Strategy use on bounded and unbounded number lines in typically developing adults and adults with dyscalculia: An eye-tracking study

Abstract

Recent research suggests that bounded number line tasks, often used to measure number sense, measure proportion estimation instead of pure number estimation. The latter is thought to be measured in recently developed unbounded number line tasks. Children with dyscalculia use less mature strategies on unbounded number lines than typically developing children. In this qualitative study, we explored strategy use in bounded and unbounded number lines in adults with (N = 8) and without dyscalculia (N = 8). Our aim was to gain more detailed insights into strategy use. Differences in accuracy and strategy use between individuals with and without dyscalculia on both number lines may enhance our understanding of the underlying deficits in individuals with dyscalculia. We combined eye-tracking and Cued Retrospective Reporting (CRR) to identify strategies on a detailed level. Strategy use and performance were highly similar in adults with and without dyscalculia on both number lines, which implies that adults with dyscalculia may have partly overcome their deficits in number sense. New strategies and additional steps and tools used to solve number lines were identified, such as the use of the previous target number. We provide gaze patterns and descriptions of strategies that give important first insights into new strategies. These newly defined strategies give a more in-depth view on how individuals approach a number lines task, and these should be taken into account when studying number estimations, especially when using the unbounded number line.

Unbounded number line estimation as a measure of numerical estimation

“…We used a smaller number range for unbounded number line estimation as there is no evidence that number range influences participants’ estimation patterns (i.e., increasing error variability with increasing target numbers). In fact, estimation patterns were virtually identical across smaller and larger ranges (e.g., 25 in [ 5 ]; 49 in [ 20 ]; 400 in [ 33 ]; 1,000 in [ 34 ]).…”

Quantity discrimination in newly hatched zebrafish suggests hardwired numerical abilities

“…Because the young of precocial species are born or hatched after a long developmental period, their brain and behavioural repertoire closely match that of adults [19][20][21][22] . Therefore, this well-developed brain might allow newborns to cope with numerical tasks with compensatory mechanisms 23,24 . To study the early appearance of cognitive abilities, it is possible to focus on vertebrate species that have evolved developmental modes as opposed to precociality [25][26][27] .…”

Eye-tracking methodology in mathematics education research: A systematic literature review

“…Learning difficulties Eye tracking has been used to characterize and analyze learning disabilities in mathematics. These eight studies (5%) compared typically developing students and students with dyscalculia (Moeller, Neuburger, et al, 2009;van der Weijden et al, 2018;van Viersen et al, 2013), Down syndrome (Abreu-Mendoza & Arias-Trejo, 2015), autism (Winoto et al, 2017), developmental coordination disorder (Gomez et al, 2017), and general mathematical learning difficulties van't Noordende et al, 2016).…”

“…Moreover, given enough time, students might use strategies and approaches that are sufficient, but not optimal. Thus, observing solution processes without interrupting students is a major challenge that can be tackled through eye tracking (e.g., Inglis & Alcock, 2012;Obersteiner & Tumpek, 2016;van der Weijden et al, 2018). b) The research included aspects of visualization and mental representations.…”