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Thinking and Reasoning

Standard 2.Understands and applies basic principles of logic and reasoning
  Level III (Grade 6-8)
   1. Uses formal deductive connectors ("if...then," "not," "and," "or") in the construction of deductive arguments
   2. Understands that some aspects of reasoning have very rigid rules but other aspects do not
   3. Understands that when people have rules that always hold for a given situation and good information about the situation, then logic can help them figure out what is true about the situation
   4. Understands that reasoning by similarities can suggest ideas but cannot be used to prove things
   5. Understands that people are using incorrect logic when they make a statement such as "if x is true, then y is true; but x isn't true, therefore y isn't true"
   6. Understands that a single example can never prove that something is true, but a single example can prove that something is not true
   7. Understands that some people invent a general rule to explain how something works by summarizing observations
   8. Understands that people overgeneralize by making up rules on the basis of only a few observations
   9. Understands that personal values influence the types of conclusions people make
   10. Recognizes situations in which a variety of conclusions can be drawn from the same information
  Level IV (Grade 9-12)
   1. Understands the differences between the formal and informal uses (e.g., in everyday situations) of the logical connectors: "if...then," "not," "and," "or"
   2. Analyzes the deductive validity of arguments based on implicit or explicit assumptions
   3. Understands the difference between formal and informal uses (e.g., in everyday situations) of the terms "sufficient" and "necessary"
   4. Understands the formal meaning of the logical quantifiers: "some," "none," and "all"
   5. Understands that formal logic is mostly about connections between statements and that these connections can be considered without attention to whether the statements themselves are true or not
   6. Understands that people sometimes reach false conclusions either by applying faulty logic to true statements or by applying valid logic to false statements
   7. Understands that a reason may be sufficient to get a result but may not be the only way to get the result (i.e., may not be necessary), or a reason may be necessary to obtain a result but not sufficient (i.e., other things are also required; some reasons may be both necessary and sufficient)
   8. Understands that logic can be used to test how well any general rule works
   9. Understands that proving a general rule to be false can be done by finding just one exception; this is much easier than proving a general rule to be true for all possible cases
   10. Understands that logic may be of limited help in finding solutions to problems if the general rules upon which conclusions are based do not always hold true; most often, we have to deal with probabilities rather than certainties
   11. Understands that once a person believes a general rule, he or she may be more likely to notice things that agree with that rule and not notice things that do not; to avoid this "confirmatory bias," scientific studies sometimes use observers who do not know what the results are supposed to be
   12. Understands that very complex logical arguments can be formulated from a number of simpler logical arguments
   13. Identifies counter examples to conclusions that have been developed
   14. Understands the distinction between deductive and inductive reasoning