram- lhes ter mais autonomia para comunicar e defender suas ideias, respeitando a opinião do colega no decorrer das discussões, ficar atentos à funcionalidade e à validade ou não de seu argumento, além de apreender símbolos e linguagem específicos da matemática
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Leandro, Ednaldo José. "Um panorma de argumentação de alunos da educação básica: O caso do fatorial." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11082.
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Previous issue date: 2006-10-20This work focuses on the mathematical object factorial. It is part of the project Argumentation and Proof in School Mathematics (AprovaME), which involves a survey of the conceptions of Brazilian students. For this survey, two questionnaires were developed, one related to the domain of algebra and the other geometry and administered to a sample composed of 2012 students aged between 14 and 16 years, studying in the 8th grade or the 1st year of High School of schools located in the state of São Paulo. The questions analyzed for this study were included in the algebra questionnaire. Following a descriptive analysis of the data collected, which indicated that the students had considerable difficulties in constructing valid mathematical arguments, the data set was subjected to a multidimensional analysis using the software CHIC. The results obtained from this analysis evidenced three distinct groups of students within the sample: those who were unable to respond to questions involving the notion of factorial; students who privileged the use of numeric calculations in their responses; and students who focused on the properties of the factorial in constructing their justifications. It was also possible to identify those students whose response profiles most contributed to the formation of these groups. In a second phase of analysis, some of these students were interviews in order to obtain additional data related to factors motivating their responses. In this phase the questionnaire was also administered to mathematics teachers in schools that made up the sample. In general, the results, both quantitative and qualitative, suggest that the question of argumentation and proof, at least in relation to multiplication and division, is not being contemplated with these students. Calculations were the principle tools used by those who managed to respond to the questions and few students were able to justify their responses using mathematical properties, such as, for example, referring to the inverse relationship between multiplication and division
Este trabalho trata do objeto matemático fatorial. Ele visa contribuir com o projeto Argumentação e Prova na Matemática Escolar (AProvaME), que tem como uma das metas elaborar um levantamento das concepções sobre argumentação e provas de estudantes brasileiros. Para este levantamento, foram elaborados dois questionários, um de Álgebra e outro de Geometria, aplicados a uma amostra composta por 2012 alunos na faixa etária entre 14 e 16 anos, matriculados na 8ª série do Ensino Fundamental ou 1ª série do Ensino Médio em escolas no Estado de São Paulo. As questões que analisamos estão inseridas no questionário de álgebra. Depois de uma análise descritiva dos dados coletados, que indicou consideráveis dificuldades dos alunos em construir argumentos válidos, uma análise multidimensional foi efetuada, utilizando o software CHIC. Com os resultados dessa análise foi possível identificar principalmente três grupos distintos de alunos os que não conseguiram resolver as questões com a noção do fatorial; os alunos que privilegiaram o uso de cálculos numéricos nas suas respostas e os alunos que enfocaram propriedades do fatorial na construção de suas justificativas. Também foi possível identificar aqueles alunos cujos perfis de respostas mais contribuíram para a formação de tais grupos. Numa segunda fase, alguns desses alunos foram entrevistados para a obtenção de mais informação em relação às motivações de suas respostas. Nessa fase, o questionário também foi aplicado aos professores de escolas participantes da amostra. Em geral, nossas análises, tanto quantitativas quanto qualitativas, sugerem que a questão de argumentação e provas, pelo menos em relação à multiplicação e divisão, não estão sendo contempladas com esses alunos. Os que conseguiram responder às questões privilegiaram o cálculo como a principal ferramenta e poucos foram os que justificaram suas respostas com o uso de propriedades, por exemplo, citando a inversa relação entre multiplicar e dividir
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Cabassut, Richard. "DEMONSTRATION , RAISONNEMENT ET VALIDATION DANS L'ENSEIGNEMENT SECONDAIRE DES MATHEMATIQUES EN FRANCE ET EN ALLEMAGNE." Phd thesis, Université Paris-Diderot - Paris VII, 2005. http://tel.archives-ouvertes.fr/tel-00009716.
