HOMEHOME Phase 1 (Introduction)Phase 1 (Introduction)

– The counter’s mistake (video) (video)

Algorithmic mistakes (graphic) (graphic) Phase 2 (Developmental Underpinnings)Phase 2 (Developmental Underpinnings)

– The perceiver’s mistake (graphic) (graphic)– The conserver’s mistake (video) (video)– Decalage– Iatrogenics– Confabulation

Phase 3 (Applications)Phase 3 (Applications)– Psychological considerations re errors– Tracking errorsTracking errors

A Checklist

– Thinking errors

LinksLocal

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Value of mistakes

Testing Mistakes

Writing Mistakes

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Signs Language based…

SES background,health, knowledgefamily, age, …

Knowledge

Problem Solving #1

Problem Solving #2Learning Styles

Assignment

Week 3 --- MetaphorWeek 3 --- Metaphor

Diagnostician Detective

Detect the thinking in these five children by Detect the thinking in these five children by examining the addition algorithm errors.examining the addition algorithm errors.

In each set of three errors the child is In each set of three errors the child is making the same mistake. If you think you making the same mistake. If you think you can see the error in the first question, you can see the error in the first question, you should be able to confirm it in the next two should be able to confirm it in the next two questions where the child makes the error. questions where the child makes the error.

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SallySally

76 205 75476 205 754 +17 +86 +28+17 +86 +28 ----- ----- ---------- ----- ----- 21 21 2621 21 26

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SethSeth

46 21 1546 21 15 +3 +8 +2+3 +8 +2 ----- ----- ---------- ----- ----- 43 13 1343 13 13

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TomTom

46 21 15 46 21 15 +3 +8 +2+3 +8 +2 ---- ---- -------- ---- ---- 79 109 3779 109 37

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EdwardEdward

48 79 2648 79 26 +3 +9 +7+3 +9 +7 ---- ---- -------- ---- ---- 411 718 213411 718 213

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BarbaraBarbara

519 345 483519 345 483 +82 +76 +57+82 +76 +57 ----- ----- ---------- ----- ----- 511 511 711511 511 711

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Detect the thinking in these five children by Detect the thinking in these five children by examining the subtraction algorithm errors.examining the subtraction algorithm errors.

In each set of three errors the child is In each set of three errors the child is making the same mistake. If you think you making the same mistake. If you think you can see the error in the first question, you can see the error in the first question, you should be able to confirm it in the next two should be able to confirm it in the next two questions where the child makes the error. questions where the child makes the error.

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SamSam

37 43 8537 43 85 -4 -1 -3-4 -1 -3 ---- ---- --------- ---- ----- 23 32 7223 32 72

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FranFran

32 50 2432 50 24 -6 -8 -5-6 -8 -5 ---- ---- -------- ---- ---- 34 58 2134 58 21

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BenBen

53 72 4553 72 45 -14 -56 -19-14 -56 -19 ---- ---- -------- ---- ---- 49 26 3649 26 36

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Sarah and SidSarah and Sid

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DiscussionDiscussion

Why

do

lear

ners

mak

e m

istak

es?

Why

do

lear

ners

mak

e m

istak

es?

-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:MedicalNeuropsychologicalPsychological/PsychometricBehavioural (Learning Theory)DevelopmentalEthologicalPolitical (Monetary)Synergistic

DecalageDecalage

A Piagetian concept that is often overlooked in A Piagetian concept that is often overlooked in education and special education. education and special education.

Vertical Decalage Horizontal Decalage

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Decalage …Decalage …

Horizontal Horizontal

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60

70

80

90

Time1 Time2 Time3 Time4

Skill1

Vertical Vertical

0

10

20

30

40

50

60

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80

90

Skill1 Skill2 Skill3 Skill4

Ability

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Part-whole perceptionPart-whole perception

Age 4/5Age 4/5

The child looks at this The child looks at this picture and when picture and when asked what he sees, asked what he sees, he is likely to reply: he is likely to reply: “suckers and candy “suckers and candy canes.”canes.”

The mistake?SEARCH

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Part-whole perceptionPart-whole perception

Age 5/6Age 5/6

The child looks at this The child looks at this picture and when picture and when asked what he sees, asked what he sees, he is likely to reply: “a he is likely to reply: “a scooter.”scooter.”

The mistake?SEARCH

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Part-whole perceptionPart-whole perception

Age 6/7Age 6/7

The child looks at this The child looks at this picture and when picture and when asked what he sees, asked what he sees, he is likely to reply: “a he is likely to reply: “a scooter made of scooter made of suckers and candy suckers and candy canes.”canes.”

