Supporting mathematical argumentation of pre-school children
In this theoretical paper, we focus on the mathematical argumentation of pre-school children about simple mathematics problems, considering the types of arguments employed and the role of the teacher in promoting or demoting certain argumentation characteristics, thus effectively establishing the ma...
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Διαθέσιμο Online: | https://pasithee.library.upatras.gr/ejupUNESCOchair/article/view/2972 |
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oai:ojs.pasithee.library.upatras.gr:article-29722019-09-12T05:38:20Z Supporting mathematical argumentation of pre-school children MOUTSIOS-RENTZOS, ANDREAS SHIAKALLI, MARIA ANGELA ZACHAROS, KONSTANTINOS Preschool mathematics education, argumentation, Toulmin, sociomathematical norms In this theoretical paper, we focus on the mathematical argumentation of pre-school children about simple mathematics problems, considering the types of arguments employed and the role of the teacher in promoting or demoting certain argumentation characteristics, thus effectively establishing the mathematical argumentation norm. We propose a model synthesising the full version of Toulmin’s argumentation scheme and a classification of the source of authority upon which the argumentation draws to identify the diverse ways that the teacher communicates the acceptable aspects of a mathematical argument. An exemplar application of the model to the collective argumentation of a class of four-year old children is presented. Urray 2019-02-20 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://pasithee.library.upatras.gr/ejupUNESCOchair/article/view/2972 10.26220/une.2972 Educational Journal of the University of Patras UNESCO Chair; Vol. 6, N. 1 (2019) - Colloque SIEST Méditerranée, Patras 2019 Educational Journal of the University of Patras UNESCO Chair; Vol. 6, N. 1 (2019) - Colloque SIEST Méditerranée, Patras 2019 2241-9152 eng https://pasithee.library.upatras.gr/ejupUNESCOchair/article/view/2972/3280 |
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Integrated teaching, decompartmentalization of academic disciplines, science and technology University Pedagogy, Flipped Classroom, e-learning Problem solving, teaching, learning, knowledge, declaratory, procedural Scientific literacy, attitudes towards science, epistemic beliefs, PISA Preschool mathematics education, argumentation, Toulmin, sociomathematical norms Educational robotics, visual programming, didactical analysis, early childhood education, computational thinking Classical Mechanics principles, Quantum Mechanics basic principles, wave in Quantum Mechanics. Copenhagen interpretation, Everett III interpretation Science textbook, physics textbook, textbook analysis, scientific practices, crosscutting concepts Intercultural competence, refugee identity, university course, candidate teachers, experiential learning Biological evolution, randomness, pupils’ conceptions, discussion with philosophic aim History, resonance, vibration, waves, cord Force, difficulties, assimilation modeling activities, conceptions Geometrical thinking, angle, rotation, simulation, Scratch Serious games, education to sustainable development, experiential learning Instrumented activity, instrumental approach, technical object, artifact, teaching-learning Variation-with-populations, population thinking, preschool, interview protocol Reasoning, semiotic modes, multimodal approach, physics teaching Preschoolers and categories, preschoolers and categorization criteria, preschoolers and category-based reasoning Sciences and technology, health education, particular teaching Promoting health, nutritional education, phytotherapy, Tunisian textbook Learning, possibilities, Piaget, constructivism, Bateson Early Childhood Education for Sustainabilit, early biology education, ‘possible futures’-approach, design research Role, school principal, Greece, NPM, autonomy Comprehension, bricolage, learning, constructivism Technical teaching, reform, Electric Engineering, French language, scientific subjects, difficulties Vocational teaching, co-design, co-teaching, educational design research Six Thinking Hats, decision-making, educational decisions, career guidance Inquiry, simulation, TACD, PCDR, mechanical wave Middle school, science learning, soil, geoscience Attrition, Science Teacher Education, Open and Distance Education, Pre-service Teachers Conceptions, socio-constructivism, learning, breathing Learning, digital technology, complexity, ICT, interdisciplinarity, didactic approach Emotional and behavioural difficulties, social and emotional learning, teacher-student relationships Autonomy, physics and chemistry, teachers, middle school Inquiry based science teaching, activity theory, professional didactics, teaching practice, intensity resonance, didactic contract Motivation, scientific career, school-university partnership, professional identity Roma, Greece, integration, exclusion, mediation, narrative Vocational activities, descriptions, differences between teachers and practitioners, implications on education Stability of teaching practices, Activity Theory, semiotic resources, video analysis Evaluation, modelisation, modeling tools, mechanical design Situational Pedagogy, skills in professional communication, professional didactics Early science teaching, children’s