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Pour étudier la démonstration nous adaptons le cadre théorique de Toulmin, sur les arguments de plausibilité et de nécessité, à la théorie anthropologique du didactique de Chevallard. Les validations de l'enseignement des mathématiques sont la double transposition des démonstrations de l'institution mathématique (qui produit le savoir) et des validations, argumentations ou preuves, d'autres institutions (comme la « vie quotidienne »). L'étude diachronique des programmes du collège-lycée en France, et du Gymnasium en Bade-Würtemberg, confirmée par l'étude de manuels, montre que la démonstration est devenue explicitement un objet à enseigner, contrairement aux cas des Hauptschule et Realschule. Ces programmes recommandent l'usage de différents types de validation (argumentation, preuve) et d'arguments (pragmatiques, sémantiques, syntaxiques) suivant leurs fonctions et les moments ; on retrouve dans des leçons sur la démonstration l'influence des fonctions de la validation dans les différents genres de tâche (découvrir, contrôler, changer de registres, ...). Malgré les difficultés linguistiques, institutionnelles et culturelles liées à la comparaison, l'examen des validations de théorèmes de cours dans les manuels et de démonstrations produites par des élèves montre des similitudes quant à la cohabitation des différents types d'arguments et différentes fonctions de la validation. On observe des différences sur les types de technologie ou de technique mis en œuvre et sur le poids donné aux types d'arguments et aux registres utilisés, avec une explication liée aux conditions institutionnelles (moment considéré, contrat, fonction privilégiée, organisation de l'enseignement ...)
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Pasini, Mirtes Fátima. "Argumentação e prova: explorações a partir da análise de uma coleção didática." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11282.
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Previous issue date: 2007-10-16Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This work is inserted the research project Argumentation and Proof in School Mathematics (AProvaME), which aims to study the teaching and learning of mathematical proofs during compulsory schooling. The main research question of this contribution to the project relates to how proof is treated in particular geometry topics in one collection of mathematics textbooks for secondary school students. More specifically, the study aims to identify how the passage from empiricism to deduction is contemplated in the textbook activities as well as to document the interventions and strategies necessary on the part of the mathematics teacher in order to manage this transition. The types of proofs in the classification of Balacheff (1988) and the functions of proof identified by de Villiers (2001) serve as the principle theoretical tools for these analyses. Following a survey of the activities related to proof and proving in topics related to the theorem of Pythagoras and properties of straight lines and triangles, teaching sequences based on these activities were developed with students from the 8th Grade of a secondary school within the public school system of the municipal of Jacupiranga in the State of São Paulo. The main findings of the study indicate that the teacher has at his or her disposal material that permit a broad approach to proof and proving, although the passage from exercises involving reliance on empirical manipulations for validation to the construction of proofs based on mathematical properties is not very explicitly addressed, with the result that intense teacher intervention is necessary at this point. A particular difficulty faced by the teacher is knowing how to intervene without assuming responsibility for the resolution of the task in question. Finally, a dynamic geometry activity is presented, as an attempt to provide a learning situation which might enable students to engage more spontaneously in the transition from evidence-based arguments to valid mathematical proofs
Nosso trabalho está inserido no Projeto Argumentação e Prova na Matemática Escolar (AProvaME), que tem como objetivo estudar o ensino e aprendizagem de provas matemáticas na Educação Básica. A questão principal da pesquisa consiste em analisar o tratamento deste tema em determinados conteúdos geométricos de uma coleção de livros didáticos do Ensino Fundamental. Mais especificamente, o estudo busca identificar como a passagem do empirismo à dedução é contemplada nas atividades dos livros e quais as intervenções e estratégias necessárias por parte do professor para gerenciar essa passagem. Os tipos de prova na classificação de Balacheff (1988) e as funções de prova identificadas por De Villiers (2001) foram as principais ferramentas teóricas utilizadas para estas análises. Após um levantamento das atividades relacionadas à prova nos conteúdos Teorema de Pitágoras, Retas Paralelas e as propriedades dos Triângulos, seqüências baseadas nessas atividades foram desenvolvidas com alunos de 8.ª Série do Ensino Fundamental de uma escola pública no Município de Jacupiranga, do Estado da São Paulo. Concluímos que o professor tem à sua disposição material consistente para trabalhar com seus alunos, embora exista o problema na passagem brusca de exercícios empíricos em diversos níveis de verificação para as demonstrações formais, sendo necessária intervenção do professor por meio de revisões pertinentes, proporcionando ao aluno esclarecimentos para desenvolver uma atividade. A principal dificuldade para o professor foi interferir sem assumir a responsabilidade de resolver a situação em questão. Por fim, apresenta-se uma atividade no ambiente de geometria dinâmica, visando proporcionar uma transição mais espontânea entre argumentos baseados em evidência e argumentos baseados em propriedades matemáticas
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Vieira, Wellington Zarur Viana. "Argumentação e prova: uma experiência em geometria espacial no ensino médio." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11286.
