Thinking and Language

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?

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

THINKING SYMBOLS

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

THINKING SYMBOLS CONCEPTS

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

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

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

THINKING SYMBOLS CONCEPTS PROTOTYPES

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

Prototype Activity

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

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?

ing Something like this?

Why not these two?

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.

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

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

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?

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.

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

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

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

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

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

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

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?”

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

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

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 _____________

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

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

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

The Three Jugs Problem

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!

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? =

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

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…

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?

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

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?

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

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.

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

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

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

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

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

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.

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

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

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!!!

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

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

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.

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

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

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

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

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