Interactive Virtual Math: Een digitale tool om context-grafieken te leren in de klas
De doelstellingen van het Interactive Virtual Math-project zijn het ontwerpen en ontwikkelen van ... more De doelstellingen van het Interactive Virtual Math-project zijn het ontwerpen en ontwikkelen van de digitale tool voor het leren van grafieken bij dynamische contexten op de middelbare school (14-17 jaar oud) en om het gebruik van nieuwe technologieën voor leren in de klas te verkennen. Onderzoek biedt enkele didactische aanwijzingen om instructies te ontwikkelen die het leren van covariationaal redeneren ondersteunen (een belangrijke aspect bij het leren van dynamische grafieken). In deze poster presenteren we het prototype van een tool die covariationaal redeneren ondersteunt: IVM (Interactive Virtua Math) en bespreken we de didactische principes achter de tool. We gebruiken hiervoor de resultaten van een kleinschalig onderzoek met vier klassen die de tool hebben gebruikt om de werking van de tool te illustreren
Designing a digital tool for reasoning with covariation graphs: didactical considerations and classroom experience
[Paper abstract]: The aims of the Interactive Virtual Math-project are to design and develop a di... more [Paper abstract]: The aims of the Interactive Virtual Math-project are to design and develop a digital tool for learning covariation graphs at high school (14-17 years old students) and to explore the use of new technologies for learning in classroom. Research provides some didactical directions to develop instruction that supports the learning of covariational reasoning. For instance, engaging students in the mental activity to visualize a situation and construct relevant quantitative relationships should be prior to determining formulas or graphs. Also, learners can be helped to focus on quantities and generalizations about relationships, connections between situations, and dynamic phenomena. Digital tools can be designed in order to meet these and other didactical requirements. In this talk we present the prototype of such tool: IVM (Interactive Virtua Math) and discuss the didactical principles behind the tool. We use results of a small scale experiment at secondary and tertiary education involving four classes and their students and teachers that used IVM during one lesson to illustrate the working of the tool and the challenges of developing digital didactical tools for learning mathematics. This abstract is submitted to the workgroep didactic considerations with respect to digital tools for the teaching of mathematics
Eighteen years after the introduction of the graphing calculator in national examinations in the ... more Eighteen years after the introduction of the graphing calculator in national examinations in the Netherlands, much has been learned about the use of technology in education. One of the key lessons was that integrating ICT as a tool for learning math is a complex task, and this complexity is often underestimated. In this article we give a current view of the use of ICT in learner practice in the Netherlands and in particular in the discipline of mathematics. Some of the topics covered include the type of technologies and learning materials used and the curriculum guidelines for math and assessment. Reflecting on experiences and challenges of the last few years is given an idea of future priorities. Directions for improving the integration of technology in mathematics education include the need to understand their role in learning and developing students' mathematical knowledge and reasoning, an investment in teacher training, the quality of digital learning materials and in more ...
Conducting a classroom dialogue for reasoning can be very challenging for teachers and, in partic... more Conducting a classroom dialogue for reasoning can be very challenging for teachers and, in particular for students-teachers. Research on classroom discussions provides examples of models that can be used to help teachers organize, analyse and conduct classroom discussions. One of these models is the five-practices framework (Stein, Engle, Smith, & Hughes, 2008). In this study we investigate how this framework has been applied in one course of mathematics' pedagogies for in-service student-teachers at the applied university of Amsterdam to support mathematics student-teachers in conducting classroom dialogue based on students reasoning. The study was conducted in the academic year 2017-18 and involved 15 in-service student-teachers and their teachers. The data concerns students written rapports to an individual assignment in which they were requested to use the five-practices in an hypothetical classroom discussion. The preliminary results confirm that the model can be useful for...
Le Centre pour la Communication Scientifique Directe - HAL - SHS, Feb 1, 2017
An essential condition to use mathematics to solve problems is the ability to recognize, imagine ... more An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students' learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions.
