Spontaneous focusing on quantitative relations as a predictor of rational number development in students. In J. McMullen (Chair), Expanding inquiries of spontaneous mathematical focusing tendency within mathematical development. Symposium conducted at the biennial meeting of the European Association for Research on Learning and Instruction (EARLI)

While a good understanding of rational numbers is an essential part of mathematical literacy, research has repeatedly shown that learners have a lot of difficulties dealing with various aspects of rational numbers (e.g. Vamvakoussi & Vosniadou, 2010). Still, little is known about the relevant contributors to learning trajectory leading to rational number understanding (McMullen, Hannula-Sormunen, & Lehtinen, 2014). Recently Lehtinen, McMullen, and Hannula-Sormunen (2014) found that Spontaneous Focusing On quantitative Relations (SFOR) was a unique contributor to the gain of rational number knowledge through instruction, even after controlling for prior knowledge of rational numbers, arithmetic fluency, and non-verbal intelligence. The goal of the present research was to replicate the study of Lehtinen and colleagues (2014) and extend it by controlling for learners’ general mathematics achievement. Results showed that SFOR was indeed a unique contributor to the gain of rational number knowledge through instruction, after taking into account previous knowledge of rational numbers, non-verbal intelligence, math fluency skills, and general mathematical skills. Both studies propose that learners who are more likely to focus on the more mathematically advanced aspect of tasks, such as the quantitative relations in a task, may gain more self-initiated practice with these skills than their peers who may only focus on less advanced aspects. This increase in self-initiated practice may contribute to mathematical skills development, particularly with regard to concepts related to rational numbers.status: publishe

The relation between learners' spontaneous focusing on quantitative relations and their rational number knowledge

Many difficulties learners have with rational number tasks can be attributed to the “natural number bias”, i.e. the tendency to inappropriately use natural number properties in rational numbers tasks (Van Hoof, 2015). McMullen and colleagues found a relevant source of individual differences in the learning of those aspects of rational numbers that are susceptible to the natural number bias, namely Spontaneous Focusing On quantitative Relations (SFOR) (McMullen, 2014). While McMullen and colleagues showed that SFOR relates to rational number knowledge as a whole, we studied its relation with several aspects of the natural number bias. Additionally, we (1) included test items addressing operations with rational numbers and (2) controlled for general mathematics achievement and age. Results showed that SFOR related strongly to rational number knowledge, even after taking into account several control variables. Results are discussed for each of the three aspects of the natural number bias separately.status: publishe