ARE STUDENTS REALLY READY TO
LEARN WHAT THEY ARE BEING
TAUGHT?
A research study based on the
cognitive development stages
of Jean Piaget
By Carry Hansen
OBJECTIVES

At the end of this presentation you will be able
to:






Explain critical biographical points of Jean Piaget
Define and explain critical theoretical concepts
relevant to the research study including key terms
Articulate the research questions that drive the study
Understand the procedure of the research study
Summarize the findings and implications
Generate new questions for additional research
JEAN PIAGET 1896-1980
Born in Switzerland
 Began as a Biologist

1st published at age 10- Albino Sparrows
 Researched Mollusks in high school
 At age 21, received a Doctorate in Natural Studies


Conflict Changed Gears
Realized that his religious and philosophical ideas
did not have scientific reasoning as their foundation
 Tried to bridge philosophy and science


“genetic epistemology” – questions concerning the origin of
knowledge and began research in child psychology
PIAGET’S RESEARCH

Influenced by his point in time



1920’s standardized testing movement
Testing soldiers for military placement
Influenced by others

Binet Lab in Paris


IQ testing of children – became very interested in the wrong
answer patterns of children because very different from
adults wrong answers– WHY?
Rousseau Institute of Geneva

Interviewed 7-12 year olds and found that before age 7,
children have a qualitative difference in their responses
Married, had children, continued children’s cognitive
development questioning
 Spent numerous years developing his theory, and
later refining his theory in response to critism

PIAGET’S THEORY
Integrated stage theory
 Developmentalist, not maturationist

The developmental change is not genetic in basis
 Development is increasingly comprehensive
 Children constantly investigate, make sense of their
environment and construct new “schema”


Invariant and universal
Although each child has their own rate
 Age norms


2/3rds nurture, 1/3 nature

All organisms have a biologic tendency, but it is
interaction with the environment that drives the
ongoing development of cognition (understanding)
KEY CONCEPTS

Organization


Schema


Using the current schema to interpret the world
Accommodation


Non-tangible cognitive structures that are constantly
adapting due to new experiences and manipulations of
the world around us
Assimilation


An organisms biologic tendency to organize (inherited)
Using the world experiences to change a schema
Disequilibrium

When the schema does not fit the situation at hand,
causing adaptation to occur
STAGES OF PIAGET’S THEORY

Sensorimotor (0-2)
First explorations, without purpose and then with
purpose
 Object permanence marks the transition to the next
stage


Preoperational (2-7)
Symbolic activity begins, language
 Cognition becomes more efficient but still limited
 Egocentric, animism, centration (one dimensional),
irreversibility, transductive reasoning
 Conservation tasks marks the transition to the next
stage

STAGES OF PIAGET’S THEORY

Concrete Operational
Logical thinking can occur IF a tangible experience
occurs
 Hypothetical and Abstract situations are not
understood
 Reversibility begins without manipulation
 Cylinder Task marks the transition to the next stage


Formal Operational
Logical thinking occurs hypothetically and abstractly
 Individual has accommodated schema to be able to
accurately make predictions about the world

WHAT IS CONSERVATION?
A cognitive development that cannot occur
 Happens spontaneously by a child
 Occurs in a certain sequence through various
tasks:







Liquid/Number
Weight/substance
Volume
Length
Surfaces
Wholes after spatial arrangements
3 reasons: identity, compensation, inversion
 The ability to determine what stays the same and
what changes in an abject after aesthetic change

STAGES-DIMENSIONS OF THINKING

Preoperational (2-7)




Illogical responses
do not address common reasons (dimensions) of an
object
An object floats because it is a ball
Concrete (7-11)
Semi logical response, logic may appear after child
can try the task (analysis afterwards)
 Addresses one dimension (property) of the object
 May make conflicting statements and cannot decide
which is correct
 An object floats because it is very large, but that
means it should be heavy so it sinks, but it floats
because…

STAGES-DIMENSIONS OF THINKING

Formal Operational (11- adulthood)





Response based on logic
Addresses multi-dimensions of an object and the
relationship between those dimensions
Hypothetical situations addressed with logic
Abstract abilities
An object floats even though it is very heavy because
it is very large. I think that object will sink even
though it is small because it is very heavy for its size.
WHERE DOES EDUCATION FIT IN?