In mathematics, sciences and economics, understanding and working with graphs are important skill... more In mathematics, sciences and economics, understanding and working with graphs are important skills. However, developing these skills has been shown to be a challenge in secondary and higher education as it involves high order thinking processes such as analysis, reflection and creativity. In this study, we present Interactive Virtual Math, a tool that supports the learning of a specific kind of graphs: dynamic graphs which represent the relation between at least two quantities that covary. The tool supports learners in visualizing abstract relations through enabling them to draw, move and modify graphs, and by combining graphs with other representations, especially interactive animations and textual explanations. This paper reports a design experiment about students' learning graphs with this tool. Results show that students with difficulty in generating acceptable graphs improve their ability while working with the tool.
An essential condition to use mathematics to solve problems is the ability to recognize, imagine ... more An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions
Aspectos envolvidos na proposição de uma tarefa com uso de recurso tecnológico: análise de uma experiência de ensino em aulas de Cálculo
Considerando o processo de elaboracao, aplicacao e refinamento de tarefas que facam uso de recurs... more Considerando o processo de elaboracao, aplicacao e refinamento de tarefas que facam uso de recursos tecnologicos configura-se como uma importante atividade no âmbito da Educacao Matematica, o objetivo deste texto e apresentar uma reflexao sobre aspectos envolvidos na proposicao de uma tarefa com uso do Geogebra, que integra um ambiente de ensino e aprendizagem de Calculo Diferencial e Integral. Para tanto, adota a metodologia de experiencia de ensino, enquanto um tipo especial de pesquisa baseada em design, e apresenta uma analise retrospectiva de dados oriundos do trabalho com tarefas para exploracao de ideias necessarias a compreensao do conceito de derivadas. Como resultados, evidenciam-se quatro aspectos do meio de aprendizagem envolvidos (a constar: a tarefa em si, o recurso tecnologico, a interpretacao das acoes e explicacoes dos estudantes e a interacao entre esses ultimos), que procuram trazer luz a questao de uma suposta “falha” na interacao com o aplicativo, o que permite ...
Collaborative learning tasks may represent an effective way to stimulate higher-order processes a... more Collaborative learning tasks may represent an effective way to stimulate higher-order processes among high-ability students in regular classrooms. This study investigated the effects of task structure and group composition on the elaboration and metacognitive activities of 11th grade pre-university students during a collaborative learning task: 102 students worked in small groups. On an ill-structured or moderately structured task. Differential effects for cognitive ability were investigated using a continuous measure. Likewise, the effects of group composition were examined using a continuous measure of the cognitive heterogeneity of the group. The group dialogues were transcribed and coded. Analysis revealed an interaction effect between task structure and cognitive ability on students' elaboration and metacognitive activities. Task structure had a negative effect on the elaborative contributions of high-ability students. For students with lower abilities, task structure had a...
Disclaimer/Complaints regulations If you believe that digital publication of certain material inf... more Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please contact the library: http://www.hva.nl/bibliotheek/contact/contactformulier/contact.html, or send a letter to: University Library (Library of the University of Amsterdam and Amsterdam University of Applied Sciences), Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
Gezamenlijk redeneren en het valideren van wiskundige ideeën : een case studie
Het gezamenlijk oplossen van wiskundige problemen creeert de gelegenheid voor leerlingen om te le... more Het gezamenlijk oplossen van wiskundige problemen creeert de gelegenheid voor leerlingen om te leren redeneren. Doordat leerlingen aan elkaar uitleg geven, worden ze bewust van bestaande kennis en mogelijke misconcepties en kunnen ze daardoor eigen kennis aanpassen en aanvullen. Leerlingen kunnen elkaar ook helpen om uitspraken en aangedragen resultaten te verbeteren met wiskundige betekenis en richting wiskundig redeneren (Dekker, Elshout-Mohr, & Wood, 2006). Bij het oplossen van schooltaken omvat wiskundig redeneren cognitieve activiteiten zoals het herroepen van kennis, verbindingen maken tussen begrippen, wiskundige representaties gebruiken, generaliseren van concrete situaties en conclusies trekken op basis van wiskundige eigenschappen (Lithner, 2008; Schoenfeld, 1992). Veel onderzoek naar gezamenlijk redeneren betreft de manier waarop leerlingen op elkaars ideeen voortbouwen maar er is weinig bekend over hoe leerlingen deze ideeen valideren (Francisco, 2013). Het doel van dit ...
