Supporting mathematical argumentation of pre-school children

• Main Authors: MOUTSIOS-RENTZOS, ANDREAS, SHIAKALLI, MARIA ANGELA, ZACHAROS, KONSTANTINOS
• Format: Online
• Language: English
• Published: Urray 2019
• Subjects: 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

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.