ideas, change of state, storytelling, drawing Educational content, blackboard, morpho-dynamics, non temporalization of displacements in the gridlines Adult secondary education, teaching of mathematics, utility PISA, press, globalisation, education policy, social imaginary Student dropout, Greece, qualitative research, interview quality, stance of universalism Hydraulics bench, energy conceptions, model-based learning, primary education Lifelong learning, perceptions, students Cognitive ergonomics, space ergonomics, computer laboratory Breathing, socioconstructivism, curriculum, curriculum didactics Block diagram, regulation, servo control, technical system Activity, artifact, instrument, instrumentalisation, integrated linear amplifier Désenchantement, enchantement, éducation, interaction Science teacher, teacher training, Science Education, pedagogical content knowledge, didactic transposition Training of teachers, training program, professionalization, universitarisation Virtual, life, inert, video games, conceptions Students, tutoring, learning, university, forum, social networks Domestic violence, women, students, academic performance, primary school, teachers Attitude, ICTs, training device, teachers training. Didactic of sciences, Task-activity, semiotic registers, energetic chain, primary school Didactical communication, teacher, student Argumentation, personal epistemology, learning, socio-scientific issues, digital Capacity, volume, didactic and ergonomic approach of practices, sciences education, teaching and learning Teaching physics, the joint action theory in didactics, contract, mechanical signal Fractions, concrete-representational-abstract approach, conceptual knowledge, low-achieving students, CRA effectiveness, instruction efficiency Proposals research, teaching didactics, impact, professional practice, exploded schema PISA, Science, test items, school-based examinations, textbooks, visual representations, functional role, type Educational robotics, teachers training, computational thinking, self-efficacy PISA, resilient students, Economic Social and Cultural Status, Finland, Portugal, Croatia Learning, education, entrepreneurship, Serious Games 3D printing technology, Activity Theory, modeling’s approach of Additive Manufacturing, fablabs Problem solving, verbal communication, cumulative talk, exploratory talk, investigative talk Cognitive development, Learning Disabilities, collaborative learning activities, Information and Communication Technologies (ICT’s) Systems Inquiry, systemic methodology, adult education, dropout Praxeology, intelligibility, traceability of objects of knowledge, movement on the grid Content and Language Integrated Learning, English, physics, didactics, upper secondary school, higher learning Secondary school students, attitudes, drugs Model, perception, abstraction, physics, Al-hiss al-mushtarak, Al-wahm, imagination Hypothesis writing, debate, inquiry, activity, speaking time Early childhood education, minerals, non-formal education, educational intervention Research and Study Courses (RSC), algebraic functions, secondary school Children’s representations, preschool education, clouds, early childhood science education Early science teaching, children’s ideas, elicitation, teachers’ beliefs and practices Device, distance, contractual teachers, teacher training education Emerging adulthood, Greece, distinctive characteristics, economic crisis Literacy in Science, knowledge-based approach, abilities, daily life Biological education, educational role of museums, zoological museum, environmental awareness, urban birds Teacher education, game-based learning, digital games-based learning Video, teachers-student, teacher training, reflection Cognitive errors, dysfunctional assumptions, cognitive psychotherapy, transformative learning Refutational text, natural number bias, multiplication makes bigger, misconceptions, rational numbers Instrumental genesis, Cabri-Geometry II, comparison, secondary school Physical magnitudes, symbolization, conventionality distended, teaching sequence, constructivism Cooperative learning, jigsaw technical, skills development, teaching/learning Physical Science teacher, teacher training, pedagogical content knowledge, didactic transposition Pedagogical alignment, assessment, formative evaluation, educational objectives School career, students, General High School, Vocational High School |
spellingShingle |
Integrated teaching, decompartmentalization of academic disciplines, science and technology University Pedagogy, Flipped Classroom, e-learning Problem solving, teaching, learning, knowledge, declaratory, procedural Scientific literacy, attitudes towards science, epistemic beliefs, PISA Preschool mathematics education, argumentation, Toulmin, sociomathematical norms Educational robotics, visual programming, didactical analysis, early childhood education, computational thinking Classical Mechanics principles, Quantum Mechanics basic principles, wave in Quantum Mechanics. Copenhagen interpretation, Everett III interpretation Science textbook, physics textbook, textbook analysis, scientific practices, crosscutting concepts Intercultural competence, refugee identity, university course, candidate teachers, experiential learning Biological evolution, randomness, pupils’ conceptions, discussion with philosophic aim History, resonance, vibration, waves, cord