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Previous issue date: 2007-10-24This work is inserted in Project AProvaME Argumentation and proof in School Mathematics - it has the objective of to do a map of conceptions about students and adolescent s argumentation and proof in schools at State of São Paulo, how this the preparation, application and valuation of the learning situations. To that we expose one sequence of activities that broach Spatial Geometry Concepts, how parallelism and perpendicularity. This sequence of activities was applied to six students age between 14 and 16 years in a State Public School, with the objective of to contribute to the development these students when they are inserted in a argumentation and proof s context on Mathematics. How assistance in this process, we used the software Cabri-Géomètre, with the hypothesis that this could to give a support to visualization of the object in study. The analysis presents that, though the students hadn t searched a level of intellectual proof. There was an important advance on search proprieties and pertinent elements of the figure to justify their answers. The situations woke-up a visible interest on the students, permitting to discuss some aspects that have to be considered in the elaboration of a Geometry proof, related principally the interference of the spatial elements of figural representation
Este trabalho está inserido no Projeto AProvaME Argumentação e Prova na Matemática Escolar que têm o objetivo de fazer um mapeamento das concepções sobre argumentação e prova de alunos adolescentes em escolas do Estado de São Paulo, bem como a elaboração, aplicação e avaliação de situações de aprendizagem sobre prova. Para isto, apresentamos uma seqüência de atividades que abordam conceitos da Geometria Espacial, em particular envolvendo paralelismo e perpendicularismo. Esta seqüência foi elaborada e aplicada a seis alunos (14-16 anos) de uma Escola Pública Estadual, com o objetivo de contribuir para o desenvolvimento desses alunos quando inseridos num contexto de argumentação e prova em Matemática. Como auxilio neste processo, usamos o software Cabri-Géomètre, com a hipótese de que este poderia dar suporte à visualização dos objetos em estudo. As análises mostram que, embora os alunos não tenham atingido um nível de prova intelectual, houve um avanço significativo na identificação de propriedades e elementos pertinentes das figuras para justificar suas respostas. As situações despertaram um visível interesse nos alunos, permitindo discutir alguns aspectos que devem ser considerados na elaboração de uma prova em Geometria, relacionados principalmente à interferência de elementos espaciais das representações figurais
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Socolowski, Regina Célia Alem Jorge. "Análise das interações tutor/participantes: um ponto de partida para avaliação de cursos de desenvolvimento profissional à distância." Pontifícia Universidade Católica de São Paulo, 2004. https://tede2.pucsp.br/handle/handle/11150.
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Previous issue date: 2004-10-08This work analyzes the interactions among participants over a Mathematics Course at Distance, aiming the professional development of Mathematics Teachers, approaching Geometry s contents. In order to achieve a better understanding of arguments included in the involved subjects speeches, the analysis main theme of this work, the Model of Argumentative Strategies MAS (Frant and Castro, 2001) has been used, based on Olbrechts and Perelman Treaty of Argumentation (1992). The methodology used in this work analysis, demanded the events organization, so that the dialogs would be obvious and the explicit and implicit participants intentions would be re-taken in their interactions, allowing confrontation with their speeches. The analysis focus on arguments included in one of the participants speeches and the Tutor, analyzing other participants speeches, only when interacting with him. This analysis privileges two views: the mathematical content and the pedagogical practice, and related to the pedagogical practice, three focus: Tutor s pedagogical practice, Anita s pedagogical practice, and the environment where the interaction was held. This essay, structured in six chapters contextualizes and presents the problem, giving an explanation referring to the national and international historical aspects and the Brazilian Legislation which approaches the Distance Education, and concludes the interactions of Argumentative Strategies of the analysis importance among the participants and the Tutor as a starting point to the Evaluation of a Professional Development Course at Distance
