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Gender, Choices, and STEM 2 Than Were Given by the Experimenter, Etc.) Spontaneous Focusing on Numerosity Is Linked to Numerosity Discrimination in Children and Adults Mattan S. Ben-Shachar1*, Svetlana Lisson1* Dalit Shotts-Peretz1, Minna Hannula-Sormunen2, and Andrea Berger 1Department of Psychology, Ben-Gurion University of the Negev, Faculty of Humanities and Social Sciences and Zlotowski Center for Neuroscience, Beer Sheva, Israel 2Department of Teacher Education, University of Turku, Finland Spontaneous focusing on numerosity (SFON) is the tendency to spontaneously address exact numerosity in the environment without prompting. While previous studies have found children’s SFON to be a stable, domain-specific predictor of mathematical abilities throughout development, it is unclear whether SFON reflects individual differences in quantitative processing. This study examined the relationship between SFON and the acuity of the Approximate Number System (ANS) in children and adults. To measure adults’ SFON, we developed a numerosity bias task (NBT). In children and adults, better ANS acuity was related to higher tendency to spontaneously focus on numerosity. Additionally, in adults, SFON was related to higher mathematical academic achievements. These findings suggest an interplay between SFON and ANS acuity, indicating a mechanism where increased ANS acuity makes numerosity elements in the environment more salient, while early self-initiated numerical practice promotes fine-tuning of the ANS. Possible implications of these reciprocal developmental pathways are discussed. Keywords: spontaneous focusing, numerosity, Weber ratio, mathematical abilities, mathematical achievements Research on mathematical development during who exhibit SFON tend to identify numerosities and preschool shows that children display considerable incorporate these impressions into decision making or individual differences in the rate of early behaviour, all without any explicit trigger, mathematical skills and knowledge acquisition, and in encouragement, or guidance to do so (Hannula and the fusion of acquired concepts and abilities (Hannula- Lehtinen 2005). Sormunen, McMullen, and Lehtinen 2019). A recent, So far, such individual differences in young growing body of research suggests that children’s children (up to 3 years of age) have been explored SFON, the process of attending to the aspect of the mainly using a number of imitation tasks, developed number of objects or incidents in a self-initiated by Hannula and Lehtinen (2005), that evaluate this manner (without being prompted by others), has an spontaneous tendency. In these tasks, the important role in early numerical development experimenter displays some numerosity properties but (Hannula and Lehtinen 2005; Hannula, Lepola, and at no point are they explicitly marked as important, Lehtinen 2010; Hannula, Räsänen, and Lehtinen 2007; and special care is taken to avoid any wording that Hannula-Sormunen, Lehtinen, and Räsänen 2015; could suggest that the tasks are mathematical or McMullen et al. 2019; Rathé et al. 2016). quantitative in nature. In these tasks, children have Environmental elements of numerosity, even if been found to differ in their tendencies to present, are not always focused on or used in one’s spontaneously focus on numerosity: Some children actions, and studies have found individual differences would imitate the exact actions of the experimenter in the tendency to focus on this aspect of the (e.g., feeding a puppet “sweets”) with no regard to environment without any guidance or numerical numerosity, whereas others would imitate the action, while also attending to the aspect of numerosity (e.g., * These authors contributed equally to this work. feeding the puppet the exact number of sweets as was Corresponding Author: Mattan S. Ben-Shachar Email: [email protected] given by the experimenter, or regarding it in other ways, such as counting the number of distributed context (Hannula and Lehtinen 2005). Individuals sweets, asking if they could give more or fewer sweets 1 Gender, Choices, and STEM 2 than were given by the experimenter, etc.). These The ANS is characterized by an imprecise ability individual differences in the children’s disposition to to distinguish quantities by relying on an estimation focus on environmental numerosites were found to be derived from a distribution of activations on the relatively stable, specifically in preschool ages, as mental number line (Izard and Dehaene 2008; Mou demonstrated by positive correlations for SFON and Van Marle 2014; Stoianov and Zorzi 2012), with scores between 4 and 5 years of age (Hannula and distribution overlap increasing in correspondence with Lehtinen 2005). an increase in numerosity (Izard and Dehaene 2008; A number of studies have demonstrated