Well, it doesn’t?
You cannot teach conservation tasks
Knowledge cannot precede readiness
The purpose of this study is to investigate if children
are cognitively at the stage that is required of them
by the curriculum. It is thought that if children show
high level of performance on specified Piagetian
conservation tasks it will positively impact their
ability to calculate density and explain in their own
language what it means for one object to be more or
less dense than another, as required by the 6th grade
science curriculum.
QUESTIONS THAT DRIVE THE STUDY:




1. Why are students struggling in science initially as they enter
middle school, and why do they continue to struggle? Are
educators trying to build a foundation of basic science concepts
that students are not ready to complete on their own cognitive
level?
2. Does the completion of specified Piagetian tasks allow a
child to have entered the early formal operational period of
thought, required for middle school science tasks such as the
concept and calculation of density?
3. Are there significant patterns of differences between ages?
4. Do the ages in which a student can complete Piagetian tasks
of conservation match the ages that Piaget originally identified,
or have these ages changed?
WHY THESE QUESTIONS TO BEGIN WITH?

PISA testing results

In the lower half of all participating countries since
2000, with the exception of reading in 2009, at 14th
out of 34 countries


Increased Standardized Testing, yet lower
performances


That was the U.S.’s BEST performance
Predicted that 80% of students would not earn a
passing mark on standardized tests in 2014
Curriculum Standards requiring early use of
abstract thought and “hurrying” children to catch
up to the world
HYPOTHESIS

The curriculum of the American school system is
not adequately preparing students for success
because it does not teach to the level in which
students are ready to learn. The curriculum is
not based on the level of the student, but instead
is based on where the level of the student is being
hurried to perform at causing the student to be
focused on attaining “right” and “correct”
answers, instead of building cognition. Through
the use of Piagetian Conservation Tasks, a
student’s “readiness” for abstract concepts and
application of knowledge can be determined.
WHAT I DID:

A Variety of Tasks
Task 1- Conservation of weight
 Task 2- Cylinder Task and Analysis
 Task 3- Conservation of weight without conservation
of volume
 Task 4

1- Floating vs. Sinking Foil- predictions and analysis
 2- Golf Ball vs. Ping Pong Ball- predictions and analysis
 3- Define Density
 4- calculate Density
 5- what do numbers mean?

