Rethinking Intensive Quantities via Guided Mediated Abduction

Autor/in	Abrahamson, Dor
Titel	Rethinking Intensive Quantities via Guided Mediated Abduction
Quelle	In: Journal of the Learning Sciences, 21 (2012) 4, S.626-649 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1050-8406
DOI	10.1080/10508406.2011.633838
Schlagwörter	Teaching Methods; Mathematics Instruction; Middle School Students; Thinking Skills; Mathematical Concepts; Cognitive Processes; Mediation Theory; Perception; Instructional Design; Epistemology; Inferences; Constructivism (Learning); Probability; Case Studies; Grade 6; Semi Structured Interviews + Suchen Sie Ihr Suchwort? Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Denkfähigkeit; Cognitive process; Kognitiver Prozess; Mediationsverfahren; Wahrnehmung; Lesson concept; Lessonplan; Unterrichtsentwurf; Erkenntnistheorie; Inference; Inferenz; Wahrscheinlichkeitsrechnung; Wahrscheinlichkeitstheorie; Case study; Fallstudie; Case Study; School year 06; 6. Schuljahr; Schuljahr 06
Abstract	Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students' sensation of an intensive quantity could serve as a powerful resource for grounding its formal expression, accepting the mathematical form requires students to align the sensation with a new way of reasoning about the phenomenon. I offer a case analysis of a middle school student who successfully came to understand the intensive quantity of likelihood. The analysis highlights a form of reasoning called "abduction" and suggests that sociocognitive processes can guide and mediate students' abductive reasoning. Interpreting the child's and tutor's multimodal action through the lens of abductive inference, I demonstrate the emergence of a proportional concept as guided mediated objectification of tacit perception. This "gestalt first" process is contrasted with traditional "elements first" approaches to building proportional concepts, and I speculate on epistemic and cognitive implications of this contrast for the design and instruction of these important concepts. In particular, my approach highlights an important source of epistemic difficulty for students as they learn intensive quantities: the difficulty in shifting from intuitive perceptual conviction to mediated disciplinary analysis. My proposed conceptualization of learning can serve as an effective synthesis of traditional and reform-based mathematics instruction. (Contains 1 table, 1 figure and 4 footnotes.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10