Este trabalho analisa as interações entre os participantes de um Curso de Matemática, à Distância, voltado para o desenvolvimento profissional de Professores de Matemática, abordando o conteúdo de Geometria. Com o propósito de melhor compreender argumentos contidos nos discursos dos sujeitos envolvidos, tema principal deste trabalho, usamos para a análise o Modelo da Estratégia Argumentativa MEA (Frant e Castro, 2001), baseado no Tratado da Argumentação de Perelman e Olbrechts (1992). A metodologia usada para a análise deste trabalho, exigiu a organização dos eventos, de modo que evidenciassem os diálogos e resgatassem as intenções explícitas e implícitas dos participantes, em suas interações, permitindo confrontá-las com seus discursos. A análise foca as argumentações contidas nos discursos de um dos participantes e do Tutor, analisando os discursos de outros participantes apenas quando interagem com ele. Essa análise privilegiou dois olhares, o do conteúdo matemático e o da prática pedagógica e, com relação à prática pedagógica três focos: a prática pedagógica do Tutor; a prática pedagógica de Anita e o ambiente onde se deram as interações. Estruturada em seis capítulos, esta dissertação contextualiza e apresenta o problema, faz uma explanação referente aos aspectos históricos nacionais e internacionais e da Legislação Brasileira que aborda a Educação à Distância, e conclui sobre a importância da análise da Estratégia Argumentativa das interações entre os participantes e o Tutor como um ponto de partida para a Avaliação de um Curso de Desenvolvimento Profissional a Distância
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Salomão, Paulo Rogério. "Argumentação e prova na matemática do ensino médio: progressões aritméticas e o uso de tecnologia." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11266.
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Previous issue date: 2007-10-02In the first term of 2005, I joined the Professional Master s degree on Mathematics Teaching at PUC/SP. In this same year, the research project AProvaME, whose goals are: investigating concepts about argumentation and proofs of teenager students at schools from São Paulo state; structuring groups composed by teachers and researchers in order to elaborate activities involving students in the building process of knowledge, arguments and proofs in Mathematics, the use of technology and the investigating the teacher s role as the mediator of this process. As a part of this project, I will structure my dissertation in order to investigate two situations. The first one to verify to what extent, by the teacher s mediation and by the activities proposed, it is possible to engage students in argument, justification and proof of conjectures about Arithmetical Progressions. On the second one, investigating if the use of technology can favor the building of arguments, justification and proofs in Arithmetical Progressions by the students. Oriented by these questions, I tried to raise some observations of how the teacher s mediation should be done, using activities related to Arithmetical Progressions to engage the students in argument, justifying and proof situations, as well as which type and how to use the technologies available: first of all, I realized the need for the teacher s mediation after each ending of a group of activities, making a closure, or else, proposing to the students that they needed to confront and discuss, giving arguments, justifying their answers, so that everyone could proceed to the following activities without compromising their conjectures; subsequently; I verified that the use of technology is an incentive to the performing of activities in any area of knowledge, because the students feel motivated to build geometrical figures in the computer to solve the Mathematics exercises, concluding, with relation to the use of technology, I noticed that in the activities of this essay the usage of one more computational tool for the validation of students answers, as the Excel software, could complement the results obtained. This essay was based, mainly on the nine types of tasks extracted from Balacheff et al. text (2001). The methodology used was the teaching experiment, always looking for an improvement, not only in the activity, but also in the teacher-studenttechnology interaction. The research involved 10th graders from the evening shift of a State public network school
No primeiro semestre de 2005, ingressei no curso de Mestrado Profissional em Ensino de Matemática na PUC/SP. Neste mesmo ano, iniciava-se o projeto de pesquisa AProvaME, cujos objetivos são: investigar concepções sobre argumentação e prova de alunos adolescentes em escolas do Estado de São Paulo; formar grupos compostos por professores e pesquisadores para elaboração de atividades envolvendo alunos em processos de construção de conhecimento, argumentos e provas em Matemática e o uso de tecnologia e investigar o papel do professor como mediador neste processo. Por fazer parte deste projeto, estruturarei minha dissertação para investigar duas situações. A primeira para verificar em que medida, por meio da mediação do professor e das atividades propostas, é possível engajar os alunos em situações de argumentar, justificar e provar conjecturas sobre Progressões Aritméticas. Na segunda, investigar se o uso de tecnologia pode favorecer a construção de argumentos, justificativas e provas em Progressões Aritméticas pelos alunos. Orientado por essas questões, procurei levantar algumas observações de como deve ser feita a mediação do professor, utilizando atividades de Progressões Aritméticas para engajar os alunos em situações de argumentações, justificativas e provas, bem