CUIN 6371 Models of Teaching Fall, 2003 Howard L. Jones Deductive Strategies… David P. Ausubel’s Efforts

Robert Gagné’s Types of Learning Basic Signal Learning – Stimulus Response Higher Order Concepts Rules/Generalizations Problem Solving Motor Skills Attitudes

Concepts Oxymoron/Pleonasm Gerrymandering Parallel Soft Diagonal Verbs, adverbs, modifiers… Model of Teaching

Elements of a Concept Jerome Bruner Every Concept has 1. A name 2. Examples and Non-Examples (positives and negatives) 3. Attributes 4. Attribute Values (essential and non-essential) A RULE, then, is the statement of the essential attributes of the concept

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.

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.

Searching for concepts and generalizations -The work of Joel Barker

Concepts Defined Generalizations Concepts Rules Principles Outcomes

Information Processing Inductive - Jerome Bruner/ Hilda Taba Deductive - David Ausubel Inquiry - J. J. Schwab/J. Richard Suchman Jean Piaget/ L. Kohlberg Memory - R. Atkinson/J. Levin/J. Lucas Creativity - W. J. J. Gordon

If a teacher lectures in the middle of the forest and nobody’s there to listen, does he actually make sense?

How to teach rules and generalizations DEDUCTIVELY (and effectively) The work of David Ausubel

Deductive Teaching The Most Common The “Guided Tour” Teaching Pattern Approach • Providing Information • Verification of information • Application of Information (after Renner) Deductive Teaching What do we know about science teaching? Most common practice of science teachers is to attempt to pass on to their pupils a mastery of content. The assumption is that once they have some information, the information can be verified and applied in some way. The GUIDED TOUR approach

Deductive Thinking Ausubel’s Postulates Thinking can be taught But not like Taba’s type - Deductive Thinking

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.

Rule and Generalization Learning (including Defined Concepts) Internal Conditions Mastery of component 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

“Preconceptions are amazingly tenacious and resistant to extinction.” Advance Organizers David P. Ausubel

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

Elements of Ausubel Lessons Advance Organizer

David P. Ausubel Advance Organizers - primary means of strengthening cognitive structures and enhancing retention of new information 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 … 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.

Other Ausubelian Big Words include: Subsumption Intellectual Scaffolding

The Ever Popular Concept Map

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

Generalization Deductive Processes data data data 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

Generalization Deductive Processes sub- sub- sub- 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

Advance Organizer Deductive Processes data data data data data data Integrative Integrative Integrative Reconciliation Reconciliation Reconciliation data data data data data data data Integrative Reconciliation data data data data data data data data data data data data data data data data

Elements of Ausubel Lessons Advance Organizer Integrative Reconciliation Progressive Differentiation

Integrative Reconciliation Advance Organizer Progressive Progressive Progressive Differentiation Differentiation Differentiation Integrative Reconciliation

Calendars

Why do we need calendars anyway?

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

The Ancient Celts … Recognized only two seasons - light and dark. This time of year was the beginning of what was called dark.

Jewish Calendar Nisan

George Washington’s Multiple Birthdays And a Third One

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)

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 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) Numa (452 BCE) adds January and February and a month called Mercedinus (22/23 days between February 23-24 every other year)

(the “year of confusion”) 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 • 365 1/4 days; but still 11 minutes,14 seconds longer than solar year • Augustus Caesar ensures regulation by 8CE • By 1580 the Spring Equinox fell on March 11, ten days earlier than it should

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… 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.

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

Council of Nicea…325 CE So what? Easter celebrated on the Sunday nearest the 14th of Nisan (Passover)… WHICH JUST HAPPENS TO BE first Sunday after the first full moon after the Spring Equinox

(October 5, 1582 became October 15) Gregorian Calendar 1582 - Pope Gregory XIII Ten days dropped from October (October 5, 1582 became October 15) February gets an extra day in “century” years that can be divided by 400 Difference between calendar and solar years now only in seconds Roman Catholic nations of Europe adopted Gregorian calendar immediately German states adopt by 1700

In 1640, when the first calendar was published for the public..... Everyone knew that its days were numbered.

So why does George Washington have three birthdays?

George Washington’s Multiple Birthdays And a Third One

In Islam, portions of 2002/3 are 1423 A.H.

Calendars through the eyes of Jigsaw II

Jigsaw II and Calendars Generalization: Calendars are affected not only by agricultural needs but also by religious and political concerns. Expert Teams focus on how the generalization holds or does not hold in the... Hebrew Calendar • Lunar calendar Islamic Calendar Months (Tishri, Nisan ...) • Portions of 2001/2002 are • Day of Atonement ... 1422 A.H. (Anno Hegirae) Dating of Year 1 • Ramadan…Eid, Haj… • Lunar calendar... Mayan Calendar • Two kinds of calendars – Chinese Calendar a sacred one of 260 days • Emperor Huang-Ti invents and another - • Naming of year - year of the ox, ... a solar calendar • Chinese new year ... • Lucky and unlucky days ... Home Teams

Lecturing is not always appropriate

The case for…and against Against Discovery 1. Takes too much time 2. Kids can’t learn as much 3. They can’t discover everything 4. What if they discover a wrong answer? For Discovery 1. Kids better remember and transfer 2. More and better interest 3. Kids learn to discover Heuristics

Direct (Expository) Teaching When to Use…. Direct (Expository) Teaching • When time is limited • When there are no readily available or easily understood materials Indirect Teaching • When time is available for discovery and higher-order thinking • When there is an abundance of understandable materials

The Lecture Method is Appropriate When… The objective is to present information Information is not available in accessible sources A particular organization is required You want to arouse interest An introduction must be made The information is original or must be integrated from different sources A summary or synthesis is required Alternative points or clarification are required Supplementary explanations are needed (after Good and Brophy, 1999; Gage and Berliner, 1992; Henson, 1988)

Ausubel Model Characteristics Interactive Deductive Sequential Uses Examples Present Present Advance Subordinate Organizer Content Differentiate Ask for Reconcile Subordinate or provide Differentiated Material examples of Material subordinate concepts or generalizations

Teaching… Inductively and Deductively

Inductive Deductive Inquiry Memory Creativity General Information Processing models are designed to assist students learn content at the same time as they learn/practice thinking skills under the guidance and direction of an active teacher. Inductive Deductive Inquiry Memory Creativity General Taba’s Concept Ausubel’s Suchman’s Science Synectics Inductive Attainment Model Inquiry Inquiry Model Model Training Models Developmental Models (Kohlberg, Piaget) Mnemonics

A Mental Movement Next Time….Memory and Creativity… Read the readings; take the S-C Inventory….

Experimentalism Education is life, not preparation for life Education is directly related to interests of the child Learning is best accomplished through problem solving The teacher’s role is not to direct but to advise Schools should encourage cooperation rather than competition Only democracy permits – in fact, encourages - the free interplay of ideas and personalities, both of which are required for true growth Lloyd Duck, Teaching With Charisma.

At Odds with Essentialism… Learning, by its nature, involves hard work and often unwilling application The initiative lies with the teacher The heart of the educational process is the absorption of prescribed subject matter The school should retain traditional methods of mental discipline Lloyd Duck, Teaching With Charisma.