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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: MOUTSIOS-RENTZOS, ANDREAS, SHIAKALLI, MARIA ANGELA, ZACHAROS, KONSTANTINOS
Μορφή: Online
Γλώσσα:English
Έκδοση: Urray 2019
Θέματα:
Διαθέσιμο Online:https://pasithee.library.upatras.gr/ejupUNESCOchair/article/view/2972
id oai:ojs.pasithee.library.upatras.gr:article-2972
record_format ojs
spelling 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
institution UPatras
collection Pasithee
language English
topic 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
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