como qual tipo e como usar as tecnologias disponíveis: em primeiro lugar, percebi a necessidade da mediação do professor a cada término de atividade ou a cada final de um grupo de atividades, fazendo um fechamento, ou seja, propondo que os alunos confrontassem e discutissem, argumentando e justificando suas respostas, para que todos pudessem prosseguir com as atividades seguintes sem comprometimento de suas conjecturas; em seguida, verifiquei que o uso de tecnologia é um incentivo para a realização de atividades em qualquer área do conhecimento, pois os alunos sentem-se motivados por construir figuras geométricas no computador para a resolução de exercícios de Matemática; ao finalizar, com relação ao uso da tecnologia, constatei que nas atividades deste trabalho a utilização de mais uma ferramenta computacional para validação das respostas dos alunos, como o software Excel, poderia complementar os resultados obtidos. Este trabalho fundamentou-se, sobretudo nos nove tipos de tarefas extraídos do texto de Balacheff et al. (2001). A metodologia utilizada foi o experimento de ensino, objetivando sempre um aperfeiçoamento, tanto das atividades, como da interação professor aluno tecnologia. A pesquisa envolveu oito alunos da 1ª série do Ensino Médio do período noturno de uma escola da rede pública estadual
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Almeida, Julio Cesar Porfirio de. "Argumentação e prova na matemática escolar do ensino básico: a soma das medidas dos ângulos internos de um triângulo." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11502.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This study is about the demonstration of amount of measure the internal angles of triangles made by 8th grade from Fundamental School and the First year of High School, from of resolution of two specified questions. This work intends to contribute with the Argumentation and Proof in School Mathematics project (AprovaME), that has as one of objectives the mapping of conceptions about teenager s argumentation and proofs in public and private schools of São Paulo (state) For this was made a questionnaire in two books, five questions of Algebra and with five questions of Geometry. They were given to 1998 pupils aged between 14 and 16 years. The two analyzed questions are in the Geometry notebook. After checking the given information, took out 50 pupils as sample, that answers were classified in four progressive levels according their form of argument used in evolution of the Pragmatic proof (first principles methods of verification) to the Intellectual proof (elaborations of reasoning from logical-deduction nature and the production of explanation characterized as mathematics demonstration). In the following phase these pupils were put in groups according with the types of answers presented, to do the individual interviews aiming explanations about their choose. Finish the work a conclusive survey based in the results of the analysis, where are suggested forms of approach of subject Proofs and Demonstrations in the classroom, contemplating the execution of dynamic activities that give privilege the construction of mathematically consistent argument based in the expression of generalized reasoning
Este estudo trata da demonstração da soma da medida dos ângulos internos de um triângulo por alunos da oitava série do Ensino Fundamental e da primeira série do Ensino Médio, a partir da resolução de duas questões específicas. Procura contribuir com o Projeto Argumentação e Prova na Matemática Escolar (AprovaME), que tem como um de seus objetivos o mapeamento das concepções sobre argumentação e prova de alunos adolescentes em escolas públicas e particulares do Estado de São Paulo. Para esse levantamento foi elaborado um questionário contendo, em dois cadernos, cinco questões de Álgebra e cinco de Geometria, aplicados a 1998 alunos na faixa etária entre 14 e 16 anos. As duas questões analisadas estão inseridas no caderno de Geometria. Após a tabulação das informações coletadas, extraiu-se dessa população uma amostra de 50 alunos, cujas respostas foram classificadas em quatro níveis progressivos quanto às formas de validação dos argumentos empregados numa evolução da categoria Prova Pragmática (métodos rudimentares de verificação) à Prova Intelectual (elaboração de raciocínios de natureza lógico-dedutiva e produção de explicações caracterizadas como demonstrações matemáticas). Na etapa seguinte, esses alunos foram agrupados de acordo com os tipos de resposta apresentados para a realização de entrevistas individuais visando à obtenção de esclarecimentos adicionais sobre suas escolhas. Encerra o trabalho um panorama conclusivo baseado no resultado da análise em que são sugeridas formas de abordagem do tema Provas e Demonstrações em sala de aula, contemplando a realização de atividades dinâmicas que privilegiem a construção de argumentos matematicamente consistentes, fundamentados na expressão de raciocínios generalizadores
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Cruz, Flávio Pereira da. "Argumentação e prova no ensino fundamental: análise de uma coleção didática de matemática." Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11291.