Stoianov and Zorzi 2012). According to the ANS correlations between SFON and children’s model, the distinction between quantities is made on mathematical abilities (Batchelor, Inglis, and Gilmore the basis of the ratio between them, in accordance 2015; Bojorque et al. 2017; Hannula and Lehtinen with Weber’s law (Dehaene 2003), which states that 2005; Hannula et al. 2010, 2007; McMullen, Hannula- the discrimination threshold between two given Sormunen, and Lehtinen 2015). For example, stimuli (of any given type of sensory modality) children’s mathematical abilities at the age of 3.5 increases by a given factor, as the intensity of the years predicted their SFON tendency at the age of 4 stimulus grows (e.g., Jordan and Brannon 2006). This years, which, in turn, predicted later mathematical discrimination ability improves as we develop, with abilities at the ages of 5 and 6 years which could not the greatest improvement occurring in the first year of be accounted for by insufficient enumeration skills, life (Brannon, Suanda, and Libertus 2007; Halberda et linguistic abilities, or difficulties in comprehending al. 2012; Lipton and Spelke 2004; Xu and Spelke task instructions (Hannula and Lehtinen 2005). Other 2000). For example, day-old infants are able to studies showed that, for kindergarten-aged children, differentiate quantities with a ratio of 1:3 (Izard et al. SFON predicted mathematical abilities over and 2009), at the age of 6 months, infants are able to above other cognitive skills either two or six years discriminate by a ratio threshold of 1:2 (Brannon et al. later -- when the children were either in second or 2007; Xu and Spelke 2000), and, at the age of 9 fifth grade -- but again did not predict their reading months, by a ratio of 2:3 (Lipton and Spelke 2003, skills at this age (Hannula et al. 2010; Hannula- 2004; Xu and Arriaga 2007). By 3-4 years of age, Sormunen et al. 2015; McMullen et al. 2015; Nanu et children are already capable of discriminating ratios of al. 2018). This particular attentional bias is considered 3:4, and adult humans can discriminate quantities with an important precursor to the exact number a ratio of 7:8, with some even succeeding with a ratio recognition process, because using exact number of 9:10 (Halberda and Feigenson 2008). The relative information in action requires analytical, conscious weight of learning experience versus brain maturation processing (Hannula and Lehtinen 2005; Hannula- on these life-long changes in ANS acuity has yet to be Sormunen et al. 2015). Simply put, one must decide to established (Geary 2013). regard specific information (among all of the Although the ANS plays a crucial role in human perceived information) as relevant, in order to act on cognition, individuals differ in their resolution of it. Although the contribution of enhanced mental quantitative processing and numerosity discrimination practice with numerosities, consequent to higher (Halberda and Feigenson 2008). One of the most well- SFON tendency, is well-established (Hannula- known computerized tasks used to measure individual Sormunen et al. 2019; McMullen, Hannula-Sormunen, discrimination ratios is the Panamath dot- and Lehtinen 2014; Rathé et al. 2016), it is unclear discrimination task (Halberda and Feigenson 2008). why numerosity elements in the environment are more During this task, participants are presented with two salient for some children compared to others. dot arrays and are asked to indicate which is more Considering the early manifestation of these numerous, with the task becoming more difficult as individual differences along with the domain- the ratio between both dot arrays decreases (as a result specificity of the SFON tendency, a possible of Weber’s law). Differences in individual Weber underlying influence could be the ANS, which is an ratios (the ratio required for successful discrimination) innate and adaptive system for processing quantities estimated using this task have been found to be a and is a congenital system of numerical representation domain-specific marker for mathematical abilities (Carey 2009; Spelke and Kinzler 2007) that is (Halberda and Feigenson 2008; Halberda, Mazzocco, common to human, and some nonhuman, animal and Feigenson 2008). For example, performance on species (Carey 2009; Feigenson, Dehaene, and Spelke the Panamath task has been found to correlate and 2004; Rugani, Vallortigara, and Regolin 2013). even predict academic mathematical achievements Gender, Choices, and STEM 3 over a 6-month period (Halberda et al. 2008; Libertus, Participants. Feigenson, and Halberda 2013). Moreover, children’s Participants were 51 preschoolers (19 boys) with performances on a symbolic math task have been ages ranging from 3.05 years to 4.9 years (M=3.03 shown to improve following
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