Interactive Virtual Math: Een digitale tool om context-grafieken te leren in de klas
De doelstellingen van het Interactive Virtual Math-project zijn het ontwerpen en ontwikkelen van ... more De doelstellingen van het Interactive Virtual Math-project zijn het ontwerpen en ontwikkelen van de digitale tool voor het leren van grafieken bij dynamische contexten op de middelbare school (14-17 jaar oud) en om het gebruik van nieuwe technologieën voor leren in de klas te verkennen. Onderzoek biedt enkele didactische aanwijzingen om instructies te ontwikkelen die het leren van covariationaal redeneren ondersteunen (een belangrijke aspect bij het leren van dynamische grafieken). In deze poster presenteren we het prototype van een tool die covariationaal redeneren ondersteunt: IVM (Interactive Virtua Math) en bespreken we de didactische principes achter de tool. We gebruiken hiervoor de resultaten van een kleinschalig onderzoek met vier klassen die de tool hebben gebruikt om de werking van de tool te illustreren
Designing a digital tool for reasoning with covariation graphs: didactical considerations and classroom experience
[Paper abstract]: The aims of the Interactive Virtual Math-project are to design and develop a di... more [Paper abstract]: The aims of the Interactive Virtual Math-project are to design and develop a digital tool for learning covariation graphs at high school (14-17 years old students) and to explore the use of new technologies for learning in classroom. Research provides some didactical directions to develop instruction that supports the learning of covariational reasoning. For instance, engaging students in the mental activity to visualize a situation and construct relevant quantitative relationships should be prior to determining formulas or graphs. Also, learners can be helped to focus on quantities and generalizations about relationships, connections between situations, and dynamic phenomena. Digital tools can be designed in order to meet these and other didactical requirements. In this talk we present the prototype of such tool: IVM (Interactive Virtua Math) and discuss the didactical principles behind the tool. We use results of a small scale experiment at secondary and tertiary education involving four classes and their students and teachers that used IVM during one lesson to illustrate the working of the tool and the challenges of developing digital didactical tools for learning mathematics. This abstract is submitted to the workgroep didactic considerations with respect to digital tools for the teaching of mathematics
Eighteen years after the introduction of the graphing calculator in national examinations in the ... more Eighteen years after the introduction of the graphing calculator in national examinations in the Netherlands, much has been learned about the use of technology in education. One of the key lessons was that integrating ICT as a tool for learning math is a complex task, and this complexity is often underestimated. In this article we give a current view of the use of ICT in learner practice in the Netherlands and in particular in the discipline of mathematics. Some of the topics covered include the type of technologies and learning materials used and the curriculum guidelines for math and assessment. Reflecting on experiences and challenges of the last few years is given an idea of future priorities. Directions for improving the integration of technology in mathematics education include the need to understand their role in learning and developing students' mathematical knowledge and reasoning, an investment in teacher training, the quality of digital learning materials and in more ...
Conducting a classroom dialogue for reasoning can be very challenging for teachers and, in partic... more Conducting a classroom dialogue for reasoning can be very challenging for teachers and, in particular for students-teachers. Research on classroom discussions provides examples of models that can be used to help teachers organize, analyse and conduct classroom discussions. One of these models is the five-practices framework (Stein, Engle, Smith, & Hughes, 2008). In this study we investigate how this framework has been applied in one course of mathematics' pedagogies for in-service student-teachers at the applied university of Amsterdam to support mathematics student-teachers in conducting classroom dialogue based on students reasoning. The study was conducted in the academic year 2017-18 and involved 15 in-service student-teachers and their teachers. The data concerns students written rapports to an individual assignment in which they were requested to use the five-practices in an hypothetical classroom discussion. The preliminary results confirm that the model can be useful for...
Le Centre pour la Communication Scientifique Directe - HAL - SHS, Feb 1, 2017
An essential condition to use mathematics to solve problems is the ability to recognize, imagine ... more An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students' learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions.
