1. Thinking and Language

2. Thinking and Language What is the sum of 362 and 499?
You found Campbell’s soup on aisle 10 at Harris Teeter; where will you find Lipton’s soup?
Chapel Hill and Duke both offer you a scholarship. How will you choose which college to attend?

3. Thinking
The mental activity that is involved in the understanding, processing, and communicating of information.
Your answer to the three questions each required a different type of thinking

4. THINKING
SYMBOLS

5. Symbols An object or an act that stands for something else
Your mental images are a type of symbol—when you think of a dog, you are thinking of a symbol of a dog

6. THINKING
SYMBOLS
CONCEPTS

7. Concepts
A mental structure used to categorize objects, people, or events that share similar characteristics
Think of an animal
What makes it an animal?
You have used the concept animal to create a new item that fits into the animal category
Now put that animal in a tree eating fruit—there is a relationship now between animal, tree, and fruit

8. Concepts ANIMALS A concept is a category containing many examples
Concepts are organized into hierarchies
ANIMALS
MAMMALS
Dogs, Whales, etc.

9. Concepts Learned through experience
Learning about concepts such as fairness, beauty, goodness more challenging than learning what is a dog, a ball, a vegetable
KEY: A concept is a type of symbol because it stands for something else

10. THINKING
SYMBOLS
CONCEPTS
PROTOTYPES

11. Prototypes
The most typical example of an object or event within a category
Think of a shoe
Any of these come to mind?

12. Prototype Activity

13. Objectives & Agenda
Continue to develop an understanding of Thinking and Language
Students will recover prior learning on symbols, concepts, and prototypes through an activity that engages your prior knowledge, encourages collaboration, and challenges your creativity
Students will study, analyze, and experiment with the several ways people use to solve problems
Students will identify obstacles to problem solving

14. Warm-up: Putting this all together…
When developing a thought, a single-word concept emerges: feathers
Now combine that concept with another: beak
Connect those concepts to a third: eggs
And one more: fly
What comes to mind?

15. ing
Something like this?

16. Why not these two?

17. Groups: Comic activity
Break into groups of three as I’ve assigned
Each group will draw a name from a hat (done) and you will create a cartoon that illustrates how people use this unit (symbol, concept, prototype) in their daily lives.

18. Cognitive processes
Watch the video and answer the questions on the viewing guide

19. Problem Solving Faced with a problem we do what?
Involves a series of processes including analyzing the problem, breaking it down into component parts, and establishing goals

20. Warm-up
A prisoner was attempting to escape from a tower. He found in his cell a rope, which was half long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. How could he have done this?  
If you have black socks and brown socks in your drawer, mixed in a ratio of 4 to 5, how many socks will you have to take out to make sure that you have a pair the same color?

21. Answers: Unwind the rope and tie the ends together
Three - if the first is brown and the second black then the third one will match either the brown or black.

22. Problem Solving
Turn in your textbook to page 180 and try and solve problems A-E; team up with someone to try and complete all six in ten minutes

23. Problem-solving strategies
Algorithm: problem solving strategy
Usually involves trying random solutions to a problem in a systematic way
𝐴=𝜋 𝑟 2 is an example
Often complex and time-consuming
Heuristics: rules of thumb, shortcuts
Faster than algorithms, not as reliable

24. C L _ F F C _ _ F F Examples Use algorithm (systematic approach)
A, E, I, O, U
C _ _ F F
Algorithm approach (slow, two letters)
Heuristic—recall linguistic rules; must have a vowel, what letters can’t follow a C

25. Another Example
C _ _ C H
Algorithm?
Heuristic?
CZECH

26. Problem-Solving Methods
Trial and error
We know the goal, have no idea how to reach it
Just keep trying different things
Similar to systematic searching
Not very reliable

28. Problem-solving methods
Difference Reduction
1) Identify goal
2) determine where we are in relation to it and the direction we must go to move closer to it
We reduce the difference between where we are (problem unresolved) and our desired situation (problem solved).
A heuristic method, not always reliable

29. Difference reduction Problem A in Figure 8.1 illustrative
One step forward, two steps back
If you want to go north, sometimes you first must go south
Sometimes must increase the distance between current location and goal to ultimately get there
Asks, “in what direction must I move to get from A to B?”

30. Means-End Analysis
Aims to reduce the difference between where we are (problem) and where we want to be (solution)
Particular action has particular effect
Asks, “what can I do to get there?”
Break a problem into parts, and then try and solve each part individually
Following a recipe

31. Working Backward Similar to means-end analysis
Begin at the end, and work way back
What is the goal—start there
Effective when you know what you need to accomplish but not sure how best to begin
Crossing a stream via stepping stones
Don’t just start from where you are—survey across the stream to identify stones in the stream beginning at other shore

32. Analogies Similarity between two or more terms, events, or situations
Consider the analogy offered in your textbook on page 184 as an analogy for solving Figure 8:1B
Always contain four parts:
Coat is to closet as car is to _____________

33. Insight and Incubation
Insight is sudden understanding—arriving at a solution to a problem all of a sudden (“A-ha!”)
Kohler chimpanzee experiment

34. Insight & incubation
Incubation effect: standing back from a problem for a period of time while some unconscious process within us continues to work it out.
Later the solution may come to us in a flash
Sometimes good to take a break from a difficult problem

35. Obstacles to problem solving
Mental set: approaching a problem with a solution that worked previously
Sometimes the same solution doesn’t work

36. The Three Jugs Problem

37. B-A-2C Problems 1-5 all solved the same way;
Problems 6-7 didn’t require as elaborate a solution (could have just worked around B)
Our mental set got in the way!

