Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Rekengroep...

Rekengroep – Ineke Imbo – Oktober 2008 Experimental Psychology – Ghent University

Rekengroep

Eerste bijeenkomst

28 oktober 2008

Volgende bijeenkomsten

25 november 200823 december 2008


Cultural differences in complex arithmetic

RekengroepGhent University

Oktober 2008

Ineke Imbo 1 & Jo-Anne LeFevre 2

1 Ghent University (Belgium)2 Carleton University (Canada)


Overview

• Study 1: Cultural differences in complex addition

‣Phonological & executive working memory‣Strategy selection, efficiency, & adaptivity

• Study 2: Cultural differences in complex subtraction & multiplication

‣Phonological & visuo-spatial working memory‣Horizontal & vertical presentation


Cultural differences• In simple arithmetic (e.g. 5 + 7)

‣ North Americans vs. Asians‧Asians are faster than North Americans‧Asians more often retrieve from long-term memory

• In complex arithmetic? (e.g. 53 + 78)• Europeans?

(e.g., Campbell & Xue, 2001; LeFevre & Liu, 1997)

→ Study 1 Belgians, Canadians, & Chinese solve complex addition problems

→ Study 2 Canadians & Chinese solve complex subtraction & multiplication problems


Working memory

• Store and manipulate temporary information

• Four components:

‣Central executive‣Phonological loop‣Visuo-spatial sketchpad‣Episodic buffer

Centralexecutive

Phonologicalloop

Visuo-spatialsketchpad

Baddeley & Hitch (1974)

Episodicbuffer

Study 1


Working memory

• Store and manipulate temporary information

• Four components:

‣Central executive‣Phonological loop‣Visuo-spatial sketchpad‣Episodic buffer

Centralexecutive

Phonologicalloop

Visuo-spatialsketchpad

Baddeley & Hitch (1974)

Episodicbuffer

Study 2


Study 1: Cultural differences in complex addition

• Method‣Participants‣Stimuli‣Choice/no-choice method‣Selective interference paradigm

• Results‣Strategy selection‣Strategy efficiency‣Strategy adaptivity

• Discussion‣Main results‣Causes


Participants

• 40 Belgians‣Born & educated in Belgium -- First language = Dutch‣Living in Belgium

• 45 Canadians‣Born & educated in Canada -- First language = English‣Living in Canada

• 40 Chinese‣Born & educated in China -- First language = Chinese ‣Living in Canada -- Second language = English


Stimuli

• Two-digit + two-digit addition problems

• Exclusion of

‣Problems involving a 0 in operand 1, operand 2, or sum‣Problems involving a 9 in operand 1 or operand 2‣Problems with a tie in the units or in the tens

• Controlled for

‣Problem size of the correct sum‣Even/uneven status of the correct sum‣Position of the largest operand (first vs. last)


Choice/no-choice method

• One choice condition

‣Participant is free to choose among all available strategies‣Units-Tens, Tens-Units, Something else‣Strategy selection (“which strategies?”)

• Two no-choice conditions

‣Participant has to use one strategy to solve all problems‣Units-Tens vs. Tens-Units‣Strategy efficiency (“how fast?” & “how accurate?”)

• Comparison of strategy selection & strategy efficiency‣Strategy adaptivity (“how adaptive?)

Siegler & Lemaire (1997)


!

500 ms

until response

Incorrect

Correct

37 + 45

Strategy?1. Units - Tens2. Tens - Units3. Something else

Strategy selectio

n

Choice condition


!

500 ms

until response

Incorrect

Correct

37 + 45

Did you succeed inusing the

requested strategy?Yes / No

Strategy efficiency

No- choice condition


Selective interference

• Primary task = solving addition problems

• Secondary task = load on working memory‣Load on central executive

‧React on high and low tones (choice reaction time task, Szmalec et al., 2005)

‣Load on phonological loop

‧Remember 4 letters


Phonological load!

500 ms

until response Incorrect

Correct

37 + 45

Strategy?!

500 ms


Correct

28 + 34

Strategy?!

500 ms


Correct

72 + 25

Strategy?

“FPKS”

Experimenter

“FPKS”

Participant


Executive load!

500 ms


Correct

37 + 45

Strategy?

beep

beep

beep

beep

beep bee

p


Strategy selection

3 x 2 x 2 ANOVA on % use of the Tens-Units strategy

• Between subjects

‣Culture (3): Belgian, Canadian, Chinese‣WM component (2): Phonological, Executive

• Within subjects

‣Load (2): No load vs. Load

Which strategies

?


