NASCO GENERATES DOT ARRAYS Running Head: NASCO METHOD TO GENERATE DOT ARRAY

9 Basic numerical abilities are generally assumed to influence more complex 10 cognitive processes involving numbers, such as mathematics. Yet measuring 11 non-symbolic number abilities remains challenging due to the intrinsic 12 correlation between numerical and non-numerical dimensions of any visual 13 scene. Several methods have been developed to generate non-symbolic stimuli 14 controlling for the latter aspects but they tend to be difficult to replicate or 15 implement. In this study, we describe the NASCO method, which is an extension 16 to the method popularized by Dehaene, Izard, & Piazza (2005). Their procedure 17 originally controlled for two visual dimensions that are mediated by Number: 18 Total Area and Item Size (i.e., N = TA/IS). Here, we additionally propose to 19 control for another twofold dimension related to the array extent, which is also 20 mediated by Number: Convex Hull Area and Mean Occupancy (i.e., N = CH/MO). 21 We illustrate the NASCO method with a MATLAB app – NASCO app – that allows 22 easy generation of dot arrays for a visually controlled assessment of non23 symbolic numerical abilities. Results from a numerical comparison task revealed 24 that the introduction of this twofold dimension manipulation substantially 25 affected young adults’ performance. In particular, we did not replicate the 26 relation between non-symbolic number abilities and arithmetic skills. Our 27 findings open the debate about the reliability of previous results that did not take 28 into account visual features related to the array extent. We then discuss the 29 strengths of NASCO method to assess numerical ability, as well as the benefits of 30 its straightforward implementation in NASCO app for researchers. 31 Abstract Word Count: 249. 32Word Count: 249. 32 NASCO GENERATES DOT ARRAYS NASCO: A new method and program to generate dot arrays for non33 symbolic number comparison tasks 34 In 1997, Dehaene formulated that humans possess a Number Sense – a 35 biologically determined ability allowing the representation and the manipulation 36 of large numerical quantities. Most authors currently consider that such 37 numerical intuition relies on a cognitive system specifically dedicated to number 38 processing (following Feigenson, Dehaene, and Spelke, 2004). This view is 39 supported by extensive empirical evidence showing that humans can 40 discriminate numerical quantities from early age (Xu & Spelke, 2000), with 41 limited knowledge of number words (Pica, Lemer, Izard, & Dehaene, 2004), or 42 without formal instruction (Nys, Ventura, Fernandes, Querido, Leybaert, & 43 Content, 2013). Recent studies further supported this perspective by showing 44 that humans have a spontaneous preference for the numerical aspect of large 45 sets rather than for other continuous visual features (Cicchini, Anobile, & Burr, 46 2016; Ferrigno, Jara-Ettinger, Piantadosi, & Cantlon, 2017). Notwithstanding 47 such findings, some authors challenged the existence of a specific cognitive 48 system devoted to numerical processing and alternatively ventured that Number 49 Sense emerges from the combined weighting of continuous perceptual 50 dimensions available in visually displayed stimulus collections (Gebuis, Cohen 51 Kadosh, & Gevers, 2016; Leibovich, Katzin, Harel, & Henik, 2016). 52 The debate about the Number Sense nature is still ongoing (see Núñez, 2017, for 53 an interesting view) because there is a peculiar methodological issue relative to 54 non-symbolic number comparison tasks: it is empirically impossible to isolate 55 the cognitive processes specifically dedicated to numerical discrimination from 56 NASCO GENERATES DOT ARRAYS those related to other continuous magnitude discrimination. The numerosity 57 (i.e., the information about the number of elements) is indeed intrinsically 58 intertwined with non-numerical magnitudes, such as the luminance or the extent 59 of the array (see for instance, Gebuis and Reynvoet, 2012). Previous studies 60 showed that numerical judgments are substantially impacted by the total surface 61 occupied by all items (Guillaume, Nys, Mussolin, and Content, 2013), by the 62 individual size of the elements (Henik, Gliksman, Kallai, & Leibovich, 2017), by 63 the item density (Dakin, Tibber, Greenwood, Kingdom, and Morgan, 2011), and 64 by the size of the convex hull (i.e., the smallest convex polygon encompassing all 65 elements; Norris, Clayton, Gilmore, Inglis, and Castronovo, 2018). 66 Critically, empirical data showed that the procedure used to handle the 67 correlation issue between magnitudes considerably influences participants’ 68 judgments, and subsequently the measurement of approximate numerical ability 69 (Smets, Gebuis, Defever, & Reynvoet, 2014; Smets, Sasanguie, Szücs, & Reynvoet, 7