Abstracts - Earli

K 1031 August 2007 08:30 - 10:30Room: 0.100ASymposiumThe development of children’s reasoning on linear and non-linearsituationsChair: Dirk De Bock, European University College Brussels, BelgiumOrganiser: Dirk De Bock, European University College Brussels, BelgiumOrganiser: Wim Van Dooren, Catholic University of Leuven, BelgiumOrganiser: Lieven Verschaffel, Catholic University of Leuven, BelgiumDiscussant: Peter Bryant, University of Oxford, United KingdomSince many years, research has demonstrated children’s difficulties to reason linearly (orproportionally), both from a technical and conceptual point of view. At the same time, recentstudies in different countries show that children also tend to over-use the linear model, i.e. theystart applying linear/proportional strategies also in non-linear situations. This symposium bringstogether research findings on the development of students’ reasoning in linear and non-linearsituations, and more specifically on their tendency to over-use linearity. The studies includestudents from various ages (from 5-year olds to adults) and pertain to a variety of mathematicaldomains. By confronting these different lines of research – each encountering the over-use oflinear methods in a particular way –, we will not only show the university and diversity of thisphenomenon, but also gain a deeper understanding of the psychological and educational processesinvolved. Ebersbach et al. found that even 5-year-old preschoolers already discriminate betweenlinear and non-linear growth processes in inductive reasoning. Nevertheless, they stillunderestimate non-linear growth in a too linear fashion. Van Dooren et al. focus on the solution ofword problems by 9-12-year-olds. They convincingly show that the number structure of a missingvalueproblem strongly affects students’ tendency to (improperly) apply linear methods. Modestouet al. further develop the knowledge on improper linear reasoning in geometrical problem solvingconcerning area and volume in 14-15-year-olds. These reasearchers found a weaker impact of thelinear model on 15-year old students’ reasoning compared to that of younger students. Finally,Hadjidemetriou et al. investigated the over-use of linearity in graphical contexts by 15-year-oldsand their teachers. They provided strong evidence for the existence of a ‘Linear Prototype’ instudents, and even in some teachers.Little, more, non-linear: How the concept of non-linearity developsMirjam Ebersbach, Leiden University, NetherlandsWilma C M Resing, Leiden University, NetherlandsMany phenomena in everyday life may be conceived of as either linear or non-linear processes:Whereas the total price of chocolate bars is usually a linear function of the total number ofchocolate bars one buys, the thickness of a folded paper increases non-linearly with the number offolds. The present study investigated whether 5-year-olds (N=54) are able to differentiate betweenboth types of processes. Children forecasted linear and quadratic growth in an inductive reasoningtask, in which the information amount initially provided, was systematically varied. As a result,the majority of children assumed a rule-based process even if only minimal information was given.Furthermore, they discriminated between linear and quadratic growth by estimating the first one– 604 –