Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction

“…Children with more than 1 year of formal instruction on fractions have demonstrated this ability (Iuculano & Butterworth, ; Siegler et al ., ). Recently, researchers investigated an early stage of formal fraction instruction in fourth graders (McMullen, Hannula‐Sormunen, & Lehtinen, ; McMullen, Laakkonen, Hannula‐Sormunen, & Lehtinen, ; Resnick et al ., ; Vamvakoussi, ). Specifically, in studying fraction magnitude understanding, Resnick et al .…”

Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches

“…Recently, researchers have started to explore children's spontaneous focusing on quantitative relations (SFOR), as a follow-up of their investigations on children's spontaneous focusing on numerosity (SFON), which has already shown to have predictive power in explaining children's later mathematical achievement (Hannula and Lehtinen 2005). McMullen, Hannula-Sormunen and Lehtinen (McMullen et al 2014) describe SFOR as 'the spontaneous (i.e. undirected) focusing of attention on quantitative relations and the use of these relations in reasoning' (p. 218).…”

“…In these situations, the recognition and use of quantitative aspects of the situation are done at the child's own initiative and thus undirected and spontaneous (e.g. Hannula and Lehtinen 2005;McMullen et al 2013McMullen et al , 2014. Therefore, studies on SFON and SFOR do not examine whether learners are able to recognise or count exact number but rather whether they spontaneously use their available number recognition or quantitative reasoning skills in situations where they are not explicitly guided or instructed to do so.…”

Spontaneous Focusing on Numerosity Is Linked to Numerosity Discrimination in Children and Adults

“…Simply put, one must decide to regard specific information (among all of the perceived information) as relevant, in order to act on it. Although the contribution of enhanced mental practice with numerosities, consequent to higher SFON tendency, is well-established McMullen, Hannula-Sormunen, and Lehtinen 2014;Rathé et al 2016), it is unclear why numerosity elements in the environment are more salient for some children compared to others. Considering the early manifestation of these individual differences along with the domain-specificity of the SFON tendency, a possible underlying influence could be the ANS, which is an innate and adaptive system for processing quantities and is a congenital system of numerical representation (Carey 2009;Spelke and Kinzler 2007) that is common to human, and some nonhuman, animal species (Carey 2009;Feigenson, Dehaene, and Spelke 2004;Rugani, Vallortigara, and Regolin 2013).…”