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The operand recognition paradigm as a method to investigate individuals’ arithmetic strategies

The operand recognition paradigm as a method to investigate individuals’ arithmetic strategies. Catherine THEVENOT. Department of Psychology UNIVERSITY OF GENEVA. San S ebastian, Saturday 1 st October 2011. How do you solve 7 + 8 ?. You know that 7 + 8 = 15

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The operand recognition paradigm as a method to investigate individuals’ arithmetic strategies

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  1. The operand recognition paradigm as a method to investigate individuals’ arithmetic strategies Catherine THEVENOT Department of Psychology UNIVERSITY OF GENEVA San Sebastian, Saturday 1st October 2011

  2. How do yousolve 7 + 8 ? You know that 7 + 8 = 15 - Direct retrieval of the resultfrom long-termmemory You know that 7 + 7 = 14, then 7 + 7 + 1 = 15 - Use of derivedfacts - Operanddecomposition

  3. How do we know how yousolve 7 + 8 ? Solution times (Groen & Parkman, 1972) Reconstructive strategies are inferredfrom long solution times = Typical in children Retrievalisinferredwhen solution times are shorter = Typical in adults

  4. How do we know how yousolve 7 + 8 ? Solution times LeFevre et al., 1996 Siegler, 1989 Solution times are averagedacrossdifferent trials . BUT, because of the variability in the proceduresused, mean solution times cannotreflect a reality.

  5. How do we know how yousolve 7 + 8 ? Verbal reports (LeFevre et al., 1996) A large variety of strategies are used by adults and children Adults report more retrievalstrategythanwhatissuggested by solution times.

  6. How do we know how yousolve 7 + 8 ? Verbal reports (Kirk & Ashcraft, 2001) Introspection is NOT bias-free Fast processes cannot reach consciousness : Retrieval !

  7. A paradigmthatdoes not rely on solution times or on verbal reports thatdoes not draw the attention of participants on the goal of the study The operand-recognition paradigm

  8. The operand Recognition paradigm Participants have to solveproblems : - Numbers are presented one by one - Participants are informed about the task to bedonebefore the first numberappears on screen - An operand recognition taskisproposedafter the problem has been solved

  9. The operand Recognition paradigm 18 18 23 A 41

  10. The operand Recognition paradigm A 23 18 41 18 Verificationtask Recognition task A calculationproceduredegrades the memory traces of the operandsinvolved in the problem. Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC Thevenot, Barrouillet & Fayol (2001), QJEP-A

  11. The operand Recognition paradigm A 23 18 41 18 Verificationtask Recognition task C 23 18 21 18 Comparisontask Recognition task Thevenot, Barrouillet, & Fayol (2001), QJEP-A

  12. The operand Recognition paradigm A 23 18 41 18 C 23 18 21 18 If recognition times are longer in A than in C a procedure have been used If recognition times are the same in A and in C the answer has been retrieved Thevenot, Barrouillet, & Fayol (2001), QJEP-A

  13. Exp.1: ADDITION IN ADULTS as a function of theirarithmeticskills Large = Two-digit numbers (e.g., 23 + 18) Small = One-digit numbers with a sum up to 10 (e.g., 3 + 5) Medium = One-digit numbers with a sum greater than 10 (e.g., 9 + 7) Thevenot, Fanget, & Fayol (2007), Memory & Cognition

  14. EXP. 2 : SUBTRACTION IN ADULTS as a function of theirarithmeticskills Large = 41 – 23 Small = 8 – 3 Medium = 16 - 9 Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

  15. EXP.2 : SUBTRACTION IN ADULTS as a function of theirarithmeticskills Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

  16. CONCLUSIONS The operand-recognition paradigm is a good tool in order to determine the strategies used by individuals to solve arithmetic problems It is more informative than verbal reports

  17. BUT An alternative interpretation of our results in terms of switch-cost A 23 18 41 18 C 23 18 21 18 SWITCH Metcalfe & Campbell, 2010 : Psy. Research Metcalfe & Campbell, 2011 : JEP - LMC

  18. BUT It is more demanding to switch from a difficult to an easy task than the other way round (Arbuthnott, 2008) > A 23 18 41 18 C 23 18 21 18 SWITCH Metcalfe & Campbell, 2010 : Psy. Research Metcalfe & Campbell, 2011 : JEP - LMC

  19. THEN Higher recognition times after addition than comparison reflect higher switch cost rather than different strategies > A 23 18 41 18 C 23 18 21 18 SWITCH Metcalfe & Campbell, 2010 : Psy. Research Metcalfe & Campbell, 2011 : JEP - LMC

  20. HOWEVER A 23 18 41 18 C 23 18 21 18 The switch-cost to the recognition task is in fact higher after a comparison than after an addition SWITCH Longer recognition task after addition cannot only reflect differential switch-cost

  21. CONCLUSIONS The operand-recognition paradigm is a good tool in order to investigate individuals’ arithmetic strategies Adults with low and higher arithmetic skills differ in the way they solve simple problems This is not revealed by verbal reports Differential switch-costs depending on the task cannot explain the entirety of our results

  22. THANK YOU FOR YOUR ATTENTION

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