THINKING STRATEGIES (PS)

Thinking hurts. However, stupidities come to world without birth pains. Bielaszewski

Discuss these problems with your partner. Make sure you both agree on the solution and write it down. Imagine you are in a room with 3 switches. In an adjacent room there are 3 bulbs (all are off at the moment), each switch belongs to one bulb. It is impossible to see from one room to another. How can you find out which switch belongs to which bulb, if you may enter the room with the bulbs only once? A man lives on the tenth floor of a building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator - or if it was raining that day - he goes back to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment. Can you explain why? How can you throw a ball as hard as you can and have it come back to you, even if it doesn't hit anything, there is nothing attached to it, and no one else catches or throws it?

Can you tell how you reached your conclusion?

REASONING InformalFormal (logical)

Informal Reasoning: HEURISTICS: Speculative formulation serving as a guide in the investigation or solution of a problem COMMON MISTAKES IN HEURISTICS: 1. The ANCHORING heuristic: they estimate the probability of an event, not by starting from scratch but adjusting an earlier estimate. 2. The REPRESENTATIVENESS heuristic: They base conclusions on whether an example Belongs in a class on how similar it is to other Items in that class. 3. The AVAILABILITY heuristic: It involves judging the Probability that an even may occur on That a hypothesis ay be true by how easily The hypothesis or examples can be brought to mind.

Formal or logical reasoning: ALGORITHMS: Methods that always reach a correct result. Formulas Rules of logic: Set of mental procedures that help us draw valid conclusions about the world SYLLOGISMS: logical arguments containing 2 or more premises and a conclusion (inference). PREMISES: Statements Example: Density = mass / volume

COMMON MISTAKES IN LOGICAL REASONING: There are cultural differences in formal reasoning. Incorrect premises Violations of the rules of logic WHY? Bias about conclusions Conversion effect Limits on working memory

Correct or incorrect? True or false? I’m a good looking woman because I eat “Special K”. If you aren’t good looking is because you don’t eat “Special K”. Some girls are beautiful. Geovanna is a girl so she’s beautiful. If I can see the sun, it’s because it’s daytime. If I can’t see the sun, it’s because it’s not daytime. All great painters are famous worldwide. Alfredo Zalce is a great painter; therefore, he’s famous worldwide. No experienced person is incompetent; Jenkins is always making silly mistakes. No competent person is always making silly mistakes. Then…

STRATEGIES FOR PROBLEM SOLVING: Decomposition: when a problem is so complicated that all of its elements cannot be held in working memory at once. Work backward Analogies: Many problems are similar to others we have encoutered before. Therefore, the similarities between currect and previos problems need to be recognized. Incubation: When the problem is very difficult, it’s helpful to allow it to “incubate”. Once we engage in unrelated mental activities for a while, the solution may suddenly appear.

CASE STUDY: A study of an individual unit, as a person, family, or social group, usually emphasizing developmental issues and relationships with the environment, esp. in order to comprar a larger group to the individual unit. Case studies (problems): - striking-feature syndrome - causal uncertainty Comparative case studies (recommended)

OBSTACLES TO PROBLEM SOLVING: Multiple Hypotheses (availability heuristic): Out of the many reasons there are, which hypotheses should be tested, and in what order? Mental Sets: Tendency for old patterns of problem solving to persist. Confirmation Bias (anchoring heuristic): it involves reluctance to abandon an initial hypothesis. Ignoring Negative Evidence: Symptoms that do not occur are less likely to be noticed and observed. People have a difficult time using the absence of symptoms to help eliminate hypothesis from consideration

How can YOU teach reasoning and problem solving techniques to your students? What kind of activities would you include in your teaching?

DECISION MAKING Risky decisions (decisions under uncertainty): decisions made when the outcome is uncertain. How can we evaluate if a decision is the best? Comparing attirbutes Estimating probabilities (expected value) Biases and Flaws in decision Making: Gains, losses, and probabilities

Do groups solve problems faster and more effectively than individuals?

High status members in a group are likely to influence group deliberations. There’s little evidence that members with the most competence always contribute more to group deliberations. Longer work periods improve group communication and give the group more opportunities to recognize and be incfluenced by its most competent members.