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

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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

Catherine

THEVENOT

Department of Psychology

UNIVERSITY OF GENEVA

San Sebastian, Saturday 1st October 2011

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

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

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.

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.

How do we know how yousolve

7 + 8 ?

Verbal reports (Kirk & Ashcraft, 2001)

Introspection is NOT bias-free

Fast processes cannot reach consciousness : Retrieval !

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

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

A 23 18 41 18

of the operandsinvolved in the problem.

Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

Thevenot, Barrouillet & Fayol (2001), QJEP-A

A 23 18 41 18

C 23 18 21 18

Thevenot, Barrouillet, & Fayol (2001), QJEP-A

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

Thevenot, Barrouillet, & Fayol (2001), QJEP-A

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

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

EXP.2 : SUBTRACTION IN ADULTS as a function of theirarithmeticskills

Thevenot, Castel, Fanget, & Fayol (2010), JEP: LMC

CONCLUSIONS

The operand-recognition paradigm is a good tool in order to determine the strategies used by individuals to solve arithmetic problems

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

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

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

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

differential switch-cost

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