To add or to multiply? An interview study on primary school children's preference for additive or multiplicative relations

edition: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 5)status: publishe

How do Flemish children solve ‘Greek’ word problems? On children’s quantitative analogical reasoning in mathematically neutral word problems

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Reconsidering SFOR: Characterizing children’s spontaneous focus on quantitative relations. In J. McMullen (Chair) Expanding inquiries of spontaneous mathematical focusing tendency within mathematical development. Symposium conducted at the Biennial Conference of the European Association for Research on Learning and Instruction (EARLI)

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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

To add or to multiply? The role of preference in erroneous word problem solving behavior

Posterstatus: publishe

To add or to multiply? An investigation of the role of preference in children's solutions of word problems

Previous research has shown that upper primary school children frequently erroneously solve additive word problems multiplicatively, while younger children frequently erroneously solve multiplicative word problems additively. It has been suggested that children's preference for additive or multiplicative relations explains these errors, besides their lacking skills, but this claim has not been tested empirically yet. Therefore, we administered four test instruments (a word problem test, a preference test, and two tests measuring additive and multiplicative computation and discrimination skill) to 246 third to sixth graders. Previous research results on errors in word problems, as well as on preference were replicated and systematized. Further, they were extended by explaining this erroneous word problem solving behavior by preference, for those children who unmistakably had acquired the necessary computation and discrimination skills. This finding provides strong evidence for the unique additional role of children's preference in erroneous additive or multiplicative word problem solving behavior.status: publishe

Verhoudingsrekenen in de basisschool: Ook voorkeuren in kaart gebracht

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Spontaneous focusing on quantitative relations: Towards a characterisation

In contrast to previous studies on Spontaneous Focusing On quantitative Relations (SFOR), the present study not only investigated the extent to which children focus on (multiplicative) quantitative relations, but also the nature of children’s quantitative focus (i.e., the types of quantitative relations that children focus on). Therefore, we offered three different SFOR tasks – a multiplicative, additive, or open SFOR task – to 315 second, fourth and sixth graders. Results revealed, first, that most children spontaneously focused on quantitative relations. Some focused on multiplicative relations, others on additive relations. Second, SFOR, and especially multiplicative SFOR, increased with grade, while the development of additive SFOR differed between tasks. Third, the open SFOR task seemed best suited to capture SFOR, since it evoked the largest number of each type of relational answers − while still showing substantial inter-individual differences in SFOR. These results indicate that a broader conceptualization and operationalisation of SFOR than the unilateral multiplicative one is warranted.status: publishe

Erroneous additive or multiplicative reasoning: The role of preference besides ability

Previous research has repeatedly shown that children erroneously reason additively in multiplicative word problems, while others erroneously reason multiplicatively in additive word problems. The present study aimed to investigate to what extent this erroneous reasoning depends on children’s preference for additive or multiplicative relations, besides their abilities. A preference test, a word problem test, and a test measuring the (procedural and conceptual) additive and multiplicative reasoning abilities were administered to 246 third to sixth graders. Results revealed that a substantial percentage of the erroneous additive reasoners or erroneous multiplicative reasoners possessed all necessary abilities, and almost all of them had a more general preference for additive resp. multiplicative relations.status: publishe

“That sounds Greek to me!” Primary children's additive and proportional responses to unreadable word problems

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