1. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Rekengroep Eerste bijeenkomst 28 oktober 2008 Volgende bijeenkomsten 25 november 2008 23 december 2008

2. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Cultural differences in complex arithmetic Rekengroep Ghent University Oktober 2008 Ineke Imbo 1 & Jo-Anne LeFevre 2 1 Ghent University (Belgium) 2 Carleton University (Canada)

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

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

5. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Working memory Store and manipulate temporary information Four components: ‣ Central executive ‣ Phonological loop ‣ Visuo-spatial sketchpad ‣ Episodic buffer Central executive Phonological loop Visuo-spatial sketchpad Baddeley & Hitch (1974) Episodic buffer Study 1

6. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Working memory Store and manipulate temporary information Four components: ‣ Central executive ‣ Phonological loop ‣ Visuo-spatial sketchpad ‣ Episodic buffer Central executive Phonological loop Visuo-spatial sketchpad Baddeley & Hitch (1974) Episodic buffer Study 2

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

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

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

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

11. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 ! 500 ms until response Incorrect Correct 37 + 45 Strategy? 1. Units - Tens 2. Tens - Units 3. Something else Strategy selectio n Choice condition

12. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 ! 500 ms until response Incorrect Correct 37 + 45 Did you succeed in using the requested strategy? Yes / No Strategy efficiency No- choice condition

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

14. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Phonological load ! 500 ms until response Incorrect Correct 37 + 45 Strategy? ! 500 ms until response Incorrect Correct 28 + 34 Strategy? ! 500 ms until response Incorrect Correct 72 + 25 Strategy? “FPKS” Experimenter “FPKS” Participant

15. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Executive load ! 500 ms until response Incorrect Correct 37 + 45 Strategy? bee p

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

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

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

19. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Culture x Load x WM component

20. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Strategy efficiency 3 x 2 x 2 x 2 ANOVA on RTs (correctly solved problems only) Between subjects ‣ Culture (3): Belgian, Canadian, Chinese ‣ WM component (2): Phonological, Executive Within subjects ‣ Load (2): No load vs. Load ‣ Strategy (2): Units-Tens vs. Tens-Units How fast? (RTs)

21. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 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 Results are considered as significant if p <.05 How fast? (RTs)

22. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 p =.06 Culture x load x WM component

23. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Strategy efficiency 3 x 2 x 2 x 2 ANOVA on % errors Between subjects ‣ Culture (3): Belgian, Canadian, Chinese ‣ WM component (2): Phonological, Executive Within subjects ‣ Load (2): No load vs. Load ‣ Strategy (2): Units-Tens vs. Tens-Units How accurate? (Errors)

24. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 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 Results are considered as significant if p <.05 How accurate? (Errors)

25. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 p =.06 Culture x WM component x Load

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

27. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 Strategy adaptivity 3 x 2 x 2 ANOVA on the adaptivity measure Between subjects ‣ Culture (3): Belgian, Canadian, Chinese ‣ WM component (2): Phonological, Executive Within subjects ‣ Load (2): No load vs. Load How adaptive?

28. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 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%) Results are considered as significant if p <.05 How adaptive?

29. Experimental Psychology – Ghent University Rekengroep – Ineke Imbo – Oktober 2008 p =.06 Culture x WM component x Load

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

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

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

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