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Models of Teaching Howard L. Jones Deductive Strategies… David P. Ausubel’s Efforts Concepts Defined Concepts Outcomes Find the Pattern Circumference Diameter 11 cm 3.5 cm 56 inches 17.8 inches 4 ft. 1.3 ft. 22 m 7 m

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models of teaching

Models of Teaching

Howard L. Jones

Deductive Strategies…

David P. Ausubel’s Efforts

slide3
Concepts Defined

Concepts

Outcomes

find the pattern
Find the Pattern

CircumferenceDiameter

11 cm 3.5 cm

56 inches 17.8 inches

4 ft. 1.3 ft.

22 m 7 m

3.1 inches 1 inch

find the pattern5
Find the Pattern

CircumferenceDiameter

11 cm 3.5 cm

56 inches 17.8 inches

4 ft. 1.3 ft.

22 m 7 m

3.1 inches 1 inch

Circumference = 3.14… x Diameter

find the pattern6
Find the Pattern

C = ∏D

CircumferenceDiameter

11 cm 3.5 cm

56 inches 17.8 inches

4 ft. 1.3 ft.

22 m 7 m

3.1 inches 1 inch

Circumference = 3.14… x Diameter

inductive teaching
Inductive Teaching

Big Idea

Smaller Ideas Smaller Ideas

Small Ideas Small Ideas

slide8
Multiple Paths to Learning
  • Teacher Gives Students Magnets
  • Students Identify What Things Are Attracted to Magnets
  • Students Determine Characteristics of Objects that Magnets Attract
  • Teacher Gives Students Other Materials
  • Students Predict Which Materials Will Be Attracted to Magnets
  • Students Verify Predictions
deductive teaching
Deductive Teaching

Big Idea (Big Deal)

Smaller Ideas Smaller Ideas

Small Ideas Small Ideas

slide10
Another Way…

Deductive Teaching

  • Teacher Writes on Board “Magnets are attracted to other metals, mostly those made of iron and steel”
  • Teacher Explains All Words, Ensures Meaningfulness
  • Teacher Asks Students For Examples
  • Teacher Gives Students Materials and Magnets
  • Students Predict Which Materials Will Be Attracted to magnets
  • Students Verify Predictions
deductive inductive
Teacher Writes the Answer on Board …

