Year: 2007
Type: dissertation
Abstract: The present dissertation focused on one aspect of mathematical knowledge: fact knowledge. More specifically, we focused on the relation between the memory representations of simple multiplication and division facts (both operands < 10), as this remains a debated issue. This dissertation contains an introductory chapter (Chapter 1), four empirical chapters (Chapters 2-5) and a general discussion (Chapter 6). In Chapter 2, we used the number-matching task (measuring automatic activation of fact knowledge) and we expected to find stronger interference effects for division problems (compared to inverse division problems) if an independent division network exists. This was not confirmed as both problem types led to automatic activation. In two subsequent studies, we focused on developmental changes in multiplication and division performance. In Chapter 3, we showed that the formation of a memory network of multiplication facts is a fast-developing process. This study laid out the foundations for Chapter 4, in which we investigated both multiplication and division performance from the moment a child acquires the multiplication and division tables until the end of fourth grade. All effects that have been robustly observed in adults were also observed in children, quickly after they acquired the tables. Moreover, all effects observed in multiplication performance were also present in division performance and strong developmental parallels between both operations were observed. These results are a necessary condition to exclude the existence of independent networks. In Chapter 5 we investigated adult multiplication and division performance by making use of a learning paradigm. Clear evidence for cross-operation transfer of learning was found, which is not in line with the idea of independent representations at high skill levels. Taken together, using different paradigms and different populations, the results of the present studies speak against the idea of independent memory networks for multiplication and division facts and show that it is more correct to consider multiplication and division as mutually dependent and interacting skills.
Author: Jolien De Brauwer
Language: English
Subfield: Developmental and Educational Psychology
Field: Psychology
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2324988085