HOW RESPONSES
WERE RECORDED:
Age: ____________ Grade as of Fall 2012 ________
Student # ______________
TASK
Question
1
1
2
2
2
(A)Do the 2 balls of clay weigh the same?
(B)Does the hot dog shape weigh more/less/the same as the ball?
(A)Do the 2 cylinders weigh the same?
(B)Did you see the water level rise?
(C)Prediction: How will the water change with the second cylinder
compared to the first?
(D) What happened and why after the heavier object was dropped
in?
(A) Do the marble and the standard weight weigh the same?
(B) Did you see the water level rise when the standard mass was
dropped?
(C ) Prediction of how the water level will change with the marble?
(D) What happened when the marble was dropped in the water and
why?
(A) Prediction: What do you think the difference will be between the
flat piece of foil and the ball of foil when both are put in the water?”
(B)What happened to both pieces of foil and why?
(C ) Prediction: Will a golf ball and Styrofoam ball act the same way
as each other in the water?
(D) What happened to each object and why?
2
3
3
3
3
4
4
4
4
4
4
4
4
(E ) Define Density:
(F) Calculated denity of golf ball:
(G) Calculated density of Styrofoam ball :
(H) Why are the numbers so different, what can you conclude about
these 2 numbers?
Response
Numerical
Value
Assigned
HOW DATA WAS ASSIGNED NUMERICAL VALUE:
Numerical
Value
Assigned
0
Numerical Values for Questions 2C, 2D, 3C, 3D, 4A, 4B, 4C, 4D, 4E, 4F&G, 4H
General Description of Possible Answers
Level of Cognitive Development
Incorrect prediction, reasoning, or response all
together that does not show at least 1
dimension (physical property) of thought. Ex.
Include “I don’t know”, “Uhhhh”, “I don’t know
how.” Answers may also be given in relation to
benefits of the child. “It sinks so I can dive and
get it.”
1
A decision is made in the form of an
observation or prediction, in which the
reasoning is based on illogical terms, but an
attempt is made: “It must sink because all
heavy things sink.” Wavering or conflict
between two reasons that appear to be
contradictory or confusing to the child are
given: “It could be the weight, or the volume,
maybe the weight”. Or, response is given in
only 1 dimension of thought : “ Only because of
an object’s weight without consideration of the
volume.”
2
Students will make observations in which two
dimensions of thought are addressed, as well as
their interactions with one another. Students
are able to makes hypotheses based on two
dimensional thought (weight and volume
together) and address the interaction of these
two components of objects. Although the
prediction may not always be the actual result,
it has a logical base and the actual outcome can
be correctly deduced by the individual.
This level of thinking is characteristic of the
preoperational stage, in which the child is still
using tactile interactions to build their
schemas about the world around them. The
child has not had enough interactions to be
able to make predictions on any basis and is
not yet capable of thinking in terms of an
object having weight or volume.
This level of thinking is characteristic of the
concrete operational stage, in which the child
has mastered conservation and understands
that an object can be manipulated in its
physical attributes, without changing the
substance. Children in this stage, however,
still rely heavily on tactile interaction in order
to explain what is occurring. Children in this
stage may not yet to understand how two
components interact, and often find
themselves struggling with which component
is at fault, when in actuality, it is the
interaction of both (weight and volume that
makes an object float or sink).
This level of thinking, the highest level
according to Piaget, is characteristic of the
formal operational stage, in which individuals
have reduced the conflict of two dimensional
thought and have assimilated schemas to the
point where hypothetical suggestions can be
made based on logical thought patterns. The
person (child) at this stage no longer required
to have tactile interactions, but can logically
partake in abstract thought.
WHAT I FOUND:
tudent
#
Student
Age
Student
Grade
Fall
2012
0
1
2
3
4
5
6
7
10.25
10.75
10.75
10.75
11.16
11.42
11.92
12.16
13.0
13.0
13.16
13.83
13.92
14.03
14.03
16.66
46.92
5
5
5
5
5
6
6
7
8
8
8
8
8
8
8
11
BS and
MBA
TASK 1 (1B)
Conservation
of Weight
Mastered?
0=no, 2=Yes
2
2
2
2
0
0
2
2
2
2
2
2
2
2
2
2
2
TASK 2 (2C)
Prediction
for
conservation
of volume
0
0
0
0.5
0
0
0
1
0
2
0
0
0
0
0
0
1.5
TASK 2 (2D)
Analysis of
Results for
Conservation
of Volume
0.5
1
0
1.5
0
1.5
2
2
1
2
2
1
1
1
2
1.5
2
TASK 3 (3C)
Prediction for
different
volumes with
the same mass
0
0
2
2
0
2
2
2
0
2
1
0
0
1.5
1
0
1
TASK 3 (3D)
Analysis of
different
volumes with
the same mass
0
2
2
2
0
2
2
1
0
1
2
2
1
1
1
2
2
WHAT I FOUND:
Student
#
Student
Age
Student
Grade
Fall 2012
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
10.25
10.75
10.75
10.75
11.16
11.42
11.92
12.16
13.0
13.0
13.16
13.83
13.92
14.03
14.03
16.66
46.92
5
5
5
5
5
6
6
7
8
8
8
8
8
8
8
11
BS and
MBA
Table 2: Task 4 Floating vs. Sinking
TASK 4 (4A)
TASK 4 (4B)
TASK 4 (4C)
Prediction
Analysis of
Prediction between
between flat foil
floating vs
golf ball and ping
and foil ball
sinking foil
pong ball
1
0
1
1
0
2
0.5
0
1.5
1.5
1
1.5
1
0
1
1.5
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
2
1
1.5
1.5
1.5
0
1
1
1
1
1
2
1.5
1.5
0.5
1
1
1.5
1
1.5
TASK 4 (4D) Analysis
of floating ball vs.
sinking ball
0
2
2
1.5
1
1
1
1
1
1
1
1.5
1
1
2
1
2
WHAT I FOUND:
Student
#
Student
Age
Table 3: Task 4- Density Tasks
Student Grade
TASK 4 (4E)
TASK 4 (4 F &G)
Fall 2012
Define Density
Calculate
Density
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
10.25
10.75
10.75
10.75
11.16
11.42
11.92
12.16
13.0
13.0
13.16
13.83
13.92
14.03
14.03
16.66
46.92
5
5
5
5
5
6
6
7
8
8
8
8
8
8
8
11
BS and MBA
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
0
2
0
0
2
1.5
2
2
2
1.5
2
2
2
2
2
2
TASK 4 (4H)
Analysis of
numerical value
of densities
0
1
1.5
2
0
1
1
2
1
1
1.5
1.5
1
1
1
1
2
WHAT I FOUND:
Student
#
Student
Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
10.25
10.75
10.75
10.75
11.16
11.42
11.92
12.16
13.0
13.0
13.16
13.83
13.92
14.03
14.03
16.66
46.92
Table 4: Averages of Each Task Segment and Overall Average
Student Average Average Average Average Average
Grade
Task 1
Task 2
Task 3
Task 4
Task 4
Fall 2012
(Foil)
(Balls)
5
2
0.25
0
0.5
1
5
2
0.5
1
0.5
2
5
2
0
2
0.25
1.75
5
2
1
2
1.25
1.5
5
0
0
0
0.5
1
6
0
0.75
2
0.75
1
6
2
1.5
2
0
1
7
2
1.5
1.5
1
1
8
2
0.5
0
0
1
8
2
2
1.5
0
1
8
2
1
1.5
1.5
1
8
2
0.5
1
1.5`
1.5
8
2
0.5
0.5
0.5
1
8
2
0.5
1.25
1
1
8
2
0.5
1
1.75
1.75
11
2
0.75
1
0.25
1
BS and
2
1.75
1.5
1.25
1.75
MBA
Average
Task 4
(Density)
0
0.66
1.5
1
0.3
1.33
0.83
2
1.3
1.33
1.6
1.5
1.33
1.3
1.33
1.33
1.66
Overall
Average
0.32
0.91
1.14
1.32
0.36
1.18
0.95
1.45
0.64
1.18
1.27
1.23
0.82
1.05
1.36
0.99
1.59
CORRELATIONS:
Graph 1: Percent of Students
Who are able to Conserve
Weight (all ages)
No
12%
Yes
88%
Prediction
Analysis
Overall Avg
CORRELATIONS
Prediction of
Foil
Analysis of
Foil
Prediction of
balls
Analysis of
balls
CORRELATIONS
CORRELATIONS
CORRELATIONS:
CORRELATIONS:
WHAT I FOUND OUT:
Students are performing on a mid-concrete level
at best
 Prediction levels were poor (formal stage),
analysis after partaking in the task was at a
higher level (concrete)
 Use of vocabulary without understanding of
vocabulary
 Students showed progression towards formal
thought with grade and age