Strategy selection

Tens-Units usage = 56%

• Main effect of culture

‣Belgians (69%) > Canadians (52%) = Chinese (44%)

• Culture x load x WM component

‣Chinese use TU strategy less frequently under executive loads

Results are considered as significant if p < .05

Which strategies

?


0

20

40

60

80

100

Chinese Belgian Canadian Chinese Belgian Canadian

Phonological Executive

TU

us

e (

%)

No load Load

Cu

lture

x L

oad

x W

M c

om

po

nen

t


Strategy efficiency

3 x 2 x 2 x 2 ANOVA on RTs (correctly solved problems only)



• Within subjects

‣Load (2): No load vs. Load‣Strategy (2): Units-Tens vs. Tens-Units

How fast?(RTs)


Strategy efficiency

• Main effect of load‣No load (3.4 sec) < Load (3.8 sec)

• Main effect of culture‣Chinese (2.6 sec) < Belgians (3.5 sec) < Canadians (4.8 sec)

• Main effect of strategy‣Tens-Units (3.4 sec) < Units-Tens (3.8 sec)

• Culture x load x WM component‣Phonological load affects Belgians only‣Executive load affects Belgians & Canadians


How fast?(RTs)


0

1

2

3

4

5

6

7



RT

(s

ec

)

No load Load

p = .06

Cu

lture

x lo

ad

x W

M c

om

po

nen

t


Strategy efficiency

3 x 2 x 2 x 2 ANOVA on % errors



• Within subjects

‣Load (2): No load vs. Load‣Strategy (2): Units-Tens vs. Tens-Units

How accurate?(Errors)


Strategy efficiency

• Main effect of load‣No load (7.4%) < Load (9.9%)

• Main effect of culture‣Chinese (7.1%) = Belgians (7.5%) < Canadians (11.4%)

• No main effect of strategy‣Units-Tens (8.7%) = Tens-Units (8.6%)

• Culture x load x WM component‣Canadians: executive load effects > phonological load effects‣Belgians & Chinese: no load effects


How accurate?(Errors)


0

5

10

15

20

25



Err

or

(%)

No load Load

p = .06

Cu

lture

x W

M c

om

pon

ent x

Loa

d


Strategy adaptivity

• Adaptivity measure

‣“1” if, in the choice condition, a participant chose the strategy that was faster on more than 50% of the trials in the no-choice condition

‣“0” otherwise

How adaptive?


Strategy adaptivity

3 x 2 x 2 ANOVA on the adaptivity measure



• Within subjects

‣Load (2): No load vs. Load

How adaptive?


Strategy adaptivity

Average adaptivity = 65%

• No main effect of load‣No load (66%) = Load (63%)

• Main effect of culture‣Chinese (53%) < Canadians (69%) = Belgians (72%)

• Culture x load x WM component‣Chinese are less adaptive under executive load (45%) than under no-load (66%)


How adaptive?


p = .06

Cu

lture

x W

M c

om

pon

ent x

Loa

d

0

20

40

60

80

100



Ad

ap

tiv

ity

No load Load


Main results

• Strategy selection

‣Tens-Units strategy use Belgians > Canadians = Chinese‣Chinese choose other strategies under an executive load

• Strategy efficiency

‣RTs & errors Canadians > Belgians ≥ Chinese‣WM load effect Canadians > Belgians ≥ Chinese

• Strategy adaptivity

‣Chinese < Belgians = Canadians‣Chinese are even less adaptive under an executive load


Causes of the cultural differences?

• Educational focus‣Focus on drill, practice & training in Eastern countries‣Focus on exploration & flexibility in Western countries

• Language of number system‣More straightforward in Chinese than in English and Dutch

‧Chinese (five ten) vs. English (fifty) and Dutch (vijftig)

• Cultural standards‣Importance of math‣Attitudes towards math: positive (motivation) vs. negative (avoidance)‣Ways to success


Overview

• Study 1: Cultural differences in complex addition

‣Phonological & executive working memory‣Strategy selection, efficiency, & adaptivity

• Study 2: Cultural differences in complex subtraction & multiplication

‣Phonological & visuo-spatial working memory‣Horizontal & vertical presentation

Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Rekengroep...

Documents

Transcript of Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Rekengroep...