The role of mental argumentation in Mathematics vis-à-vis property perception and the operational mode

• Main Author: MΑΜΟΝΑ-DΟWNS, JOANNA
• Format: Online
• Language: English
• Published: Urray 2012
• Subjects: Science education, scientific revolution, history and philosophy of science and; Science and mathematics education; education; Participation, early mathematics, mathematising process, children’s initiatives, play pedagogies; Primary education, investigative approach, scientific and technological activities; Material and virtual resources, praxeology, task, technique, technology, register, number sense, place-value system, Chinese abacus; Science, pseudoscience, expert, media, television, media format; Chemical reaction, MBL, Lebanon, labwork; Spatial skills, programming cards, Scratch Jr, tangible material, code learning; Contradictions, conflicts, turning points, early childhood, science education, motives, demands, everyday concepts, scientific concepts; Explanations construction, teaching, sciences, preschool; Avalanche, joint action theory for didactics (JATD), physics, resources, science communication; Museology, science education, archaeological museum, interdisciplinary interpretation of museum collections, archaeometry; Science disaffection, aims of science education, didactics, educational policy and administration; Technology education, curriculum, gender; Content analysis, qualitative research, primary school, scientific research activity; PhD studies, PhD student, supervisor, research problem; Science education, chemistry, conceptions, teaching practices, atomic models; Health literacy, kindergarten teacher, qualitative research, content analysis; Environmental education, environmental issues, social representations, word associations, environmental conceptions; Indigenous education, biology education, models, living beings classification; Digital technology, documentation work, programming, students’ autonomy, teacher education; Science education, precursor models construction, flotation, teaching and learning strategy, preschool education.; Science, investigation, école primaire, élèves en situation de handicap; Scolarisation des élèves handicapés; habiletés éducatives; gestes professionnels d’ajustement; auxiliaire de vie scolaire; école primaire française; Teacher training, mathematics teaching, scheme, instrument; Teaching physics, energy concept, systems of signs, inscriptions, semiotic resources; Concept force, didactic transposition, mathematical approach, students’ difficulties misconceptions; France, history of science, teaching, experimental sciences, Volta.; Inquiry based teaching, formulation of hypotheses, buoyancy, manipulation, students' ideas; Inquiry-Based Science Education, biology in early childhood education, teaching practices in kindergarten, learning practices in kindergarten; Early childhood science, drawing, young children’s ideas, change of state; Science Education, Mathematics Education, international testing, school curricula; Problems solving, knowledge, task, declarative, procedural, hierarchy; Earth science curriculum, student learning, quality assessment, validity and reliability study, survey development; Health education, educational styles, biomedical model, health promotion, textbooks; Learning material; knowledge structures; WPW learning model; content specialization; engagement; heteroglossia; Educative robotics, primary school, learning, micro-genetics approach, activity analysis; Ethical issues, Biological Sciences, PCK, Scientific Argumentation; Conception, learning, complexity, ecosystem; Early childhood, graphical sign lexicons, repertoires, children’s mathematical graphics, emergent learners; Young children’s thinking, sociocultural/cultural-historical theory, methodology, early childhood science; Ancient remains, amphorae, mediation; Why-questions, knowledge-statements, belief-statements, epistemic status of scientific theories; Preparation, physics and technology teachers, science and technology education, Greece; Logical-mathematical games, logical reasoning, operations and logical deductions, recurrence of logical-mathematical games in daily educational activities; IBSE, primary school, Intentio, institutional science education project; Gender, relationship to scientific knowledge, ROSE project, French student, secondary school science, science education; Evaluation, professional competences, initial teachers, didactic roles; Canadian science museums, mission statements, museum mission statements, roles, science centres, science museums; Monologue, egocentric speech, thought, enunciative dimension, education; Relativity of simultaneity, theory of conceptual fields, secondary school, Special Theory of Relativity; Adequacy training-employment, epistemology, professional identity, occupational integration, teaching practices, professional knowledge, school knowledge; Science education, participatory science, authenticity of learning, teaching practices, school-scientist partnerships; Methodology, exploratory data analysis, inquiry based science education, teachers representations; Representations, ICT uses; ICT practices; university students; digital skills; Nature of science, teacher education, key-ideas, matrix of stages and strands, didactical units; Bloodstream, scientific debate, language interactions, cognitive work; Inquiry-based science education, previous experience, previous knowledge; Mental argumentation, property based thinking, meaning in mathematics, thinking globally, the role of symbols; Prospective teachers, elementary school, pedagogical competency, scientific competency, science and technology; Energy, epistemological awareness, scientific constructs, trans-phenomenological aspect, system analysis; Science exhibitions, technoscientific issues, practice and process, communicating controversy in science, critical viewer, negotiation; Contextual issues, history of science, effective learning, physics education; Early childhood science education; children’s ideas; communication; drawing activity; group discussion; research methods; Earth’s shape; day/night cycle; Spatial awareness, direction, orientation, programmable toy Bee-Bot, educational scenario, preschool children’s representations; Professional development, learning trajectories, student teachers, learning trajectories, expertise; Problem solving, conceptual understanding, square, construction, pre-school education; Visual methods, participation, early childhood, competency, Mosaic approach; Early year education, decomposition, recycling, constructivist learning environment; Transition, mathematics, coping styles, higher education, assessment; History and Philosophy of Science, History and Philosophy of Mathematics, HP&ST; Chemical education; car catalyst; students’ misconceptions; mental models; Scientific education, continuing education, teachers, high school, participatory museum, society museums, museum of civilisation, exhibition media, community of practice; Semiotic representation registers, proportionality, problem solving, tabular register, graphical register; Metalinguistic function, scientific code, early childhood education, theatre semiotics

In this article, mental argumentation concerning the doing of mathematics is characterized by that part of reasoning dealing with the perception of properties, in contrast to that involving an operational mode of thinking. In particular, the role of mental argumentation is argued in terms of semantics, holism, the usage of symbolism and what reasoning can be achieved without pen and paper. The discourse is based on a succession of mathematical tasks, stated in the text together with solutions and comments on how the solutions could be reached. What transpires is that there is a mutual dependence between mental argumentation and operational working, even though at first the two might seem to represent opposites. A partial account of the nature of this interaction is given.