Force, difficulties, assimilation modeling activities, conceptions Geometrical thinking, angle, rotation, simulation, Scratch Serious games, education to sustainable development, experiential learning Instrumented activity, instrumental approach, technical object, artifact, teaching-learning Variation-with-populations, population thinking, preschool, interview protocol Reasoning, semiotic modes, multimodal approach, physics teaching Preschoolers and categories, preschoolers and categorization criteria, preschoolers and category-based reasoning Sciences and technology, health education, particular teaching Promoting health, nutritional education, phytotherapy, Tunisian textbook Learning, possibilities, Piaget, constructivism, Bateson Early Childhood Education for Sustainabilit, early biology education, ‘possible futures’-approach, design research Role, school principal, Greece, NPM, autonomy Comprehension, bricolage, learning, constructivism Technical teaching, reform, Electric Engineering, French language, scientific subjects, difficulties Vocational teaching, co-design, co-teaching, educational design research Six Thinking Hats, decision-making, educational decisions, career guidance Inquiry, simulation, TACD, PCDR, mechanical wave Middle school, science learning, soil, geoscience Attrition, Science Teacher Education, Open and Distance Education, Pre-service Teachers Conceptions, socio-constructivism, learning, breathing Learning, digital technology, complexity, ICT, interdisciplinarity, didactic approach Emotional and behavioural difficulties, social and emotional learning, teacher-student relationships Autonomy, physics and chemistry, teachers, middle school Inquiry based science teaching, activity theory, professional didactics, teaching practice, intensity resonance, didactic contract Motivation, scientific career, school-university partnership, professional identity Roma, Greece, integration, exclusion, mediation, narrative Vocational activities, descriptions, differences between teachers and practitioners, implications on education Stability of teaching practices, Activity Theory, semiotic resources, video analysis Evaluation, modelisation, modeling tools, mechanical design Situational Pedagogy, skills in professional communication, professional didactics Early science teaching, children’s ideas, change of state, storytelling, drawing Educational content, blackboard, morpho-dynamics, non temporalization of displacements in the gridlines Adult secondary education, teaching of mathematics, utility PISA, press, globalisation, education policy, social imaginary Student dropout, Greece, qualitative research, interview quality, stance of universalism Hydraulics bench, energy conceptions, model-based learning, primary education Lifelong learning, perceptions, students Cognitive ergonomics, space ergonomics, computer laboratory Breathing, socioconstructivism, curriculum, curriculum didactics Block diagram, regulation, servo control, technical system Activity, artifact, instrument, instrumentalisation, integrated linear amplifier Désenchantement, enchantement, éducation, interaction Science teacher, teacher training, Science Education, pedagogical content knowledge, didactic transposition Training of teachers, training program, professionalization, universitarisation Virtual, life, inert, video games, conceptions Students, tutoring, learning, university, forum, social networks Domestic violence, women, students, academic performance, primary school, teachers Attitude, ICTs, training device, teachers training. Didactic of sciences, Task-activity, semiotic registers, energetic chain, primary school Didactical communication, teacher, student Argumentation, personal epistemology, learning, socio-scientific issues, digital Capacity, volume, didactic and ergonomic approach of practices, sciences education, teaching and learning Teaching physics, the joint action theory in didactics, contract, mechanical signal Fractions, concrete-representational-abstract approach, conceptual knowledge, low-achieving students, CRA effectiveness, instruction efficiency Proposals research, teaching didactics, impact, professional practice, exploded schema PISA, Science, test items, school-based examinations, textbooks, visual representations, functional role, type Educational robotics, teachers training, computational thinking, self-efficacy PISA, resilient students, Economic Social and Cultural Status, Finland, Portugal, Croatia Learning, education, entrepreneurship, Serious Games 3D printing technology, Activity Theory, modeling’s approach of Additive Manufacturing, fablabs Problem solving, verbal communication, cumulative talk, exploratory talk, investigative talk Cognitive development, Learning Disabilities, collaborative learning activities, Information and Communication Technologies (ICT’s) Systems Inquiry, systemic methodology, adult education, dropout Praxeology, intelligibility, traceability of objects of knowledge, movement on the grid Content and Language Integrated Learning, English, physics, didactics, upper secondary school, higher learning Secondary school students, attitudes, drugs Model, perception, abstraction, physics, Al-hiss al-mushtarak, Al-wahm, imagination Hypothesis writing, debate, inquiry, activity, speaking time Early childhood education, minerals, non-formal education, educational intervention Research and Study Courses (RSC), algebraic