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Rekengroep

Rekengroep. Eerste bijeenkomst 28 oktober 2008 Volgende bijeenkomsten 25 november 2008 23 december 2008. Cultural differences in complex arithmetic. Rekengroep Ghent University Oktober 2008 Ineke Imbo 1 & Jo-Anne LeFevre 2 1 Ghent University (Belgium)

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Rekengroep

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  1. Rekengroep • Eerste bijeenkomst • 28 oktober2008 • Volgende bijeenkomsten • 25 november 2008 • 23 december 2008 Rekengroep – Ineke Imbo – Oktober 2008

  2. Cultural differences in complex arithmetic • Rekengroep • Ghent University • Oktober2008 • Ineke Imbo 1 & Jo-Anne LeFevre 2 • 1 Ghent University (Belgium) • 2 Carleton University (Canada) Rekengroep – Ineke Imbo – Oktober 2008

  3. 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 Rekengroep – Ineke Imbo – Oktober 2008

  4. 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 Rekengroep – Ineke Imbo – Oktober 2008

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

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

  7. Method Participants Stimuli Choice/no-choice method Selective interference paradigm Results Strategy selection Strategy efficiency Strategy adaptivity Discussion Main results Causes Study 1: Cultural differences in complex addition Rekengroep – Ineke Imbo – Oktober 2008

  8. 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 Rekengroep – Ineke Imbo – Oktober 2008

  9. 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) Rekengroep – Ineke Imbo – Oktober 2008

  10. 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) Rekengroep – Ineke Imbo – Oktober 2008

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

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

  13. 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 Rekengroep – Ineke Imbo – Oktober 2008

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

  15. ! beep 37 + 45 500 ms beep Correct until response beep Incorrect beep beep beep Strategy? Executive load Rekengroep – Ineke Imbo – Oktober 2008

  16. Method Participants Stimuli Choice/no-choice method Selective interference paradigm Results Strategy selection Strategy efficiency Strategy adaptivity Discussion Main results Causes Study 1: Cultural differences in complex addition Rekengroep – Ineke Imbo – Oktober 2008

  17. Which strategies? 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 Rekengroep – Ineke Imbo – Oktober 2008

  18. 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 Rekengroep – Ineke Imbo – Oktober 2008

  19. Culture x Load x WM component Rekengroep – Ineke Imbo – Oktober 2008

  20. How fast? (RTs) 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 Rekengroep – Ineke Imbo – Oktober 2008

  21. 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 Results are considered as significant if p < .05 Rekengroep – Ineke Imbo – Oktober 2008

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

  23. How accurate? (Errors) 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 Rekengroep – Ineke Imbo – Oktober 2008

  24. 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 Results are considered as significant if p < .05 Rekengroep – Ineke Imbo – Oktober 2008

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

  26. How adaptive? 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 Rekengroep – Ineke Imbo – Oktober 2008

  27. How adaptive? 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 Rekengroep – Ineke Imbo – Oktober 2008

  28. 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%) Results are considered as significant if p < .05 Rekengroep – Ineke Imbo – Oktober 2008

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

  30. Method Participants Stimuli Choice/no-choice method Selective interference paradigm Results Strategy selection Strategy efficiency Strategy adaptivity Discussion Main results Causes Study 1: Cultural differences in complex addition Rekengroep – Ineke Imbo – Oktober 2008

  31. 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 Rekengroep – Ineke Imbo – Oktober 2008

  32. 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 Rekengroep – Ineke Imbo – Oktober 2008

  33. 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 Rekengroep – Ineke Imbo – Oktober 2008

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