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Previous issue date: 2008-02-15Secretaria da Educação do Estado de São Paulo
This dissertation aims to analyze how the collection Mathematics and Reality approaches argumentation and proof when it refers to the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras. It s inserted in the Project AProvaME (Argumentation and Proof in School Mathematics) that proposes the investigation of conceptions of argumentation and proof in the teaching of mathematics in schools in the state of São Paulo and to form a group of researchers to elaborate situations of learning involving arguments and proof to be investigated in the classroom. The analysis of the collection, in our research, is based on the work done by BALACHEFF et. al. (2001) which presents possible activities that may involve argumentation and proof classifying them into various types and levels. We have used this classification, when it refers to the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras, to consider the theoretical text and the respective exercises presented in the collection that are related to argumentation and proof. We have noticed that the proposed activities may basically be classified as "tasks of initiation to proof." We conclude, in our analysis, that the collection is not designed to work with argumentation and proof to develop such skills in students when presenting the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras, and also when proposing its activities. We propose, at the end of our work, dynamic activities that may complement those that are present in the collection, aiming to help in the development of new approaches on argumentation and proof in the classroom
Este trabalho tem o objetivo de analisar como a coleção Matemática e Realidade aborda argumentação e prova quando trata do Teorema Fundamental da Aritmética e do Teorema de Pitágoras. Ele está inserido no projeto AProvaME - (Argumentação e Prova na Matemática Escolar) que propõe a investigação de concepções de argumentação e prova no ensino de matemática em escolas do estado de São Paulo e formar grupo de pesquisadores para elaborar situações de aprendizagem envolvendo argumentação e prova para serem investigadas em sala de aula. A análise da coleção, em nossa pesquisa, tem como fundamento o trabalho desenvolvido por BALACHEFF et. al. (2001) que apresenta possíveis atividades que possam envolver argumentação e prova classificando-as em vários tipos e níveis. Utilizamos esta classificação para analisar, quando trata do Teorema Fundamental da Aritmética e do Teorema de Pitágoras, o texto teórico e os respectivos exercícios apresentados na coleção e que estejam relacionados com argumentação e prova. Constatamos que são propostas basicamente atividades que podem ser classificadas como de tarefas de iniciação a prova . Concluímos, em nossa análise, que a coleção não visa o trabalho com argumentação e prova para desenvolver tais competências nos alunos quando apresenta os temas Teorema Fundamental da Aritmética e Teorema de Pitágoras e também quando propõe as respectivas atividades. Propomos ao final de nosso trabalho, atividades dinâmicas que podem complementar as que estão presentes na coleção, com o propósito de contribuir na elaboração de novas abordagens sobre argumentação e prova em sala de aula
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Kim, Hee-Joon. "An exploratory study of teachers’ use of mathematical knowledge for teaching to support mathematical argumentation in middle-grades classrooms." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-12-4696.
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Mathematical argumentation is fundamental to doing mathematics and developing
new knowledge. Working from the view that mathematical argumentation is also integral
to teaching and learning mathematics, this study investigated teachers’ use of
mathematical knowledge for teaching (MKT) to support student participation in
mathematical argumentation. Classroom observations were made of three case-study
teachers’ implementation of a three-day curriculum unit on mathematical argumentation
and supplemented with paper and pencil assessments of teachers’ MKT. Teaching moves,
or teachers’ actions directed toward supporting argumentation, were identified as a unit
of discourse in which MKT-in-action appeared. Teachers’ MKT showed up in three types
of teaching moves including: Revoicing by Reformulation, Responding to Student
Difficulties, and Pressing for Generalization in Defining. MKT that was evident in these
moves included knowledge of core information in argument, heuristic methods, and
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formulation of mathematical definition through and in argumentation. Findings highlight
that supporting mathematical argumentation requires teachers to have a sophisticated
understanding of the subject matter as well as how concepts develop through
argumentation. Findings have limitations in understanding complex teaching practices by
considering MKT as a single factor. The study has implications on teacher learning and
MKT assessments.text