Formal Operational Thinking in Piaget’s Theory of

Cognitive DevelopmentBy Kaitlyn Lissner

Jean Piaget

Born in Switzerland in 1896

Published first article at age 10

Received doctorate at 21 and began research on child psychology and development and genetic epistemology at age 23

Began work at Rousseau Institute in Geneva in 1921

Studied development of his own children

Piaget’s Stage Theory

Four periods Sensorimotor Intelligence Preoperational Thought Concrete Operations Formal Operations

NOT genetically determined

Assimilation

Accommodation

Organization

Equilibrium******

Active Construction Process

Stage concept*** Invariant Qualitatively different

patterns General characteristics Hierarchic integration

Sets of executive strategies

Cross-cultural Cognitive performance vs.

cognitive competence

Stages of Cognitive Development

Period I: Sensorimotor Intelligence (birth to 2 years) Stage 1:The Use of Reflexes Stage 2: Primary Circular Reactions Stage 3: Secondary Circular Reactions Stage 4: Coordination of Secondary Schemes Stage 5: Tertiary Circular Reactions Stage 6: Beginnings of Thought

Period II: Preoperational Thought (2 to 7 years)

Period III: Concrete Operations

Period IV: Formal Operation

Concrete Operations

The third period, (7 to 11 years)

Internal contradiction

Conservation Identity Compensation Inversion

Classification

Decrease in egocentrism

Moral autonomy

Decrease in animism

Concrete objects and real activities

Formal Operations

Fourth and final period, (11 years to adulthood)

Hypothetico-deductive reasoning and abstract thinking

Control-of-variable strategy

Highest level of equilibrium

Application to social life, as well as math and science

Application to social life, as well as math and science

‘New’ egocentrism

Relevant Research

There have been studies that have both supported and challenged Piaget’s research in Geneva. Pendulum task

Factors such as different types schools or social environments have shown a more significant number of children stuck in concrete

Questions

Do college freshman demonstrate all aspects of the formal operation stage?

Which aspects of the formal operational stage are they most likely and least likely to demonstrate?

Are there patterns of significance between male and female students?

Hypotheses

College freshmen will display formal operations in many, if not all, of the tests.

College freshmen will be most successful with the inferential reasoning test and struggle the most with the ‘Three Brothers Test.”

Female college freshman will have a slightly firmer grasp of formal operations.

Methodology

Participants Convenience sample of 10 UD freshman (age 18-19)

5 girls 5 boys

Setting Various locations on the University of Dallas campus

Procedure1. Have participant read and sign consent form

2. Ask participant the four questions

3. Record responses

Limitations and Assumptions

Limitations Only 10 participants Distractions Understanding of the

questions

Assumptions Cooperation Effort

The Test

Question 1: Inferential Reasoning Test“If Kelly is taller than Ali, and Ali is

taller than Jo, who is the tallest?”

Question 2: Piaget’s Third Eye Problem “Where would you put an extra eye ,

if you had a third one , and why?”

Question 3: Card ProblemEach card has a letter on one side and a

number on the other. If there is a vowel on one side of the card, then there has to be an even number on the other. Which of the four ‘cards’ shown here do you have to turn over before you can tell whether they follow this rule? Why?

E 7K 4

Question 4: Three Brothers Problem“Find the contradiction in this statement—I

have three sisters, Sally, Jane and myself.”

Evaluation

Answers scored between 1 and 3 1-Concrete/low level formal operations 2-Moderate formal opeations 3-Formal operations

Question 1: Objective Correct answer is Kelly Use of materials

Question 2: Subjective Creativity Reasoning

Question 3:The E card and the 7 card. The E card

absolutely must have an even number on the other side. Since 7 is an odd number, you have to turn the 7 card over to make sure there is no vowel on the other side, because that would break the rule. Since the rule does not say anything about what should be on the other side of a card with a consonant, such as K, and does not say that there has to be a vowel on the other side of a card with an even number, such as 4, you do not need to check those cards.

Objective/subjectiveReasoning

Question 4:Ability to identify the contradictionExplain why there is contradiction

Type 1-Participant does not see myself as sisters; he forgets or does not know that myself am a sister to my sisters

Type 2-Participant realizes that if I have two sisters, than I must be their sister

Type 3-Participant puts myself on equal level with the sisters; he sees the problem as a lack of a third name

Type 4-Participant finds the real solution; either I have only two sisters or there is a missing, unnamed sister

Responses

Subject Age Question 1 Question 2 Question 3 Question 4

Female 1 18 Kelly probably on my shoulder cuz it wouldn’t be in the way and I could see behind me and cover it if I needed to

the E to see if there is an even and the 7 to make sure there is not a vowel

the myself because if you had three siters you would have listed another because you cannot be your own sister.

Female 2 19 Kelly in my hand so I could stick it into rooms without people seeing me

E to see if there is an even number, and K to see if there was an odd

that’s not three sisters. Its three children. Myself is not your sister.