The mistake?SEARCH

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Conservation of NumberConservation of Number

Age 4/5, 5/6, 6/7, 9Age 4/5, 5/6, 6/7, 9

Watch the video clip and note the Watch the video clip and note the cognitive underpinnings with respect cognitive underpinnings with respect to the conservation of number.to the conservation of number.

Does this child approach the task at Does this child approach the task at each age level in a manner each age level in a manner comparable to the child approaching comparable to the child approaching the scooter made from candies? the scooter made from candies?

11stst details, … 2 details, … 2ndnd gestaltgestalt, … , …

33rdrd both…both…

CLICK on the VideoCLICK on the Video

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DecalageDecalage

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Preoperational Stage Concrete-Operational Stage

MistakesMistakes

Mistakes are allies! Mistakes are allies!

Mistakes:Mistakes:–Often show the reasoning in the errorOften show the reasoning in the error–Point to a developmental levelPoint to a developmental level–Ensure constructivism is operativeEnsure constructivism is operative–Demonstrate risk-taking behaviorsDemonstrate risk-taking behaviors–Can flag significant processing problemsCan flag significant processing problems–Can be the occasion of great harmCan be the occasion of great harm

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Iatrogenics Iatrogenics Prescription drugs are now the third leading cause Prescription drugs are now the third leading cause

of death in America killing 200,000 every year.of death in America killing 200,000 every year. INTERNATIONAL COALITION FOR DRUG AWARENESSINTERNATIONAL COALITION FOR DRUG AWARENESS http://members.aol.com/atracyphd/mission.htmhttp://members.aol.com/atracyphd/mission.htm

80,000 die from medical malpractice (est 44,000 to 80,000 die from medical malpractice (est 44,000 to 98,000 by Institute of Medicine Report)98,000 by Institute of Medicine Report)

http://abcnews.go.com/onair/http://abcnews.go.com/onair/2020/2020_000405_medicalerrors_feature.html2020/2020_000405_medicalerrors_feature.html

41,000 die in auto accidents41,000 die in auto accidents

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Iatrogenic mistakes or problems in education?Iatrogenic mistakes or problems in education?

Can you think of an instance where a teacher might harm Can you think of an instance where a teacher might harm rather than help even though the intention was to help?rather than help even though the intention was to help?

Teaching reading before the child is ready…Teaching reading before the child is ready…

Expecting an adolescent to engage a task at the formal Expecting an adolescent to engage a task at the formal operational level when they aren’t there yet.operational level when they aren’t there yet.

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Remember it isn’t just developmental level, or Remember it isn’t just developmental level, or carelessness in making mistakes…carelessness in making mistakes…

And then (spoofing And then (spoofing me) there’s… me) there’s… Learning Styles

-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

ConfabulationConfabulation

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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.

Group activity-at least three different majors in your group-hand in assignment with participants names

Mistakes in ThinkingMistakes in Thinking

Illusions of Knowing.. Logic Errors

Testing Mistakes

Writing Mistakes

Signs

If there is a mistake in thinking here what is it?If there is a mistake in thinking here what is it? Allan and Bill are young adolescent students. They are Allan and Bill are young adolescent students. They are

debating the question: “Is it necessary to teach young students debating the question: “Is it necessary to teach young students computers in order to develop their intelligence?” Allan argues computers in order to develop their intelligence?” Allan argues that it is necessary in order to develop their intelligence. Bill that it is necessary in order to develop their intelligence. Bill argues that it is not necessary. Allan says, “It is necessary to argues that it is not necessary. Allan says, “It is necessary to teach young children computers in order to develop their teach young children computers in order to develop their intelligence, because it is known that most of the intelligent intelligence, because it is known that most of the intelligent students in school learned computers when they were young.”students in school learned computers when they were young.”

Alice and Betty are young adolescents who have been listening Alice and Betty are young adolescents who have been listening to their parents discuss taxes. Both have seen their parents pay to their parents discuss taxes. Both have seen their parents pay for services via the underground economy with the statement for services via the underground economy with the statement “no taxes!” When taxes are discussed in a school civics lesson “no taxes!” When taxes are discussed in a school civics lesson Alice argues that it is fair to avoid paying taxes. Betty argues 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 that it is not fair. Alice makes the point that “it is fair to avoid paying taxes because most people avoid paying their taxes.”paying taxes because most people avoid paying their taxes.”

Andrew and Bonnie are discussing whether or not God exists. Andrew and Bonnie are discussing whether or not God exists. Andrew makes the claim that God exists. Bonnie says, “no Andrew makes the claim that God exists. Bonnie says, “no way.” Andrew responds, “No one has proven that God does not way.” Andrew responds, “No one has proven that God does not exist, therefore we can conclude that God does exist.”exist, therefore we can conclude that God does exist.”

