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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
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Nonsymbolic approximate arithmetic
“Phylogenetically widespread approximate magnitude system”(Barth, Starr & Sullivan, 2009)
Preschool children
(Barth, Beckmann, & Spelke, 2008)
The Dot task
*WM role!
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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.
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Hypotheses
o Nonsymbolic approximate arithmetic processing would depend on VSSP components (Rasmussen & Bisanz, 2005)
o Memory updating on the elements presented, thus CE involvement. (Morris & Jones, 1990)
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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 interference4. Spatial interference5. CE interference.
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Material – Primary Task
o Primary task : the Dot-task
New: Reaction Time registration
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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
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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)
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Material – Secondary Tasks
+
Dot-task
+
+
Same or different? Same or different?
Also conducted in stand alone control conditions with a 15 sec delay replacing the primary task.
Dual
Stand -alone
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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.
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Results Primary task
• Accuracy: 60.21%, chance = 50%, t(61) = 7.18, p < .001)
• Ratio effect: F(2,122)=31.21, p <.001
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Results
Interference Conditions: accuracy
Conditions x ratios Conditions
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Results
Interference Conditions: RTs
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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).
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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).
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Conclusions...
“Non-symbolic approximate
representations are central to
human knowledge of mathematics”
(Gilmore & Spelke, 2008)
• Enhancement of later math development prediction and early intervention