Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

Abstract

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made ''ordered'' or ''non-ordered'' judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.Citation: Rubinsten O, Sury D (2011) Processing Ordinality and Quantity: The Case of Developmental Dyscalculia. PLoS ONE 6(9): e24079.

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity

“…This is in clear contrast with Rubinsten and Sury (2011) who proposed that these skills represented two independent, parallel core systems. Our findings also prompt at least some reconsideration of claims about the independence of comparison and ordering skills (e.g., Goffin & Ansari, 2016;Lyons & Beilock, 2013).…”

“…These studies most often used symbolic and non-symbolic comparison tasks. Nevertheless, recent studies (starting with Beilock, 2011, andRubinsten &Sury, 2011) also highlighted the importance of number-ordering skills in mathematical abilities. Indeed, Lyons et al (2014) showed that beyond a certain point in development, number-ordering abilities become the strongest predictors of arithmetic skills (although number comparison performance also continues to be a significant predictor).…”

“…Lyons, Price, Vaessen, Blomert, and Ansari (2014) found that whereas number comparison performance (i.e., participants' ability to quickly decide which of two numerals represents a larger quantity) was a better predictor of early symbolic number skills than numerical order processing, from around Grade 6, numerical order processing was the best predictor of children's arithmetic performance (as compared to seven other numerical predictors of arithmetic skills). There is also newly emerging evidence for an order processing deficit in both adults (Rubinsten & Sury, 2011) and children with developmental dyscalculia (Attout & Majerus, 2015). Finally Attout, Noël, and Majerus (2014) demonstrated that memory for order information was a robust predictor of the development of symbolic number skills in young children.…”

Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic

“…This is true of efforts to understand how the brain represents basic numerical representations, as well as research into how these basic processes underpin more sophisticated mathematical thinking. In the past few years, there has been a steady uptick in work on how we process the relative order of numbers (e.g., Brannon, ; Colomé & Noël, ; Delazer & Butterworth, ; Fias, Lammertyn, Caessens, & Orban, ; Franklin & Jonides, ; Franklin, Jonides, & Smith, ; Jou, ; Knops & Willmes, ; LeFevre & Bisanz, ; LeFevre, Kulak, & Bisanz, ; Lyons & Beilock, , , ; Lyons, Price, Vaessen, Blomert, & Ansari, ; Rubinsten & Sury, ; Turconi, Campbell, & Seron, ; Turconi & Seron, ; Zorzi, Di Bono, & Fias, ). Intriguingly, this work suggests that ordinality may be a key to understanding how we represent numbers symbolically (e.g., as Indo‐Arabic numerals; Delazer & Butterworth, ; Lyons & Beilock, , ; Turconi & Seron, ).…”

Using basic number processing tasks in determining students with mathematics disorder risk

“…Second, there might be still other tasks to be included in the screening tool. For example, the task of comparing analog quantities (34), both small and large quantities, ordering numbers (35), and transcoding tasks could be included in the screening tool. Further research can include the fMRI and eye tracking methodology to reveal the brain bases of MD.…”