Formal Operational Thinking
in Piaget’s Theory of Cognitive
Development
By 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
 Equilibrium******
 Active Construction Process
 Stage concept***
 Invariant
 Qualitatively different patterns
 General characteristics
 Assimilation
 Hierarchic integration
 Accommodation
 Cross-cultural
 Organization
 Cognitive performance vs.
cognitive competence

Sets of executive strategies
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
 Procedure
1.
2.
3.
Have participant read and sign consent form
Ask participant the four questions
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 Problem
 Each 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
K
4
7
 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/subjective
 Reasoning
 Question 4:
 Ability to identify the contradiction
 Explain 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
Female 1
18
Kelly
Female 2
19
Kelly
Female 3
18
Kelly
Female 4
19
Kelly
Female 5
18
Kelly
Question 3
probably on my shoulder cuz it
the E to see if there is an
wouldn’t be in the way and I could even and the 7 to make sure
see behind me and cover it if I
there is not a vowel
needed to
Question 4
the myself because if you
had three siters you would
have listed another
because you cannot be
your own sister.
in my hand so I could stick it into E to see if there is an even that’s not three sisters. Its
rooms without people seeing me number, and K to see if there three children. Myself is
was an odd
not your sister.
back of my head so I could see
all of them because E is a
myself is wrong because if
what is behind me
vowel and K is a consonant. you have three sisters, you
in order to prove the vowel shouldn’t include yourself.
has an even you have to turn Where is the other sister?
that one and the consonant
to see if it has an odd. Turn
the numbers to see if there
are vowels
back of my head so I could see
I have no idea, maybe like
you only said two sisters
people coming
turn over the numbers to see and you mentioned
what letters are on the back yourself
if I was a guy I would put it on the you would have to turn them yourself is not a sister
back of my head, but I have too all over too see if they follow
much hair, but I think I'll still just the rule
go with that
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 E never said that the even
see behind
numbers had vowels
Male 3
18 Kelly
Male 4
19 Kelly
Male 5
19 Kelly
palm so you could look around
all of them. A law says that it
corners, if it was on the back of
works ever single time. So to
your head it would be covered by prov ethat you would have to
your hair unless you shaved a spot test the law as many times as
on your head
possible, so you need to flip
every card
I don’t think it would look very
E because it’s the only vowel
good, so maybe right peripheral and 4 and 7 could still have
since im right dominant but I
consonant
don’t think it would very helpful,
not aesthetically pleasing and
hard with sunglassess
foread because I don’t want it
E because of the rule. if it’s a
anywhere else plus I don’t need vowel you have to figure out if it
another
has an even number
you're not your own siter, who
is your other sister? Unless
myself is a name, which would
suck
You are not your own sister. You
are three sisters but you only
have two
you are referring to yourself as
a sister, unless you have a sister
whose name is myself which
mean your parents are high
myself is not a sister. You can't
be your own sister.
Results
 Question 1: Inferential Reasoning
6
Kelly
Ali
5
Jo
4
3
2
1
0
Males
Females
*None of the
subjects needed
to write to answer
the question
 Question 2: Piaget’s Third Eye Test
3.5
3
2.5
Forehead
2
Back of the Head
Hand
1.5
Shoulder
1
Temple
0.5
0
Male
Female
 Question 3: Card Problem
1
E
K
4
7
All
0
FemaleFemaleFemaleFemaleFemale Male 1 Male 2 Male 3 Male 4 Male 5
1
2
3
4
5
 Question 4: Three Brothers Problem
1
Type 1
Type 2
Type 3
Type 4
0
FemaleFemaleFemaleFemaleFemale Male 1 Male 2 Male 3 Male 4 Male 5
1
2
3
4
5
Overall Results
3
Score
2
Question 1
Question 2
1
Question 3
Question 4
0
1-Cocnrete/low formal
operations
2-Moderate formal
operations
3-Formal operations
Overall Averages
Score
3.5
3
2.5
2
1.5
1
0.5
0
3.5
3
2.5
2
1.5
1
0.5
0
Averages by Question
Average by Gender
2.35
2.3
Score
Score
Averages
2.25
2.2
2.15
Males
Females
Question 1
Question 2
Question 3
Question 4
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.