In mathematics, sciences and economics, understanding and working with graphs are important skill... more In mathematics, sciences and economics, understanding and working with graphs are important skills. However, developing these skills has been shown to be a challenge in secondary and higher education as it involves high order thinking processes such as analysis, reflection and creativity. In this study, we present Interactive Virtual Math, a tool that supports the learning of a specific kind of graphs: dynamic graphs which represent the relation between at least two quantities that covary. The tool supports learners in visualizing abstract relations through enabling them to draw, move and modify graphs, and by combining graphs with other representations, especially interactive animations and textual explanations. This paper reports a design experiment about students' learning graphs with this tool. Results show that students with difficulty in generating acceptable graphs improve their ability while working with the tool.
An essential condition to use mathematics to solve problems is the ability to recognize, imagine ... more An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions
Aspectos envolvidos na proposição de uma tarefa com uso de recurso tecnológico: análise de uma experiência de ensino em aulas de Cálculo
Considerando o processo de elaboracao, aplicacao e refinamento de tarefas que facam uso de recurs... more Considerando o processo de elaboracao, aplicacao e refinamento de tarefas que facam uso de recursos tecnologicos configura-se como uma importante atividade no âmbito da Educacao Matematica, o objetivo deste texto e apresentar uma reflexao sobre aspectos envolvidos na proposicao de uma tarefa com uso do Geogebra, que integra um ambiente de ensino e aprendizagem de Calculo Diferencial e Integral. Para tanto, adota a metodologia de experiencia de ensino, enquanto um tipo especial de pesquisa baseada em design, e apresenta uma analise retrospectiva de dados oriundos do trabalho com tarefas para exploracao de ideias necessarias a compreensao do conceito de derivadas. Como resultados, evidenciam-se quatro aspectos do meio de aprendizagem envolvidos (a constar: a tarefa em si, o recurso tecnologico, a interpretacao das acoes e explicacoes dos estudantes e a interacao entre esses ultimos), que procuram trazer luz a questao de uma suposta “falha” na interacao com o aplicativo, o que permite ...
Collaborative learning tasks may represent an effective way to stimulate higher-order processes a... more Collaborative learning tasks may represent an effective way to stimulate higher-order processes among high-ability students in regular classrooms. This study investigated the effects of task structure and group composition on the elaboration and metacognitive activities of 11th grade pre-university students during a collaborative learning task: 102 students worked in small groups. On an ill-structured or moderately structured task. Differential effects for cognitive ability were investigated using a continuous measure. Likewise, the effects of group composition were examined using a continuous measure of the cognitive heterogeneity of the group. The group dialogues were transcribed and coded. Analysis revealed an interaction effect between task structure and cognitive ability on students' elaboration and metacognitive activities. Task structure had a negative effect on the elaborative contributions of high-ability students. For students with lower abilities, task structure had a...
Disclaimer/Complaints regulations If you believe that digital publication of certain material inf... more Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please contact the library: http://www.hva.nl/bibliotheek/contact/contactformulier/contact.html, or send a letter to: University Library (Library of the University of Amsterdam and Amsterdam University of Applied Sciences), Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
Gezamenlijk redeneren en het valideren van wiskundige ideeën : een case studie
Het gezamenlijk oplossen van wiskundige problemen creeert de gelegenheid voor leerlingen om te le... more Het gezamenlijk oplossen van wiskundige problemen creeert de gelegenheid voor leerlingen om te leren redeneren. Doordat leerlingen aan elkaar uitleg geven, worden ze bewust van bestaande kennis en mogelijke misconcepties en kunnen ze daardoor eigen kennis aanpassen en aanvullen. Leerlingen kunnen elkaar ook helpen om uitspraken en aangedragen resultaten te verbeteren met wiskundige betekenis en richting wiskundig redeneren (Dekker, Elshout-Mohr, & Wood, 2006). Bij het oplossen van schooltaken omvat wiskundig redeneren cognitieve activiteiten zoals het herroepen van kennis, verbindingen maken tussen begrippen, wiskundige representaties gebruiken, generaliseren van concrete situaties en conclusies trekken op basis van wiskundige eigenschappen (Lithner, 2008; Schoenfeld, 1992). Veel onderzoek naar gezamenlijk redeneren betreft de manier waarop leerlingen op elkaars ideeen voortbouwen maar er is weinig bekend over hoe leerlingen deze ideeen valideren (Francisco, 2013). Het doel van dit ...
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