To add or to multiply? An investigation of children's preference for additive or multiplicative relations

Multiplicative reasoning is not only omnipresent in numerous daily life situations, it also plays a critical role in the learning of advanced mathematical topics as well as in other fields of study (Lamon, 1993; Lamon & Lesh, 1992; Lesh, Post, & Behr, 1988; Vergnaud, 1988). For these reasons, the development of multiplicative reasoning has been frequently studied. However, it is not achieved easily. Numerous studies indicated that young children inappropriately reason additively in multiplicative word problems (e.g. Kaput & West, 1994; Karplus, Pulos, & Stage, 1983; Noelting, 1980; Resnick & Singer, 1993). The inverse error has been found too, that is, older children inappropriately reason multiplicatively in additive word problems (Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2005; Van Dooren, De Bock, & Verschaffel, 2010). Although those errors were traditionally explained by children's lacking skills to make the necessary computations and to discriminate between additive and multiplicative models underlying word problems, these explanations purely in terms of lacking computation and discrimination skills do not seem to suffice, since children may have acquired these two skills but still produce errors. The present doctoral dissertation generally aimed to shed a new light on the development of children's additive and multiplicative reasoning, by investigating their preference for additive or multiplicative relations as an additional explanation - besides their lacking skills - for their inappropriate word problem solving behavior. This dissertation consists of two research lines. A first research line, which consists of studies presented in Chapters 1 to 4, showed the existence of a subject characteristic that can be identified as a preference for additive or multiplicative relations, by means of diverse problems that are open to additive and multiplicative relations. This research line also yielded insight in the development of those relational preferences throughout primary school, and revealed some task (e.g., open vs. additive vs. multiplicative task, continuous vs. discrete quantities, integer vs. non-integer number ratios) and subject characteristics (e.g., computation skill) that impact children's preference. In a second research line, we demonstrated the importance (Chapter 5) and explored the nature of children's relational preference (Chapter 6). Relating to its importance, we provided evidence for the unique explanatory role of children's preference in inappropriate word problem solving behavior, in children who possessed the necessary computation and discrimination skills. Further, we investigated (1) the perseverance of children's preference, that is the extent to which children perseveringly held on to their preference when being confronted with alternative answers to open problems, and (2) the deliberateness of their preference, that is the extent to which their preferential answer was given deliberately.

Jaar van publicatie:2019

Toegankelijkheid:Closed