functions, secondary school Children’s representations, preschool education, clouds, early childhood science education Early science teaching, children’s ideas, elicitation, teachers’ beliefs and practices Device, distance, contractual teachers, teacher training education Emerging adulthood, Greece, distinctive characteristics, economic crisis Literacy in Science, knowledge-based approach, abilities, daily life Biological education, educational role of museums, zoological museum, environmental awareness, urban birds Teacher education, game-based learning, digital games-based learning Video, teachers-student, teacher training, reflection Cognitive errors, dysfunctional assumptions, cognitive psychotherapy, transformative learning Refutational text, natural number bias, multiplication makes bigger, misconceptions, rational numbers Instrumental genesis, Cabri-Geometry II, comparison, secondary school Physical magnitudes, symbolization, conventionality distended, teaching sequence, constructivism Cooperative learning, jigsaw technical, skills development, teaching/learning Physical Science teacher, teacher training, pedagogical content knowledge, didactic transposition Pedagogical alignment, assessment, formative evaluation, educational objectives School career, students, General High School, Vocational High School MOUTSIOS-RENTZOS, ANDREAS SHIAKALLI, MARIA ANGELA ZACHAROS, KONSTANTINOS Supporting mathematical argumentation of pre-school children |
topic_facet |
Integrated teaching, decompartmentalization of academic disciplines, science and technology University Pedagogy, Flipped Classroom, e-learning Problem solving, teaching, learning, knowledge, declaratory, procedural Scientific literacy, attitudes towards science, epistemic beliefs, PISA Preschool mathematics education, argumentation, Toulmin, sociomathematical norms Educational robotics, visual programming, didactical analysis, early childhood education, computational thinking Classical Mechanics principles, Quantum Mechanics basic principles, wave in Quantum Mechanics. Copenhagen interpretation, Everett III interpretation Science textbook, physics textbook, textbook analysis, scientific practices, crosscutting concepts Intercultural competence, refugee identity, university course, candidate teachers, experiential learning Biological evolution, randomness, pupils’ conceptions, discussion with philosophic aim History, resonance, vibration, waves, cord Force, difficulties, assimilation modeling activities, conceptions Geometrical thinking, angle, rotation, simulation, Scratch Serious games, education to sustainable development, experiential learning Instrumented activity, instrumental approach, technical object, artifact, teaching-learning Variation-with-populations, population thinking, preschool, interview protocol Reasoning, semiotic modes, multimodal approach, physics teaching Preschoolers and categories, preschoolers and categorization criteria, preschoolers and category-based reasoning Sciences and technology, health education, particular teaching Promoting health, nutritional education, phytotherapy, Tunisian textbook Learning, possibilities, Piaget, constructivism, Bateson Early Childhood Education for Sustainabilit, early biology education, ‘possible futures’-approach, design research Role, school principal, Greece, NPM, autonomy Comprehension, bricolage, learning, constructivism Technical teaching, reform, Electric Engineering, French language, scientific subjects, difficulties Vocational teaching, co-design, co-teaching, educational design research Six Thinking Hats, decision-making, educational decisions, career guidance Inquiry, simulation, TACD, PCDR, mechanical wave Middle school, science learning, soil, geoscience Attrition, Science Teacher Education, Open and Distance Education, Pre-service Teachers Conceptions, socio-constructivism, learning, breathing Learning, digital technology, complexity, ICT, interdisciplinarity, didactic approach Emotional and behavioural difficulties, social and emotional learning, teacher-student relationships Autonomy, physics and chemistry, teachers, middle school Inquiry based science teaching, activity theory, professional didactics, teaching practice, intensity resonance, didactic contract Motivation, scientific career, school-university partnership, professional identity Roma, Greece, integration, exclusion, mediation, narrative Vocational activities, descriptions, differences between teachers and practitioners, implications on education Stability of teaching practices, Activity Theory, semiotic resources, video analysis Evaluation, modelisation, modeling tools, mechanical design Situational Pedagogy, skills in professional communication, professional didactics Early science teaching, children’s ideas, change of state, storytelling, drawing Educational content, blackboard, morpho-dynamics, non temporalization of displacements in the gridlines Adult secondary education, teaching of mathematics, utility PISA, press, globalisation, education policy, social imaginary Student dropout, Greece, qualitative research, interview quality, stance of universalism Hydraulics bench, energy conceptions, model-based learning, primary education Lifelong learning, perceptions, students Cognitive ergonomics, space ergonomics, computer laboratory Breathing, socioconstructivism, curriculum, curriculum didactics Block diagram, regulation, servo