Abstracts - Earli

During learning and problem solving they can strengthen, complement, or hinder each other indifferent ways. In the symposium we will investigate the roles of external and internal knowledgerepresentations, and, especially, the roles of their interactions in children’s mathematics learning.Empirical studies from the domains of numerical estimation, probability theory, graphcompetence, and understanding of algebraic expressions will highlight aspects of this wide fieldand elaborate on them with the help of different methodological approaches, such as experimentaland developmental designs, eye-tracking, interviews, and path analyses. The discussion willaddress commonalities and differences of external and internal knowledge representations, theimplications of the presented studies from the viewpoints of cognitive science as well aspedagogy, and relations between the two disciplines that became apparent during thepresentations.The role of internal representations of magnitude in numerical estimationJulie Booth, Carnegie Mellon University, USARobert Siegler, Carnegie Mellon University, USAThis study examined developmental and individual differences in choice of numericalrepresentation for four types of numerical estimation; it also aimed to determine whether theseindividual differences were related to students’ general mathematics ability. Second and fourthgrade students completed four different tasks on the 0-1000 scale: number line, measurement,numerosity, and computational estimation. Estimates improved between second and fourth gradefor all four tasks. At both grade levels, all types of estimation were consistently intercorrelated,and each was also correlated with individual differences in children’s math achievement. Inaddition, we replicated the previously observed shift between second and fourth grade fromreliance on a logarithmic representation of numbers to use of a linear one on the 0-1000 scale, notonly on the number line task, but on the measurement and numerosity tasks as well. The threemeasures of linearity were also related to math achievement, though their intercorrelationsremained when math achievement was controlled for. Results from this study suggest thatdifficulty in choosing the appropriate, linear representation of numbers may explain children’spoor performance on a variety of estimation and other mathematics tasks.Children’s access to representations of magnitude and the development of mathematicaldisabilitiesBert De Smedt, K.U. Leuven, BelgiumAnn Swillen, K.U. Leuven, BelgiumLieven Verschaffel, K.U. Leuven, BelgiumPol Ghesquiere, K.U. Leuven, BelgiumIt has been demonstrated that the speed and efficiency of accessing representations of magnitude isan important determinant of the development of mathematical skills in primary school children.Moreover, recent research suggests that mathematical disabilities (MD) are due to a domainspecificdeficit in the speed and efficiency of accessing such magnitude representations of number.The present study examined children’s access to representations of magnitude and its relation tomathematical functioning in children with a genetic disorder who are at risk for math disability,namely children with Velo-Cardio-Facial Syndrome (VCFS). Performance of twenty-five primaryschool children with VCFS was compared with an individually matched control group. A classicnumber comparison task was administered to measure children’s access to representations ofmagnitude. All children completed assessments of various mathematical abilities (single-digitarithmetic, multidigit arithmetic, word problem solving). A number reading task was administered– 292 –