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 Phase 1 (Introduction)
– The counter’s mistake (video)
Value of mistakes
 Algorithmic mistakes (graphic)
 Phase 2 (Developmental Underpinnings)
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The perceiver’s mistake (graphic)
The conserver’s mistake (video)
Decalage
Iatrogenics
Confabulation
Assignment
Signs
Testing Mistakes
SES background,
health, knowledge
family, age, …
Writing Mistakes
 Phase 3 (Applications)
– Psychological considerations re errors
– Tracking errors
Problem Solving #1
 A Checklist
– Thinking errors
SEARCH
Problem Solving #2
Learning Styles
Week 3 --- Metaphor
Diagnostician
Detective
Detect the thinking in these five children by
examining the addition algorithm errors.
 In each set of three errors the child is
making the same mistake. If you think you
can see the error in the first question, you
should be able to confirm it in the next two
questions where the child makes the error.
SEARCH
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Sally
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76 205
+17 +86
----- ----21
21
SEARCH
754
+28
----26
A
Seth
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46 21 15
+3 +8 +2
----- ----- ----43 13 13
SEARCH
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Tom
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46 21 15
+3 +8 +2
---- ---- ---79 109 37
SEARCH
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Edward
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48
+3
---411
SEARCH
79 26
+9 +7
---- ---718 213
A
Barbara
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519 345
+82 +76
----- ----511 511
SEARCH
483
+57
----711
Detect the thinking in these five children by
examining the subtraction algorithm errors.
 In each set of three errors the child is
making the same mistake. If you think you
can see the error in the first question, you
should be able to confirm it in the next two
questions where the child makes the error.
SEARCH
A
Sam
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37 43 85
-4
-1 -3
---- ---- ----23 32 72
SEARCH
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Fran
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32 50 24
-6 -8 -5
---- ---- ---34 58 21
SEARCH
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Ben
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53
-14
---49
SEARCH
72 45
-56 -19
---- ---26 36
Sarah and Sid
SEARCH
A
Discussion
-Thinking
-Background information
-Brain Damage
-Sensory deficits
-Culture
-Intelligence
-Lack of Skills
-Fatigue
-Impulsivity
-Attention Deficits
-Hierarchy of Needs (Maslow)
-Language Limitations
-Peers
-Teachers
-Learning (Faulty or Incorrect)
-Developmental Level
Paradigms:
Medical
Neuropsychological
Psychological/Psychometric
Behavioural (Learning Theory)
Developmental
Ethological
Political (Monetary)
Synergistic
Decalage
A
A Piagetian concept that is often overlooked in
education and special education.
Vertical Decalage
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Horizontal Decalage
A
Decalage …
Horizontal
Vertical
90
90
80
80
70
60
70
60
50
50
Ability
40
30
20
10
0
Skill1
Skill2
Skill3
Skill4
Skill1
40
30
20
10
0
Time1
Time2
Time3
Time4
A
Part-whole perception
 Age 4/5
 The child looks at this
picture and when
asked what he sees,
he is likely to reply:
“suckers and candy
canes.”
SEARCH
The mistake?
A
Part-whole perception
 Age 5/6
 The child looks at this
picture and when
asked what he sees,
he is likely to reply: “a
scooter.”
SEARCH
The mistake?
A
Part-whole perception
 Age 6/7
 The child looks at this
picture and when
asked what he sees,
he is likely to reply: “a
scooter made of
suckers and candy
canes.”
SEARCH
The mistake?
Conservation of Number
 Age 4/5, 5/6, 6/7, 9
 Watch the video clip and note the
cognitive underpinnings with respect
to the conservation of number.
 Does this child approach the task at
each age level in a manner
comparable to the child approaching
the scooter made from candies?
 1st details, … 2nd gestalt, …
3rd
both…
 CLICK on the Video
SEARCH
A
Decalage
Preoperational Stage
SEARCH
A
Concrete-Operational Stage
Mistakes
A
Mistakes are allies!
Mistakes:
–Often show the reasoning in the error
–Point to a developmental level
–Ensure constructivism is operative
–Demonstrate risk-taking behaviors
–Can flag significant processing problems
–Can be the occasion of great harm
SEARCH
A
Iatrogenics
 Prescription drugs are now the third leading cause
of death in America killing 200,000 every year.
 INTERNATIONAL COALITION FOR DRUG AWARENESS
 http://members.aol.com/atracyphd/mission.htm
 80,000 die from medical malpractice (est 44,000 to
98,000 by Institute of Medicine Report)
 http://abcnews.go.com/onair/2020/2020_000405_m
edicalerrors_feature.html
 41,000 die in auto accidents
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A
 Iatrogenic mistakes or problems in education?
