Subitizing and Finger Gnosis Predict Calculation Fluency in Adults

Subitizing and Finger Gnosis Predict Calculation Fluency in Adults Marcie Penner-Wilger (mpennerw@uwo.ca) Department of Psychology, King’s University College at Western University 266 Epworth Avenue, London, ON, Canada N6A 2M3 Rylan J. Waring (rwaring2@uwo.ca) Department of Psychology, King’s University College at Western University 266 Epworth Avenue, London, ON, Canada N6A 2M3 Adam T. Newton (anewton9@uwo.ca) Department of Psychology, King’s University College at Western University 266 Epworth Avenue, London, ON, Canada N6A 2M3 Abstract Both subitizing, the ability to enumerate small sets without counting, and finger gnosis, the ability to mentally represent one’s fingers, have been found to predict calculation skill in children (Penner-Wilger et al., 2007, 2009). In the current paper, we examined whether these same relations hold for young adults. Consistent with the developmental data, both subitizing and finger gnosis were significantly related to university students’ (N = 51) calculation fluency, jointly accounting for 33% of variability in fluency. The findings demonstrate that early precursor skills to mathematics remain similarly related into adulthood. Introduction The calculation skills of young adults are falling (LeFevre et al., 2014; Mulhern & Wylie, 2004). LeFevre et al. (2014) report data showing that the arithmetic fluency of university students has declined by 24% across a 12-year span. This decline is problematic, because without basic calculation skills students have insufficient resources to grasp more advanced material (Walcyzk & Griffith-Ross, 2006). Also, strong calculation skills are related to positive employment outcomes including obtaining and retaining a job, higher employment income, and home ownership (Bynner & Parsons, 1997; Parsons & Bynner, 1997; Ritchie & Bates, 2013). Indeed, the links are stronger for numeracy than for literacy skills. Recent research has identified foundational capacities that underlie the development of calculation skills in children (Butterworth, 2010; Penner-Wilger et al. 2007). In the current paper, we examine whether these childhood precursors to calculation skill, subitizing and finger gnosis, remain related to calculation skill into young adulthood. The answer to this research question will address whether the relation in childhood simply reflects the cognitive strategies employed by children while learning arithmetic or a more fundamental and enduring relation. Subitizing, the ability to enumerate small sets without counting, predicts calculation skill in children (Penner- Wilger et al., 2007; Reeve, Reynolds, Humberstone, & Butterworth, 2012). Children can typically subitize to three items, whereas adults can typically subitize to four items (Svenson & Sjoberg, 1983). Penner-Wilger et al. (2007) examined the relation between subitizing and calculation skill in Grade 1 children. Children completed an enumeration task, where they were shown a set of dots and asked to verbally report how many dots were shown. The response time (RT) slope as a function of set size across 1-3 items was used as the subitizing measure. A slope close to zero indicates subitizing (items enumerated in parallel) and a positive slope indicates counting. Calculation skill was measured using the calculation subtest from the Woodcock- Johnson Psycho-Educational Battery-Revised (Woodcock & Johnson, 1989). Penner-Wilger et al. found that subitizing was significantly related to calculation skill [r(145) = -. 31] concurrently in Grade 1. Children with better subitizing ability, indicated by flatter slopes, displayed better calculation skills. These findings were extended by Reeve et al. (2012) who found that subitizing ability at six years of age was related to calculation skill both concurrently and also longitudinally at nine and eleven years of age. Children with developmental dyscalculia, a deficit in numeracy and/or arithmetic, have poorer subitizing abilities than typically developing children (Andersson & Ostergren, 2012; Landerl, 2013; Schleifer & Landerl, 2011). Schleifer and Landerl (2011) found that dyscalculic children in Grades 2, 3 and 4 had response time slopes across 1-3 items that were twice as steep as the slopes of their typically developing peers. Landerl (2013) replicated the finding that dyscalculic children in Grades 2-4 have steeper RT slopes than typically developing children for dot enumeration across 1-3 items. Thus, there is evidence for a relation between subitizing ability and calculation skill both within typically developing samples and when comparing between typically developing and dyscalculic samples. Why does subitizing predict calculation skill? Butterworth (1999; 2010) proposed that the capacity to abstractly represent numerosity, the number of items in a set, is a foundational ability for building calculation skill. The dot enumeration task indexes this capacity to abstractly represent numerosities by requiring the mapping of an abstract symbol (e.g., 3 or “three”) onto a set. In a test of