Abstracts - Earli

C 129 August 2007 08:30 - 10:30Room: KonferenciaEARLI Invited SymposiumConstruction of mathematical knowledge: new conceptual andmethodological developmentsChair: Lieven Verschaffel, Katholieke Universiteit Leuven, BelgiumOrganiser: Lieven Verschaffel, Katholieke Universiteit Leuven, BelgiumDiscussant: Brian Greer, University of Portland, USADiscussant: Andreas Demetriou, University of Cyprus, CyprusDevelopment in the domain of mathematics from birth through the end of adolescence generatesincreasingly more complex, abstract, and rule-governed concepts, and more versatile, flexible, andplanfull problem solving skills (Demetriou, 2006). Nothwithstanding major work done bydevelopmental psychologists and mathematics educators like Baroody and Dowker (2003),Hiebert (1986), Rittle-Johnson and Siegler (1998), Star (2005), and many others, the respectiveroles of procedural and conceptual knowledge in students’ learning of mathematics continues to bea topic of animated debate. Recent theoretical and methodological developments, with importantimplications for both research and practice, have led to new approaches to this topical issue.Compared to previous research, this recent work is characterized, first, by a greater reliance tolongitudinal and intervention methods that seriously take into account the impact of people’sinstructional histories and, second, by the use of more advanced and sophisticated methods andtechniques for data gathering and data analysis The present symposium comprises four papers oforiginal research programmes addressing the above pivotal issue, followed by two discussionpapers, one by a developmental psychologist and one by a mathematics educator.Children’s understanding and use of the inverse relation between addition and subtraction.Peter Bryant, University of Oxford, United KingdomTerezinha Nunes, University of Oxford, United KingdomResearch on the understanding of the inverse relation between addition and subtraction hasconcentrated, almost entirely, on the procedural question of the "short-cut strategy". This researchdeals with the extent to which children are able to solve a+b-b problems rapidly and correctlywithout having to calculate. However, the underlying development which leads to this insight hasbeen rather neglected. We shall report studies which show that a crucial change in children’sunderstanding of the inverse relation takes place in the pre-school years. At this time manychildren progress from understanding the inversion of identity (if you add some stuff to an objectand then take the same stuff away, you restore the status quo) to understanding the inversion ofquantity (if you add 3 items to a set, and then take 3 different items away from it, the number ofitems in the set is as it was in the first place). We shall also show that children’s understanding ofinversion at this time is not restricted to exact cancellation: they are as likely to judge correctlythat a+b-c=>a when b>c as that a+b-b=a. During the pre-school period there are large individualvariations among children in their success with inversion problems, and our evidence suggests thatthese persist into the school years. We shall argue that there is a link between the strength ofchildren’s underlying understanding of the inverse addition-subtraction relation and their ability toadopt "short-cut" inversion procedures.– 119 –