The development of children’s additive and multiplicative reasoning in open problems

Additive reasoning was traditionally assumed to be a precursor of multiplicative reasoning. This was postulated after numerous studies indicating that young children erroneously reason additively in multiplicative word problems (for an overview, see e.g. Van Dooren, De Bock, & Verschaffel, 2010). However, this assumption has been recently questioned by the finding that young children already show some multiplicative reasoning abilities (Nunes & Bryant, 2010). Moreover, older children erroneously reason multiplicatively in additive word problems, despite their additive reasoning abilities (e.g. Van Dooren et al., 2010). Children’s incorrect reasoning in word problems seems not merely dependent on their (in)ability to reason additively or multiplicatively, but also on their preference for additive or multiplicative reasoning. We studied the development of third to sixth graders' preference for additive or multiplicative reasoning by means of schematic problems that were open to both additive and multiplicative reasoning, i.e. arrow schemes wherein three numbers were given and a fourth one was missing. While children in Study 1 were asked to fill out the missing number in an open answer format, in Study 2 another group of children was asked to indicate all possible answers amongst a set of given alternatives. In both studies, most answers were additive, but a substantial number of multiplicative answers was given too. This indicates the existence of a multiplicative preference besides an additive preference. Second, additive answers decreased, while multiplicative answers increased across grades. Third, problems with integer number ratios evoked fewer additive and more multiplicative answers than non-integer problems, especially in fifth grade. Study 2 moreover revealed that children rarely considered both the additive and the multiplicative answer. This occurred more often by older children in upper primary education and in integer problems. In sum, our results resemble previous findings of word problem research (e.g., Van Dooren et al., 2010), suggesting that getting a view on preference next to ability is indispensable in order to fully understand the development of additive and multiplicative reasoning.status: publishe