Teacher Explains All Words, Ensures Meaningfulness

Teacher Asks Students For Examples

Teacher Gives Students Materials and Magnets

Students Predict Which Materials Will Be Attracted to Magnets

Students Verify Predictions

Teacher Gives Students Magnets

Students Identify What Things Are Attracted to Magnets

Students Generate Answer Based on heir Observations

Teacher Gives Students Other Materials and Magnets

Students Predict Which Materials Will Be Attracted to Magnets

Students Verify Predictions

Deductive Inductive
deductive inductive12
Teacher Writes the Answer on Board …

Teacher Explains All Words, Ensures Meaningfulness

Teacher Asks Students For Examples

Teacher Gives Students Materials and Magnets

Students Predict Which Materials Will Be Attracted to Magnets

Students Verify Predictions

Teacher Gives Students Magnets

Students Identify What Things Are Attracted to Magnets

Students Generate Answer Based on heir Observations

Teacher Gives Students Other Materials and Magnets

Students Predict Which Materials Will Be Attracted to Magnets

Students Verify Predictions

Deductive Inductive
slide13
But There are Other Outcomes

Concepts Defined Generalizations

Concepts Rules

Principles

Outcomes

a generalization
A Generalization
  • has a broad level of application.
  • contains two or more concepts.
  • states the relationship which exists between (among) the concepts found in the generalization.
slide15
Objects in motion tend to stay in motion unless acted upon by an outside force
  • He more mass an object has the greater the force necessary to accelerate it
  • For every action there is an equal and opposite reaction
slide16
Objects in motiontend to stay in motion unless interacted upon by an outsideforce
  • He moremass an object has the greater the forcenecessary to accelerate it
  • For everyaction there is an equal and oppositereaction
slide17
As the size of a place changes the kinds of goods and services found in that place tend to change.
slide18
As the size of a place changes the kinds of goods and services found in that place tend to change.
  • When two or more societies interact, each tends to acquire some of the characteristics of the other society.
slide19
As the size of a place changes the kinds of goods and services found in that place tend to change.
  • When two or more societies interact, each tends to acquire some of the characteristics of the other society.
  • When two or more groups of people wish to use the same land in different ways, a conflict usually results.
slide20
When the people in a society feel that they are not being governed in their best interests they usually attempt top change the government to suit their interests.
slide21
How to teach rules and generalizations DEDUCTIVELY (and effectively)

The work of David Ausubel

ausubel s postulates
Ausubel’s Postulates
  • Thinking can be taught

Deductive Thinking

deductive thinking
Deductive Thinking

General

Specific

basic postulates
Basic Postulates
  • Learning is more than passive listening
  • Teacher must present generalizations that govern the meaningfulness of new information
  • The purpose of teaching is to strengthen cognitive structures
david p ausubel
David P. Ausubel

“Preconceptions are amazingly tenacious and resistant to extinction.”

Advance Organizers

elements of ausubel lessons
Elements of Ausubel Lessons
  • Advance Organizer

Introductory material presented ahead of the learning task and at a higher level of abstraction and inclusiveness than the learning task itself.

organizers we have organizers
Organizers, we have organizers …

Concept Definition Landforms are land surfaces

that have characteristic

shapes and sizes.

Analogy Two-paragraph comparison

between river systems and

the body’s circulatory system

Generalization The more technology and

knowledge humans possess,

the less limiting are the

influences of nature on

human life.

organizers we have organizers28
Organizers, we have organizers …

Concept Definition Landforms are land surfaces

that have characteristic

shapes and sizes.

Analogy Two-paragraph comparison

between river systems and

the body’s circulatory system

Generalization The more technology and

knowledge humans possess,

the less limiting are the

influences of nature on

human life.

slide29
A chemical bond is a state in which the atoms of two or more elements are at lower energy levels than they would be if they existed separately.
  • A Spanish verb is like a good mystery; it tells who did it and when.
  • A season is an arbitrary period of time with distinctive features.
  • When the ing ending is placed on words ending with vowel-consonant-e (e.g. mate, live), the e is dropped.
slide30
The more technology and knowledge humans possess, the less limiting are the influences of nature on human life.

Agriculture Resource Manufacturing

Extractions

Technology Persistent

Problems

Irrigation Seed Energy

Fertilization Mechanization

Transportation

slide31
The more technology and knowledge humans possess, the less limiting are the influences of nature on human life.

Agriculture Resource Manufacturing

Extractions

Technology Persistent

Problems

Irrigation Seed Energy

Fertilization Mechanization

Transportation

Intelectual Scaffolding

slide33
The more technology and knowledge humans possess, the less limiting are the influences of nature on human life.

Agriculture Resource Manufacturing

Extractions

Technology Persistent

Problems

Irrigation Seed Energy

Fertilization Mechanization

Transportation

Subsumption

rule and generalization learning including defined concepts
External Conditions

Teacher informs student what is expected

Teacher invokes recall of component concepts

Student makes statement in own words

Student demonstrates in another situation

Reinforcement

Internal Conditions

Mastery of component concepts

Rule and Generalization Learning(including Defined Concepts)
slide35
Deductive Processes

Generalization

data data data data data data

data data data

conglomerate conglomerate conglomerate

data data data data data data data

data conglomerate

data

data data data data data data data

data data data data data

data data data

slide36
Deductive Processes

Generalization

data data data data data data

sub- sub- sub-

generalization generalization generalization

data data data data data data data

sub generalization

data

data data data data data data data

data data data data data

data data data

slide37
Deductive Processes

Advance Organizer

data data data data data data

Integrative Integrative Integrative

Reconciliation Reconciliation Reconciliation

data data data data data data data

IntegrativeReconciliation

data

data data data data data data data

data data data data data

data data data

slide38
If a teacher lectures in the middle of

the forest and nobody’s there to

listen, does he actually make sense?

