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Nonsymbolic approximate arithmetic and working memory: A dual-task study with preschoolers Iro Xenidou-Dervou, Ernest C. D.M. van Lieshout & Menno van der Schoot
(Barth, Beckmann, & Spelke, 2008) Nonsymbolic approximate arithmetic The Dot task “Phylogenetically widespread approximate magnitude system”(Barth, Starr & Sullivan, 2009) Preschool children *WM role!
Working Memory • Working Memory (WM) predictor Baddeley’s Tripartite WM Model. • 1. Visual-Spatial SketchPad(VSSP) • 2.Phonological Loop (PL) • 3. Central Executive (CE) • No previous study has examined: • the relation between approximate math and WM. • the specific WM resources which are allocated for nonsymbolic arithmetic processing.
Hypotheses • Nonsymbolic approximate arithmetic processing would depend on VSSP components (Rasmussen & Bisanz, 2005) • Memory updating on the elements presented, thus CE involvement. (Morris & Jones, 1990)
Method • Participants: 62 children (25 boys; mean age: 5.95 years) • Design: • Each subject 5 sessions with the nonsymbolic approximate arithmetic task (primary task): • 1. without interference (baseline) • 2. PL interference, • 3. Visual interference • 4. Spatial interference • 5. CE interference.
Material – Primary Task • Primary task : the Dot-task New: Reaction Time registration
Material – Primary Task • 24 trials; numerocities: 6-70 • Controlling for total surface area/density/circumference • 3 ratios: 4:7, 4:6, 4:5 • Controlling for non-addition strategies with ratio-based differences
Material – Secondary Tasks • 1. PL - adapted Letter Span task (LS), 2.Visual– adapted Abstract Patterns task (AP), 3.Spatial – adapted Corsi Blocks (CB) 4.CE – Continuous Choice Reaction Time Task-Random (CRT-R task)
+ + + Dot-task Material – Secondary Tasks Dual Stand -alone • Also conducted in stand alone control conditions with a 15 sec delay replacing the primary task. Same or different? Same or different?
Procedure • Childrencounterbalanced based on intelligence (Raven) between two task-order presentation conditions: • 1. AP, LS, CB, CRT-R, dual-AP, dual-LS, dual-CB, dual-CRT-R & Dot-task • 2.Or the opposite order.
Results • Primary task • Accuracy: 60.21%, chance = 50%, t(61) = 7.18, p < .001) • Ratio effect: F(2,122)=31.21, p <.001
Results • Interference Conditions: accuracy Conditions x ratios Conditions
Results • Interference Conditions: RTs
Results • Secondary Tasks • WM demands are indexed by performance breakdowns on either the primary or the secondary tasks. • Children performed worse on the CE (t(60) = 8.12; p < .001) but also, surprisingly, on the PL (t(61) = 2.24; p < .05).
Conclusions • Central Executive: • The process of updating WM most important for NA math processing. • Phonological Loop involvement • Effect of instructions during dot-task (e.g.“look”) • Attempt to phonologically code the numerical magnitudes they saw in order to process them (Krajewski & Schneider, 2009).
Conclusions... • Enhancement of later math development prediction and early intervention “Non-symbolic approximate representations are central to human knowledge of mathematics” (Gilmore & Spelke, 2008) • Does approximate math play a role in later development? • Or are WM components that mediate approximate math performance more important?
for your attention! Contact: I.XenidouDervou@psy.vu.nl Websites: http://vu.mathchild.nl http://mathchild.nl/