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
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 • 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?
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?
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 • is an example • Often complex and time-consuming • Heuristics: rules of thumb, shortcuts • Faster than algorithms, not as reliable
Examples • C L _ F F • 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
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