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

Nonsymbolic approximate arithmetic  “Phylogenetically widespread approximate magnitude system” (Barth, Starr & Sullivan, 2009)  Preschool children (Barth, Beckmann, & Spelke, 2008) The Dot task *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 oNonsymbolic approximate arithmetic processing would depend on VSSP components (Rasmussen & Bisanz, 2005) o Memory updating on the elements presented, thus CE involvement. (Morris & Jones, 1990)

Method o Participants: 62 children (25 boys; mean age: 5.95 years) o 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 oPrimary 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)

Material – Secondary Tasks + Dot-task + + Same or different? Also conducted in stand alone control conditions with a 15 sec delay replacing the primary task. Dual Stand -alone

Procedure Children counterbalanced 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 ratiosConditions

Results  Interference Conditions: RTs

Results  Secondary Tasks o WM demands are indexed by performance breakdowns on either the primary or the secondary tasks. o 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... “Non-symbolic approximate representations are central to human knowledge of mathematics” (Gilmore & Spelke, 2008) Enhancement of later math development prediction and early intervention Does approximate math play a role in later development? Or are WM components that mediate approximate math performance more important?

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