1. Models of Teaching Howard L. Jones Deductive Strategies… David P. Ausubel’s Efforts

3. ConceptsDefined Concepts Outcomes

4. Find the Pattern CircumferenceDiameter 11 cm 3.5 cm 56 inches17.8 inches 4 ft. 1.3 ft. 22 m 7 m 3.1 inches 1 inch

5. Find the Pattern CircumferenceDiameter 11 cm 3.5 cm 56 inches17.8 inches 4 ft. 1.3 ft. 22 m 7 m 3.1 inches 1 inch Circumference = 3.14… x Diameter

6. Find the Pattern CircumferenceDiameter 11 cm 3.5 cm 56 inches17.8 inches 4 ft. 1.3 ft. 22 m 7 m 3.1 inches 1 inch Circumference = 3.14… x Diameter

7. Big IdeaSmaller IdeasSmall Ideas Inductive Teaching

8. Multiple Paths to Learning l Teacher Gives Students Magnets l Students Identify What Things Are Attracted to Magnets l Students Determine Characteristics of Objects that Magnets Attract l Teacher Gives Students Other Materials l Students Predict Which Materials Will Be Attracted to Magnets l Students Verify Predictions

9. Deductive Teaching D Big Idea (Big D eal)Smaller IdeasSmall Ideas

10. 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 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 Another Way… Another Way… Deductive Teaching Deductive Teaching

11. 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

12. DeductiveInductive 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

13. ConceptsDefinedGeneralizations Concepts Rules Principles Outcomes But There are Other Outcomes

14. 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.

15. 1. Objects in motion tend to stay in motion unless acted upon by an outside force 2. He more mass an object has the greater the force necessary to accelerate it 3. For every action there is an equal and opposite reaction

16. 1. Objects in motion tend to stay in motion unless interacted upon by an outside force 2. He more mass an object has the greater the force necessary to accelerate it 3. For every action there is an equal and opposite reaction

17. As the size of a place changes the kinds of goods and services found in that place tend to change.

18. When two or more societies interact, each tends to acquire some of the characteristics of the other society.

19. 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.

20. 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.

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

22. Ausubel’s Postulates Thinking can be taught Deductive Thinking

23. General Specific

24. 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

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

26. 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.

27. Organizers, we have organizers … Concept DefinitionLandforms are land surfaces that have characteristic shapes and sizes. AnalogyTwo-paragraph comparison between river systems and the body’s circulatory system GeneralizationThe more technology and knowledge humans possess, the less limiting are the influences of nature on human life.

28. Organizers, we have organizers … Concept DefinitionLandforms are land surfaces that have characteristic shapes and sizes. AnalogyTwo-paragraph comparison between river systems and the body’s circulatory system GeneralizationThe more technology and knowledge humans possess, the less limiting are the influences of nature on human life.

29. 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.

30. The more technology and knowledge humans possess, the less limiting are the influences of nature on human life. Agriculture Resource Manufacturing Extractions TechnologyPersistent Problems Irrigation SeedEnergy Fertilization Mechanization Transportation

31. The more technology and knowledge humans possess, the less limiting are the influences of nature on human life. Agriculture Resource Manufacturing Extractions TechnologyPersistent Problems Irrigation SeedEnergy Fertilization Mechanization Transportation

32. The Ever Popular Concept Map

33. The more technology and knowledge humans possess, the less limiting are the influences of nature on human life. Agriculture Resource Manufacturing Extractions TechnologyPersistent Problems Irrigation SeedEnergy Fertilization Mechanization Transportation

34. Rule and Generalization Learning (including Defined Concepts) External Conditions 1. Teacher informs student what is expected 2. Teacher invokes recall of component concepts 3. Student makes statement in own words 4. Student demonstrates in another situation 5. Reinforcement Internal Conditions Mastery of component concepts

35. Deductive Processes Generalization data data data conglomerate conglomerate conglomerate datadatadatadatadatadata data data conglomerate data data datadatadatadatadatadata data data data data data datadata data data datadatadatadata data

36. Deductive Processes Generalization sub- sub- sub- generalization generalization generalization datadatadatadatadatadata data sub generalization data data datadatadatadatadatadata data data data data data datadata data data datadatadatadata data

37. Deductive Processes Advance Organizer Integrative Integrative Integrative Reconciliation Reconciliation Reconciliation datadatadatadatadatadata data Integrative Reconciliation data data datadatadatadatadatadata data data data data data datadata data data datadatadatadata data

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

39. Calendars

40. Why do we need calendars anyway?

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

43. The Ancient Celts … Recognized only two seasons - light and dark. This time of year was still called dark.

44. Jewish Calendar Nisan

45. And a Third One George Washington’s Multiple Birthdays

46. 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)

47. George Washington was first in war, first in peace… And the first to have his birthday juggled to make a long weekend. - Ashley Cooper

48. Early Roman Calendar Apparently borrowed from Greeks (Romulus founds Rome in 738 BCE)

49. 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)

50. 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)

51. 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)

52. Julian Calendar By 46 BCE winter occurs in September

53. Julian Calendar By 46 BCE winter occurs in September 46 BCE declared to have 445 days (the “year of confusion”)

54. 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

55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

61. Dionysius Exiguus ca. 525 CE Dates birth of Jesus and misses by at least four years

62. Don’t fool with the religious elements of the calendar… Mathematicians make mistakes…Take Geronimo Cardano, a resident of strictly religious Italy in the 16 th century. He tried running a horoscope on Jesus and wound up in prison.

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

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