Female 3 18 Kelly back of my head so I could see what is behind me

all of them because E is a vowel and K is a consonant. in order to prove the vowel has an even you have to turn that one and the consonant to see if it has an odd. Turn the numbers to see if there are vowels

myself is wrong because if you have three sisters, you shouldn’t include yourself. Where is the other sister?

Female 4 19 Kelly back of my head so I could see people coming

I have no idea, maybe like turn over the numbers to see what letters are on the back

you only said two sisters and you mentioned yourself

Female 5 18 Kelly if I was a guy I would put it on the back of my head, but I have too much hair, but I think I'll still just go with that

you would have to turn them all over too see if they follow the rule

yourself is not a sister

Subject Age Question 1 Question 2 Question 3 Question 4

Male 1 18 Kelly forehead, otherwise the line of sight wouldn't match with the other eyes and your brain wouldn't be able to interpret and blend the different directions

all 4. you would have to flip all of them because you need to know if the letters have letters or the numbers have numbers.

the myself part. You can't be your own sister unless you have multiple personalities or something

Male 2 19 Kelly back of the head so that you could see behind

E never said that the even numbers had vowels

you're not your own siter, who is your other sister? Unless myself is a name, which would suck

Male 3 18 Kelly palm so you could look around corners, if it was on the back of your head it would be covered by your hair unless you shaved a spot on your head

all of them. A law says that it works ever single time. So to prov ethat you would have to test the law as many times as possible, so you need to flip every card

You are not your own sister. You are three sisters but you only have two

Male 4 19 Kelly I don’t think it would look very good, so maybe right peripheral since im right dominant but I don’t think it would very helpful, not aesthetically pleasing and hard with sunglassess

E because it’s the only vowel and 4 and 7 could still have consonant

you are referring to yourself as a sister, unless you have a sister whose name is myself which mean your parents are high

Male 5 19 Kelly foread because I don’t want it anywhere else plus I don’t need another

E because of the rule. if it’s a vowel you have to figure out if it has an even number

myself is not a sister. You can't be your own sister.

Results

Question 1: Inferential Reasoning

Males Females0

1

2

3

4

5

6Kelly

Ali

Jo

*None of the subjects needed to write to answer the question

Question 2: Piaget’s Third Eye Test

Male Female0

0.5

1

1.5

2

2.5

3

3.5

ForeheadBack of the HeadHandShoulderTemple

Question 3: Card Problem

Fem

ale

1

Fem

ale

2

Fem

ale

3

Fem

ale

4

Fem

ale

5

Mal

e 1

Mal

e 2

Mal

e 3

Mal

e 4

Mal

e 5

0

1

EK47All

Question 4: Three Brothers Problem

Fem

ale

1

Fem

ale

2

Fem

ale

3

Fem

ale

4

Fem

ale

5

Mal

e 1

Mal

e 2

Mal

e 3

Mal

e 4

Mal

e 5

0

1

Type 1Type 2Type 3Type 4

Overall Results

Fem

ale

1

Fem

ale

2

Fem

ale

3

Fem

ale

4

Fem

ale

5

Mal

e 1

Mal

e 2

Mal

e 3

Mal

e 4

Mal

e 5

0

1

2

3

Question 1Question 2Question 3Question 4

Score

1-Cocnrete/low formal operations2-Moderate formal operations3-Formal operations

Averages

Fem

ale

1

Fem

ale

2

Fem

ale

3

Fem

ale

4

Fem

ale

5

Mal

e 1

Mal

e 2

Mal

e 3

Mal

e 4

Mal

e 5

0

1

2

3

Overall Averages

Score

0

1

2

3

Averages by Question

Question 1Question 2Question 3Question 4

Sco

re

Males Females2.15

2.2

2.25

2.3

2.35

Average by Gender

Score

Conclusions

Overall, college freshman showed a moderate grasp of formal operation, thus supporting the hypothesis.

College freshman were most successful with the Inferential Reasoning test, but least successful with the Card Problem. The hypothesis was both supported and rejected.

Girls scored higher than the boys by 0.1. The value is too small to state that the difference is significant.

Improvements

More tests to encompass more diversity

More complicated tests

Better evaluation methods

Clearer question wording

Record participants’ areas of interest

Record participants’ type of schooling

Works Cited

Crain, William. “Piaget’s Cognitive-Developmental Theory.” In Theories of Development: Concepts and Applications, 118-156. 6th ed.

Upper Saddle Ridge, New Jersey: Prentice Hall, Inc., 2011.

Day, Mary Carol. “Thinking at Piaget’s Stage of Formal Operations.” Educational Leadership, October (1981): 44-47.

Dubuc, Bruno. “Piaget’s Model of Cognitive Thinking.” The Brain From Top to Bottom. Accessed October 15, 2024. http://

thebrain.mcgill.ca/flash/a/a_09/a_09_p/a_09_p_dev/ a_09_p_dev.html

Piaget, Jean. “Formal Thought and Relational Judgments.” In Judgment And Reasoning In The Child. New York: Harcourt, Brace and Company, 1928.

-------. Science of Education and the Psychology of the Child. New York, New York: The Viking Press, Inc., 1971.