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

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)

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.

Material – Primary Task

o 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)

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

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 ratios Conditions

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

for your attention!

Contact: I.XenidouDervou@psy.vu.nlWebsites:http://vu.mathchild.nl http://mathchild.nl/