title: Categories of Large Numbers in Line Estimation.
abstract: How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words-thousand, million, billion-to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time are expected near the boundaries between categories. In contrast to previous work (Landy, Silbert, & Goldin, 2013) that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers.
authors.affiliation: Indiana University.|University of Richmond.
authors.forename: David
authors.initials: D
authors.lastname: Landy
authors.affiliation: University of Richmond.
authors.forename: Arthur
authors.initials: A
authors.lastname: Charlesworth
authors.affiliation: Worchester Polytechnic Institute.
authors.forename: Erin
authors.initials: E
authors.lastname: Ottmar
mesh_terms: D003071:Cognition / Q000502:physiology*; D006801:Humans; D007600:Judgment / Q000502:physiology*; D008433:Mathematics; D011340:Problem Solving / Q000502:physiology*; D011930:Reaction Time / Q000502:physiology
keywords: Category adjustment theory; Concepts; Mathematical cognition; Mathematical misconceptions; Neural reuse; Number line; Numerical magnitude; Numerical reasoning