control, technical system Activity, artifact, instrument, instrumentalisation, integrated linear amplifier Désenchantement, enchantement, éducation, interaction Science teacher, teacher training, Science Education, pedagogical content knowledge, didactic transposition Training of teachers, training program, professionalization, universitarisation Virtual, life, inert, video games, conceptions Students, tutoring, learning, university, forum, social networks Domestic violence, women, students, academic performance, primary school, teachers Attitude, ICTs, training device, teachers training. Didactic of sciences, Task-activity, semiotic registers, energetic chain, primary school Didactical communication, teacher, student Argumentation, personal epistemology, learning, socio-scientific issues, digital Capacity, volume, didactic and ergonomic approach of practices, sciences education, teaching and learning Teaching physics, the joint action theory in didactics, contract, mechanical signal Fractions, concrete-representational-abstract approach, conceptual knowledge, low-achieving students, CRA effectiveness, instruction efficiency Proposals research, teaching didactics, impact, professional practice, exploded schema PISA, Science, test items, school-based examinations, textbooks, visual representations, functional role, type Educational robotics, teachers training, computational thinking, self-efficacy PISA, resilient students, Economic Social and Cultural Status, Finland, Portugal, Croatia Learning, education, entrepreneurship, Serious Games 3D printing technology, Activity Theory, modeling’s approach of Additive Manufacturing, fablabs Problem solving, verbal communication, cumulative talk, exploratory talk, investigative talk Cognitive development, Learning Disabilities, collaborative learning activities, Information and Communication Technologies (ICT’s) Systems Inquiry, systemic methodology, adult education, dropout Praxeology, intelligibility, traceability of objects of knowledge, movement on the grid Content and Language Integrated Learning, English, physics, didactics, upper secondary school, higher learning Secondary school students, attitudes, drugs Model, perception, abstraction, physics, Al-hiss al-mushtarak, Al-wahm, imagination Hypothesis writing, debate, inquiry, activity, speaking time Early childhood education, minerals, non-formal education, educational intervention Research and Study Courses (RSC), algebraic functions, secondary school Children’s representations, preschool education, clouds, early childhood science education Early science teaching, children’s ideas, elicitation, teachers’ beliefs and practices Device, distance, contractual teachers, teacher training education Emerging adulthood, Greece, distinctive characteristics, economic crisis Literacy in Science, knowledge-based approach, abilities, daily life Biological education, educational role of museums, zoological museum, environmental awareness, urban birds Teacher education, game-based learning, digital games-based learning Video, teachers-student, teacher training, reflection Cognitive errors, dysfunctional assumptions, cognitive psychotherapy, transformative learning Refutational text, natural number bias, multiplication makes bigger, misconceptions, rational numbers Instrumental genesis, Cabri-Geometry II, comparison, secondary school Physical magnitudes, symbolization, conventionality distended, teaching sequence, constructivism Cooperative learning, jigsaw technical, skills development, teaching/learning Physical Science teacher, teacher training, pedagogical content knowledge, didactic transposition Pedagogical alignment, assessment, formative evaluation, educational objectives School career, students, General High School, Vocational High School |
format |
Online |
author |
MOUTSIOS-RENTZOS, ANDREAS SHIAKALLI, MARIA ANGELA ZACHAROS, KONSTANTINOS |
author_facet |
MOUTSIOS-RENTZOS, ANDREAS SHIAKALLI, MARIA ANGELA ZACHAROS, KONSTANTINOS |
author_sort |
MOUTSIOS-RENTZOS, ANDREAS |
title |
Supporting mathematical argumentation of pre-school children |
title_short |
Supporting mathematical argumentation of pre-school children |
title_full |
Supporting mathematical argumentation of pre-school children |
title_fullStr |
Supporting mathematical argumentation of pre-school children |
title_full_unstemmed |
Supporting mathematical argumentation of pre-school children |
title_sort |
supporting mathematical argumentation of pre-school children |
description |
In this theoretical paper, we focus on the mathematical argumentation of pre-school children about simple mathematics problems, considering the types of arguments employed and the role of the teacher in promoting or demoting certain argumentation characteristics, thus effectively establishing the mathematical argumentation norm. We propose a model synthesising the full version of Toulmin’s argumentation scheme and a classification of the source of authority upon which the argumentation draws to identify the diverse ways that the teacher communicates the acceptable aspects of a mathematical argument. An exemplar application of the model to the collective argumentation of a class of four-year old children is presented. |
publisher |
Urray |
publishDate |
2019 |
url |
https://pasithee.library.upatras.gr/ejupUNESCOchair/article/view/2972 |
work_keys_str_mv |
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