1. Department of Psychology
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 you solve 7 + 8 ? You know that 7 + 8 = 15?
You know that = 15
- Direct retrieval of the result from long-term memory
You know that = 14, then = 15
- Use of derived facts
- Operand decomposition

3. How do we know how you solve?
Solution times (Groen & Parkman, 1972)
Reconstructive strategies are inferred from long solution times = Typical in children
Retrieval is inferred when solution times are shorter = Typical in adults

4. How do we know how you solve?
Solution times
LeFevre et al., 1996
Siegler, 1989
Solution times are averaged across different trials .
BUT, because of the variability in the procedures used, mean solution times cannot reflect a reality.

5. How do we know how you solve?
Verbal reports (LeFevre et al., 1996)
A large variety of strategies are used by adults and children
Adults report more retrieval strategy than what is suggested by solution times.

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

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

8. Participants have to solve problems :
The operand Recognition paradigm
Participants have to solve problems :
- Numbers are presented one by one
- Participants are informed about the task to be done before the first number appears on screen
- An operand recognition task is proposed after the problem has been solved

9. The operand Recognition paradigm18 23 18 A 41

10. A calculation procedure degrades the memory traces
The operand Recognition paradigm A
Verification task
Recognition task
Thevenot, Barrouillet & Fayol (2001), QJEP-A
A calculation procedure degrades the memory traces
of the operands involved in the problem.
Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

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

12. If recognition times are longer in A than in C
The operand Recognition paradigm A C
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. Large = Two-digit numbers (e.g., 23 + 18)
Exp.1: ADDITION IN ADULTS as a function of their arithmetic skills
Large = Two-digit numbers (e.g., )
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. Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC
EXP. 2 : SUBTRACTION IN ADULTS as a function of their arithmetic skills
Large = 41 – 23
Small = 8 – 3
Medium =
Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

15. Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC
EXP.2 : SUBTRACTION IN ADULTS as a function of their arithmetic skills
Large
Medium
Small
Good solvers
Not so good
Not- so- good
Not -so -good
Retrieval 4 1 45 50 95 92
Counting down 2 3 5
Counting up 12
Decomposition 52 27 6 13
Transformation 41 64 25 15
Addition Reference
Others 8
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 C
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 C
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 C
SWITCH
Metcalfe & Campbell, 2010 : Psy. Research
Metcalfe & Campbell, 2011 : JEP - LMC

20. HOWEVER A C
SWITCH
The switch-cost to the recognition task is in fact higher after a comparison than after an addition
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