38. Functional Fixedness: tendency to think of objects only in terms of their usual functions.
How did functional fixedness stand in the way of solving problems D & E? =

39. Problem Solving & Creativity
Functional fixedness can be overcome by creativity
Requires DIVERGENT rather than CONVERGENT thinking
Convergent thinking—limited to available facts
Divergent thinking—explore all options

40. Divergent thinking exercise
Take two minutes and write down everything you can do with a
BRICK
Following that, I have two other things for you to complete…

41. Agenda
Students will be expert problem-solvers and able to differentiate between deductive and inductive reasoning
Recover prior learning: the ABCDE’s of problem solving
Introduction to Reasoning
What is deductive reasoning
What is inductive reasoning
Work independently to create study cards
Introduction to Decision Making & Judgment
Collaborative work on decision making balance sheet
Exit ticket: How do inductive and deductive reasoning differ?

42. The ABCDEs of Problem Solving
Assess the problem
Brainstorm approaches to the problem
Choose the approach that seems most likely to work
Do it—try the most likely approach.
Evaluate the results

43. Bell-work
No problem in life is too big to solve if you use the correct problem-solving method. Do you agree or disagree—EXPLAIN WHY?

44. Tower of Hanoi
Your task is to move the tower from the left peg to the right peg, moving only one disk at a time and never putting a larger disk on a smaller one

45. Tower of Hanoi
Solution: Move smallest disk to third peg; move middle disk to second peg; place smallest disk on top of middle disk; move largest disk to third peg; move smallest disk to first peg; place middle disk on top of largest disk; move smallest disk on top of middle disk.

46. Reasoning The use of information to reach conclusions
Two primary kinds of reasoning
Deductive
Inductive

47. Deductive Reasoning “Top-down” reasoning or logic
Reasoning from one or more general statements (premises) to reach a conclusion
Premise: idea or statement that provides basic information that allows us to draw conclusions

48. Deductive Reasoning Premise 1: All men are mortal.
Premise 2: Aristotle is a man.
Conclusion?
Aristotle is mortal.

49. Deductive Reasoning Aristotle (384-322 BC) Greek philosopher
Taught Alexander the Great
Syllogisms: form of deductive reasoning
Major premise
Minor premise
Conclusion

50. Deductive Reasoning Aristotle (384-322 BC) All virtues are admirable
Patience is a virtue
Therefore…
Patience is admirable
His goal: to construct valid arguments & valid conclusions if true premises could be discovered

51. Deductive reasoning South Korea is in Asia
The city of Seoul is in South Korea
Therefore…Seoul is in Asia.
Conclusion is always true when the premises are true.

52. Deductive Reasoning Faulty premises
Countries that are near each other have similar languages
The United States and Mexico are near each other
Therefore, the United States and Mexico have similar languages
monty python

53. Inductive Reasoning
Reason in the other direction—from individual facts/cases to reach a general conclusion
Sometimes the conclusions are wrong even when the premises are correct

54. Inductive Reasoning DOES NOT LOGICALLY FOLLOW!!!
The United States and Canada are near each other and have similar languages.
Mexico, Nicaragua, and Guatemala are near each other and have similar languages.
Therefore, countries that are near each other have similar languages.
DOES NOT LOGICALLY FOLLOW!!!

55. Inductive Reasoning
Often impossible to prove an assumption reached by inductive reasoning to be true
Confirmation bias: tendency to look for information that confirms one’s preconceived notions
We use inductive reasoning all the time
Until we prove a hypothesis false, we assume it is true

56. Inductive Reasoning
Today, I left for work at 8 o’clock and arrived at work on time.
Therefore, every day that I leave for work at 8 o’clock I will arrive at work on time.
Illogical to assume an entire premise just because one set of data suggests it

57. Inductive Reasoning Uses in scientific theory
100% of biological life forms that we know of depend on liquid water to exist.
Therefore, if we discover a new biological life form it will probably depend on liquid water to exist.

58. Reasoning Deductive Reasoning Inductive Reasoning “Top-down”
Reasoning from one or more premises (true) to a conclusion (true)
A=B
B=C
Therefore, A=C
If premises are true, conclusion is ALWAYS true
“Bottom-up”
Reasoning from individual facts or cases to reach a general conclusion
All books by Jones are great
Jones’ new book must be great
Confirmation bias
Inherently uncertain

59. Study cards
Using notecards supplied, create cards for both inductive and deductive reasoning
Definition and at least two examples
Find a partner and exchange cards, offering advice and comments on clarity and accuracy
10 minutes for activity

60. Decision Making and Moral Judgment
Brainstorm—what are some big decisions you have to make in life?
What makes those decisions difficult?
Weighing the pluses and the minuses
Can’t always weight pluses and minuses; sometimes we have to proceed with limited information

61. Decision Making & Judgment
Balance sheet—weighing the pro’s, the con’s, and need for additional information
Textbook page 192
Work in groups; in each group develop a list of difficult decisions facing teens
Choose one challenge, each member of the group creates a balance sheet to assess the pros and cons of each choice (independent)
Reconvene as a group and evaluate your information and come to a GROUP consensus
30 minutes for activity

62. Closure Ticket out the door
How do deductive and inductive reasoning differ?