# List of Benchmarks for 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 |