Later than Piaget suggested
6th graders performing at a solid concrete level,
8th graders between concrete and formal
WHAT THIS MEANS:

Curriculum is demanding formal operational
level…but the students are not ready
Hypothesis, abstract methods, abstract concepts
 Density is based on two dimensions
 Curriculum is focused on right vs. wrong answers, not
getting to the answer
 PISA performance will continue to be low because students
are not accommodating schema



Lack of tangible interaction, manipulation to create
schemas capable of leading to formal operational
thought, increases technology which is abstract will
continue to compound disconnect
Hurrying and not building foundations
HYPOTHESIS TRUE OR FALSE?

TRUE!


Students are not ready to handle the demands of the
curriculum in the way that it is presented
Data from the research supported that most students are still
operating at or near a concrete level:






5th = 0.81
6th = 1.07
7th = 1.45
8th = 1.08
11th =0.99
Adult = 1.59
very early concrete
concrete
between concrete and formal operational
concrete
concrete
transitioning to formal

Students are ready for the analysis of actions!

Students are capable- just not yet


Can present the concepts, but teachers need to give experiences and present
abstract concepts in tangible ways and offer time for discussion and discovery
Take pressure off of the “right” answer
REFERENCES













Armario, Christine. “Wake Up Call : US Students Trail Global Leaders”. MSNBC, The Associated Press,
December 7, 2010. Web. June 23, 2012. <www.msnbc.msn.com>
Berger, Carl. “A Piagetian Like Task Considering the Double Variables of Mass and Volume by
Preservice
and Inservice Elementary School Science Teachers.” University of Michigan,
presented and the National Association of Research in Science Teaching. Web:
www.personal.umich.edu/cberger/marbles_water.html, 6/11/12
Blake, Anthony and Anton Lawson and Floyd Norland. “Piagetian Tasks Clarified: The use of Metal
Cylinders.” The American Biology Teacher April 194: 209-211.
Crain, William. Theories of Development Concepts and Applications, 4th edition. New Jersey: Prentice
Hall. 2000.
Inhelder, Barbel and Jean Piaget. The Growth of Logical Thinking: From Childhood to Adolescence.
United States: Basic Books, Inc., 1958. Or France: Presses Universitairies de France
Inhelder, Barbel and Jean Piaget. The Psychology of the Child. New York: Basic Books, Inc., 1969.
“Is the use of Standardized Tests Improving Education in America.” ProCon.org, 14 Sept, 2011. Web. 23
June 2012. <http://Standardizedtests.procon.org>
Lefton, Lester. Interactive Psychology Online. Boston: Allyn and Bacon, 2001.
OECD Statistics (PISA results, 2003, 2006, 2009). “OECD Statistics (GDP, Unemployment,
Education, Income…).” Oecd, Dec. 2004, 2007, 2010. Web. 23 June 2012.< http://stats.oec.org>
“Piagetian Tasks Conservation of Number, Mass and Weight”. Introduction of Early Childhood Studies.
Ohlone College, 2007. Web. 12 June 2012. <www2.ohlone.edu/people>



“Piaget’s Theory of Conservation: When One Cup of Water is Less Than One Cup of Water.” Science
Buddies. Science Buddies, 10 Nov. 2009. Web. 8 June 2012. <www.sciencebuddies.org/sciencefair-projects/Project_ideas?HumBeh_p049.shtml>
Zwiers, Jeff. Building Reading Comprehension Habits in Grades 6-12: A Toolkit of Classroom
Activities.
Newark: International Reading Association, Inc. 2010.
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