slide41
Calendars are affected not only by agricultural needs but also by religious and political concerns
slide42
hat's my Advance Organizer

Calendars are affected not only by agricultural needs but also by religious and political concerns

the ancient celts
The Ancient Celts …
  • Recognized only two seasons - light and dark. This time of year was still called dark.
george washington s birthday celebrations
George Washington’s Birthday Celebrations
  • February 11, 1732

(Band of Fourth Continental Army serenades him at Valley Forge in 1778)

• February 22, 1732

(Generally observed from 1796)

• President's Day

(Third Monday of February - P. L. 90-363;

effective 1971)

slide47
George Washington was first in war, first in peace…

And the first to have his birthday juggled to make a long weekend.

-Ashley Cooper

early roman calendar
Early Roman Calendar
  • Apparently borrowed from Greeks

(Romulus founds Rome in 738 BCE)

early roman calendar49
Early Roman Calendar
  • Apparently borrowed from Greeks

(Romulus founds Rome in 738 BCE)

  • Ten months and 304 days

(60 days in middle of winter ignored)

early roman calendar50
Early Roman Calendar
  • Apparently borrowed from Greeks

(Romulus founds Rome in 738 BCE)

  • Ten months and 304 days

(60 days in middle of winter ignored)

  • Names of months

(Martius, Aprilis, Maius, Junius, Quintilis,Sextilis, September, October, November, December)

early roman calendar51
Early Roman Calendar
  • Apparently borrowed from Greeks

(Romulus founds Rome in 738 BCE)

  • Ten months and 304 days

(60 days in middle of winter ignored)

  • Names of months

(Martius, Aprilis, Maius, Junius, Quintilis,Sextilis, September, October, November, December)

  • Legend has it that Numa Pompilius (452 BCE) adds January and February and a month called Mercedinus

(22/23 days between February 23-24 every other year)

julian calendar
Julian Calendar
  • By 46 BCE winter occurs in September
julian calendar53
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

julian calendar54
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
julian calendar55
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days

Finally

julian calendar56
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days
  • Quintilis renamed July
julian calendar57
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days
  • Quintilis renamed July
  • Sextilis renamed August
julian calendar58
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days
  • Quintilis renamed July
  • Sextilis renamed August
  • Moved Beginning of Year to January 1
julian calendar59
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days
  • Quintilis renamed July
  • Sextilis renamed August
  • Moved Beginning of Year to January 1
  • 3651/4 days; but still 11 minutes,14 seconds longer than solar year
julian calendar60
Julian Calendar
  • By 46 BCE winter occurs in September
  • 46 BCE declared to have 445 days

(the “year of confusion”)

  • Every four years, February (which had 28 days) was given an additional day
  • Every year thereafter to have 365 days
  • Quintilis renamed July
  • Sextilis renamed August
  • Moved Beginning of Year to January 1
  • 3651/4 days; but still 11 minutes,14 seconds longer than solar year
  • Augustus Caesar ensures regulation by 8CE
dionysius exiguus ca 525 ce
Dionysius Exiguus ca. 525 CE
  • Dates birth of Jesus and misses by at least four years
don t fool with the religious elements of the calendar
Don’t fool with the religious elements of the calendar…

Mathematicians make mistakes…Take Geronimo Cardano, a resident of strictly religious Italy in the 16th century. He tried running a horoscope on Jesus and wound up in prison.

slide63
But…

By 1580 CE, the Spring Equinox fell on March 11, ten days before it should

so what
So what?

Council of Nicea…325 CE

Easter celebrated on the first Sunday after the 14th of Nisan (Passover)…

WHICH JUST HAPPENS TO BE

first Sunday after the first full moon after the Spring Equinox

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