 Can you think of an instance where a teacher might harm
rather than help even though the intention was to help?
 Teaching reading before the child is ready…
 Expecting an adolescent to engage a task at the formal
operational level when they aren’t there yet.
Remember it isn’t just developmental level, or
carelessness in making mistakes…
-Thinking
-Background information
-Brain Damage
-Sensory deficits
-Culture
-Intelligence
-Lack of Skills
-Fatigue
-Impulsivity
-Attention Deficits
-Hierarchy of Needs (Maslow)
-Language Limitations
-Peers
-Teachers
-Developmental Level
 And then (spoofing
me) there’s…
Learning Styles
Group activity
-at least three different
majors in your group
-hand in assignment
with participants names
Create a list of ten important
points (possibly related to
the philosophy of mistakes,
the psychology of mistakes,
the pedagogy of mistakes,
the history of mistakes, the
politics of mistakes, and so
on) that might emerge from
the lecture material and
textbook information for
today.
SEARCH
A
Confabulation
Mistakes in Thinking
 Illusions of Knowing.
 Logic Errors
Testing Mistakes
Signs
Writing Mistakes
If there is a mistake in thinking here what is it?
A
 Allan and Bill are young adolescent students. They are
debating the question: “Is it necessary to teach young students
computers in order to develop their intelligence?” Allan argues
that it is necessary in order to develop their intelligence. Bill
argues that it is not necessary. Allan says, “It is necessary to
teach young children computers in order to develop their
intelligence, because it is known that most of the intelligent
students in school learned computers when they were young.”
 Alice and Betty are young adolescents who have been listening
to their parents discuss taxes. Both have seen their parents pay
for services via the underground economy with the statement
“no taxes!” When taxes are discussed in a school civics lesson
Alice argues that it is fair to avoid paying taxes. Betty argues
that it is not fair. Alice makes the point that “it is fair to avoid
paying taxes because most people avoid paying their taxes.”
 Andrew and Bonnie are discussing whether or not God exists.
Andrew makes the claim that God exists. Bonnie says, “no
way.” Andrew responds, “No one has proven that God does not
exist, therefore we can conclude that God does exist.”
A
Value
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Mistakes are developmental
Mistakes are normal
Mistakes are learning experiences
Mistakes are diagnostic
Mistakes are linked to risk-taking
Mistakes are/should be encouraged
Mistakes are opportunities for teachers
Mistakes are.…
SEARCH
Put it together…
A
 The psychology of making mistakes.
 Causes (carelessness, developmental level,
attention, memory, language, thinking, history,
culture, disability, attitude, impulsivity, sensory
deficits, and so on…)
 Why might a child make spelling errors,
math errors, thinking errors… etc?
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Identify the error.
Identify the type of error the child consistently makes.
Identify what the child is thinking, or doing, or not doing.
Develop a checklist to monitor error sources.
SEARCH
A
Tracking
 If you wanted to conduct an error analysis for
spelling errors you could draw up a checklist of
things to monitor. Suppose you have a child in
your class who is making numerous errors. You
decide to record three of her errors each day, and
then after a few weeks see if there is any pattern
in the errors. What might your checklist look like?
SEARCH
Spelling Errors
Error Response
Pronunciation
Too few letters
Too many letters
Substituted letter
Incorrect Sequencing
Visual (Initial Position)
Visual (Medial Position)
Visual (Final Position)
Consonant
Blend
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A
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A
Error Analysis
 Plot the following errors on the checklist you
construct/design.
 What might the errors indicate about this child’s
problem/s?
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cak (cake)
ma (mat)
kat (cat)
ned (need)
rak (rake)
sen (sent)
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bel (bell)
book (books)
cand (candy)
pene (penny)
duk (duck)
drak (drake)
Spelling Errors
Error Response
Pronunciation
Too few letters
Too many letters
Substituted letter
Incorrect Sequencing
Visual (Initial Position)
Visual (Medial Position)
Visual (Final Position)
Consonant
Vowel
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2
3
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5
6
7
A
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14
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Problem Solving #1
I
Identify Problems
D Define Goal
E
Explore possible
strategies
A Anticipate outcomes /
Act
L
Look back / Learn
SEARCH
Problem Solving #2
I
Identify Problems
D
Define Goal
E
Explore possible
strategies
A
Anticipate outcomes
/ Act
L
Look back / Learn
SEARCH
Learning From Mistaks
 Mistakes people make:
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Math
Spelling
Language
Thinking
Bullying
Being bullied
Smoking
Drug use
Fighting/Violence
Eating
Apathy
Suicidal ideation
Racism
Sexism
Etc.
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-Post (1-2 Polished pages)
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