Post hoc e

rgo pro

pter hoc f

allacy

Ad populum argument

Ad ignora

tium arg

ument

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Value Value

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Mistakes are developmentalMistakes are developmental Mistakes are normalMistakes are normal Mistakes are learning experiencesMistakes are learning experiences Mistakes are diagnosticMistakes are diagnostic Mistakes are linked to risk-takingMistakes are linked to risk-taking Mistakes are/should be encouragedMistakes are/should be encouraged Mistakes are opportunities for teachersMistakes are opportunities for teachers Mistakes are.…Mistakes are.…

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Put it together…Put it together… The psychology of making mistakes. The psychology of making mistakes. Causes Causes (carelessness, developmental level, (carelessness, developmental level,

attention, memory, language, thinking, history, attention, memory, language, thinking, history, culture, disability, attitude, impulsivity, sensory culture, disability, attitude, impulsivity, sensory deficits, and so on…)deficits, and so on…)

Why might a child make spelling errors, Why might a child make spelling errors, math errors, thinking errors… etc?math errors, thinking errors… etc?– Identify the error.Identify the error.– Identify the type of error the child consistently makes. Identify the type of error the child consistently makes. – Identify what the child is thinking, or doing, or not doing.Identify what the child is thinking, or doing, or not doing.– Develop a checklist to monitor error sources. Develop a checklist to monitor error sources.

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TrackingTracking If you wanted to conduct an error analysis for If you wanted to conduct an error analysis for

spelling errors you could draw up a checklist of spelling errors you could draw up a checklist of things to monitor. Suppose you have a child in things to monitor. Suppose you have a child in your class who is making numerous errors. You your class who is making numerous errors. You decide to record three of her errors each day, and decide to record three of her errors each day, and then after a few weeks see if there is any pattern then after a few weeks see if there is any pattern in the errors. What might your checklist look like?in the errors. What might your checklist look like?

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Spelling ErrorsSpelling ErrorsError Response 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1

5

Pronunciation

Too few letters

Too many letters

Substituted letter

Incorrect Sequencing

Visual (Initial Position)

Visual (Medial Position)

Visual (Final Position)

Consonant

Blend

Digraph

Short vowel

Long vowel

Vowel combinations

Silent e

Phonetically Appropriate

Phonetically Inappropriate

A

K a

tX

XX

Error AnalysisError Analysis Plot the following errors on the checklist you Plot the following errors on the checklist you

construct/design.construct/design. What might the errors indicate about this child’s What might the errors indicate about this child’s

problem/s?problem/s?

cak (cake)cak (cake) ma (mat)ma (mat) kat (cat)kat (cat) ned (need)ned (need) rak (rake)rak (rake) sen (sent)sen (sent)

bel (bell)bel (bell) book (books)book (books) cand (candy)cand (candy) pene (penny)pene (penny) duk (duck)duk (duck) drak (drake)drak (drake)

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Spelling ErrorsSpelling ErrorsError Response 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1

5

Pronunciation

Too few letters

Too many letters

Substituted letter

Incorrect Sequencing

Visual (Initial Position)

Visual (Medial Position)

Visual (Final Position)

Consonant

Vowel

Digraph

Short vowel

Long vowel

Vowel combinations

Silent e

Phonetically Appropriate

Phonetically Inappropriate

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K a

t/cat

XX

X

Sen/

sent

Ten/

tent

bel/b

ell

Duk

/duc

kBo

ok/b

ooks

Bud/

bed

XX

XX

XX

XX

XX

XX

XX

X X XX

Problem Solving #1Problem Solving #1

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Identify Problems

Define Goal

Explore possible strategies

Anticipate outcomes / Act

Look back / Learn

I

D

E

A

L

Problem Solving #2Problem Solving #2

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Identify Problems

Define Goal

Explore possible strategies

Anticipate outcomes / Act

Look back / Learn

I

D

E

A

L

Learning From MistaksLearning From Mistaks Mistakes people make:Mistakes people make:

– MathMath– SpellingSpelling– LanguageLanguage– ThinkingThinking– BullyingBullying– Being bulliedBeing bullied– SmokingSmoking– Drug useDrug use– Fighting/ViolenceFighting/Violence– EatingEating– ApathyApathy– Suicidal ideationSuicidal ideation– RacismRacism– SexismSexism– Etc.Etc.

A Protocol for Using Mistakes

•Be creative

•Be practical

•Be instructive

•Be application-oriented

•Be constructive

•Build

•Two pages

•It could be posted for others

-Draft (1-2 rough pages)-Post (1-2 Polished pages)-Newsletter

Impu

lsivit

y